## Simulation of a Correlated Random Walk

### Description

This function simulates a correlated random walk

### Usage

```simm.crw(date=1:100, h = 1, r = 0,
x0=c(0,0), id="A1", burst=id,
typeII=TRUE, proj4string=CRS())
```

### Arguments

 `date` a vector indicating the date (in seconds) at which relocations should be simulated. This vector can be of class `POSIXct`. *Note that the time lag between two relocations should be constant* (regular trajectories required) `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 `help(ltraj)`) `burst` a character string indicating the identity of the simulated burst (see `help(ltraj)`) `typeII` logical. Whether the simulated trajectory should be of type II (`TRUE`, time recorded) or not (`FALSE`, time not recorded). See `help(ltraj)`. `proj4string` a valid CRS object containing the projection information (see `?CRS` from the package `sp`).

### Details

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`.

### Value

an object of class `ltraj`

### Note

This function requires the package `CircStats`.

### Author(s)

Clement Calenge clement.calenge@ofb.gouv.fr
Stephane Dray dray@biomserv.univ-lyon1.fr
Manuela Royer royer@biomserv.univ-lyon1.fr
Daniel Chessel chessel@biomserv.univ-lyon1.fr

### References

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`

### Examples

```
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)

```