Kullback-Leibler information as a basis for strong inference in ecological studies

Abstract

We describe an information-theoretic paradigm for analysis of ecological data, based on Kullback-Leibler information, that is an extension of likelihood theory and avoids the pitfalls of null hypothesis testing. Information-theoretic approaches emphasise a deliberate focus on the a priori science in developing a set of multiple working hypotheses or models. Simple methods then allow these hypotheses (models) to be ranked from best to worst and scaled to reflect a strength of evidence using the likelihood of each model (gi), given the data and the models in the set (i.e. L(gi | data)). In addition, a variance component due to model-selection uncertainty is included in estimates of precision. There are many cases where formal inference can be based on all the models in the a priori set and this multi-model inference represents a powerful, new approach to valid inference. Finally, we strongly recommend inferences based on a priori considerations be carefully separated from those resulting from some form of data dredging. An example is given for questions related to age- and sex-dependent rates of tag loss in elephant seals (Mirounga leonina).