# Trajectory Analysis using the Residence Time Method These functions can be used to apply the residence time method (Barraquand and Benhamou, 2008). ```r 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, ...) ``` ## Arguments - `lt`: an object of class `ltraj` - `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 `TRUE`, then the residence time method is added as a variable in the `infolocs` component of the object `lt`. If `FALSE` this function returns an object of class `resiti` - `units`: a character string indicating the time units of `maxt` - `x`: an object of class `"resiti"` - `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 ## Details 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. ## Returns 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. ## References Barraquand, F. and Benhamou, S. (2008) Animal movement in heterogeneous landscapes: identifying profitable places and homogeneous movement bouts. **Ecology**, 89 , 3336--3348. ## Author(s) Clement Calenge clement.calenge@ofb.gouv.fr ## See Also `lavielle` for the partitionning of the trajectory based on the residence time. ## Examples ```r ## 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) ```

residenceTime function