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), or a list of these, one per row of xy

simOU.capthist - single-session capthist object for secr

Arguments

xy: numeric vector of x,y coordinates for one animal, or 2-column matrix
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. This step is skipped to save time if `traps' has detector type ``multi'' and ... is empty.

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 default `verify' step in reduce.capthist may also be suppressed (set verify = FALSE in simOU.capthist()).

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 (blue dots), movements (grey), and AC (triangles)
plot(pop, pch = 2, cex = 1, border = 4)
plot(ch, rad = 0.2, tracks = TRUE, varycol = FALSE, add = TRUE,
    gridlines = FALSE)
symbols(grid$x, grid$y, circles = rep(0.25,64), inches = FALSE, fg = 'red', 
    add = TRUE)
sapply(attr(ch, 'path'), lines, col = 'grey')

# fit a misspecified HHN model
# density estimates show a small negative bias 
# sigma estimates show a large negative bias 
# lambda0 cannot be compared
fit <- secr.fit(capthist = ch, buffer = 8, detectfn = 14, trace = FALSE)
predict(fit)

# }