| Title: | Analysis of Animal Movements |
|---|---|
| Description: | A collection of tools for the analysis of animal movements. |
| Authors: | Clement Calenge [aut, cre], Stephane Dray [ctb], Manuela Royer [ctb] |
| Maintainer: | Clement Calenge <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.3.28 |
| Built: | 2024-11-05 04:57:46 UTC |
| Source: | https://github.com/clementcalenge/adehabitatlt |
The functions acfdist.ltraj and acfang.ltraj compute
(and by default plot) a correlogram-like function .
acfdist.ltraj(x, which = c("dist", "dx", "dy"), nrep = 999, lag = 1, plot = TRUE, xlab = "Lag", ylab = "autocorrelation") acfang.ltraj(x, which = c("absolute", "relative"), nrep = 999, lag = 1, plot = TRUE, xlab = "Lag", ylab = "autocorrelation")acfdist.ltraj(x, which = c("dist", "dx", "dy"), nrep = 999, lag = 1, plot = TRUE, xlab = "Lag", ylab = "autocorrelation") acfang.ltraj(x, which = c("absolute", "relative"), nrep = 999, lag = 1, plot = TRUE, xlab = "Lag", ylab = "autocorrelation")
x |
an object of the class |
which |
to select on which parameter the autocorrelation should be computed (see details). |
nrep |
the number of repetitions used to test the significance of autocorrelation for each lag value. |
lag |
maximum lag at which to calculate the autocorrelation. Default is 1. |
plot |
logical. If 'TRUE' (the default) the autocorrelation is plotted. |
xlab |
a title for the x axis |
ylab |
a title for the y axis |
The function acfdist.ltraj is used to compute a correlogram for
linear descriptors and acfang.ltraj for angular descriptors
(see as.ltraj for a description of these descriptors).
Statistics used are defined in Dray et al. (in press). They are based on squared differences between successive values. For angular descriptors, the statistic is based on the chord distance.
In the case of missing data, the computation of the correlograms is restricted to the pairs of successive observed data and only observed data are permuted (i.e. the structure of the missing data is kept constant under permutation).
The grey area represents a 95 % interval obtained after permutation of the data. If the observed data is outside this region, it is considered as significant and represetend by a black symbol. Note that no multiple-comparison adjustement is performed.
A list of matrices. Each matrix corresponds to a 'burst'. The matrix
contains for each lag value (column), the values of autocorrelation
(observed, and the 2.5 %, 50 % and 97.5 % quantiles of for the set
of nrep permutations of values).
Stephane Dray [email protected]
Dray, S., Royer-Carenzi, M. and Calenge, C. The exploratory analysis
of autocorrelation in animal movement studies. Ecological
Research, in press.
Calenge, C., Dray, S. and Royer-Carenzi, M. (2009) The concept of animals trajectories from a data analysis perspective. Ecological Informatics, 4,34–41.
as.ltraj for additional information on the class
ltraj, wawotest for a simple test of the
autocorrelation of the descriptive parameters on the trajectory.
## Not run: data(puechcirc) puechcirc acfang.ltraj(puechcirc, lag=5) acfdist.ltraj(puechcirc, lag=5) ## End(Not run)## Not run: data(puechcirc) puechcirc acfang.ltraj(puechcirc, lag=5) acfdist.ltraj(puechcirc, lag=5) ## End(Not run)
This data set contains the relocations of 6 adult albatross monitored in the Crozets Islands by the team of H. Weimerskirch from the CEBC-CNRS (Centre d'Etudes Biologiques de Chize, France).
data(albatross)data(albatross)
This data set is an object of class ltraj.
The coordinates are given in meters (UTM - zone 42).
http://suivi-animal.u-strasbg.fr/index.htm
data(albatross) plot(albatross)data(albatross) plot(albatross)
The class ltraj is intended to store trajectories of
animals. Trajectories of type II correspond to trajectories for which the
time is available for each relocation (mainly GPS and
radio-tracking). Trajectories of type I correspond to trajectories for which
the time has not been recorded (e.g. sampling of tracks in the snow).
as.ltraj creates an object of this class.
summary.ltraj returns the number of relocations (and missing
values) for each "burst" of relocations and each animal.
rec recalculates the descriptive parameters of an object of
class ltraj (e.g. after a modification of the contents of this object,
see examples)
as.ltraj(xy, date, id, burst = id, typeII = TRUE, slsp = c("remove", "missing"), infolocs = data.frame(pkey = paste(id, date, sep="."), row.names=row.names(xy)), proj4string = CRS()) ## S3 method for class 'ltraj' print(x, ...) ## S3 method for class 'ltraj' summary(object, ...) rec(x, slsp = c("remove", "missing"))as.ltraj(xy, date, id, burst = id, typeII = TRUE, slsp = c("remove", "missing"), infolocs = data.frame(pkey = paste(id, date, sep="."), row.names=row.names(xy)), proj4string = CRS()) ## S3 method for class 'ltraj' print(x, ...) ## S3 method for class 'ltraj' summary(object, ...) rec(x, slsp = c("remove", "missing"))
x, object
|
an object of class |
xy |
a data.frame containing the x and y coordinates of the relocations |
date |
for trajectories of type II, a vector of class |
id |
either a character string indicating the identity of the
animal or a factor with length equal to |
burst |
either a character string indicating the identity of the
burst of relocations or a factor with length equal to
|
typeII |
logical. |
slsp |
a character string used for the computation of the turning angles (see details) |
infolocs |
if not |
proj4string |
an object of class CRS storing the projection information of the relocations. |
... |
For other functions, arguments to be passed to the generic
functions |
Objects of class ltraj allow the analysis of animal
movements. They contain the descriptive parameters of the moves
generally used in such studies (coordinates of the relocations, date,
time lag, relative and absolute angles, length of moves, increases
in the x and y direction, and dispersion R2n, see below), as well as
optionally metadata on the relocations (precision, etc.).
The computation of turning angles may be problematic when successive
relocations are located at the same place. In such cases, at least
one missing value is returned. For example, let r1, r2, r3 and r4 be
4 successive relocations of a given animal (with coordinates (x1,y1),
(x2,y2), etc.). The turning angle in r2 is computed between the moves
r1-r2 and r2-r3. If r2 = r3, then a missing value is returned for the
turning angle at relocation r2. The argument slsp controls the
value returned for relocation r3 in such cases. If slsp ==
"missing", a missing value is returned also for the relocation r3.
If slsp == "remove", the turning angle computed in r3 is the
angle between the moves r1-r2 and r3-r4.
For a given individual, trajectories are often sampled as "bursts"
of relocations. For example, when an animal is monitored using
radio-tracking, the data may consist of several circuits of activity
(two successive relocations on one circuit are often highly
autocorrelated, but the data from two circuits may be sampled at long
intervals in time). These bursts are indicated by the attribute
burst. Note that the bursts should be unique: do not use the
same burst id for bursts collected on different animals.
Two types of trajectories can be stored in objects of class
ltraj: trajectories of type I correspond to trajectories where
the time of relocations is not recorded. It may be because it could
not be noted at the time of sampling (e.g. sampling of animals' tracks
in the snow) or because the analyst decided that he did not want to
take it into account, i.e. to study only its geometrical
properties. In this case, the variable date in each burst of
the object contains a vector of integer giving the order of the
relocations in the trajectory (i.e. 1, 2, 3, ...). Trajectories of
type II correspond to trajectories for which the time is available for
each relocation. It is stored as a vector of class POSIXct in
the column date of each burst of relocations. The type of
trajectory should be defined when the object of class ltraj is
defined, with the argument typeII. Note that the time zone of
dates in objects of type II should be the same for all bursts (this is
checked by the functions of adehabitatLT).
Concerning trajectories of type II, in theory, it is expected that the
time lag between two relocations is constant in all the bursts and all
the ids of one object of class
ltraj (don't mix animals located every 10 minutes and animals
located every day in the same object). Indeed, some of the
descriptive parameters of the trajectory do not have any sense when
the time lag varies. For example, the distribution of relative
angles (angles between successive moves) depends on a given time
scale; the angle between two during 10-min moves of a whitestork
does not have the same biological meaning as the angle between two
1-day move. If the time lag varies, the underlying process varies
too. For this reason, most functions of adehabitatLT have been
developed for "regular" trajectories, i.e. trajectories with a
constant time lag (see help(sett0)). Furthermore, several
functions are intended to help the user to transform an object of
class ltraj into a regular object (see for example
help(sett0), and particularly the examples to see how regular
trajectories can be obtained from GPS data).
Nevertheless, the class ltraj allows for variable time lag,
which often occur with some modes of data collection (e.g. with Argos
collars). But *we stress that their analysis is still an open
question!!*
Finally, the class ltraj deals with missing values in the
trajectories. Missing values are frequent in the trajectories of
animals collected using telemetry: for example, GPS collar may not
receive the signal of the satellite at the time of relocation. Most
functions dealing with the class ltraj have a specified
behavior in case of missing values.
It is recommended to store the missing values in the data *before*
the creation of the object of class ltraj. For example, the
GPS data imported within R contain missing values. It is recommended
to *not remove* these missing values before the creation of the
object!!! These missing values may present patterns (e.g. failure to
locate the animal at certain time of the day or in certain habitat
types), and *the analysis of these missing values should be part of the
analysis of the trajectory* (e.g. see help(runsNAltraj) and
help(plotNAltraj).
However, sometimes, the data come without any information concerning
the location of these missing values. If the trajectory is
approximately regular (i.e. approximately constant time lag), it is
possible to determine where these missing values should occur in the
object of class ltraj. This is the role of the function
setNA.
One word now about the attribute infolocs of the object of
class ltraj. This attribute is intended to store metadata
concerning the relocations building the trajectory (the precision
of the relocations, the value of environmental variables at this
place, etc.). There are constraints on the structure of this
attribute. Although any variable can be stored in this attribute, it
is required that: (i) all the relocations take a value (or a missing
value) for all variables, (ii) all the variables are measured (or
correspond to missing values) for all bursts and ids. This means for
example that the function c.ltraj cannot be used to combine an
object where only variable "A" is stored as metadata and an object
where only variable "B" is stored as metadata. The function
removeinfo can be used to remove this attribute. Note also
that the data.frames in the list infolocs should have the same
row.names as the corresponding elements in the object of class
"ltraj".
Finally, note that an object of class ltraj *can* have an
attribute named "proj4string", storing the projection
information of the object. The package adehabitatLT does not manage
projection information, but this attribute can be useful when an
object of class ltraj is converted to other classes (in
particular spatial classes). Note that this attribute can be NULL
(identical to a NA CRS).
summary.ltraj returns a data frame.
All other functions return objects of class ltraj. An object
of class ltraj is a list with one component per burst of
relocations. Each component is a data frame with two attributes and
one optionnal attribute:
the attribute "id" indicates the identity of the animal, and
the attribute "burst" indicates the identity of the
burst. An optional attribute "infolocs" contains any
additional information desired by the user (precision, etc.).
Each main data frame stores the following columns:
x |
the x coordinate for each relocation |
y |
the y coordinate for each relocation |
date |
the date for each relocation (type II) or a vector of integer giving the order of the relocations in the trajectory. |
dx |
the increase of the move in the x direction. At least two
successive relocations are needed to compute |
dy |
the increase of the move in the y direction. At least two
successive relocations are needed to compute |
dist |
the length of each move. At least two
successive relocations are needed to compute |
dt |
the time interval between successive relocations |
R2n |
the squared net displacement between the current relocation and the first relocation of the trajectory |
abs.angle |
the angle between each move and the x axis. At least two
successive relocations are needed to compute |
rel.angle |
the turning angles between successive moves. At least
three successive relocations are needed to compute |
Clement Calenge [email protected]
Stephane Dray [email protected]
Calenge, C., Dray, S. and Royer, M. (2009) The concept of animals' trajectories from a data analysis perspective. Ecological Informatics, 4: 34–41.
is.regular and sett0 for additional
information on "regular" trajectories. setNA and
runsNAltraj for additional information on missing values
in trajectories. c.ltraj to combine several objects of
class ltraj, Extract.ltraj to extract or replace
bursts of relocations, plot.ltraj and
trajdyn for graphical displays, gdltraj to
specify a time period.
data(puechabonsp) locs <- puechabonsp$relocs head(locs) xy <- coordinates(locs) df <- as.data.frame(locs) id <- df[,1] ###################################################### ## ## Example of a trajectory of type I (time not recorded) (litrI <- as.ltraj(xy, id = id, typeII=FALSE)) plot(litrI) ## The components of the object of class "ltraj" head(litrI[[1]]) ###################################################### ## ## Example of a trajectory of type II (time recorded) ### Conversion of the date to the format POSIX da <- as.character(df$Date) da <- as.POSIXct(strptime(as.character(df$Date),"%y%m%d", tz="Europe/Paris")) ### Creation of an object of class "ltraj", with for ### example the first animal (tr1 <- as.ltraj(xy[id=="Brock",], date = da[id=="Brock"], id="Brock")) ## The components of the object of class "ltraj" head(tr1[[1]]) ## With all animals (litr <- as.ltraj(xy, da, id = id)) ## Change something manually in the first burst: head(litr[[1]]) litr[[1]][3,"x"] <- 700000 ## Recompute the trajectory litr <- rec(litr) ## Note that descriptive statistics have changed (e.g. dx) head(litr[[1]]) ###################################################### ## ## Example of a trajectory of type II (time recorded) ## with an infolocs attribute: data(capreochiz) head(capreochiz) ## Create an object of class "ltraj" cap <- as.ltraj(xy = capreochiz[,c("x","y")], date = capreochiz$date, id = "Roe.Deer", typeII = TRUE, infolocs = capreochiz[,4:8]) capdata(puechabonsp) locs <- puechabonsp$relocs head(locs) xy <- coordinates(locs) df <- as.data.frame(locs) id <- df[,1] ###################################################### ## ## Example of a trajectory of type I (time not recorded) (litrI <- as.ltraj(xy, id = id, typeII=FALSE)) plot(litrI) ## The components of the object of class "ltraj" head(litrI[[1]]) ###################################################### ## ## Example of a trajectory of type II (time recorded) ### Conversion of the date to the format POSIX da <- as.character(df$Date) da <- as.POSIXct(strptime(as.character(df$Date),"%y%m%d", tz="Europe/Paris")) ### Creation of an object of class "ltraj", with for ### example the first animal (tr1 <- as.ltraj(xy[id=="Brock",], date = da[id=="Brock"], id="Brock")) ## The components of the object of class "ltraj" head(tr1[[1]]) ## With all animals (litr <- as.ltraj(xy, da, id = id)) ## Change something manually in the first burst: head(litr[[1]]) litr[[1]][3,"x"] <- 700000 ## Recompute the trajectory litr <- rec(litr) ## Note that descriptive statistics have changed (e.g. dx) head(litr[[1]]) ###################################################### ## ## Example of a trajectory of type II (time recorded) ## with an infolocs attribute: data(capreochiz) head(capreochiz) ## Create an object of class "ltraj" cap <- as.ltraj(xy = capreochiz[,c("x","y")], date = capreochiz$date, id = "Roe.Deer", typeII = TRUE, infolocs = capreochiz[,4:8]) cap
These data contain the relocations of one female brown bear monitored using GPS collars during May 2004 in Sweden.
data(bear)data(bear)
Scandinavian Bear Research Project. Skandinaviska Bjornprojektet. Tackasen - Kareliusvag 2. 79498 Orsa, Sweden. email: [email protected]
data(bear) plot(bear)data(bear) plot(bear)
This data set contains the relocations of an African buffalo (Syncerus caffer) monitored in the W National Park (Niger) by D. Cornelis, as well as the habitat map of the study area.
data(buffalo)data(buffalo)
This dataset is a list containing an object of class ltraj and
a SpatialPixelsDataFrame.
The "infolocs" component of the ltraj stores the proportion of the time duration between relocation i-1 and relocation i during which the animal was active.
Cornelis D., Benhamou S., Janeau G., Morellet N., Ouedraogo M. & de Vissher M.-N. (submitted). The spatiotemporal segregation of limiting resources shapes space use patterns of West African savanna buffalo. Journal of Mammalogy.
data(buffalo) plot(buffalo$traj, spixdf=buffalo$habitat)data(buffalo) plot(buffalo$traj, spixdf=buffalo$habitat)
Functions to get or set the attribute "id", "burst", and
"infolocs" of the components of an object of class
ltraj.
burst(ltraj) burst(ltraj) <- value id(ltraj) id(ltraj) <- value infolocs(ltraj, which) infolocs(ltraj) <- value removeinfo(ltraj)burst(ltraj) burst(ltraj) <- value id(ltraj) id(ltraj) <- value infolocs(ltraj, which) infolocs(ltraj) <- value removeinfo(ltraj)
ltraj |
an object of class |
value |
for the assignment functions |
which |
an optional character vector containing the names of the
variables in the |
The functions id, burst and infolocs are
accessor functions, and id<- and burst<- are
replacement function. removeinfo removes the attribute
infolocs from the object ltraj (see the help page of
as.ltraj).
For id and burst, a character vector of the same length
as ltraj. For infolocs, the data frame containing the
information on the relocations. removeinfo returns an object
of class ltraj.
For id<- and burst<-, the updated object. (Note that
the value of burst(x) <- value is that of the assignment,
value, not the return value from the left-hand side.)
Clement Calenge [email protected]
data(puechcirc) puechcirc ## To see the ID and the burst id(puechcirc) burst(puechcirc) ## Change the burst burst(puechcirc) <- c("glou", "toto", "titi") puechcirc burst(puechcirc)[2] <- "new name" puechcirc ## Change the ID id(puechcirc)[id(puechcirc)=="CH93"] <- "WILD BOAR" puechcirc ## example of an object with an attribute "infolocs" data(capreochiz) head(capreochiz) ## Create an object of class "ltraj" cap <- as.ltraj(xy = capreochiz[,c("x","y")], date = capreochiz$date, id = "Roe.Deer", typeII = TRUE, infolocs = capreochiz[,4:8]) cap cap2 <- removeinfo(cap) cap2 infolocs(cap)data(puechcirc) puechcirc ## To see the ID and the burst id(puechcirc) burst(puechcirc) ## Change the burst burst(puechcirc) <- c("glou", "toto", "titi") puechcirc burst(puechcirc)[2] <- "new name" puechcirc ## Change the ID id(puechcirc)[id(puechcirc)=="CH93"] <- "WILD BOAR" puechcirc ## example of an object with an attribute "infolocs" data(capreochiz) head(capreochiz) ## Create an object of class "ltraj" cap <- as.ltraj(xy = capreochiz[,c("x","y")], date = capreochiz$date, id = "Roe.Deer", typeII = TRUE, infolocs = capreochiz[,4:8]) cap cap2 <- removeinfo(cap) cap2 infolocs(cap)
This function combines several objects of class ltraj.
## S3 method for class 'ltraj' c(...)## S3 method for class 'ltraj' c(...)
... |
objects of class |
An object of class ltraj.
Clement Calenge [email protected]
ltraj for further information on the class
ltraj, Extract.ltraj to extract or replace
bursts of relocations, plot.ltraj and
trajdyn for graphical
displays, gdltraj to specify a time period
data(puechcirc) (i <- puechcirc[1]) (j <- puechcirc[3]) (toto <- c(i,j))data(puechcirc) (i <- puechcirc[1]) (j <- puechcirc[3]) (toto <- c(i,j))
This dataset contains the relocations of a roe deer collected using GPS collars in the Chize reserve (Deux-Sevres, France) by the ONCFS (Office national de la chasse et de la faune sauvage).
data(capreochiz)data(capreochiz)
This dataset is a data.frame containing the relocations and metadata on these relocations (DOP, status, etc.).
Sonia Said, Office national de la chasse et de la faune sauvage, CNERA-CS, 1 place Exelmans, 55000 Bar-le-Duc (France).
data(capreochiz) head(capreochiz)data(capreochiz) head(capreochiz)
This dataset contains the relocations of a roe deer collected from May 1st to May 4th 2004 (every 5 minutes) using GPS collars in the wildlife reserve of Trois-Fontaines (Haute Marne, France) by the ONCFS (Office national de la chasse et de la faune sauvage).
data(capreotf)data(capreotf)
This dataset is a regular object of class ltraj (i.e. constant
time lag).
Sonia Said, Office national de la chasse et de la faune sauvage, CNERA-CS, 1 place Exelmans, 55000 Bar-le-Duc (France).
data(capreotf) plot(capreotf)data(capreotf) plot(capreotf)
Density, distribution function, quantile function and random
generation for the chi distribution with df degrees of
freedom.
dchi(x, df = 2) pchi(q, df = 2, lower.tail = TRUE, ...) qchi(p, df = 2, lower.tail = TRUE) rchi(n, df = 2)dchi(x, df = 2) pchi(q, df = 2, lower.tail = TRUE, ...) qchi(p, df = 2, lower.tail = TRUE) rchi(n, df = 2)
x, q
|
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. If |
df |
degrees of freedom (non-negative, but can be non-integer). |
lower.tail |
logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]. |
... |
additional arguments to be passed to the function
|
The chi distribution with df = n > 0 degrees of freedom
has density
for x > 0. This distribution is used to describe the square root of a variable distributed according to a chi-square distribution.
dchi gives the density, pchi gives the distribution
function, qchi gives the quantile function, and rchi
generates random deviates.
Clement Calenge [email protected]
Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, 3rd ed. Wiley, New York.
opar <- par(mfrow = c(2,2)) hist(rchi(100), ncla = 20, main="The Chi distribution") plot(tutu <- seq(0, 5, length=20), dchi(tutu, df = 2), xlab = "x", ylab = "probability density", type = "l") plot(tutu, pchi(tutu), xlab = "x", ylab = "Repartition function", type = "l") par(opar)opar <- par(mfrow = c(2,2)) hist(rchi(100), ncla = 20, main="The Chi distribution") plot(tutu <- seq(0, 5, length=20), dchi(tutu, df = 2), xlab = "x", ylab = "probability density", type = "l") plot(tutu, pchi(tutu), xlab = "x", ylab = "Repartition function", type = "l") par(opar)
The function cutltraj split the bursts in an object of class
ltraj into several "sub-bursts", according to some specified
criterion.
The function bindltraj binds the bursts an object of class
ltraj with the same attributes "id" into one unique
burst.
cutltraj(ltraj, criterion, value.NA = FALSE, nextr = TRUE, ...) bindltraj(ltraj, ...)cutltraj(ltraj, criterion, value.NA = FALSE, nextr = TRUE, ...) bindltraj(ltraj, ...)
ltraj |
an object of class |
criterion |
a character string giving any syntactically correct R
logical expression implying the descriptive parameters in |
value.NA |
logical. The value that should be used to replace the missing values. |
nextr |
logical. Whether the current "sub-burst" should stop
after ( |
... |
additional arguments to be passed to other functions |
Splitting a trajectory may be of interest in many situations. For example, if it is known that two kinds of activities of the monitored animals correspond to different properties of, say, the distance between successive relocations, it may be of interest to split the trajectory according to the values of these distances.
The criterion used to cut the trajectory may imply any of the
parameters describing a trajectory in the object ltraj (e.g.,
"dt", "dist", "dx", etc. see the help page of
as.ltraj), as well as any variable stored in the attribute
"infolocs" of the object.
Two options are available in cutltraj, depending on the value
of nextr. If nextr = FALSE, any sequence of
successive relocations that *do not* match the criterion is considered
as a new burst. For example, if for a given burst, the criterion
returns the vector (FALSE, FALSE, FALSE, TRUE, TRUE, TRUE,
FALSE, FALSE, FALSE), then the function cutltraj creates
two new bursts of relocations, the first one containing the first 3
relocations and the second one the last 3 relocations.
If nextr = TRUE, any sequence of successive relocations that
*do not* match the criterion, *as well as the first relocation that
does match it after this sequence* is considered as a new burst.
This option is available because many of the descriptive parameters
associated to a given relocation in an object of class ltraj
measure some specific feature concerning the position of the next
relocation. For example, one may want to consider as a burst any
sequence of relocations for which the time lag is below one hour (the
criterion is "dt > 3600". The first relocation for which this
criterion is TRUE belong to the burst, and it is the next one which
is excluded from the burst. For example, if for a given burst, the
criterion returns the vector (FALSE, FALSE, FALSE, TRUE, TRUE,
TRUE, FALSE, FALSE, FALSE), then the function cutltraj
creates two new bursts of relocations, the first one containing the
first 4 relocations and the second one the last 3 relocations.
An object of class ltraj.
Clement Calenge [email protected]
ltraj for additional information about objects
of class ltraj (and especially concerning the names of the
descriptive parameters that can be used in
cutltraj). is.sd (especially the examples of this
help page) for other examples of use of this function
## Not run: ####################################################### ## ## GPS monitoring of one bear data(bear) ## We want to study the trajectory of the day at the scale ## of the day. We define one trajectory per day. The trajectory should begin ## at 22H00 ## The following function returns TRUE if the date is comprised between ## 21H00 and 22H00 (i.e. correspond to the relocation taken at 21H30) foo <- function(date) { da <- as.POSIXlt(date, "UTC") ho <- da$hour + da$min/60 return(ho>21&ho<22) } ## We cut the trajectory into bursts after the relocation taken at 21H30: bea1 <- cutltraj(bear, "foo(date)", nextr = TRUE) bea1 ## Remove the first and last burst: bea2 <- bea1[-c(1,length(bea1))] ####################################################### ## ## Bind the trajectories bea3 <- bindltraj(bea2) bea3 ## End(Not run)## Not run: ####################################################### ## ## GPS monitoring of one bear data(bear) ## We want to study the trajectory of the day at the scale ## of the day. We define one trajectory per day. The trajectory should begin ## at 22H00 ## The following function returns TRUE if the date is comprised between ## 21H00 and 22H00 (i.e. correspond to the relocation taken at 21H30) foo <- function(date) { da <- as.POSIXlt(date, "UTC") ho <- da$hour + da$min/60 return(ho>21&ho<22) } ## We cut the trajectory into bursts after the relocation taken at 21H30: bea1 <- cutltraj(bear, "foo(date)", nextr = TRUE) bea1 ## Remove the first and last burst: bea2 <- bea1[-c(1,length(bea1))] ####################################################### ## ## Bind the trajectories bea3 <- bindltraj(bea2) bea3 ## End(Not run)
Extract or replace subsets of objects of class ltraj.
## S3 method for class 'ltraj' x[i, id, burst] ## S3 replacement method for class 'ltraj' x[i, id, burst] <- value## S3 method for class 'ltraj' x[i, id, burst] ## S3 replacement method for class 'ltraj' x[i, id, burst] <- value
x |
an object of class |
i |
numeric. The elements to extract or replace |
id |
a character vector indicating the identity of the animals to extract or replace |
burst |
a character vector indicating the identity of the bursts of relocations to extract or replace |
value |
an object of class |
Objects of class ltraj contain several bursts of
relocations. This function subsets or replaces these bursts, based
on their indices or on the attributes id *or* burst.
When replacement is done, it is required that value and
x have the same variables in attribute infolocs (i.e.,
both contain the same variables or both do not contain any variable,
see the help page of as.ltraj)
An object of class ltraj.
Clement Calenge [email protected]
data(puechcirc) puechcirc ## Extract the second and third bursts (toto <- puechcirc[2:3]) ## Extracts all bursts collected on the animal JE puechcirc[id = "JE93"] ## Replace one burst toto[2] <- puechcirc[1] totodata(puechcirc) puechcirc ## Extract the second and third bursts (toto <- puechcirc[2:3]) ## Extracts all bursts collected on the animal JE puechcirc[id = "JE93"] ## Replace one burst toto[2] <- puechcirc[1] toto
These functions compute the first passage time using trajectories of
class "ltraj" of type II (time recorded).
fpt(lt, radii, units = c("seconds", "hours", "days")) varlogfpt(f, graph = TRUE) meanfpt(f, graph = TRUE) ## S3 method for class 'fipati' plot(x, scale, warn = TRUE, ...)fpt(lt, radii, units = c("seconds", "hours", "days")) varlogfpt(f, graph = TRUE) meanfpt(f, graph = TRUE) ## S3 method for class 'fipati' plot(x, scale, warn = TRUE, ...)
lt |
an object of class |
radii |
a numeric vector giving the radii of the circles |
units |
The time units of the results |
f, x
|
an object of class |
graph |
logical. Whether the results should be plotted |
scale |
the value of the radius to be plotted |
warn |
logical. Whether the function should warn the user when
the given scale does not correspond to possible radii available in
the object of class |
... |
additional arguments to be passed to the generic function
|
The first passage time (FPT) is a parameter often used to describe the
scale at which patterns occur in a trajectory. For a given scale r,
it is defined as the time required by the animals to pass through a
circle of radius r. Johnson et al. (1992) indicated that the mean
first passage time scales proportionately to the square of the radius
of the circle for an uncorrelated random walk. They used this
property to differenciate facilitated diffusion and impeded diffusion,
according to the value of the coefficient of the linear regression
log(FPT) = a * log(radius) + b. Under the hypothesis of a
random walk, a should be equal to 2 (higher for impeded
diffusion, and lower for facilitated diffusion). Note however, that
the value of a converges to 2 only for large values of radius.
Fauchald & Tveraa (2003) proposed another use of the FPT. Instead of computing the mean of FPT, they propose the use of the variance of the log(FPT). This variance should be high for scales at which patterns occur in the trajectory (e.g. area restricted search). This method is often used to determine the scale at which an animal seaches for food.
fpt computes the FPT for each relocation and each radius, and
for each animals. This function returns an object of class
"fipati", i.e. a list with one component per animal. Each
component is a data frame with each column corresponding to a value
of radii and each row corresponding to a relocation. An object
of class fipati has an attribute named "radii"
corresponding to the argument radii of the function
fpt.
meanfpt and varlogfpt return a data frame giving
respectively the mean FPT and the variance of the log(FPT) for each
animal (rows) and rach radius (column). These objects also have an
attribute "radii".
Clement Calenge [email protected]
Johnson, A. R., Milne, B.T., & Wiens, J.A. (1992) Diffusion in fractal landscapes: simulations and experimental studies of tenebrionid beetle movements. Ecology 73: 1968–1983.
Fauchald, P. & Tveraa, T. (2003) Using first passage time in the analysis of area restricted search and habitat selection. Ecology 84: 282–288.
ltraj for additional information on objects of
class ltraj
data(puechcirc) i <- fpt(puechcirc, seq(300,1000, length=30)) plot(i, scale = 500, warn = FALSE) toto <- meanfpt(i) toto attr(toto, "radii") toto <- varlogfpt(i) toto attr(toto, "radii")data(puechcirc) i <- fpt(puechcirc, seq(300,1000, length=30)) plot(i, scale = 500, warn = FALSE) toto <- meanfpt(i) toto attr(toto, "radii") toto <- varlogfpt(i) toto attr(toto, "radii")
Gets the parts of the trajectories stored in an object of class
ltraj of type II (time recorded), corresponding to a specified
time period.
gdltraj(x, min, max, type = c("POSIXct", "sec", "min", "hour", "mday", "mon", "year", "wday", "yday"))gdltraj(x, min, max, type = c("POSIXct", "sec", "min", "hour", "mday", "mon", "year", "wday", "yday"))
x |
an object of class |
min |
numeric. The beginning of the period to consider |
max |
numeric. The end of the period to consider |
type |
character. The time units of |
The limits of the period to consider may correspond to any of the
components of the list of class POSIXlt (hour, day, month,
etc.; see help(POSIXlt)), or to dates stored in objects of
class POSIXct (see examples). The corresponding metadata in
the attribute infolocs are also returned.
an object of class ltraj.
Clement Calenge [email protected]
ltraj for further information about objects of
class ltraj, POSIXlt for further information
about objects of class POSIXlt
data(puechcirc) plot(puechcirc, perani = FALSE) ## Gets all the relocations collected ## between midnight and 3H AM toto <- gdltraj(puechcirc, min = 0, max = 3, type="hour") plot(toto, perani = FALSE) ## Gets all relocations collected between the 15th ## and the 25th august 1993 lim <- as.POSIXct(strptime(c("15/08/1993", "25/08/1993"), "%d/%m/%Y", tz="Europe/Paris")) tutu <- gdltraj(puechcirc, min = lim[1], max = lim[2], type="POSIXct") plot(tutu, perani = FALSE)data(puechcirc) plot(puechcirc, perani = FALSE) ## Gets all the relocations collected ## between midnight and 3H AM toto <- gdltraj(puechcirc, min = 0, max = 3, type="hour") plot(toto, perani = FALSE) ## Gets all relocations collected between the 15th ## and the 25th august 1993 lim <- as.POSIXct(strptime(c("15/08/1993", "25/08/1993"), "%d/%m/%Y", tz="Europe/Paris")) tutu <- gdltraj(puechcirc, min = lim[1], max = lim[2], type="POSIXct") plot(tutu, perani = FALSE)
hbrown estimates the scaling factor h (used in the
Brownian motion, see help(simm.brown)) from a trajectory.
hbrown(x)hbrown(x)
x |
an object of class |
a vector with one estimate per burst of the object of class
ltraj.
Clement Calenge [email protected]
toto <- simm.brown(1:200, h=4) hbrown(toto) toto <- simm.brown(1:200, h=20) hbrown(toto)toto <- simm.brown(1:200, h=4) hbrown(toto) toto <- simm.brown(1:200, h=20) hbrown(toto)
This function draws an histogram of any tranformation of the
descriptive parameters of a trajectory in objects of class
ltraj.
## S3 method for class 'ltraj' hist(x, which = "dx/sqrt(dt)", ...)## S3 method for class 'ltraj' hist(x, which = "dx/sqrt(dt)", ...)
x |
an object of class |
which |
a character string giving any syntactically correct R
expression implying the descriptive elements in |
... |
parameters to be passed to the generic function
|
a list of objects of class "histogram"
Clement Calenge [email protected]
hist, ltraj for additional
information on the descriptive parameters of the trajectory,
qqnorm.ltraj for examination of distribution.
## Simulation of a Brownian Motion a <- simm.brown(c(1:300, seq(301,6000,by=20))) plot(a, addpoints = FALSE) ## dx/sqrt(dt) and dy/sqrt(dt) are normally distributed (see ## ?qqchi) hist(a, "dx/sqrt(dt)", freq = FALSE) lines(tutu <- seq(-5,5, length=50), dnorm(tutu), col="red") hist(a, "dy/sqrt(dt)", freq = FALSE) lines(tutu, dnorm(tutu), col="red") ## Look at the distribution of distances between ## successive relocations hist(a, "dist/sqrt(dt)", freq = FALSE) lines(tutu <- seq(0,5, length=50), dchi(tutu), col="red")## Simulation of a Brownian Motion a <- simm.brown(c(1:300, seq(301,6000,by=20))) plot(a, addpoints = FALSE) ## dx/sqrt(dt) and dy/sqrt(dt) are normally distributed (see ## ?qqchi) hist(a, "dx/sqrt(dt)", freq = FALSE) lines(tutu <- seq(-5,5, length=50), dnorm(tutu), col="red") hist(a, "dy/sqrt(dt)", freq = FALSE) lines(tutu, dnorm(tutu), col="red") ## Look at the distribution of distances between ## successive relocations hist(a, "dist/sqrt(dt)", freq = FALSE) lines(tutu <- seq(0,5, length=50), dchi(tutu), col="red")
This data set contains the trajectory of one hooded seal.
data(hseal)data(hseal)
The dataset hseal is an object of class ltraj. The
coordinates are stored in meters (UTM - zone 21).
Jonsen, I.D., Flemming, J.M. and Myers, R.A. (2005). Robust state-space modeling of animal movement data. Ecology, 86, 2874–2880.
data(hseal) plot(hseal)data(hseal) plot(hseal)
This dataset is an object of class "ltraj" (regular trajectory, relocations every 4 hours) containing the GPS relocations of four ibex during 15 days in the Belledonne mountain (French Alps).
data(ibex)data(ibex)
Office national de la chasse et de la faune sauvage, CNERA Faune de Montagne, 95 rue Pierre Flourens, 34000 Montpellier, France.
data(ibex) plot(ibex)data(ibex) plot(ibex)
This dataset is an object of class "ltraj" (irregular trajectory, relocations roughly every 4 hours) containing the raw GPS relocations of four ibex during 15 days in the Belledonne mountain (French Alps).
data(ibexraw)data(ibexraw)
This dataset is nearly the same as the dataset ibex, except
that the timing of relocations has not been rounded and the missing
values have not been placed in the trajectory.
Office national de la chasse et de la faune sauvage, CNERA Faune de Montagne, 95 rue Pierre Flourens, 34000 Montpellier, France.
data(ibexraw) plot(ibexraw)data(ibexraw) plot(ibexraw)
The function indmove tests for the independence between
successive components c(dx, dy) for each burst in a regular
object of class ltraj.
The function indmove.detail tests for the independence between
successive dx or dy for each burst in a regular object
of class ltraj.
The function testang.ltraj tests for the independence between
successive angles (relative or absolute) for each burst in a regular
object of class ltraj.
The function testdist.ltraj tests for the independence between
successive distances between successive relocations for each burst in
a regular object of class ltraj.
indmove(ltr, nrep = 200, conflim = seq(0.95, 0.5, length=5), sep = ltr[[1]]$dt[1], units = c("seconds", "minutes", "hours", "days"), plotit = TRUE) testang.ltraj(x, which = c("absolute", "relative"), nrep = 999, alter = c("two-sided","less","greater")) testdist.ltraj(x, nrep = 999, alter = c("two-sided","less","greater")) indmove.detail(x, detail=c("dx","dy"), nrep=999, alter = c("two-sided","less","greater"))indmove(ltr, nrep = 200, conflim = seq(0.95, 0.5, length=5), sep = ltr[[1]]$dt[1], units = c("seconds", "minutes", "hours", "days"), plotit = TRUE) testang.ltraj(x, which = c("absolute", "relative"), nrep = 999, alter = c("two-sided","less","greater")) testdist.ltraj(x, nrep = 999, alter = c("two-sided","less","greater")) indmove.detail(x, detail=c("dx","dy"), nrep=999, alter = c("two-sided","less","greater"))
ltr, x
|
an object of class |
conflim |
a vector giving the limits of the confidence intervals to be plotted |
nrep |
number of simulations |
units |
a character string indicating the time units for the result |
alter |
a character string specifying the alternative hypothesis, must be one of "greater", "less" or "two-sided" (default) |
which |
a character string indicating whether the absolute or relative angles are under focus |
detail |
a character string indicating whether |
plotit |
logical. Whether the results should be plotted on a graph |
sep |
used in the case of variable time lag between relocations. Indicates the theoretical time lag between two relocations |
The function indmove randomises the order of the increments
c(dx, dy) in a trajectory. The criteria of the test is the
Mean Squared Displacement (R^2_n) (Root & Kareiva 1984).
The function testang.ltraj randomises the order of the angles in a
trajectory. The criteria of the test is f^2 = sum_(i=1)^(n-1) 2*(1 -
cos(angle[i+1] - angle[i])). This measure corresponds to the
mean squared length of the segment joining two successive angles on
the trigonometric circle (see examples for an illustration).
The function testdist.ltraj randomises the order of the
distances between successive relocations in a trajectory. The
criteria of the test is sum_(i=1)^(n-1) (dist[i+1] -
dist[i])^2 (Neuman 1941, Neuman et al. 1941). The same criteria is
used in indmove.detail().
Note that these functions require "regular" trajectories, i.e. trajectories for which the relocations are separated by a constant time lag.
Finally, note that the functions testang.ltraj and
testdist.ltraj are not affected by the presence of missing
values in the bursts of relocations. The function indmove may
be greatly affected by these missing values (they are removed prior to
the test).
indmove() returns a list with one component per burst. Each
component is a list of two data frames. The data frame Time
contains the time points at which R2n is computed for the
observation (first column) and the simulations (other ones). The data
frame R2n contains the values for the R2n (same dimensions).
testang.ltraj(), testdist.ltraj and
indmove.detail return lists of
objects of class randtest.
Clement Calenge [email protected]
Stephane Dray [email protected]
Root, R.B. & Kareiva, P.M. (1984) The search for resources by cabbage butterflies (Pieris Rapae): Ecological consequences and adaptive significance of markovian movements in a patchy environment. Ecology, 65: 147–165.
Neumann, J.V., Kent, R.H., Bellinson, H.R. & Hart, B.I. (1941) The mean square successive difference. Annals of Mathematical Statistics, 12: 153–162.
Neumann, J.V. (1941) Distribution of the ration of the mean square successive difference to the variance. The Annals of Mathematical Statistics, 12: 367–395.
## Not run: ## theoretical independence between br <- simm.brown(1:1000) testang.ltraj(br) testdist.ltraj(br) indmove(br) ## End(Not run) ## Illustration of the statistic used for the test of the independence ## of the angles opar <- par(mar = c(0,0,4,0)) plot(0,0, asp=1, xlim=c(-1, 1), ylim=c(-1, 1), ty="n", axes=FALSE, main="Criteria f for the measure of independence between successive angles at time i-1 and i") box() symbols(0,0,circle=1, inches=FALSE, lwd=2, add=TRUE) abline(h=0, v=0) x <- c( cos(pi/3), cos(pi/2 + pi/4)) y <- c( sin(pi/3), sin(pi/2 + pi/4)) arrows(c(0,0), c(0,0), x, y) lines(x,y, lwd=2, col="red") text(0, 0.9, expression(f^2 == 2*sum((1 - cos(alpha[i]-alpha[i-1])), i==1, n-1)), col="red") foo <- function(t, alpha) { xa <- sapply(seq(0, alpha, length=20), function(x) t*cos(x)) ya <- sapply(seq(0, alpha, length=20), function(x) t*sin(x)) lines(xa, ya) } foo(0.3, pi/3) foo(0.1, pi/2 + pi/4) foo(0.11, pi/2 + pi/4) text(0.34,0.18,expression(alpha[i]), cex=1.5) text(0.15,0.11,expression(alpha[i-1]), cex=1.5) par(opar)## Not run: ## theoretical independence between br <- simm.brown(1:1000) testang.ltraj(br) testdist.ltraj(br) indmove(br) ## End(Not run) ## Illustration of the statistic used for the test of the independence ## of the angles opar <- par(mar = c(0,0,4,0)) plot(0,0, asp=1, xlim=c(-1, 1), ylim=c(-1, 1), ty="n", axes=FALSE, main="Criteria f for the measure of independence between successive angles at time i-1 and i") box() symbols(0,0,circle=1, inches=FALSE, lwd=2, add=TRUE) abline(h=0, v=0) x <- c( cos(pi/3), cos(pi/2 + pi/4)) y <- c( sin(pi/3), sin(pi/2 + pi/4)) arrows(c(0,0), c(0,0), x, y) lines(x,y, lwd=2, col="red") text(0, 0.9, expression(f^2 == 2*sum((1 - cos(alpha[i]-alpha[i-1])), i==1, n-1)), col="red") foo <- function(t, alpha) { xa <- sapply(seq(0, alpha, length=20), function(x) t*cos(x)) ya <- sapply(seq(0, alpha, length=20), function(x) t*sin(x)) lines(xa, ya) } foo(0.3, pi/3) foo(0.1, pi/2 + pi/4) foo(0.11, pi/2 + pi/4) text(0.34,0.18,expression(alpha[i]), cex=1.5) text(0.15,0.11,expression(alpha[i-1]), cex=1.5) par(opar)
is.regular tests whether a trajectory is regular (i.e. constant
time lag between successive relocations).
is.regular(ltraj)is.regular(ltraj)
ltraj |
an object of class |
is.regular returns a logical value
Clement Calenge [email protected]
data(capreotf) is.regular(capreotf) plotltr(capreotf, "dt") data(albatross) is.regular(albatross) plotltr(albatross, "dt")data(capreotf) is.regular(capreotf) plotltr(capreotf, "dt") data(albatross) is.regular(albatross) plotltr(albatross, "dt")
is.sd tests whether the bursts of relocations in an object of
class ltraj contain the same number of relocations, and cover
the same duration ("sd" = "same duration").sd2df gets one of the descriptive parameters of a regular "sd"
trajectory (e.g. "dt", "dist", etc.) and returns a data
frame with one relocation per row, and one burst per column.
is.sd(ltraj) sd2df(ltraj, what)is.sd(ltraj) sd2df(ltraj, what)
ltraj |
an object of class |
what |
a character string indicating the descriptive parameter of the trajectory to be exported |
is.sd returns a logical value.sd2df returns a data frame with one column per burst of
relocations, and one row per relocation.
Clement Calenge [email protected]
set.limits for additional information about
"sd" regular trajectories
## Not run: ## Takes the example from the help page of cutltraj (bear): data(bear) ## We want to study the trajectory of the animal at the scale ## of the day. We define one trajectory per day. The trajectory should begin ## at 22H00. ## The following function returns TRUE if the date is comprised between ## 21H00 and 22H00 and FALSE otherwise (i.e. correspond to the ## relocation taken at 21H30) foo <- function(date) { da <- as.POSIXlt(date, "UTC") ho <- da$hour + da$min/60 return(ho>21.1&ho<21.9) } ## We cut the trajectory into bursts after the relocation taken at 21H30: bea1 <- cutltraj(bear, "foo(date)", nextr = TRUE) bea1 ## Remove the first and last burst: bea2 <- bea1[-c(1,length(bea1))] ## Is the resulting object "sd" ? is.sd(bea2) ## Converts to data frame: df <- sd2df(bea2, "dist") ## Plots the average distance per hour meandi <- apply(df[-nrow(df),], 1, mean, na.rm = TRUE) sedi <- apply(df[-nrow(df),], 1, sd, na.rm = TRUE) / sqrt(ncol(df)) plot(seq(0, 23.5, length = 47), meandi, ty = "b", pch = 16, xlab = "Hours (time 0 = 22H00)", ylab="Average distance covered by the bear in 30 mins", ylim=c(0, 500)) lines(seq(0, 23.5, length = 47), meandi+sedi, col="grey") lines(seq(0, 23.5, length = 47), meandi-sedi, col="grey") ## End(Not run)## Not run: ## Takes the example from the help page of cutltraj (bear): data(bear) ## We want to study the trajectory of the animal at the scale ## of the day. We define one trajectory per day. The trajectory should begin ## at 22H00. ## The following function returns TRUE if the date is comprised between ## 21H00 and 22H00 and FALSE otherwise (i.e. correspond to the ## relocation taken at 21H30) foo <- function(date) { da <- as.POSIXlt(date, "UTC") ho <- da$hour + da$min/60 return(ho>21.1&ho<21.9) } ## We cut the trajectory into bursts after the relocation taken at 21H30: bea1 <- cutltraj(bear, "foo(date)", nextr = TRUE) bea1 ## Remove the first and last burst: bea2 <- bea1[-c(1,length(bea1))] ## Is the resulting object "sd" ? is.sd(bea2) ## Converts to data frame: df <- sd2df(bea2, "dist") ## Plots the average distance per hour meandi <- apply(df[-nrow(df),], 1, mean, na.rm = TRUE) sedi <- apply(df[-nrow(df),], 1, sd, na.rm = TRUE) / sqrt(ncol(df)) plot(seq(0, 23.5, length = 47), meandi, ty = "b", pch = 16, xlab = "Hours (time 0 = 22H00)", ylab="Average distance covered by the bear in 30 mins", ylim=c(0, 500)) lines(seq(0, 23.5, length = 47), meandi+sedi, col="grey") lines(seq(0, 23.5, length = 47), meandi-sedi, col="grey") ## End(Not run)
These functions allow to perform a non-parametric segmentation of a
time series using the penalized contrast method of Lavielle (1999,
2005). The function lavielle computes the contrast matrix
(i.e., the matrix used to segment the series) either from a series of
observations or from an animal trajectory. The function
chooseseg can be used to estimate the number of segments
building up the trajectory. The function findpath can be used
to find the limits of the segments (see Details).
lavielle(x, ...) ## Default S3 method: lavielle(x, Lmin, Kmax, ld = 1, type = c("mean", "var", "meanvar"), ...) ## S3 method for class 'ltraj' lavielle(x, Lmin, Kmax, ld = 1, which = "dist", type = c("mean", "var", "meanvar"), ...) ## S3 method for class 'lavielle' print(x, ...) chooseseg(lav, S = 0.75, output = c("full","opt"), draw = TRUE) findpath(lav, K, plotit = TRUE)lavielle(x, ...) ## Default S3 method: lavielle(x, Lmin, Kmax, ld = 1, type = c("mean", "var", "meanvar"), ...) ## S3 method for class 'ltraj' lavielle(x, Lmin, Kmax, ld = 1, which = "dist", type = c("mean", "var", "meanvar"), ...) ## S3 method for class 'lavielle' print(x, ...) chooseseg(lav, S = 0.75, output = c("full","opt"), draw = TRUE) findpath(lav, K, plotit = TRUE)
x |
for |
Lmin |
an integer value indicating the minimum number of
observations in each segment. Should be a multiple of |
Kmax |
an integer value indicating the maximum number of segments expected in the series |
ld |
an integer value indicating the resolution for the
calculation of the contrast function. The contrast function will be
evaluated for segments containing the observations |
type |
the type of contrast function to be used to segment the series (see Details) |
which |
a character string giving any syntactically correct R
expression implying the descriptive elements in |
lav |
an object of class |
S |
a value indicating the threshold in the second derivative of the contrast function |
output |
type of output expected (see the section value) |
draw |
a logical value indicating whether the decrease in the contrast function should be plotted |
K |
The number of segments |
plotit |
a logical value indicating whether the segmentation should be plotted |
... |
additional arguments to be passed from or to other functions |
The method of Lavielle (1999, 2005) per se finds the best segmentation
of a time series, given that it is built by K segments. It
searches the segmentation for which a contrast function (measuring the
contrast between the actual series and the segmented series) is
minimized. Different contrast functions are available measuring
different aspects of the variation of the series from one segment to
the next: when type = "mean", we suppose that only
the mean of the segments varies between segments; when type =
"var", we suppose that only the variance of the segments varies
between segments; when type = "meanvar", we suppose that both
the mean and the variance varies between segments. It is required to
specify a value for the minimum number of observations Lmin in
a segment, as well as the maximum number of segments Kmax in
the series.
There are several approaches to estimate the best number of segments
K to partition the time series. One possible approach is
the graphical examination of the decrease of the contrast function
with the number of segments. In theory, there should be a clear
"break" in the decrease of this function after the optimal value of
K. Lavielle (2005) suggested an alternative way to estimate
automatically the optimal number of segments, also relying on the
presence of a "break" in the decrease of the contrast function. He
proposed to choose the last value of K for which the second
derivative of a standardized constrast function is greater than a
threshold S (see Lavielle, 2005 for details). Based on
numerical experiments, he proposed to choose the value S =
0.75. Note, however, that for short time series (i.e. less than 500
observations) some simulations indicated that this value may not be
optimal and may depend on the value of Kmax, so that the
graphical method is maybe more appropriate.
The function lavielle.default returns a list of class
lavielle, with an attribute "typeseg" set to
"default". This list contains the following elements:
contmat |
The contrast matrix |
sumcont |
The optimal contrast |
matpath |
The matrix of the paths from the first to the last observation |
Kmax |
The maximum number of segments |
Lmin |
The minimum number of observations in a segment |
ld |
the value of the resolution |
series |
The time series |
The function lavielle.ltraj also returns a list of class
lavielle, with an attribute "typeseg" set to
"ltraj".
The function chooseseg returns the optimal number of segments
when output = "opt", and a dataframe containing the value of
the contrast function Jk and of the second derivative D
of the standardized contrast function for each possible value of
K, if output = "full".
The function findpath return a list containing vectors giving
the index of the first and last observations in each segment, when the
object of class "lavielle" passed as argument is characterized
by an attribute "typeseg" set to "default". When the
attribute "typeseg" is set to "ltraj", this function
returns an object of class ltraj where each burst correspond to a
segment.
The contrast matrix is a matrix of size n*n (with n the
number of observations in the series). If n is large, memory
problems may occur. In this case, setting ld to a value
greater than one will allow to reduce the size of this matrix (i.e. it
will be of size k*k, where k = floor(n/ld)). However,
this will also reduce the resolution of the segmentation, so that the
segment limits will be less precisely estimated.
Clement Calenge [email protected]. The code is a C translation based on the Matlab code of M. Lavielle
Lavielle, M. (1999) Detection of multiple changes in a sequence of dependent variables. Stochastic Processes and their Applications, 83: 79–102.
Lavielle, M. (2005) Using penalized contrasts for the change-point problem. Report number 5339, Institut national de recherche en informatique et en automatique.
################################################# ## ## A simulated series suppressWarnings(RNGversion("3.5.0")) set.seed(129) seri <- c(rnorm(100), rnorm(100, mean=2), rnorm(100), rnorm(100, mean=-3), rnorm(100), rnorm(100, mean=2)) plot(seri, ty="l", xlab="time", ylab="Series") ## Segmentation: (l <- lavielle(seri, Lmin=10, Kmax=20)) ## choose the number of segments chooseseg(l) ## There is a clear break in the ## decrease of the contrast function after K = 6 ## Moreover, Jk(6) >> 0.75 and Jk(7) << 0.75 ## We choose 6 segments: fp <- findpath(l, 6) fp ## This list gives the limits of the segments ## for example, to get the first segment: seg <- 1 firstseg <- seri[fp[[seg]][1]:fp[[seg]][2]] #################################################### ## ## Now, changes of variance ## A simulated series suppressWarnings(RNGversion("3.5.0")) set.seed(129) seri <- c(rnorm(100), rnorm(100, sd=2), rnorm(100), rnorm(100, sd=3), rnorm(100), rnorm(100, sd=2)) plot(seri, ty="l", xlab="time", ylab="Series") ## Segmentation: (l <- lavielle(seri, Lmin=10, Kmax=20, type="var")) ## choose the number of segments chooseseg(l) ## There is a clear break in the ## decrease of the contrast function after K = 6 ## Moreover, Jk(6) >> 0.75 and Jk(7) << 0.75 ## We choose 6 segments: fp <- findpath(l, 6) fp ## This list gives the limits of the segments ## for example, to get the first segment: seg <- 1 firstseg <- seri[fp[[seg]][1]:fp[[seg]][1]] ################################################# ## ## Example of segmentation of a trajectory ## Show the trajectory data(porpoise) gus <- porpoise[1] plot(gus) ## Show the changes in the distance between ## successive relocations with the time plotltr(gus, "dist") ## Segmentation of the trajectory based on these distances lav <- lavielle(gus, Lmin=2, Kmax=20) ## Choose the number of segments chooseseg(lav) ## 4 segments seem a good choice ## Show the partition kk <- findpath(lav, 4) plot(kk)################################################# ## ## A simulated series suppressWarnings(RNGversion("3.5.0")) set.seed(129) seri <- c(rnorm(100), rnorm(100, mean=2), rnorm(100), rnorm(100, mean=-3), rnorm(100), rnorm(100, mean=2)) plot(seri, ty="l", xlab="time", ylab="Series") ## Segmentation: (l <- lavielle(seri, Lmin=10, Kmax=20)) ## choose the number of segments chooseseg(l) ## There is a clear break in the ## decrease of the contrast function after K = 6 ## Moreover, Jk(6) >> 0.75 and Jk(7) << 0.75 ## We choose 6 segments: fp <- findpath(l, 6) fp ## This list gives the limits of the segments ## for example, to get the first segment: seg <- 1 firstseg <- seri[fp[[seg]][1]:fp[[seg]][2]] #################################################### ## ## Now, changes of variance ## A simulated series suppressWarnings(RNGversion("3.5.0")) set.seed(129) seri <- c(rnorm(100), rnorm(100, sd=2), rnorm(100), rnorm(100, sd=3), rnorm(100), rnorm(100, sd=2)) plot(seri, ty="l", xlab="time", ylab="Series") ## Segmentation: (l <- lavielle(seri, Lmin=10, Kmax=20, type="var")) ## choose the number of segments chooseseg(l) ## There is a clear break in the ## decrease of the contrast function after K = 6 ## Moreover, Jk(6) >> 0.75 and Jk(7) << 0.75 ## We choose 6 segments: fp <- findpath(l, 6) fp ## This list gives the limits of the segments ## for example, to get the first segment: seg <- 1 firstseg <- seri[fp[[seg]][1]:fp[[seg]][1]] ################################################# ## ## Example of segmentation of a trajectory ## Show the trajectory data(porpoise) gus <- porpoise[1] plot(gus) ## Show the changes in the distance between ## successive relocations with the time plotltr(gus, "dist") ## Segmentation of the trajectory based on these distances lav <- lavielle(gus, Lmin=2, Kmax=20) ## Choose the number of segments chooseseg(lav) ## 4 segments seem a good choice ## Show the partition kk <- findpath(lav, 4) plot(kk)
The two functions ld and dl are useful to quickly
convert objects of class ltraj from and to dataframes.
ld(ltraj) dl(x, proj4string=CRS())ld(ltraj) dl(x, proj4string=CRS())
ltraj |
an object of class |
x |
an object of class |
proj4string |
a valid CRS object containing the projection information. |
The function ld concatenates all bursts in an object of class
ltraj, adds two columns named id and burst, and,
when it is present, also adds the variables in the infolocs
component.
The function dl creates an object of class ltraj from a
data.frame. If no column named id exists, a random ID
is generated. If no column named burst exists, the ID is used
as burst. The columns named "dx", "dy", "dist", "dt", "R2n",
"abs.angle" and "rel.angle" are recomputed by the function (see
?as.ltraj). Additional columns are used as the infolocs
component.
ld returns an object of class data.frame.dl returns an object of class ltraj.
Clement Calenge [email protected]
as.ltraj for additional information about objects of
class ltraj
data(puechcirc) puechcirc ## class ltraj uu <- ld(puechcirc) head(uu) dl(uu)data(puechcirc) puechcirc ## class ltraj uu <- ld(puechcirc) head(uu) dl(uu)
These functions convert the class "ltraj" available in adehabitatLT toward
classes available in the package sp.
ltraj2spdf converts an object of class ltraj into an
object of class SpatialPointsDataFrame.
ltraj2sldf converts an object of class ltraj into an
object of class SpatialLinesDataFrame.
ltraj2spdf(ltr) ltraj2sldf(ltr, byid = FALSE)ltraj2spdf(ltr) ltraj2sldf(ltr, byid = FALSE)
ltr |
an object of class |
byid |
logical. If |
Clement Calenge [email protected]
ltraj for objects of class
ltraj.
## Not run: if (require(sp)) { ######################################### ## ## Conversion ltraj -> SpatialPointsDataFrame ## data(puechcirc) plot(puechcirc) toto <- ltraj2spdf(puechcirc) plot(toto) ######################################### ## ## Conversion ltraj -> SpatialLinesDataFrame ## toto <- ltraj2sldf(puechcirc) plot(toto) } ## End(Not run)## Not run: if (require(sp)) { ######################################### ## ## Conversion ltraj -> SpatialPointsDataFrame ## data(puechcirc) plot(puechcirc) toto <- ltraj2spdf(puechcirc) plot(toto) ######################################### ## ## Conversion ltraj -> SpatialLinesDataFrame ## toto <- ltraj2sldf(puechcirc) plot(toto) } ## End(Not run)
Objects of class ltraj are often created with data collected
using some form of telemetry (radio-tracking, G.P.S., etc.). However,
the relocations of the monitored animals are always somewhat
imprecise. The function mindistkeep considers that when
the distance between two successive relocations is lower than a given
threshold distance, the animal actually does not move (and replaces
the coordinates of relocation i+1 by the coordinates of relocation
i).
mindistkeep(x, threshold)mindistkeep(x, threshold)
x |
An object of class |
threshold |
The minimum distance under which is is considered that the animal does not move |
An object of class ltraj
Clement Calenge [email protected]
data(puechcirc) plot(puechcirc) i <- mindistkeep(puechcirc, 10) plot(i)data(puechcirc) plot(puechcirc) i <- mindistkeep(puechcirc, 10) plot(i)
These functions partition a trajectory into several segments corresponding to different behaviours of the animal.
modpartltraj is used to generate the models to which the trajectory
is compared.
bestpartmod is used to compute the optimal number of segments
of the partition.
partmod.ltraj is used to partition the trajectory into
npart segments. plot.partltraj can be used to plot the
results.
modpartltraj(tr, limod) ## S3 method for class 'modpartltraj' print(x, ...) bestpartmod(mods, Km = 30, plotit = TRUE, correction = TRUE, nrep = 100) partmod.ltraj(tr, npart, mods, na.manage = c("prop.move","locf")) ## S3 method for class 'partltraj' print(x, ...) ## S3 method for class 'partltraj' plot(x, col, addpoints = TRUE, lwd = 2, ...)modpartltraj(tr, limod) ## S3 method for class 'modpartltraj' print(x, ...) bestpartmod(mods, Km = 30, plotit = TRUE, correction = TRUE, nrep = 100) partmod.ltraj(tr, npart, mods, na.manage = c("prop.move","locf")) ## S3 method for class 'partltraj' print(x, ...) ## S3 method for class 'partltraj' plot(x, col, addpoints = TRUE, lwd = 2, ...)
tr |
an object of class |
limod |
a list of syntactically correct R expression giving the
models for the trajectory, implying one or several elements in
|
x, mods
|
an object of class |
na.manage |
a character string indicating what should be done
with the missing values located between two segments. With
|
npart |
the number of partitions of the trajectory |
Km |
the maximum number of partitions of the trajectory |
plotit |
logical. Whether the results should be plotted. |
correction |
logical. Whether the log-likelihood should be corrected (see details). |
nrep |
logical. The number of Monte Carlo simulations used to correct the log-likelihood for each number of segments. |
col |
the colors to be used for the models |
addpoints |
logical. Whether the relocations should be added to the graph |
lwd |
the line width |
... |
additional arguments to be passed to other functions |
A trajectory is made of successive steps traveled by an organism in the geographical space. These steps (the line connecting two successive relocations) can be described by a certain number of descriptive parameters (relative angles between successive steps, length of the step, etc.). One aim of the trajectory analysis is to identify the structure of the trajectory, i.e. the parts of the trajectory where the steps have homogeneous properties. Indeed, an animal may have a wide variety of behaviours (feeding, traveling, escape from a predator, etc.). As a result, partitioning a trajectory occupies a central place in trajectory analysis.
These functions are to be used to partition a trajectory based on Markov models of animal movements. For example, one may suppose that a normal distribution generated the step lengths, with a different mean for each type of behaviour. These models and the value of their parameters are supposed a priori by the analyst. These functions allow, based on these a priori models, to find both the number and the limits of the segments building up the trajectory (see examples). Any model can be supposed for any parameter of the steps (the distance, relative angles, etc.), provided that the model is Markovian.
The rationale behind this algorithm is the following. First, the user
should propose a set of model describing the movements of the animals,
in the different segments of the trajectory. For example, the user may
define two models of normal distribution for the step length, with
means equal to 10 meters (i.e. a trajectory with relatively small steps)
and 100 meters (i.e. a trajectory with longer step lengths). For a
given step of the trajectory, it is possible to compute the probability
density that the step has been generated by each model of the set.
The function modpartltraj computes the matrix containing the
probability densities associated to each step (rows), under each model
of the set (columns). This matrix is of class modpartltraj.
Then, the user can estimate the optimal number of segments in the
trajectory, given the set of a priori models, using the function
bestpartmod, taking as argument the matrix of class
modpartltraj. If correction = FALSE, this function
returns the log of the probability (log-likelihood) that the trajectory
is actually made of K segments, with each one described by one
model. The resulting graph can be used to choose an optimal number of
segment for the partition. Note that Gueguen (2009) noted that this
algorithm tends to overestimate the number of segments in a
trajectory. He proposed to correct this estimation using Monte Carlo
simulations of the independence of the steps within the trajectory. At
each step of the randomization process, the order of the rows of the
matrix is randomized, and the curve of log-likelihood is computed for
each number of segments, for the randomized trajectory. Then, the
observed log-likelihood is corrected by these simulations: for a given
number of segments, the corrected log-likelihood is equal to the
observed log-likelihood minus the simulated log-likelihood. Because
there is a large number of simulations of the independence, a
distribution of corrected log-likelihoods is available for each number
of segments. The "best" number of segments is the one for which the
median of the distribution of corrected log-likelihood is maximum.
Finally, once the optimal number of segments npart has been
chosen, the function partmod.ltraj can be used to compute the
partition.
The mathematical rationale underlying these two functions is the
following: given an optimal k-partition of the trajectory, if the ith
step of the trajectory belongs to the segment k predicted by the model d,
then either the relocation (i-1) belongs to the same segment, in which
case the segment containing (i-1) is predicted by d, or the relocation
(i-1) belongs to another segment, and the other (k-1) segments
together constitute an optimal (k-1) partition of the trajectory
1-(i-1). These two probabilities are computed recursively by the
functions from the matrix of class partmodltraj, observing that
the probability of a 1-partition of the trajectory from 1 to i described
by the model m (i.e. only one segment describing the trajectory) is
simply the product of the probability densities of the steps from 1 to
i under the model m. Further details can be found in Gueguen (2001, 2009).
partmodltraj returns a matrix of class partmodltraj
containing the probability densities of the steps of the trajectory
(rows) for each model (columns).
bestpartmod returns a list with two elements: (i) the element
mk is a vector containing the values of the log-probabilities
for each number of segments (varying from 1 to Km), and (ii)
the element correction contains either "none" or a
matrix containing the corrected log-likelihood for each number of
segments (rows) and each simulation of the independence (column).
partmod.ltraj returns a list of class partltraj with the
following components: ltraj is an object of class ltraj
containing the segmented trajectory (one burst of relocations per segment
of the partition); stats is a list containing the following
elements:
locs |
The number ID of the relocations starting the segments (except the last one which ends the last segment) |
Mk |
The value of the cumulative log-probability for the Partition (i.e. the log-probability associated to a K-partition is equal to the log-probability associated to the (K-1)-partition plus the log-probability associated to the Kth segment) |
mod |
The number ID of the model chosen for each segment |
which.mod |
the name of the model chosen for each segment |
Clement Calenge [email protected]
Calenge, C., Gueguen, L., Royer, M. and Dray, S. (unpublished) Partitioning the trajectory of an animal with Markov models.
Gueguen, L. (2001) Segmentation by maximal predictive partitioning according to composition biases. Pp 32–44 in: Gascuel, O. and Sagot, M.F. (Eds.), Computational Biology, LNCS, 2066.
Gueguen, L. (2009) Computing the likelihood of sequence segmentation under Markov modelling. Arxiv preprint arXiv:0911.3070.
## Not run: ## Example on the porpoise data(porpoise) ## Keep the first porpoise gus <- porpoise[1] plot(gus) ## First test the independence of the step length indmove(gus) ## There is a lack of independence between successive distances ## plots the distance according to the date plotltr(gus, "dist") ## One supposes that the distance has been generated ## by normal distribution, with different means for the ## different behaviours ## The means of the normal distribution range from 0 to ## 130000. We suppose a standard deviation equal to 5000: tested.means <- round(seq(0, 130000, length = 10), 0) (limod <- as.list(paste("dnorm(dist, mean =", tested.means, ", sd = 5000)"))) ## Build the probability matrix mod <- modpartltraj(gus, limod) ## computes the corrected log-likelihood for each ## number of segments bestpartmod(mod) ## The best number of segments is 4. Compute the partition: (pm <- partmod.ltraj(gus, 4, mod)) plot(pm) ## Shows the partition on the distances: plotltr(gus, "dist") lapply(1:length(pm$ltraj), function(i) { lines(pm$ltraj[[i]]$date, rep(tested.means[pm$stats$mod[i]], nrow(pm$ltraj[[i]])), col=c("red","green","blue")[as.numeric(factor(pm$stats$mod))[i]], lwd=2) }) ## Computes the residuals of the partition res <- unlist(lapply(1:length(pm$ltraj), function(i) { pm$ltraj[[i]]$dist - rep(tested.means[pm$stats$mod[i]], nrow(pm$ltraj[[i]])) })) plot(res, ty = "l") ## Test of independence of the residuals of the partition: wawotest(res) ## End(Not run)## Not run: ## Example on the porpoise data(porpoise) ## Keep the first porpoise gus <- porpoise[1] plot(gus) ## First test the independence of the step length indmove(gus) ## There is a lack of independence between successive distances ## plots the distance according to the date plotltr(gus, "dist") ## One supposes that the distance has been generated ## by normal distribution, with different means for the ## different behaviours ## The means of the normal distribution range from 0 to ## 130000. We suppose a standard deviation equal to 5000: tested.means <- round(seq(0, 130000, length = 10), 0) (limod <- as.list(paste("dnorm(dist, mean =", tested.means, ", sd = 5000)"))) ## Build the probability matrix mod <- modpartltraj(gus, limod) ## computes the corrected log-likelihood for each ## number of segments bestpartmod(mod) ## The best number of segments is 4. Compute the partition: (pm <- partmod.ltraj(gus, 4, mod)) plot(pm) ## Shows the partition on the distances: plotltr(gus, "dist") lapply(1:length(pm$ltraj), function(i) { lines(pm$ltraj[[i]]$date, rep(tested.means[pm$stats$mod[i]], nrow(pm$ltraj[[i]])), col=c("red","green","blue")[as.numeric(factor(pm$stats$mod))[i]], lwd=2) }) ## Computes the residuals of the partition res <- unlist(lapply(1:length(pm$ltraj), function(i) { pm$ltraj[[i]]$dist - rep(tested.means[pm$stats$mod[i]], nrow(pm$ltraj[[i]])) })) plot(res, ty = "l") ## Test of independence of the residuals of the partition: wawotest(res) ## End(Not run)
This dataset is an object of class "ltraj" (regular trajectory, relocations every 20 minutes) containing the GPS relocations of one mouflon during two week-ends in the Caroux mountain (South of France).
data(mouflon)data(mouflon)
Office national de la chasse et de la faune sauvage, CNERA Faune de Montagne, 95 rue Pierre Flourens, 34000 Montpellier, France.
data(mouflon) plot(mouflon)data(mouflon) plot(mouflon)
na.omit.ltraj can be used to remove missing relocations from a
trajectory.
## S3 method for class 'ltraj' na.omit(object, ...)## S3 method for class 'ltraj' na.omit(object, ...)
object |
an object of class |
... |
additionnal arguments to be passed to or from other methods |
An object of class ltraj
Clement Calenge [email protected]
setNA to place the missing values in the trajectory
data(puechcirc) puechcirc na.omit(puechcirc)data(puechcirc) puechcirc na.omit(puechcirc)
This functions allows to set an offset value from the date in an
object of class ltraj of type II (time recorded).
offsetdate(ltraj, offset, units = c("sec", "min", "hour", "day"))offsetdate(ltraj, offset, units = c("sec", "min", "hour", "day"))
ltraj |
an object of class |
offset |
a numeric value indicating the offset to be deducted from the date |
units |
a character string indicating the time units for
|
The use of offset is a convenient way to define reference dates in an
object of class ltraj. For example, if the animal is monitored
every night, from 18H00 to 06H00, the fact that the beginning and the
end of the monitoring do not correspond to the same day may cause
difficulties to handle the trajectory. Though these difficulties are
not unsurmountable, it is often convenient to deduct an offset to the
trajectory, so that the first relocation is collected at 0H and the
last one at 12H00 the same day (i.e., in this example, an offset of
18 hours).
an object of class ltraj
Clement Calenge [email protected]
ltraj for additional information on objects of
class ltraj
data(puechcirc) plotltr(puechcirc, "dt") toto <- offsetdate(puechcirc, 17, "hour") plotltr(puechcirc, "dt")data(puechcirc) plotltr(puechcirc, "dt") toto <- offsetdate(puechcirc, 17, "hour") plotltr(puechcirc, "dt")
plot.ltraj allows various graphical displays of the
trajectories.
## S3 method for class 'ltraj' plot(x, id = unique(unlist(lapply(x, attr, which = "id"))), burst = unlist(lapply(x, attr, which = "burst")), spixdf = NULL, spoldf = NULL, xlim = NULL, ylim = NULL, colspixdf = gray((240:1)/256), colspoldf = "green", addpoints = TRUE, addlines = TRUE, perani = TRUE, final = TRUE, ...)## S3 method for class 'ltraj' plot(x, id = unique(unlist(lapply(x, attr, which = "id"))), burst = unlist(lapply(x, attr, which = "burst")), spixdf = NULL, spoldf = NULL, xlim = NULL, ylim = NULL, colspixdf = gray((240:1)/256), colspoldf = "green", addpoints = TRUE, addlines = TRUE, perani = TRUE, final = TRUE, ...)
x |
an object of class |
id |
a character vector containing the identity of the individuals of interest |
burst |
a character vector containing the burst levels of interest |
spixdf |
an object of class |
spoldf |
an object of class |
xlim |
the ranges to be encompassed by the x axis |
ylim |
the ranges to be encompassed by the y axis |
colspixdf |
a character vector giving the colors of the map
|
colspoldf |
a character vector giving the colors of the polygon contour
map, when |
addpoints |
logical. If |
addlines |
logical. If |
perani |
logical. If |
final |
logical. If |
... |
arguments to be passed to the generic
function |
Clement Calenge [email protected]
For further information on the class ltraj,
ltraj.
data(puechcirc) plot(puechcirc) plot(puechcirc, perani = FALSE) plot(puechcirc, id = "JE93", perani = FALSE) data(puechabonsp) plot(puechcirc, perani = FALSE, spixdf = puechabonsp$map[,1]) cont <- getcontour(puechabonsp$map[,1]) plot(puechcirc, spoldf = cont)data(puechcirc) plot(puechcirc) plot(puechcirc, perani = FALSE) plot(puechcirc, id = "JE93", perani = FALSE) data(puechabonsp) plot(puechcirc, perani = FALSE, spixdf = puechabonsp$map[,1]) cont <- getcontour(puechabonsp$map[,1]) plot(puechcirc, spoldf = cont)
This function allows a graphical examination of the changes in
descriptive parameters in objects of class ltraj
plotltr(x, which = "dist", pch = 16, cex = 0.7, addlines = TRUE, addpoints = TRUE,...)plotltr(x, which = "dist", pch = 16, cex = 0.7, addlines = TRUE, addpoints = TRUE,...)
x |
An object of class |
which |
a character string giving any syntactically correct R
expression implying the descriptive elements in |
pch |
the type of points on the plot (see |
cex |
the size of points on the plot (see |
addlines |
logical. Indicates whether lines should be added to the plot. |
addpoints |
logical. Indicates whether points should be added to the plot. |
... |
additional parameters to be passed to the generic
function |
Clement Calenge [email protected]
ltraj for additional information about
objects of class ltraj, and sliwinltr for a
sliding window smoothing
data(puechcirc) plotltr(puechcirc, "cos(rel.angle)") plotltr(puechcirc, "dist") plotltr(puechcirc, "dx")data(puechcirc) plotltr(puechcirc, "cos(rel.angle)") plotltr(puechcirc, "dist") plotltr(puechcirc, "dx")
This data set contains the relocations of 3 porpoises
data(porpoise)data(porpoise)
This data set is a regular object of class ltraj (i.e. constant
time lag of 24H).
The coordinates are given in meters (UTM - zone 19).
http://whale.wheelock.edu/
data(porpoise) plot(porpoise)data(porpoise) plot(porpoise)
This data set is an object of class ltraj, giving the results of the
monitoring of 2 wild boars by radio-tracking at Puechabon (Mediterranean
habitat, South of France). These data have been
collected by Daniel Maillard (Office national de la chasse et de la
faune sauvage), and correspond to the activity period of the wild boar
(during the night, when the animals forage. The data set
puechabonsp in the package adehabitatMA describes the
resting sites).
data(puechcirc)data(puechcirc)
This object has, in total, 204 relocations distributed among two
animals and three bursts of relocations (CH930803, CH930824,
CH930827, and JE930827).
Maillard, D. (1996). Occupation et utilisation de la garrigue et du vignoble mediterraneens par le Sanglier. Universite d'Aix-Marseille III: PhD thesis.
The functions allow the examination of the distribution of trajectories descriptors (see Details).
## Chi distribution of the increment length / sqrt(dt) qqchi(y, ...) ## Default S3 method: qqchi(y, df = 2, ylim, main = "Chi Q-Q Plot", xlab = "Theoretical Quantiles", ylab = "Sample Quantiles", plot.it = TRUE, datax = FALSE, ...) ## S3 method for class 'ltraj' qqchi(y, xlab = "Theoretical Quantiles", ylab = "Sample Quantiles (Distances)", ...) ## Normal Distribution of dx/sqrt(dt) or dy/sqrt(dt) ## S3 method for class 'ltraj' qqnorm(y, which=c("dx","dy"), ...)## Chi distribution of the increment length / sqrt(dt) qqchi(y, ...) ## Default S3 method: qqchi(y, df = 2, ylim, main = "Chi Q-Q Plot", xlab = "Theoretical Quantiles", ylab = "Sample Quantiles", plot.it = TRUE, datax = FALSE, ...) ## S3 method for class 'ltraj' qqchi(y, xlab = "Theoretical Quantiles", ylab = "Sample Quantiles (Distances)", ...) ## Normal Distribution of dx/sqrt(dt) or dy/sqrt(dt) ## S3 method for class 'ltraj' qqnorm(y, which=c("dx","dy"), ...)
y |
a vector containing the data sample for |
df |
the number of degrees of freedom of the Chi distribution (default to 2). |
xlab, ylab, main
|
plot labels. |
plot.it |
logical. Should the result be plotted? |
datax |
logical. Should data values be on the x-axis? |
which |
a character string indicating the component (dx or dy) to be examined. |
ylim, ...
|
graphical parameters. |
Among the numerous statistics that can be used to describe the
movements of an animal, the length of the increment between two
successive relocations is very common. This increment can be
described by a vector i = c(dx, dy). Under the hypothesis
of a Brownian motion, dx and dy should be normally distributed with
mean = 0 and variance = dt (where dt is the time interval between the
two relocations). Therefore, dx/sqrt(dt) and
dy/sqrt(dt) should be normally distributed with mean = 0 and
variance = 1. The function qqnorm.ltraj performs a
quantile-quantile plot of dx/sqrt(dt) or dy/sqrt(dt)
vs. a normal distribution to verify wether the Brownian motion
assumption is correct.
Furthermore, the quantity (dx^2 + dy^2)/dt should be
distributed according to a Chi-squared distribution with two degrees
of freedom. Thus, the quantity distance / sqrt(dt) should be
distributed according to a Chi distribution with two degrees of
freedom (where distance is the distance between the two
relocations). The function qqchi.ltraj performs
quantile-quantile plot of distance/sqrt(dt) vs. a Chi
distribution to verify wether the Brownian motion
assumption is correct.
for functions dealing with objects of class ltraj, a list with
components being themselves lists, with components:
x |
The x coordinates of the points that were/would be plotted |
y |
The original |
Clement Calenge [email protected]
## Example with an Arithmetic Brownian Process toto <- simm.mba(1:500, sig = diag(c(5, 5))) qqnorm(toto, "dx") qqnorm(toto, "dy") qqchi(toto) ## Example of wild boar data(puechcirc) qqnorm(puechcirc, "dx") qqnorm(puechcirc, "dy") qqchi(puechcirc)## Example with an Arithmetic Brownian Process toto <- simm.mba(1:500, sig = diag(c(5, 5))) qqnorm(toto, "dx") qqnorm(toto, "dy") qqchi(toto) ## Example of wild boar data(puechcirc) qqnorm(puechcirc, "dx") qqnorm(puechcirc, "dy") qqchi(puechcirc)
The function rasterize.ltraj allows to rasterize a trajectory.
rasterize.ltraj(ltr, map)rasterize.ltraj(ltr, map)
ltr |
An object of class |
map |
An object inheriting the class |
A list of objects of class SpatialPointsDataFrame, with one
component per burst in the object of class ltraj. Each object
contains the coordinates of the pixels of the maps traversed by the
trajectory. The number of the step that traverse each pixel is
indicated.
Clement Calenge [email protected]
as.ltraj for additional information about objects of
class ltraj
data(puechabonsp) data(puechcirc) ## Show the trajectories on the map plot(puechcirc, spixdf = puechabonsp$map) ## rasterize the trajectories ii <- rasterize.ltraj(puechcirc, puechabonsp$map) ## show, e.g. the first rasterized trajectory tr1 <- ii[[1]] head(tr1) plot(tr1) ## so, for example, to see the pixels traversed by the third step of the ## trajectory points(tr1[tr1[[1]]==3,], col="red") ## So, if we want to calculate the mean elevation for each step: mel <- over(tr1, puechabonsp$map) mo <- tapply(mel[[1]], tr1[[1]], mean) plot(mo, ty="l") ## It is clear that elevation decreases at the middle of the monitoring ## and increases again at the end (the animal sleeps on the plateau ## and goes down in the vineyards during the night). ## Now define an infolocs component in puechcirc corresponding to the ## mean elevation: val <- lapply(1:length(ii), function(i) { ## get the rasterized trajectory tr <- ii[[i]] ## get the pixels of the map mel <- over(tr, puechabonsp$map) ## calculate the mean elevation mo <- tapply(mel[[1]], tr[[1]], mean) ## prepare the output elev <- rep(NA, nrow(puechcirc[[i]])) ## place the average values at the right place ## names(mo) contains the step number (i.e. relocation ## number +1) elev[as.numeric(names(mo))+1] <- mo ## Checks that the row.names are the same for ## the result and the ltraj component df <- data.frame(elevation = elev) row.names(df) <- row.names(puechcirc[[i]]) return(df) }) ## define the infolocs component infolocs(puechcirc) <- val ## and draw the trajectory plotltr(puechcirc, "elevation")data(puechabonsp) data(puechcirc) ## Show the trajectories on the map plot(puechcirc, spixdf = puechabonsp$map) ## rasterize the trajectories ii <- rasterize.ltraj(puechcirc, puechabonsp$map) ## show, e.g. the first rasterized trajectory tr1 <- ii[[1]] head(tr1) plot(tr1) ## so, for example, to see the pixels traversed by the third step of the ## trajectory points(tr1[tr1[[1]]==3,], col="red") ## So, if we want to calculate the mean elevation for each step: mel <- over(tr1, puechabonsp$map) mo <- tapply(mel[[1]], tr1[[1]], mean) plot(mo, ty="l") ## It is clear that elevation decreases at the middle of the monitoring ## and increases again at the end (the animal sleeps on the plateau ## and goes down in the vineyards during the night). ## Now define an infolocs component in puechcirc corresponding to the ## mean elevation: val <- lapply(1:length(ii), function(i) { ## get the rasterized trajectory tr <- ii[[i]] ## get the pixels of the map mel <- over(tr, puechabonsp$map) ## calculate the mean elevation mo <- tapply(mel[[1]], tr[[1]], mean) ## prepare the output elev <- rep(NA, nrow(puechcirc[[i]])) ## place the average values at the right place ## names(mo) contains the step number (i.e. relocation ## number +1) elev[as.numeric(names(mo))+1] <- mo ## Checks that the row.names are the same for ## the result and the ltraj component df <- data.frame(elevation = elev) row.names(df) <- row.names(puechcirc[[i]]) return(df) }) ## define the infolocs component infolocs(puechcirc) <- val ## and draw the trajectory plotltr(puechcirc, "elevation")
This functions rediscretizes one or several trajectories in an object
of class ltraj.
redisltraj(l, u, burst = NULL, samplex0 = FALSE, addbit = FALSE, nnew = 5, type = c("space", "time"))redisltraj(l, u, burst = NULL, samplex0 = FALSE, addbit = FALSE, nnew = 5, type = c("space", "time"))
l |
an object of class |
u |
the new step length in units of the coordinates or step duration in seconds |
burst |
The burst identity of trajectories to be rediscretized. |
samplex0 |
Whether the first relocation of the trajectory should be sampled |
addbit |
logical. When |
nnew |
optionnally, you may specify the maximum ratio between number of relocations of the new trajectory. If not specified, this maximum is equal to 5 times the number of relocations of the raw trajectory. |
type |
a character string indicating whether the step duration
( |
The rediscretization of trajectory has been advocated by several authors in the literature (Turchin 1998, Bovet & Benhamou 1988). It is also the first step of the computation of the fractal dimension of the path (Sugihara & May 1990).
When type="time", a linear interpolation is performed to find
new relocations separated by the given time lag.
An object of class "ltraj"
Clement Calenge [email protected]
Bovet, P., & Benhamou, S. (1988) Spatial analysis of animal's movements using a correlated random walk model. Journal of Theoretical Biology 131: 419–433.
Turchin, P. (1998) Quantitative analysis of movement, Sunderland, MA.
Sugihara, G., & May, R. (1990) Applications of fractals in Ecology. Trends in Ecology and Evolution 5: 79–86.
ltraj for further information on objects of
class ltraj
##################################### ## ## Example of space rediscretization data(puechcirc) puechcirc ## before rediscretization plot(puechcirc, perani = FALSE) ## after rediscretization toto <- redisltraj(puechcirc, 100) plot(toto, perani = FALSE) ##################################### ## ## Example of time rediscretization data(buffalo) tr <- buffalo$traj ## Show the time lag before rediscretization plotltr(tr, "dt") ## Rediscretization every 1800 seconds tr <- redisltraj(tr, 1800, type="time") ## Show the time lag after rediscretization plotltr(tr, "dt")##################################### ## ## Example of space rediscretization data(puechcirc) puechcirc ## before rediscretization plot(puechcirc, perani = FALSE) ## after rediscretization toto <- redisltraj(puechcirc, 100) plot(toto, perani = FALSE) ##################################### ## ## Example of time rediscretization data(buffalo) tr <- buffalo$traj ## Show the time lag before rediscretization plotltr(tr, "dt") ## Rediscretization every 1800 seconds tr <- redisltraj(tr, 1800, type="time") ## Show the time lag after rediscretization plotltr(tr, "dt")
These functions can be used to apply the residence time method (Barraquand and Benhamou, 2008).
residenceTime(lt, radius, maxt, addinfo = FALSE, units = c("seconds", "hours", "days")) ## S3 method for class 'resiti' print(x, ...) ## S3 method for class 'resiti' plot(x, addpoints = FALSE, addlines = TRUE, ...)residenceTime(lt, radius, maxt, addinfo = FALSE, units = c("seconds", "hours", "days")) ## S3 method for class 'resiti' print(x, ...) ## S3 method for class 'resiti' plot(x, addpoints = FALSE, addlines = TRUE, ...)
lt |
an object of class |
radius |
the radius of the patch (in units of the coordinates) |
maxt |
maximum time threshold that the animal is allowed to spend outside the patch before that we consider that the animal actually left the patch (see Details) |
addinfo |
logical value. If |
units |
a character string indicating the time units of
|
x |
an object of class |
addpoints |
logical. Whether points should be added to the plot. |
addlines |
logical. Whether lines should be added to the plot. |
... |
additionnal arguments to be passed to or from other methods |
Barraquand and Benhamou (2008) proposed a new approach to identify the
places where the animals spend the most of their time, relying on the
calculation of their residence time in the various places where they
have been relocated. This approach is similar to the
first passage time method: for a given value of radius and for
a given relocation, the first passage time is defined as the time
required by the animal to pass through a circle of given radius
centred on the relocation (see the help page of the function
fpt for additional details). The residence time associated to
a given relocation corresponds to the first passage time calculated at
this place plus the passage times that occurred in this circle
before or after the current relocation, *given* that
the animal did not spent a time greater than maxt before
reentering the circle (see Barraquand and Benhamou, 2008, for
details). It is therefore computed by determining the various times
at which the path intersects the perimeter of the circle
centred on the current relocation, both forward and backward, and
then by summing the durations associated with the
various portions of the path occurring within the circle. The
graphical examination of the changes with time allow to identify the
dates and places where the animal spent most of its time.
A partitionning method can be used to segment the series formed by the
residence time into homogeneous segments. Barraquand and Benhamou
(2008) propose the method of Lavielle (1999, 2005). See the function
lavielle for details about this method.
If addinfo = FALSE, the function residenceTime returns a
list of class "resiti" where each element corresponds to a
burst of the object lt. Each element is a data.frame
with two columns: the date and the residence time associated with the
date.
Clement Calenge [email protected]
Barraquand, F. and Benhamou, S. (2008) Animal movement in heterogeneous landscapes: identifying profitable places and homogeneous movement bouts. Ecology, 89, 3336–3348.
lavielle for the partitionning of the trajectory based
on the residence time.
## Not run: data(albatross) ltr <- albatross[1] ## show the distances between successive relocations as a function ## of date plotltr(ltr) ## focus on the first period ltr <- gdltraj(ltr, as.POSIXct("2001-12-15", tz="UTC"), as.POSIXct("2003-01-10", tz="UTC")) plot(ltr) ## We identify places that seem to be a patch and, with locator, ## we measure approximately their size. ## The approximate patch radius can be set equal to 100 km as a first try plotltr(ltr, "dt") ## As a first try, we could set maxt equal to 15000 seconds, i.e. ## approximately 4 hours ## calculation of the residence time res <- residenceTime(ltr, radius = 100000, maxt=4, units="hour") plot(res) ## There seems to be about 10 segments. Let us try the method ## of Lavielle (1999, 2005) to segment this series: ## First calculate again the residence time as the infolocs attribute ## of the trajectory res <- residenceTime(ltr, radius = 100000, maxt=4, addinfo = TRUE, units="hour") res ## Note that the residence time is now an attribute of the infolocs ## component of res ## Now, use the Lavielle method, with Kmax set to 2-3 times the ## "optimal" number of segments, assessed visually according ## to the recommendations of Barraquand and Benhamou (2008) ## We set the minimum number of relocations in each segment to ## 10 observations (given that the relocations were theoretically ## taken every hour, this defines a patch as a place where the animal ## stays at least 10 hours: this also defines the scale of our study) ii <- lavielle(res, which="RT.100000", Kmax=20, Lmin=10) ## Both the graphical method and the automated method to choose ## the optimal number of segments indicate 4 segments ## (see ?lavielle for a description of these methods): chooseseg(ii) ## We identify the 4 segments: the method of Lavielle seems to do a good ## job: (pa <- findpath(ii, 4)) ## and we plot this partition: plot(pa, perani=FALSE) ## Now, we could try a study at a smaller scale (patch = 50km): res <- residenceTime(ltr, radius = 50000, maxt=4, addinfo = TRUE, units="hour") ii <- lavielle(res, which="RT.50000", Kmax=20, Lmin=10) ## 5 segments seem a good choice: chooseseg(ii) ## There is more noise in the residence time, but ## the partition is still pretty clear: (pa <- findpath(ii, 5)) ## show the partition: plot(pa, perani = FALSE) ## Now try at a larger scale (patch size=250 km) res <- residenceTime(ltr, radius = 250000, maxt=4, addinfo = TRUE, units="hour") ii <- lavielle(res, which="RT.250000", Kmax=15, Lmin=10) ## 5 segments seem a good choice again: chooseseg(ii) ## There is more noise in the residence time, but ## the partition is still pretty clear: (pa <- findpath(ii, 5)) ## show the partition: plot(pa, perani = FALSE) ## End(Not run)## Not run: data(albatross) ltr <- albatross[1] ## show the distances between successive relocations as a function ## of date plotltr(ltr) ## focus on the first period ltr <- gdltraj(ltr, as.POSIXct("2001-12-15", tz="UTC"), as.POSIXct("2003-01-10", tz="UTC")) plot(ltr) ## We identify places that seem to be a patch and, with locator, ## we measure approximately their size. ## The approximate patch radius can be set equal to 100 km as a first try plotltr(ltr, "dt") ## As a first try, we could set maxt equal to 15000 seconds, i.e. ## approximately 4 hours ## calculation of the residence time res <- residenceTime(ltr, radius = 100000, maxt=4, units="hour") plot(res) ## There seems to be about 10 segments. Let us try the method ## of Lavielle (1999, 2005) to segment this series: ## First calculate again the residence time as the infolocs attribute ## of the trajectory res <- residenceTime(ltr, radius = 100000, maxt=4, addinfo = TRUE, units="hour") res ## Note that the residence time is now an attribute of the infolocs ## component of res ## Now, use the Lavielle method, with Kmax set to 2-3 times the ## "optimal" number of segments, assessed visually according ## to the recommendations of Barraquand and Benhamou (2008) ## We set the minimum number of relocations in each segment to ## 10 observations (given that the relocations were theoretically ## taken every hour, this defines a patch as a place where the animal ## stays at least 10 hours: this also defines the scale of our study) ii <- lavielle(res, which="RT.100000", Kmax=20, Lmin=10) ## Both the graphical method and the automated method to choose ## the optimal number of segments indicate 4 segments ## (see ?lavielle for a description of these methods): chooseseg(ii) ## We identify the 4 segments: the method of Lavielle seems to do a good ## job: (pa <- findpath(ii, 4)) ## and we plot this partition: plot(pa, perani=FALSE) ## Now, we could try a study at a smaller scale (patch = 50km): res <- residenceTime(ltr, radius = 50000, maxt=4, addinfo = TRUE, units="hour") ii <- lavielle(res, which="RT.50000", Kmax=20, Lmin=10) ## 5 segments seem a good choice: chooseseg(ii) ## There is more noise in the residence time, but ## the partition is still pretty clear: (pa <- findpath(ii, 5)) ## show the partition: plot(pa, perani = FALSE) ## Now try at a larger scale (patch size=250 km) res <- residenceTime(ltr, radius = 250000, maxt=4, addinfo = TRUE, units="hour") ii <- lavielle(res, which="RT.250000", Kmax=15, Lmin=10) ## 5 segments seem a good choice again: chooseseg(ii) ## There is more noise in the residence time, but ## the partition is still pretty clear: (pa <- findpath(ii, 5)) ## show the partition: plot(pa, perani = FALSE) ## End(Not run)
runsNAltraj performs a runs test to detect any autocorrelation
in the location of missing relocations, for each burst of an object of
class ltraj.
summaryNAltraj returns a summary of the number and proportion
of missing values for each burst of an object of class
ltraj.
plotNAltraj plots the missing values in an object of class
ltraj against the time.
runsNAltraj(x, nrep = 500, plotit = TRUE, ...) summaryNAltraj(x) plotNAltraj(x, ...)runsNAltraj(x, nrep = 500, plotit = TRUE, ...) summaryNAltraj(x) plotNAltraj(x, ...)
x |
An object of class |
nrep |
Number of randomisations |
plotit |
logical. Whether the results should be plotted on a graph |
... |
Further arguments to be passed to the generic function
|
The statistics used here for the test is the number of runs in the sequence of relocations. For example, the sequence reloc-NA-NA-reloc-reloc-reloc-NA-NA-NA-reloc contains 5 runs, 3 runs of successful relocations and 2 runs of missing values. Under the hypothesis of random distribution of the missing values in the sequence, the theoretical expectation and standard deviation of the number of runs is known. The runs test is a randomization test that compares the standardized value of the number of runs (i.e. (value-expectation)/(standard deviation)) to the distribution of values obtained after randomizing the distribution of the NA in the sequence. Thus, a negative value of this standardized number of runs indicates that the missing values tend to be clustered together in the sequence.
runsNAltraj returns a list of objects of class
randtest (if a burst does not contain any missing value, the
corresponding component is NULL).
In the versions of adehabitatLT prior to 0.3.21, a bug occurred in the calculation of the P-value (the test actually presented the value 1-P). This bug is now corrected.
Clement Calenge [email protected]
ltraj for additional information about objects of
class ltraj, setNA for additional information
about missing values in such objects
## Two relocations are theoretically separated by ## 10 minutes (600 seconds) data(puechcirc) puechcirc ## plot the missing values plotNAltraj(puechcirc) ## Test for an autocorrelation pattern in the missing values (runsNAltraj(puechcirc))## Two relocations are theoretically separated by ## 10 minutes (600 seconds) data(puechcirc) puechcirc ## plot the missing values plotNAltraj(puechcirc) ## Test for an autocorrelation pattern in the missing values (runsNAltraj(puechcirc))
This dataset is an object of class "ltraj" (regular trajectory, relocations every 20 minutes) containing the GPS relocations of two chamois during one day in the Bauges mountain (French Alps).
data(rupicabau)data(rupicabau)
Office national de la chasse et de la faune sauvage, CNERA Faune de Montagne, 95 rue Pierre Flourens, 34000 Montpellier, France.
data(rupicabau) plot(rupicabau)data(rupicabau) plot(rupicabau)
This function sets the same time limits for several bursts in a regular trajectory.
set.limits(ltraj, begin, dur, pattern, units = c("sec", "min", "hour", "day"), tz = "", ...)set.limits(ltraj, begin, dur, pattern, units = c("sec", "min", "hour", "day"), tz = "", ...)
ltraj |
an object of class |
begin |
a character string which is used to determine the time of beginning of the study period (see below) |
dur |
the duration of the study period |
pattern |
a character string indicating the conversion
specifications for |
units |
a character string indicating the time units of
|
tz |
A timezone specification to be used for the conversion of
|
... |
additional arguments to be passed to other functions |
Some studies are intended to compare regular trajectories of the same duration collected at different period. For example, the aim may be to identify the differences/similarities between different days (each one corresponding to a burst of relocation) in the pattern of movements of an animal between 05H00 and 08H00, with a time lag of 5 minutes. In such cases, it is often convenient that the relocations of the bursts are paired (e.g. the fifth relocation correspond to the position of the animal at 5H30 for all bursts).
The function set.limits is intended to ensure that the time of
beginning, the end, and the duration of the trajectory is the same for
all bursts of the object ltraj. If relocations are collected
outside the limits, they are removed (and so is the corresponding
metadata in the attribute infolocs). If the actual time limits
of the burst cover a shorter period than those specified, missing values
are added to the trajectory (and in the corresponding
metadata in the attribute infolocs).
Note that "time of beginning" is not a synonym for "date". That is,
two trajectories of the same animal, both beginning at 05H00 and
ending at 08H00, have the same time of beginning, but are necessarily
not sampled on the same day, which implies that they correspond to
different dates. For this reason, the time of beginning is indicated
to the function set.limits by a character string, and the
parameter pattern should indicate the conversion specifications.
These conversions specifications are widely documented on the help
page of the function strptime. For example, to indicate that the
trajectory begins at 5H00, the value for begin should be
"05:00" and the value for pattern should be
"%H:%M". If the trajectory should begin on january 10th, the
value for begin should be "01:10" and pattern
should be "%m:%d". Note that the only conversion
specifications allowed in this function are %S (seconds),
%M (minutes), %H (hours), %d (day), %m
(month), %Y (year with century), %w (weekday), and
%j (yearday). See help(strptime) for additional
information on these convention specifications.
an object of class ltraj
Clement Calenge [email protected]
ltraj for additional information on objects of
class ltraj, sett0 for additional
information on regular trajectories, and sd2df for
additionnal information about regular trajectories of the same
duration. See also strptime for further information
about conversion specifications for dates.
## load data on the ibex data(ibex) ibex ## The monitoring of the 4 ibex should start and end at the same time ## define the time limits ib2 <- set.limits(ibex, begin="2003-06-01 00:00", dur=14, units="day", pattern="%Y-%m-%d %H:%M", tz="Europe/Paris") ib2 is.sd(ib2) ## All the trajectories cover the same study period ## Relocations are collected at the same time. This dataset can now be ## used for studies of interactions between animals## load data on the ibex data(ibex) ibex ## The monitoring of the 4 ibex should start and end at the same time ## define the time limits ib2 <- set.limits(ibex, begin="2003-06-01 00:00", dur=14, units="day", pattern="%Y-%m-%d %H:%M", tz="Europe/Paris") ib2 is.sd(ib2) ## All the trajectories cover the same study period ## Relocations are collected at the same time. This dataset can now be ## used for studies of interactions between animals
This function places missing values in an (approximately) regular trajectory, when a relocation should have been collected, but is actually missing.
setNA(ltraj, date.ref, dt, tol = dt/10, units = c("sec", "min", "hour", "day"), ...)setNA(ltraj, date.ref, dt, tol = dt/10, units = c("sec", "min", "hour", "day"), ...)
ltraj |
an object of class |
date.ref |
an object of class |
dt |
the time lag between relocations |
tol |
the tolerance, which measures the imprecision in the timing of data collection (see below) |
units |
a character string indicating the time units for
|
... |
additional arguments to be passed to the function
|
During the field study, the collection of the relocations of a
trajectory may sometimes fail, which results into missing values. The
class ltraj deal with these missing values, so that it is
recommended to store the missing values in the data *before* the
creation of the object of class ltraj. For example, GPS
collars often fail to locate the animal, so that the GPS data imported
within R contain missing values. It is recommended to *not remove*
these missing values.
However, sometimes, the data come without any information concerning
the placement of these missing values. If the trajectory is
approximately regular (i.e. approximately constant time lag), it is
possible to determine where these missing values should occur in the
object of class ltraj (and in the optional attribute
infolocs). This is the role of the function setNA.
The relocations in the object of class ltraj may not have been
collected at exactly identical time lag (e.g. a relocation is
collected at 17H57 instead of 18H00). The function setNA
requires that the imprecision in the timing is at most equal to
tol. Because of this imprecision, it is necessary to pass a
reference date as argument to the function setNA. This
reference date is used to determine at which time the missing values
should be placed.
The reference date is chosen so that the rest of the division of
(date.relocations - reference.date) by the time lag dt is equal
to zero. For example, if it is known that one of the relocations of the
trajectory has been collected on January 16th 1996 at 18H00,
and if the theoretical time lag between two relocations is of one
hour, the date of reference could be (for example) the August 1st 2017
at 05H00, because these two dates are separated by an exact number of
hours (i.e. an exact number of dt). Therefore, any date
fulfilling this condition could be passed as reference date.
Alternatively, the August 1st 2007 at 05H30 is an uncorrect reference
date, because the number of hours separating these two dates is not an
integer.
An object of class ltraj
Clement Calenge [email protected]
ltraj for additional information about objects
of class ltraj. sett0 (especially the examples
of this help page) and is.regular for additional
information about regular trajectories.
data(porpoise) foc <- porpoise[1] ## the list foc does not contain any missing value: foc plotNAltraj(foc) ## we remove the second to tenth relocation foc[[1]] <- foc[[1]][-c(2:10),] foc <- rec(foc) ## The missing values are not visible: foc plotNAltraj(foc) ## The porpoise is located once a day. ## We use the first relocation as the reference date foc2 <- setNA(foc, foc[[1]]$date[1], 24*3600) ## Missing values are now present foc2 plotNAltraj(foc2)data(porpoise) foc <- porpoise[1] ## the list foc does not contain any missing value: foc plotNAltraj(foc) ## we remove the second to tenth relocation foc[[1]] <- foc[[1]][-c(2:10),] foc <- rec(foc) ## The missing values are not visible: foc plotNAltraj(foc) ## The porpoise is located once a day. ## We use the first relocation as the reference date foc2 <- setNA(foc, foc[[1]]$date[1], 24*3600) ## Missing values are now present foc2 plotNAltraj(foc2)
This function rounds the timing of collection of relocations in an
object of class ltraj to obtain a regular trajectory, based on
a reference date.
sett0(ltraj, date.ref, dt, correction.xy = c("none", "cs"), tol = dt/10, units = c("sec", "min", "hour", "day"), ...)sett0(ltraj, date.ref, dt, correction.xy = c("none", "cs"), tol = dt/10, units = c("sec", "min", "hour", "day"), ...)
ltraj |
an object of class |
date.ref |
an object of class |
dt |
the time lag between relocations |
correction.xy |
the correction for the coordinates.
|
tol |
the tolerance, which measures the imprecision in the timing of data collection (see below) |
units |
the time units for |
... |
additional arguments to be passed to the function
|
Trajectories are stored in adehabitatLT as lists of "bursts" of
successive relocations with the timing of relocation. Regular
trajectories are characterized by a constant time lag dt
between successive relocations (don't mix animals located every 10
minutes and animals located every day in a regular trajectory).
However, in many cases, the actual time lag in the data may not be
equal to the theoretical time lag dt: there may be some
negligible imprecision in the time of collection of the data (e.g. an
error of a few seconds on a time lag of one hour).
But many functions of adehabitatLT require exact regular
trajectories. sett0 allows to round the date so that all the
successive relocations are separated exactly by dt. The
function sett0 requires that the imprecision is at most equal
to tol. To proceed, it is necessary to pass a reference date as
argument.
The reference date is chosen so that the rest of the division of
(date.relocations - reference.date) by dt is equal to zero.
For example, if it is known that one of the relocations of the
trajectory should have been collected on January 16th 1996 at 18H00,
and if the theoretical time lag between two relocations is of one
hour, the date of reference could be (for example) the August 1st 2017
at 05H00, because these two dates are separated by an exact number of
hours. Alternatively, the August 1st 2007 at 05H30 is an uncorrect
reference date, because the number of hours separating these two dates
is not an integer.
Note that this rounding adds an error on the relocation. For example,
the position of a moving animal at 17H57 is not the same as its
position at 18H00. If the time imprecision in the data collection is
negligible (e.g. a few seconds, while dt is equal to an hour),
this "noise" in the relocations can be ignored, but if it is more
important, a correction on the relocation is needed. The function
sett0 may correct the relocations based on the hypothesis of
constant speed (which is not necessarily biologically relevant, see
examples).
Note finally that missing values can be present in the trajectory.
Indeed, there are modes of data collection that fail to locate the
animal at some dates. These failures should appear as missing values
in the regular trajectory. It is often convenient to use the function
setNA before the function sett0 to set the missing
values in a (nearly) regular trajectory.
an object of class ltraj containing a regular trajectory.
Clement Calenge [email protected]
ltraj for additional information on objects of
class ltraj, is.regular for regular trajectories,
setNA to place missing values in the trajectory and
cutltraj to cut a trajectory into several bursts based
on a criteria.
## Not run: ######################################################################### ## ## ## Transform a GPS monitoring on 4 ibex into a regular trajectory ## data(ibexraw) is.regular(ibexraw) ## the data are not regular: see the distribution of dt (in hours) ## according to the date plotltr(ibexraw, "dt/3600") ## The relocations have been collected every 4 hours, and there are some ## missing data ## The reference date: the hour should be exact (i.e. minutes=0): refda <- strptime("00:00", "%H:%M", tz="Europe/Paris") refda ## Set the missing values ib2 <- setNA(ibexraw, refda, 4, units = "hour") ## now, look at dt for the bursts: plotltr(ib2, "dt") ## dt is nearly regular: round the date: ib3 <- sett0(ib2, refda, 4, units = "hour") plotltr(ib3, "dt") is.regular(ib3) ## ib3 is now regular ## End(Not run)## Not run: ######################################################################### ## ## ## Transform a GPS monitoring on 4 ibex into a regular trajectory ## data(ibexraw) is.regular(ibexraw) ## the data are not regular: see the distribution of dt (in hours) ## according to the date plotltr(ibexraw, "dt/3600") ## The relocations have been collected every 4 hours, and there are some ## missing data ## The reference date: the hour should be exact (i.e. minutes=0): refda <- strptime("00:00", "%H:%M", tz="Europe/Paris") refda ## Set the missing values ib2 <- setNA(ibexraw, refda, 4, units = "hour") ## now, look at dt for the bursts: plotltr(ib2, "dt") ## dt is nearly regular: round the date: ib3 <- sett0(ib2, refda, 4, units = "hour") plotltr(ib3, "dt") is.regular(ib3) ## ib3 is now regular ## End(Not run)
This function simulates a brownian bridge motion
simm.bb(date = 1:100, begin = c(0, 0), end = begin, id = "A1", burst = id, proj4string=CRS())simm.bb(date = 1:100, begin = c(0, 0), end = begin, id = "A1", burst = id, proj4string=CRS())
date |
a vector indicating the date (in seconds) at which
relocations should be simulated. This vector can be of class
|
begin |
a vector of length 2 giving the x and y coordinates of the location beginning of the trajectory |
end |
a vector of length 2 giving the x and y coordinates of the location ending the trajectory |
id |
a character string indicating the identity of the simulated
animal (see |
burst |
a character string indicating the identity of the
simulated animal (see |
proj4string |
a valid CRS object containing the projection
information (see |
An object of class ltraj.
Clement Calenge [email protected]
Stephane Dray [email protected]
Manuela Royer [email protected]
Daniel Chessel [email protected]
plot(simm.bb(1:1000, end=c(100,100)), addpoints = FALSE)plot(simm.bb(1:1000, end=c(100,100)), addpoints = FALSE)
This function simulates a Bivariate Brownian Motion.
simm.brown(date = 1:100, x0 = c(0, 0), h = 1, id = "A1", burst = id, proj4string=CRS())simm.brown(date = 1:100, x0 = c(0, 0), h = 1, id = "A1", burst = id, proj4string=CRS())
date |
a vector indicating the date (in seconds) at which
relocations should be simulated. This vector can be of class
|
x0 |
a vector of length 2 containing the coordinates of the startpoint of the trajectory |
h |
Scaling parameter for the brownian motion (larger values give smaller dispersion) |
id |
a character string indicating the identity of the simulated
animal (see |
burst |
a character string indicating the identity of the simulated
burst (see |
proj4string |
a valid CRS object containing the projection
information (see |
A bivariate Brownian motion can be described by a vector
B2(t) = (Bx(t), By(t)), where Bx and By are
unidimensional Brownian motions. Let F(t) the set of all
possible realisations of the process (B2(s), 0 < s < t).
F(t) therefore corresponds to the known information at time
t. The properties of the bivariate Brownian motion are
therefore the following: (i) B2(0)= c(0,0) (no uncertainty at
time t = 0); (ii) B2(t) - B2(s) is independent of
F(s) (the next increment does not depend on the present or past
location); (iii) B2(t) - B2(s) follows a bivariate normal
distribution with mean c(0,0) and with variance equal to
(t-s).
Note that for a given parameter h, the process 1/h * B2(
t * h^2 ) is a Brownian motion. The function simm.brown
simulates the process B2(t * h^2). Note that the function
hbrown allows the estimation of this scaling factor from data.
An object of class ltraj
Clement Calenge [email protected]
Stephane Dray [email protected]
Manuela Royer [email protected]
Daniel Chessel [email protected]
~put references to the literature/web site here ~
plot(simm.brown(1:1000), addpoints = FALSE) ## Note the difference in dispersion: plot(simm.brown(1:1000, h = 4), addpoints = FALSE)plot(simm.brown(1:1000), addpoints = FALSE) ## Note the difference in dispersion: plot(simm.brown(1:1000, h = 4), addpoints = FALSE)
This function simulates a correlated random walk
simm.crw(date=1:100, h = 1, r = 0, x0=c(0,0), id="A1", burst=id, typeII=TRUE, proj4string=CRS())simm.crw(date=1:100, h = 1, r = 0, x0=c(0,0), id="A1", burst=id, typeII=TRUE, proj4string=CRS())
date |
a vector indicating the date (in seconds) at which
relocations should be simulated. This vector can be of class
|
h |
the scaling parameter for the movement length |
r |
The concentration parameter for wrapped normal distribution of turning angles |
x0 |
a vector of length 2 containing the coordinates of the startpoint of the trajectory |
id |
a character string indicating the identity of the simulated
animal (see |
burst |
a character string indicating the identity of the simulated
burst (see |
typeII |
logical. Whether the simulated trajectory should be of
type II ( |
proj4string |
a valid CRS object containing the projection
information (see |
Since the seminal paper of Kareiva and Shigesada (1983), most
biologists describe the trajectories of an animal with the help of
two distributions: the distribution of distances between successive
relocations, and the distribution of turning angles between successive
moves (relative angles in the class ltraj). The CRW is
built iteratively. At each step of the simulation process,
the orientation of the move is drawn from a wrapped normal
distribution (with concentration parameter r). The length of
the move is drawn from a chi distribution, multiplied by h *
sqrt(dt). h is a scale parameter (the same as in the
function simm.brown(), and the distribution is
multiplied by sqrt(t) to make it similar to the discretized Brownian
motion if r == 0.
an object of class ltraj
This function requires the package CircStats.
Clement Calenge [email protected]
Stephane Dray [email protected]
Manuela Royer [email protected]
Daniel Chessel [email protected]
Kareiva, P. M. & Shigesada, N. (1983) Analysing insect movement as a correlated random walk. Oecologia, 56: 234–238.
chi, rwrpnorm,
simm.brown, ltraj,
simm.crw, simm.mba
suppressWarnings(RNGversion("3.5.0")) set.seed(876) u <- simm.crw(1:500, r = 0.99, burst = "r = 0.99") v <- simm.crw(1:500, r = 0.9, burst = "r = 0.9", h = 2) w <- simm.crw(1:500, r = 0.6, burst = "r = 0.6", h = 5) x <- simm.crw(1:500, r = 0, burst = "r = 0 (Uncorrelated random walk)", h = 0.1) z <- c(u, v, w, x) plot(z, addpoints = FALSE, perani = FALSE)suppressWarnings(RNGversion("3.5.0")) set.seed(876) u <- simm.crw(1:500, r = 0.99, burst = "r = 0.99") v <- simm.crw(1:500, r = 0.9, burst = "r = 0.9", h = 2) w <- simm.crw(1:500, r = 0.6, burst = "r = 0.6", h = 5) x <- simm.crw(1:500, r = 0, burst = "r = 0 (Uncorrelated random walk)", h = 0.1) z <- c(u, v, w, x) plot(z, addpoints = FALSE, perani = FALSE)
This function simulates a Levy walk
simm.levy(date = 1:500, mu = 2, l0 = 1, x0 = c(0, 0), id = "A1", burst = id, typeII = TRUE, proj4string=CRS())simm.levy(date = 1:500, mu = 2, l0 = 1, x0 = c(0, 0), id = "A1", burst = id, typeII = TRUE, proj4string=CRS())
date |
a vector indicating the date (in seconds) at which
relocations should be simulated. This vector can be of class
|
mu |
The exponent of the Levy distribution |
l0 |
The minimum length of a step |
x0 |
a vector of length 2 containing the coordinates of the startpoint of the trajectory |
id |
a character string indicating the identity of the simulated
animal (see |
burst |
a character string indicating the identity of the simulated
burst (see |
typeII |
logical. Whether the simulated trajectory should be of
type II ( |
proj4string |
a valid CRS object containing the projection
information (see |
This function simulates a Levy flight with exponent mu.
This is done by sampling a random relative angle from a uniform
distribution (-pi, pi) for each step, and a step length generated by
dt * (l0 * (runif(1)^(1/(1 - mu))))
an object of class ltraj
Clement Calenge [email protected]
Bartumeus, F., da Luz, M.G.E., Viswanathan, G.M. Catalan, J. (2005) Animal search strategies: a quantitative random-walk analysis. Ecology, 86: 3078–3087.
chi, rwrpnorm,
simm.brown, ltraj,
simm.crw, simm.mba,
simm.levy
suppressWarnings(RNGversion("3.5.0")) set.seed(411) w <- simm.levy(1:500, mu = 1.5, burst = "mu = 1.5") u <- simm.levy(1:500, mu = 2, burst = "mu = 2") v <- simm.levy(1:500, mu = 2.5, burst = "mu = 2.5") x <- simm.levy(1:500, mu = 3, burst = "mu = 3") par(mfrow=c(2,2)) lapply(list(w,u,v,x), plot, perani=FALSE)suppressWarnings(RNGversion("3.5.0")) set.seed(411) w <- simm.levy(1:500, mu = 1.5, burst = "mu = 1.5") u <- simm.levy(1:500, mu = 2, burst = "mu = 2") v <- simm.levy(1:500, mu = 2.5, burst = "mu = 2.5") x <- simm.levy(1:500, mu = 3, burst = "mu = 3") par(mfrow=c(2,2)) lapply(list(w,u,v,x), plot, perani=FALSE)
This function simulates an Arithmetic Brownian Motion.
simm.mba(date = 1:100, x0 = c(0, 0), mu = c(0, 0), sigma = diag(2), id = "A1", burst = id, proj4string=CRS())simm.mba(date = 1:100, x0 = c(0, 0), mu = c(0, 0), sigma = diag(2), id = "A1", burst = id, proj4string=CRS())
date |
a vector indicating the date (in seconds) at which
relocations should be simulated. This vector can be of class
|
x0 |
a vector of length 2 containing the coordinates of the startpoint of the trajectory |
mu |
a vector of length 2 describing the drift of the movement |
sigma |
a 2*2 positive definite matrix |
id |
a character string indicating the identity of the simulated
animal (see |
burst |
a character string indicating the identity of the simulated
burst (see |
proj4string |
a valid CRS object containing the projection
information (see |
The arithmetic Brownian motion (Brillinger et al. 2002) can be described by the stochastic differential equation:
Coordinates of the animal at time t are contained in the vector
z(t). dz = c(dx, dy) is the increment of the
movement during dt. dB2(t) is a bivariate brownian Motion (see
?simm.brown). The vector mu measures the drift of the
motion. The matrix Sigma controls for perturbations due to the
random noise modeled by the Brownian motion. It can also be used to
take into account a potential correlation between the components dx
and dy of the animal moves during dt (see Examples).
An object of class ltraj
Clement Calenge [email protected]
Stephane Dray [email protected]
Manuela Royer [email protected]
Daniel Chessel [email protected]
Brillinger, D.R., Preisler, H.K., Ager, A.A. Kie, J.G. & Stewart, B.S. (2002) Employing stochastic differential equations to model wildlife motion. Bulletin of the Brazilian Mathematical Society 33: 385–408.
simm.brown, ltraj,
simm.crw, simm.mou
suppressWarnings(RNGversion("3.5.0")) set.seed(253) u <- simm.mba(1:1000, sigma = diag(c(4,4)), burst = "Brownian motion") v <- simm.mba(1:1000, sigma = matrix(c(2,-0.8,-0.8,2), ncol = 2), burst = "cov(x,y) > 0") w <- simm.mba(1:1000, mu = c(0.1,0), burst = "drift > 0") x <- simm.mba(1:1000, mu = c(0.1,0), sigma = matrix(c(2, -0.8, -0.8, 2), ncol=2), burst = "Drift and cov(x,y) > 0") z <- c(u, v, w, x) plot(z, addpoints = FALSE, perani = FALSE)suppressWarnings(RNGversion("3.5.0")) set.seed(253) u <- simm.mba(1:1000, sigma = diag(c(4,4)), burst = "Brownian motion") v <- simm.mba(1:1000, sigma = matrix(c(2,-0.8,-0.8,2), ncol = 2), burst = "cov(x,y) > 0") w <- simm.mba(1:1000, mu = c(0.1,0), burst = "drift > 0") x <- simm.mba(1:1000, mu = c(0.1,0), sigma = matrix(c(2, -0.8, -0.8, 2), ncol=2), burst = "Drift and cov(x,y) > 0") z <- c(u, v, w, x) plot(z, addpoints = FALSE, perani = FALSE)
This function simulates a bivariate Ornstein-Uhlenbeck process for animal movement.
simm.mou(date = 1:100, b = c(0, 0), a = diag(0.5, 2), x0 = b, sigma = diag(2), id = "A1", burst = id, proj4string=CRS())simm.mou(date = 1:100, b = c(0, 0), a = diag(0.5, 2), x0 = b, sigma = diag(2), id = "A1", burst = id, proj4string=CRS())
date |
a vector indicating the date (in seconds) at which
relocations should be simulated. This vector can be of class
|
b |
a vector of length 2 containing the coordinates of the attraction point |
a |
a 2*2 matrix |
x0 |
a vector of length 2 containing the coordinates of the startpoint of the trajectory |
sigma |
a 2*2 positive definite matrix |
id |
a character string indicating the identity of the simulated
animal (see |
burst |
a character string indicating the identity of the simulated
burst (see |
proj4string |
a valid CRS object containing the projection
information (see |
The Ornstein-Uhlenbeck process can be used to take into account an "attraction point" into the animal movements (Dunn and Gipson 1977). This process can be simulated using the stochastic differential equation:
The vector b contains the coordinates of the attraction
point. The matrix a (2 rows and 2 columns) contains
coefficients controlling the force of the attraction. The matrix
Sigma controls the noise added to the movement (see
?simm.mba for details on this matrix).
An object of class ltraj
Clement Calenge [email protected]
Stephane Dray [email protected]
Manuela Royer [email protected]
Daniel Chessel [email protected]
Dunn, J.E., & Gipson, P.S. (1977) Analysis of radio telemetry data in studies of home range. Biometrics 33: 85–101.
simm.brown, ltraj,
simm.crw, simm.mba
suppressWarnings(RNGversion("3.5.0")) set.seed(253) u <- simm.mou(1:50, burst="Start at the attraction point") v <- simm.mou(1:50, x0=c(-3,3), burst="Start elsewhere") w <- simm.mou(1:50, a=diag(c(0.5,0.1)), x0=c(-3,3), burst="Variable attraction") x <- simm.mou(1:50, a=diag(c(0.1,0.5)), x0=c(-3,7), burst="Both") z <- c(u,v,w,x) plot(z, addpoints = FALSE, perani = FALSE)suppressWarnings(RNGversion("3.5.0")) set.seed(253) u <- simm.mou(1:50, burst="Start at the attraction point") v <- simm.mou(1:50, x0=c(-3,3), burst="Start elsewhere") w <- simm.mou(1:50, a=diag(c(0.5,0.1)), x0=c(-3,3), burst="Variable attraction") x <- simm.mou(1:50, a=diag(c(0.1,0.5)), x0=c(-3,7), burst="Both") z <- c(u,v,w,x) plot(z, addpoints = FALSE, perani = FALSE)
This function applies a function on an object of class "ltraj", using a sliding window.
sliwinltr(ltraj, fun, step, type = c("locs", "time"), units = c("sec", "min", "hour", "day"), plotit = TRUE, ...)sliwinltr(ltraj, fun, step, type = c("locs", "time"), units = c("sec", "min", "hour", "day"), plotit = TRUE, ...)
ltraj |
an object of class |
fun |
the function to be applied, implying at least one of the
descriptive parameters in the object of class |
step |
the half-width of the sliding window. If
|
type |
character string. If |
units |
if |
plotit |
logical. Whether the result should be plotted |
... |
additional arguments to be passed to the function
|
An object of class ltraj is a list with one component per burst of
relocations. The function fun is applied to each burst of
relocations. This burst of relocations should be refered as x
in fun. For example, to compute the mean of the distance
between successive relocations, the function fun is equal to
function(x) mean(x$dist).
Do not forget that some of the descriptive parameters in the object
ltraj may contain missing values (see
help(ltraj)). The function should therefore specify how to
manage these missing values.
If type=="locs", a list with one component per burst of
relocation containing the smoothed values for each relocation.
If type=="locs", a list with one component per burst of
relocation. Each component is a data frame containing the time and
the corresponding smoothed values for each date.
Clement Calenge [email protected]
ltraj for additional information about objects
of class ltraj
## Not run: data(capreotf) ## computes the average speed of the roe deer in a moving window of width ## equal to 60 minutes toto <- sliwinltr(capreotf, function(x) mean(x$dist/x$dt, na.rm = TRUE), step = 30, type = "time", units = "min") ## zoom before the peak head(toto[[1]]) plot(toto[[1]][1:538,], ty="l") ## End(Not run)## Not run: data(capreotf) ## computes the average speed of the roe deer in a moving window of width ## equal to 60 minutes toto <- sliwinltr(capreotf, function(x) mean(x$dist/x$dt, na.rm = TRUE), step = 30, type = "time", units = "min") ## zoom before the peak head(toto[[1]]) plot(toto[[1]][1:538,], ty="l") ## End(Not run)
This function subsamples a regular trajectory (i.e. changes the time lag between successive relocations).
subsample(ltraj, dt, nlo = 1, units = c("sec", "min", "hour", "day"), ...)subsample(ltraj, dt, nlo = 1, units = c("sec", "min", "hour", "day"), ...)
ltraj |
an object of class |
dt |
numeric value. The new time lag (should be a multiple of
the time lag in |
nlo |
an integer, or a vector of integers (with length equal to
the number of bursts in |
units |
character string. The time units of |
... |
additional arguments to be passed to other functions |
An object of class ltraj
Clement Calenge [email protected]
ltraj for additional information on objects of
class ltraj, is.regular for regular trajectories.
data(capreotf) plot(capreotf) toto <- subsample(capreotf, dt = 900) plot(toto)data(capreotf) plot(capreotf) toto <- subsample(capreotf, dt = 900) plot(toto)
This dataset describes the location and date of recovery of 800 teal ringed in Camargue, southern France between January 1952 and February 1978 using standard dabbling duck funnel traps hidden in the vegetation.
data(teal)data(teal)
The following variables are given for each recovery:
xa numeric vector giving the longitude of the recovery
ya numeric vector giving the latitude of the recovery
datea vector of class POSIXct containing the date of recovery. Actually, only the day and month have been indicated. The year of recovery has been set to 1900 or 1901, and should not be taken into account in the analysis.
The Camargue teal ringing program led to the recovery of 9,114 teals after the ringing of 59,187 birds. These 800 recoveries of this dataset are a subsample of the 4,652 birds recovered during the first year following ringing. Note that both the coordinates and the date have been jittered to preserve copyright on the data.
La Tour du Valat. A research centre for the conservation of Mediterranean wetlands. Le Sambuc - 13200 Arles, France. http://en.tourduvalat.org/
data(teal) plot(teal[,1:2], asp=1, xlab="longitude", ylab="latitude", main="Capture site (red) and recoveries") points(attr(teal, "CaptureSite"), pch=16, cex=2, col="red")data(teal) plot(teal[,1:2], asp=1, xlab="longitude", ylab="latitude", main="Capture site (red) and recoveries") points(attr(teal, "CaptureSite"), pch=16, cex=2, col="red")
The functions NMs.* allow to define "single null models" (see
details). The function NMs2NMm can be used on an object of
class "NMs" to define "multiple null models". The function
testNM can be used to simulate the defined null models.
NMs.randomCRW(ltraj, rangles = TRUE, rdist = TRUE, fixedStart = TRUE, x0 = NULL, rx = NULL, ry = NULL, treatment.func = NULL, treatment.par = NULL, constraint.func = NULL, constraint.par = NULL, nrep = 999) NMs.randomShiftRotation(ltraj, rshift = TRUE, rrot = TRUE, rx = NULL, ry = NULL, treatment.func = NULL, treatment.par = NULL, constraint.func = NULL, constraint.par = NULL, nrep = 999) NMs.CRW(N = 1, nlocs = 100, rho = 0, h = 1, x0 = c(0,0), treatment.func = NULL, treatment.par = NULL, constraint.func = NULL, constraint.par = NULL, nrep = 999) NMs.randomCs(ltraj, Cs = NULL, rDistCs = TRUE, rAngleCs = TRUE, rCentroidAngle = TRUE, rCs = TRUE, newCs = NULL, newDistances = NULL, treatment.func = NULL, treatment.par = NULL, constraint.func = NULL, constraint.par = NULL, nrep=999) NMs2NMm(NMs, treatment.func = NULL, treatment.par = NULL, constraint.func = NULL, constraint.par = NULL, nrep = 999) ## S3 method for class 'NMm' print(x, ...) ## S3 method for class 'NMs' print(x, ...) testNM(NM, count = TRUE)NMs.randomCRW(ltraj, rangles = TRUE, rdist = TRUE, fixedStart = TRUE, x0 = NULL, rx = NULL, ry = NULL, treatment.func = NULL, treatment.par = NULL, constraint.func = NULL, constraint.par = NULL, nrep = 999) NMs.randomShiftRotation(ltraj, rshift = TRUE, rrot = TRUE, rx = NULL, ry = NULL, treatment.func = NULL, treatment.par = NULL, constraint.func = NULL, constraint.par = NULL, nrep = 999) NMs.CRW(N = 1, nlocs = 100, rho = 0, h = 1, x0 = c(0,0), treatment.func = NULL, treatment.par = NULL, constraint.func = NULL, constraint.par = NULL, nrep = 999) NMs.randomCs(ltraj, Cs = NULL, rDistCs = TRUE, rAngleCs = TRUE, rCentroidAngle = TRUE, rCs = TRUE, newCs = NULL, newDistances = NULL, treatment.func = NULL, treatment.par = NULL, constraint.func = NULL, constraint.par = NULL, nrep=999) NMs2NMm(NMs, treatment.func = NULL, treatment.par = NULL, constraint.func = NULL, constraint.par = NULL, nrep = 999) ## S3 method for class 'NMm' print(x, ...) ## S3 method for class 'NMs' print(x, ...) testNM(NM, count = TRUE)
ltraj |
an object of class |
rangles |
logical. Whether the turning angles should be randomized. |
rdist |
logical. Whether the distances between successive relocations should be randomized. |
fixedStart |
logical. If |
x0 |
a vector of length 2 giving the x and y coordinates of the
first relocations. If |
rx |
a vector of length 2 giving the x coordinates of the bounding box where the first location of the trajectory should be sampled |
ry |
a vector of length 2 giving the range (min, max) of the y coordinates of the bounding box where the first location of the trajectory should be sampled |
treatment.func |
any function taking two arguments |
treatment.par |
the R object that will be passed as
an argument to the parameter |
constraint.func |
any function taking two arguments |
constraint.par |
The R object that will be passed as an argument
to the parameter |
nrep |
The number of repetitions of the null model |
rshift |
logical. Whether the trajectory should be shifted over the study area. |
rrot |
logical. Whether the trajectory should be rotated around its barycentre. |
N |
The number of animals to simulate. |
nlocs |
The number of relocations building up each trajectory |
rho |
The concentration parameter for wrapped normal distribution
of turning angles (see |
h |
the scaling parameter for the movement length (see
|
Cs |
a list of vectors of length 2. Each vector should contain
the x and y coordinates of the capture sites of the animals in
|
rDistCs |
logical. Whether the distances between the barycentre of the trajectories and the corresponding capture sites should be randomized among trajectories |
rAngleCs |
logical. Whether the angle between the east direction and the line connecting the capture site and the barycentre of the trajectory should be drawn from an uniform distribution. |
rCentroidAngle |
logical. Whether the trajectory should be randomly rotated around its barycentre. |
rCs |
logical. Whether the trajectory should be randomly associated to a new capture site. |
newCs |
a list of vectors of length 2. Each vector should contain
the x and y coordinates of new capture sites. If |
newDistances |
a vector of new distances that will be used to
define the distances between capture sites and centroid of simulated
trajectories if |
NM, x
|
a null model of class |
NMs |
a null model of class |
count |
whether the iterations should be displayed |
... |
additionnal arguments to be passed to or from other methods |
The null model approach has been considered as a useful approach in many fields of ecology to study biological processes. According to Gotelli and Graves (1996), "A null model is a pattern-generating model that is based on randomization of ecological data or random sampling from a known or imagined distribution. The null model is designed with respect to some ecological or evolutionary process of interest. Certain elements of the data are held constant, and others are allowed to vary stochastically to create new assemblage patterns. The randomization is designed to produce a pattern that would be expected in the absence of a particular ecological mechanism".
This approach can be very useful to test hypotheses related to animal
movements. The package adehabitatLT propose several general null
models that can be used to test biological hypotheses. For example,
imagine that we want to test the hypothesis that no habitat selection
occurs when the animal moves. The shape of the trajectory, under this
hypothesis would be the pure result of changing activity (moving,
foraging, resting). Therefore, a possible approach to test whether
habitat selection actually occurs would be to randomly rotate the
trajectory around its barycentre and shifting it over the study area.
The function NMs.randomShiftRotation can be used to define such
a model. It is possible to constrain the randomization by defining a
"constraint function" (e.g. to keep only the randomized trajectories
satisfying a given criterion). It is required to specify a "treatment
function" (i.e., a function that will be applied to each randomized
trajectory). Once the null model has been defined, it is then possible
to perform the randomizations using the function testNM. We
give below the details concerning the available null models, as well
as the constraint and the treatment functions.
First, two types of null models can be defined: single (NMs) and
multiple (NMm) null models. Consider an object of class
"ltraj" containing N bursts. With NMs, the treatment
function will be applied to each randomized burst of relocations. Thus,
for example, if nrep repetitions of the null model are
required, nrep repetitions of the null models will be carried
out for each burst separately. The treatment function will be applied
on each randomized burst. With NMm, for each repetition, N
randomized bursts of relocations are generated. The treatment is then
applied, for each repetition, to the whole set of N randomized
bursts. Thus, NMs are useful to test hypothesis on each
trajectory separately (e.g. individual habitat selection), whereas
NMm are useful to test hypotheses relative to the whole set of
animals stored in an object of class ltraj (e.g. interactions
between animals). The only current way to define an object of class
NMm is to first define an object of class NMs and then
use the function NMs2NMm to indicate the treatment function
that should be applied on the whole set of trajectories.
The constraint function should be user-defined. It should return a
logical value indicating whether the constraint is satisfied. With
NMs, this function should take only two parameters: x
and par. The argument x is a data frame with three
columns describing a trajectory (the X and Y coordinates, and the date
as a vector of class "POSIXct"), and the argument par
can be any R object required by the constraint function (e.g. if the
constraint to keep 80% of the relocations of the randomized
trajectories within a given habitat type, the parameter par
can be a raster map, or a list of raster maps). With
NMm, this function should also take only the two parameters
x and par. The argument par can be any R object
required by the constraint function. However, when "NMm" are
defined, the argument x of the constraint function should be an
object of class "ltraj". If the function NMs2NMm is
used to define the object of class "NMm", two types of
constraint can therefore be defined: at the individual level (in the
function NMs.*) and for the whole set of animals (in the
function NMs2NMm). In this case, some constraints will be
satisfied at the individual level, and others at the scale of the
whole set of animals. If no constraint function is defined by the
user, a constraint function always returning TRUE is
automatically defined internally.
The treatment function can be any function defined by the user, but
should take two arguments x and par, identical to those
passed to the constraint function (i.e., x should be a data
frame with three columns for NMs and an object of class
"ltraj" for NMm. Note that only one treatment function
can be applied to the randomization: if NMs2NMm is used to
define an object of class NMm, the treatment function defined
in the function NMs.* will be ignored, and only the treatment
function defined in the function NMs2NMm will be taken into
account. If no treatment function is defined by the user, a treatment
function will be defined internally, simply returning the randomized
trajectory (i.e. a data.frame with three columns for NMs, and
an object of class ltraj for NMm).
We now describe the list of available null models:
NMs.CRW: this model is a purely parametric model. It
simulates a correlated random walk with specified parameters (see
?simm.crw for a complete description of this model).
NMs.randomCRW: this model also simulates a correlated
random walk, but the distributions of the turning angles and/or
distances between successive relocations are derived from the
trajectories passed as arguments. It is possible to randomize the
turning angles, the distances between successive relocations, or
both (default).
NMs.randomShiftRotation: this model randomly rotates the
trajectory around its barycentre and randomly shifts it over the study
area (but does not change its shape). The function allows for a
random rotation, a random shift or both operations (default).
NMs.randomCs: this model is similar to the previous one:
it keeps the shape of the trajectory unchanged. However, it
randomizes the position of the trajectories with respect to a set of
capture sites (it can be
used to take into account the fact that a the home range of a
sedentary animal captured at a given place is likely to be close to
this place). First a
capture site may be randomly drawn from a list of capture sites
(either the actual capture sites or a list passed by the user). Then,
the angle between the east direction and the line connecting the
capture site of the animal and the barycentre of its trajectory is
randomly drawn from a uniform distribution. Then, the distance
between this barycentre and the capture site is randomly drawn from
the observed distribution of distances between capture sites and
trajectory barycentre (or from a set of distances passed as
argument). Finally, the trajectory is randomly rotated around its
barycentre.
For objects of class "NMs" a list of N elements (where
N is the number of trajectories in the object of class
"ltraj" passed as argument, with each element is a list storing
the nrep results of the treatment function applied to each randomized
trajectory.
For objects of class "NMm", a list of nrep elements,
each element storing the result of the treatment function applied to
each set of N randomized trajectories.
Clement Calenge [email protected]
Gotelli, N. and Graves, G. (1996) Null models in Ecology. Smithsonian Institution Press.
Richard, E., Calenge, C., Said, S., Hamann, J.L. and Gaillard, J.M. (2012) Studying spatial interactions between sympatric populations of large herbivores: a null model approach. Ecography, in press.
as.ltraj for additional information about objects of
class "ltraj"
## Not run: ######################################## ## ## example using NMs.randomShiftRotation ## first load the data: data(puechcirc) data(puechabonsp) map <- puechabonsp$map ## Consider the first animal ## on an elevation map anim1 <- puechcirc[1] plot(anim1, spixdf=map[,1]) ## We define a very simple treatment function ## for a NMs model: it just plots the randomized trajectory ## over the study area ## As required, the function takes two arguments: ## x is a data.frame storing a randomized trajectory (three ## columns: the x, y coordinates and the date) ## par contains the map of the study area myfunc <- function(x, par) { par(mar = c(0,0,0,0)) ## first plot the map image(par) ## then add the trajectory lines(x[,1], x[,2], lwd=2) } ## Then we define the null model ## ## We define the range of the study area where the trajectory ## will be shifted: rxy <- apply(coordinates(map),2,range) rxy ## We define the null model with 9 repetitions nmo <- NMs.randomShiftRotation(na.omit(anim1), rshift = TRUE, rrot = TRUE, rx = rxy[,1], ry = rxy[,2], treatment.func = myfunc, treatment.par = map, nrep=9) ## Then apply the null model par(mfrow = c(3,3)) tmp <- testNM(nmo) ## You may try variations, by setting rshift or rrot to FALSE, to see ## the differences ## Note that some of the randomized trajectories are located outside the ## study area, although all barycentres are located within the X and Y ## limits of this study area. ## We may define a constraint function returning TRUE only if all ## relocations are located within the study area ## again, note that the two parameters are x and par consfun <- function(x, par) { ## first convert x to the class SpatialPointsDataFrame coordinates(x) <- x[,1:2] ## then use the function over from the package sp ## to check whether all points in x are located inside ## the study area ov <- over(x, geometry(map)) return(all(!is.na(ov))) } ## Now fit again the null model under these constraints: nmo2 <- NMs.randomShiftRotation(na.omit(anim1), rshift = TRUE, rrot = TRUE, rx = rxy[,1], ry = rxy[,2], treatment.func = myfunc, treatment.par = map, constraint.func = consfun, constraint.par = map, nrep=9) ## Then apply the null model par(mfrow = c(3,3)) tmp <- testNM(nmo2) ## all the relocations are now inside the study area. ######################################## ## ## example using NMs.randomCRW ## We generate correlated random walks with the same starting ## point as the original trajectory, the same turning angle ## distribution, and the same distance between relocation ## distribution. We use the same constraint function as previously ## (all relocations falling within the study area), and we ## use the same treatment function as previously (just plot ## the result). mo <- NMs.randomCRW(na.omit(anim1), rangles=TRUE, rdist=TRUE, treatment.func = myfunc, treatment.par = map, constraint.func=consfun, constraint.par = map, nrep=9) par(mfrow = c(3,3)) tmp <- testNM(mo) ## Now, try a different treatment function: e.g. measure ## the distance between the first and last relocation, ## to test whether the animal is performing a return trip myfunc2 <- function(x, par) { sqrt(sum(unlist(x[1,1:2] - x[nrow(x),1:2])^2)) } ## Now fit again the null model with this new treatment and 499 repetitions: mo2 <- NMs.randomCRW(na.omit(anim1), rangles=TRUE, rdist=TRUE, treatment.func = myfunc2, treatment.par = map, constraint.func=consfun, constraint.par = map, nrep=499) ## Then apply the null model suppressWarnings(RNGversion("3.5.0")) set.seed(298) ## to make the calculation reproducible rand <- testNM(mo2) ## rand is a list with one element (there is one trajectory in anim1). length(rand[[1]]) ## The first element of rand is a list of length 499 (there are 499 ## randomizations). head(rand[[1]]) ## unlist this list: rand2 <- unlist(rand[[1]]) ## calculate the observed average elevation: obs <- myfunc2(na.omit(anim1)[[1]][,1:3], map) ## and performs a randomization test: (rt <- as.randtest(rand2, obs, alter="less")) plot(rt) ## Comparing to a model where the animal is moving randomly, and based ## on the chosen criterion (distance between the first and last ## relocation), we can see that the distance between the first and last ## relocation is rarely observed. It seems to indicate that the animal ## tends to perform a loop. ######################################## ## ## example using NMs2NMm ## Given the previous results, we may try to see if all ## the trajectories in puechcirc are characterized by return ## trips ## We need a NMm approach. Because we have 3 burst in puechcirc ## we need a summary criterion. For example, the mean ## distance between the first and last relocation. ## We program a treatment function: it also takes two arguments, but x ## is now an object of class "ltraj" ! ## par is needed, but will not be used in the function myfunm <- function(x, par) { di <- unlist(lapply(x, function(y) { sqrt(sum(unlist(y[1,1:2] - y[nrow(y),1:2])^2)) })) return(mean(di)) } ## Now, prepare the NMs object: we do not indicate any treatment ## function (it would not be taken into account when NMs would be ## transformed to NMm). However, we keep the constraint function ## the simulated trajectories should fall within the study area mo2s <- NMs.randomCRW(na.omit(puechcirc), constraint.func=consfun, constraint.par = map) ## We convert this object to NMm, and we pass the treatment function mo2m <- NMs2NMm(mo2s, treatment.func = myfunm, nrep=499) ## and we fit the model suppressWarnings(RNGversion("3.5.0")) set.seed(908) resu <- testNM(mo2m) ## We calculate the observed mean distance between the ## first and last relocation obs <- myfunm(na.omit(puechcirc)) ## and performs a randomization test: (rt <- as.randtest(unlist(resu), obs, alter="less")) plot(rt) ## The test is no longer significant ######################################## ## ## example using NMs.randomCs ## Consider this sample of 5 capture sites: cs <- list(c(701184, 3161020), c(700164, 3160473), c(698797, 3159908), c(699034, 3158559), c(701020, 3159489)) image(map) lapply(cs, function(x) points(x[1], x[2], pch=16)) ## Consider this sample of distances: dist <- c(100, 200, 150) ## change the treatment function so that the capture sites are showed as ## well. Now, par is a list with two elements: the first one is the map ## and the second one is the list of capture sites myfunc <- function(x, par) { par(mar = c(0,0,0,0)) ## first plot the map image(par[[1]]) lapply(par[[2]], function(x) points(x[1], x[2], pch=16)) ## then add the trajectory lines(x[,1], x[,2], lwd=2) } ## Now define the null model, with the same constraints ## and treatment as before mod <- NMs.randomCs(na.omit(anim1), newCs=cs, newDistances=dist, treatment.func=myfunc, treatment.par=list(map, cs), constraint.func=consfun, constraint.par=map, nrep=9) ## apply the null model par(mfrow = c(3,3)) tmp <- testNM(mod) ## End(Not run)## Not run: ######################################## ## ## example using NMs.randomShiftRotation ## first load the data: data(puechcirc) data(puechabonsp) map <- puechabonsp$map ## Consider the first animal ## on an elevation map anim1 <- puechcirc[1] plot(anim1, spixdf=map[,1]) ## We define a very simple treatment function ## for a NMs model: it just plots the randomized trajectory ## over the study area ## As required, the function takes two arguments: ## x is a data.frame storing a randomized trajectory (three ## columns: the x, y coordinates and the date) ## par contains the map of the study area myfunc <- function(x, par) { par(mar = c(0,0,0,0)) ## first plot the map image(par) ## then add the trajectory lines(x[,1], x[,2], lwd=2) } ## Then we define the null model ## ## We define the range of the study area where the trajectory ## will be shifted: rxy <- apply(coordinates(map),2,range) rxy ## We define the null model with 9 repetitions nmo <- NMs.randomShiftRotation(na.omit(anim1), rshift = TRUE, rrot = TRUE, rx = rxy[,1], ry = rxy[,2], treatment.func = myfunc, treatment.par = map, nrep=9) ## Then apply the null model par(mfrow = c(3,3)) tmp <- testNM(nmo) ## You may try variations, by setting rshift or rrot to FALSE, to see ## the differences ## Note that some of the randomized trajectories are located outside the ## study area, although all barycentres are located within the X and Y ## limits of this study area. ## We may define a constraint function returning TRUE only if all ## relocations are located within the study area ## again, note that the two parameters are x and par consfun <- function(x, par) { ## first convert x to the class SpatialPointsDataFrame coordinates(x) <- x[,1:2] ## then use the function over from the package sp ## to check whether all points in x are located inside ## the study area ov <- over(x, geometry(map)) return(all(!is.na(ov))) } ## Now fit again the null model under these constraints: nmo2 <- NMs.randomShiftRotation(na.omit(anim1), rshift = TRUE, rrot = TRUE, rx = rxy[,1], ry = rxy[,2], treatment.func = myfunc, treatment.par = map, constraint.func = consfun, constraint.par = map, nrep=9) ## Then apply the null model par(mfrow = c(3,3)) tmp <- testNM(nmo2) ## all the relocations are now inside the study area. ######################################## ## ## example using NMs.randomCRW ## We generate correlated random walks with the same starting ## point as the original trajectory, the same turning angle ## distribution, and the same distance between relocation ## distribution. We use the same constraint function as previously ## (all relocations falling within the study area), and we ## use the same treatment function as previously (just plot ## the result). mo <- NMs.randomCRW(na.omit(anim1), rangles=TRUE, rdist=TRUE, treatment.func = myfunc, treatment.par = map, constraint.func=consfun, constraint.par = map, nrep=9) par(mfrow = c(3,3)) tmp <- testNM(mo) ## Now, try a different treatment function: e.g. measure ## the distance between the first and last relocation, ## to test whether the animal is performing a return trip myfunc2 <- function(x, par) { sqrt(sum(unlist(x[1,1:2] - x[nrow(x),1:2])^2)) } ## Now fit again the null model with this new treatment and 499 repetitions: mo2 <- NMs.randomCRW(na.omit(anim1), rangles=TRUE, rdist=TRUE, treatment.func = myfunc2, treatment.par = map, constraint.func=consfun, constraint.par = map, nrep=499) ## Then apply the null model suppressWarnings(RNGversion("3.5.0")) set.seed(298) ## to make the calculation reproducible rand <- testNM(mo2) ## rand is a list with one element (there is one trajectory in anim1). length(rand[[1]]) ## The first element of rand is a list of length 499 (there are 499 ## randomizations). head(rand[[1]]) ## unlist this list: rand2 <- unlist(rand[[1]]) ## calculate the observed average elevation: obs <- myfunc2(na.omit(anim1)[[1]][,1:3], map) ## and performs a randomization test: (rt <- as.randtest(rand2, obs, alter="less")) plot(rt) ## Comparing to a model where the animal is moving randomly, and based ## on the chosen criterion (distance between the first and last ## relocation), we can see that the distance between the first and last ## relocation is rarely observed. It seems to indicate that the animal ## tends to perform a loop. ######################################## ## ## example using NMs2NMm ## Given the previous results, we may try to see if all ## the trajectories in puechcirc are characterized by return ## trips ## We need a NMm approach. Because we have 3 burst in puechcirc ## we need a summary criterion. For example, the mean ## distance between the first and last relocation. ## We program a treatment function: it also takes two arguments, but x ## is now an object of class "ltraj" ! ## par is needed, but will not be used in the function myfunm <- function(x, par) { di <- unlist(lapply(x, function(y) { sqrt(sum(unlist(y[1,1:2] - y[nrow(y),1:2])^2)) })) return(mean(di)) } ## Now, prepare the NMs object: we do not indicate any treatment ## function (it would not be taken into account when NMs would be ## transformed to NMm). However, we keep the constraint function ## the simulated trajectories should fall within the study area mo2s <- NMs.randomCRW(na.omit(puechcirc), constraint.func=consfun, constraint.par = map) ## We convert this object to NMm, and we pass the treatment function mo2m <- NMs2NMm(mo2s, treatment.func = myfunm, nrep=499) ## and we fit the model suppressWarnings(RNGversion("3.5.0")) set.seed(908) resu <- testNM(mo2m) ## We calculate the observed mean distance between the ## first and last relocation obs <- myfunm(na.omit(puechcirc)) ## and performs a randomization test: (rt <- as.randtest(unlist(resu), obs, alter="less")) plot(rt) ## The test is no longer significant ######################################## ## ## example using NMs.randomCs ## Consider this sample of 5 capture sites: cs <- list(c(701184, 3161020), c(700164, 3160473), c(698797, 3159908), c(699034, 3158559), c(701020, 3159489)) image(map) lapply(cs, function(x) points(x[1], x[2], pch=16)) ## Consider this sample of distances: dist <- c(100, 200, 150) ## change the treatment function so that the capture sites are showed as ## well. Now, par is a list with two elements: the first one is the map ## and the second one is the list of capture sites myfunc <- function(x, par) { par(mar = c(0,0,0,0)) ## first plot the map image(par[[1]]) lapply(par[[2]], function(x) points(x[1], x[2], pch=16)) ## then add the trajectory lines(x[,1], x[,2], lwd=2) } ## Now define the null model, with the same constraints ## and treatment as before mod <- NMs.randomCs(na.omit(anim1), newCs=cs, newDistances=dist, treatment.func=myfunc, treatment.par=list(map, cs), constraint.func=consfun, constraint.par=map, nrep=9) ## apply the null model par(mfrow = c(3,3)) tmp <- testNM(mod) ## End(Not run)
This function provides an interactive version of plot.ltraj,
for the exploration of objects of class ltraj.
trajdyn(x, burst = attr(x[[1]], "burst"), hscale = 1, vscale = 1, recycle = TRUE, display = c("guess", "windows", "tk"), ...)trajdyn(x, burst = attr(x[[1]], "burst"), hscale = 1, vscale = 1, recycle = TRUE, display = c("guess", "windows", "tk"), ...)
x |
an object of class |
burst |
a character string indicating the burst identity to explore |
hscale |
passed to tkrplot |
vscale |
passed to tkrplot |
recycle |
logical. Whether the trajectory should be recycled at the end of the display |
display |
type of display. The default |
... |
additional arguments to be passed to the function
|
Clement Calenge [email protected]
ltraj for further information on the class
ltraj, and plot.ltraj for information on arguments
that can be passed to this function.
## Not run: ## Without map data(puechcirc) trajdyn(puechcirc) ## With map data(puechabonsp) trajdyn(puechcirc, spixdf = puechabonsp$map) ## End(Not run)## Not run: ## Without map data(puechcirc) trajdyn(puechcirc) ## With map data(puechabonsp) trajdyn(puechcirc, spixdf = puechabonsp$map) ## End(Not run)
This function transforms a trajectory of type II (time recorded) into a trajectory of type I (time not recorded).
typeII2typeI(x)typeII2typeI(x)
x |
a object of class "ltraj" of type II |
An object of class "ltraj"
Clement Calenge [email protected]
as.ltraj for additional information on the
objects of class "ltraj"
data(puechcirc) puechcirc typeII2typeI(puechcirc)data(puechcirc) puechcirc typeII2typeI(puechcirc)
The function wawotest.default performs a Wald Wolfowitz test of
the random distribution of the values in a vector. The function
wawotest.ltraj performs this tests for the descriptive
parameters dx, dy and dist in an object of class
ltraj. The function wawotest is generic.
wawotest(x, ...) ## Default S3 method: wawotest(x, alter = c("greater", "less"), ...) ## S3 method for class 'ltraj' wawotest(x, ...)wawotest(x, ...) ## Default S3 method: wawotest(x, alter = c("greater", "less"), ...) ## S3 method for class 'ltraj' wawotest(x, ...)
x |
for |
alter |
a character string specifying the alternative hypothesis, must be one of "greater" (default), "less" or "two-sided" |
... |
additional arguments to be passed to other functions |
The statistic of the test is equal to A = sum(y(i) y(i+1)), with y(N+1) = y(1). Under the hypothesis of a random distribution of the values in the vector, this statistic is normally distributed, with theoretical means and variances given in Wald & Wolfowitz (1943).
wawotest.default returns a vector containing the value of the
statistic (a), its esperance (ea), its variance
(va), the normed statistic (za) and the
P-value. wawotest.ltraj returns a table giving these values for
the descriptive parameters of the trajectory.
Stephane Dray [email protected]
Wald, A. & Wolfowitz, J. (1943) An exact test for randomness in the non-parametric case based on serial correlation. Ann. Math. Statist., 14, 378–388.
indmove and runsNAltraj for other
tests of independence to be used with objects of class "ltraj"
data(puechcirc) puechcirc wawotest(puechcirc)data(puechcirc) puechcirc wawotest(puechcirc)
This data set contains the relocations of one right whale.
data(whale)data(whale)
This data set is a regular object of class ltraj (i.e. constant
time lag of 24H00)
The coordinates are given in decimal degrees (Longitude - latitude).
http://whale.wheelock.edu/Welcome.html
data(whale) plot(whale)data(whale) plot(whale)
This function identifies the relocations fullfilling a condition in an
object of class ltraj.
which.ltraj(ltraj, expr)which.ltraj(ltraj, expr)
ltraj |
an object of class |
expr |
a character string giving any syntactically correct R
logical expression implying the descriptive elements in
|
A data frame giving the ID, the Bursts and the relocations for which
the condition described by expr is verified.
Clement Calenge [email protected]
ltraj for additional information about objects
of class ltraj
data(puechcirc) puechcirc ## Identifies the relocations for which time lag is ## upper than one hour which.ltraj(puechcirc, "dt>3600") puechcirc[burst="CH930824"][[1]][27:28,] ## Identifies the speed between successive ## relocations upper than 0.8 meters/second which.ltraj(puechcirc, "dist/dt > 0.8") ## This is the case for example for the ## relocations #28, 58, 59 and 60 of "CH930824" puechcirc[burst="CH930824"][[1]][c(28,58,59,60),]data(puechcirc) puechcirc ## Identifies the relocations for which time lag is ## upper than one hour which.ltraj(puechcirc, "dt>3600") puechcirc[burst="CH930824"][[1]][27:28,] ## Identifies the speed between successive ## relocations upper than 0.8 meters/second which.ltraj(puechcirc, "dist/dt > 0.8") ## This is the case for example for the ## relocations #28, 58, 59 and 60 of "CH930824" puechcirc[burst="CH930824"][[1]][c(28,58,59,60),]