Mid-domain models of species richness gradients: assumptions, methods and evidence

1. Patterns of species richness along latitudinal, elevational and depth gradients often exhibit a mid-gradient peak. Similar patterns with a mid-domain peak in richness are produced, as a result of geometric constraints on species distributions, by models that randomize species range size and placement over a bounded gradient. 2. Proponents of these so-called mid-domain models argue that they provide an appropriate null hypothesis for examining species richness patterns along spatial gradients. Furthermore, some claim that because these models seem to explain a large proportion of the large-scale spatial variation in richness, geometric constraints on species distribution are in fact the cause of these patterns. 3. A critical examination of model assumptions reveals that some are unrealistic, conceptually flawed or internally inconsistent. Additionally, tests of mid-domain models have suffered from methodological deficiencies derived from arbitrariness and circularity in the definition of domain boundaries, collapsing two-dimensional (2-D) patterns into a single dimension (1-D), and the use of interpolated ranges, all of which can bias test results in favour of the models. Tests have also been statistically naive by using fairly insensitive measures of deviation between observed and predicted patterns and ignoring the increased probability of Type I error that can result in analyses of spatially autocorrelated data. 4. In spite of this, a review of the empirical evidence indicates that most studies do not show a high degree of concordance between observed and predicted species richness patterns, particularly in 2-D. Additionally, spatial patterns of variation in range size and species turnover do not unequivocally support mid-domain models. Thus, the models do not adequately describe observed species richness gradients and thus fail to explain them. 5. Although mid-domain models have served a useful purpose in drawing attention to the need to clarify the null expectation in the study of species richness gradients, their use appears to be severely limited by difficulties associated with the treatment of ranges, boundary definitions and a lack of clarity regarding the extent to which the observed data should be used to generate the null patterns.