Ecological boundary detection using Carlin-Chib Bayesian model selection

Sharp ecological transitions in space (ecotones, edges, boundaries) often are where ecologically important events occur, such as elevated or reduced biodiversity or altered ecological functions (e.g. changes in productivity, pollination rates or parasitism loads, nesting success). While human observers often identify these transitions by using intuitive or gestalt assignments (e.g. the boundary between a remnant woodland patch and the surrounding farm paddock seems obvious), it is clearly desirable to make statistical assessments based on measurements. These assessments often are straightforward to make if the data are univariate, but identifying boundaries or transitions using compositional or multivariate data sets is more difficult. There is a need for an intermediate step in which pairwise similarities between points or temporal samples are computed. Here, I describe an approach that treats points along a transect as alternative hypotheses (models) about the location of the boundary. Carlin and Chib (1995) introduced a Bayesian technique for comparing non-hierarchical models, which I adapted to compute the probabilities of each boundary location (i.e. a model) relative to the ensemble of models constituting the set of possible points of the boundary along the transect. Several artificial data sets and two field data sets (on vegetation and soils and on cave-dwelling invertebrates and microclimates) are used to illustrate the approach. The method can be extended to cases in with several boundaries along a gradient, such as where there is an ecotone of non-zero thickness.