# simm.mou: Simulation of a Bivariate Ornstein-Uhlenbeck Process In adehabitatLT: Analysis of Animal Movements

 simm.mou R Documentation

## Simulation of a Bivariate Ornstein-Uhlenbeck Process

### Description

This function simulates a bivariate Ornstein-Uhlenbeck process for animal movement.

### Usage

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())


### Arguments

 date a vector indicating the date (in seconds) at which relocations should be simulated. This vector can be of class POSIXct 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 help(ltraj)) burst a character string indicating the identity of the simulated burst (see help(ltraj)) proj4string a valid CRS object containing the projection information (see ?CRS from the package sp).

### Details

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:

d\mathbf{z} = \mathbf{a} ( \mathbf{b} - \mathbf{z}(t)) dt + \mathbf{\Sigma} d \mathbf{B2(t)}

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).

### Value

An object of class ltraj

### 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

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

### Examples


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)



adehabitatLT documentation built on April 6, 2023, 5:18 p.m.