Models for vectors and vector-borne diseases.

The development of models for species' distributions is briefly reviewed, concentrating on logistic regression and discriminant analytical methods. Improvements in each type of modelling approach have led to increasingly accurate model predictions. This review addresses several key issues that now confront those wishing to choose the "right" sort of model for their own application. One major issue is the number of predictor variables to retain in the final model. Another is the problem of sparse datasets, or of data reported to administrative levels only, not to points. A third is the incorporation of spatial co-variance and auto-covariance in the modelling process. It is suggested that many of these problems can be resolved by adopting an information-theoretic approach whereby a group of reasonable potential models is specified in advance, and the "best" candidate model is selected among them. This approach of model selection and multi-model inference, using various derivatives of the Kullback-Leibler information or distance statistic, puts the biologist, with her or his insight, back in charge of the modelling process that is usually the domain of statisticians. Models are penalized when they contain too many variables; careful specification of the right set of candidate models may also be used to identify the importance of each predictor variable individually; and finally the degree to which the current "best" model improves on all the other models in the candidate set may be quantified. The ability definitely to exclude some models from the realm of all possible models appropriate for any particular distribution problem may be as important as the ability to identify the best current model.