simOU.capthist: Simulate Detections For Ornstein-Uhlenbeck Movement

Description

The usual SECR model ignores the sequential locations of an individual within its home range. Movement models predict serial correlation of detections in space. The Ornstein-Uhlenbeck (OU) model is a convenient example that over long durations leads to a bivariate normal distribution of locations.

Movements of a single animal according to the OU model are simulated in discrete time with simOU.

Detections of a population of individuals with pre-defined activity centres are simulated with simOU.capthist. Detection happens when the location of an individual at time $t$ (occasion $t$) is within distance epsilon $\epsilon$ of a detector.

Usage

simOU(xy, tau, sigma, noccasions, start = NULL)
simOU.capthist(traps, popn, detectpar, noccasions, seed = NULL,
    savepopn = FALSE, savepath = FALSE, ...)

Value

simOU - matrix of locations dim = c(noccasions, 2)

simOU.capthist - single-session capthist object for secr

Arguments

xy: numeric vector of x,y coordinates for one animal
tau: numeric parameter of serial correlation = $1 / \beta$
sigma: numeric spatial scale parameter
noccasions: integer number of time steps
start: numeric vector of x,y coordinates for initial location (optional)
traps: secr traps object
popn: secr popn object or a 2-column matrix of x-y coordinates of activity centres
detectpar: list with values of detection parameters epsilon, sigma, and tau
seed: either NULL or an integer that will be used in a call to set.seed
savepopn: logical; if TRUE the population is saved as an attribute
savepath: logical; if TRUE the movement paths are saved as an attribute
...: other arguments passed to reduce.capthist

Details

The first location for simOU by default is drawn at random from the asymptotic distribution.

The detection parameters are:

epsilon	radius within which individual detected with certainty
sigma	spatial scale of asymptotic bivariate normal
tau	serial correlation parameter 1/beta

In a final step, `simOU.capthist' uses the reduce method for capthist objects to coerce the simulated capthist object to the detector type of the traps argument.

The ... argument may be used to pass the 'by' argument to reduce.capthist. For example, 'by = "ALL"' collapses the initially binary data for a single detector on noccasions to a single integer. Alternatively, 'by = 10' collapses the original occasions in groups of 10. Data will be lost unless the input traps object has detector type 'count'.

The x- and y-dimensions are simulated separately, assuming circularity. The distribution of location on the $x$ axis at time $t+1$ conditional on the location at time $t$ is then $$x_{t+1} | x_{t} \sim N(\mu_x + e^{\frac{-1}{\tau}(x_{t} - \mu_x)}, \; \sigma^2 (1 - e^{\frac{-2}{\tau}}),$$ where $\mu = (\mu_x, \mu_y)$ is the long-term activity centre and $\tau$ (tau) is a parameter for the strength of serial correlation ($\tau = 1/\beta$ in other formulations). The scale of the long-term (asymptotic) bivariate normal home range is governed by $\sigma$ as usual. Steps are implicitly of length 1 occasion so $\Delta t$ is omitted.

Examples

Run this code


# one animal
locs <- simOU(c(0,0), 20, 1, 100)
par(pty = 's')
plot(locs, type = 'o', xlim = c(-2.5,2.5), ylim = c(-2.5,2.5))
points(0,0, pch = 16, col = 'red')

# \donttest{

# simulate some capture data
set.seed(123)
grid <- make.grid(8, 8, spacing = 2)
pop <- sim.popn(D = 1000, core = grid, buffer = 4)
ch <- simOU.capthist(grid, pop, detectpar=list(tau = 50, sigma = 1, epsilon = 0.25), 
   noccasions = 100, savepath = TRUE)

# plot simulated capthist with overlay of movements and AC
plot(ch, rad = 0.1, tracks = TRUE, varycol = FALSE, border = 4)
sapply(attr(ch, 'path'), lines, col = 'grey')
plot(pop, add = TRUE, pch = 16, cex = 0.6)

# fit a model
fit <- secr.fit(capthist = ch, buffer = 8, detectfn = 14, trace = FALSE)
predict(fit)

# }