secr (version 2.5.0)

secr.model.density: Density Models

Description

SECR can fit an inhomogeneous Poisson model to describe the distribution of animals. This may be viewed as a surface of expected density across the study area. The log likelihood is evaluated in secr.fit by summing values at points on a `habitat mask'. Each point in a habitat mask represents a grid cell of potentially occupied habitat (their combined area may be almost any shape and may include disjunct patches). The density model may take one of two forms: a user-provided Rfunction or a linear model on the link scale (see the link argument of secr.fit; the default link for density is `log'). User-provided functions are described in the accompanying vignette ../doc/secr-densitysurfaces.pdf. Here we focus on linear models. The full design matrix for density (D) has one row for each point in the mask. The design matrix has one column for the intercept (constant) term and one for each predictor. Predictors may be based on Cartesian coordinates (e.g. `x' for an east-west trend), a continuous habitat variable (e.g. vegetation cover) or a categorical (factor) habitat variable. Predictors must be known for all points in the mask (non-habitat excluded). The variables `x', `y', `x2', `y2', `xy', `session', `Session' and `g' are provided automatically. Other covariates should be named columns in the `covariates' attribute of the habitat mask. lll{ Variable Description Data source x x-coordinate automatic y y-coordinate automatic x2 x-coordinate^2 automatic y2 y-coordinate^2 automatic xy x-coordinate * y-coordinate automatic session session factor automatic Session session number 0:(R-1) automatic g group factor automatic [user] mask covariate covariates(mask) as named in formula } The submodel for density (D) is a named component of the list used in the model argument of secr.fit. It is expressed in Rformula notation by appending terms to $\sim{~}$. Density surfaces resulting from the fitting of SECR models are manipulated in secr as objects of class `Dsurface'. See the vignette ../doc/secr-densitysurfaces.pdf for details and examples, including functions for prediction and plotting.

References

Borchers, D. L. and Efford, M. G. (2008) Spatially explicit maximum likelihood methods for capture--recapture studies. Biometrics 64, 377--385.

See Also

secr models, secr detection models, secr.fit, Dsurface, predictDsurface, plot.Dsurface

Examples

D = ~ 1      ## constant density (homogeneous Poisson)
D = ~ x      ## east-west trend
D = ~ cover  ## requires 'cover' as a mask covariate