An Autologistic Model for the Spatial Distribution of Wildlife

Abstract

1. A new method for estimating the geographical distribution of plant and animal species from incomplete field survey data is developed. 2. Wildlife surveys are often conducted by dividing a study region into a regular grid and collecting data on abundance or on presence/absence from some or all of the squares in the grid. Generalized linear models (GLMs) can be used to model the spatial distribution of a species within such a grid by relating the response variable (abundance or presence/absence) to spatially referenced covariates. 3. Such models ignore or at best indirectly model dependence on unmeasured covariates, and the intrinsic spatial autocorrelation arising for example in gregarious populations. 4. We describe a procedure for use with presence/absence data in which spatial autocorrelation is modelled explicitly. We achieve this by extending a logistic model to include an extra covariate which is derived from the responses at neighbouring squares. The extended model is known as an autologistic model. 5. To allow fitting of the autologistic model when only a random sample of squares is surveyed, we use the Gibbs sampler to predict presence/absence at unsurveyed squares. 6. We compare the autologistic model with the ordinary logistic model using red deer census data. Both models are fitted to a subsample of 20% of the data and results are compared with the 'true' abundance and spatial distribution indicated by the full census. We conclude that the autologistic model is superior for estimating the spatial distribution of the deer, whereas the ordinary logistic model yields more precise estimates of the overall number of squares occupied by deer at the time of the survey.