Limiting Similarity, Species Packing, and System Stability for Hierarchical Competition‐Colonization Models

Hierarchical competition-colonization models have been used to explain limiting similarities among species, successional dynamics, and species loss under habitat destruction. This class of models assumes that there is an inverse relationship between competitive ability and colonization ability and that competitively superior species exclude competitively inferior species when both occupy the same site. This hierarchical model of performance trade-offs, however, exhibits some unusual behaviors in the high-diversity limit, including infinitesimally close species packing, pathologically slow dynamics, and fundamentally important regularities in trait-abundance relationships. In particular, under the condition of constant mortality across species, a 3/2-power-law relationship emerges between abundance and fecundity under infinite packing (abundance of a species with fecundity f is inversely proportional to f to the 3/2 power). In this article, we explore the high-diversity limit of the hierarchical competition-colonization model, with particular emphasis on patterns of species packing, species-abundance relationships, and system stability. Because of the potential for pathologically slow dynamics following perturbations and infinitesimally close species packing in the high-diversity limit for this class of models, the models may need to be modified to include more realistic mechanisms governing the extent and timing of interspecific competitive exclusion in order to effectively capture the structure and dynamics of real-world ecosystems.