Statistical models for spatially explicit biological data.

Existing algorithms for predicting species' distributions sit on a continuum between purely statistical and purely biological approaches. Most of the existing algorithms are aspatial because they do not consider the spatial context, the occurrence of the species or conditions conducive to the species' existence, in neighbouring areas. The geostatistical techniques of kriging and cokriging are presented in an attempt to encourage biologists more frequently to consider them. Unlike deterministic spatial techniques they provide estimates of prediction errors. The assumptions and applications of common geostatistical techniques are presented with worked examples drawn from a dataset of the bluetongue outbreak in northwest Europe in 2006. Emphasis is placed on the importance and interpretation of weights in geostatistical calculations. Covarying environmental data may be used to improve predictions of species' distributions, but only if their sampling frequency is greater than that of the species' or disease data. Cokriging techniques are unable to determine the biological significance or importance of such environmental data, because they are not designed to do so.