Power Fraction: A New Explanation of Relative Abundance Patterns in Species-Rich Assemblages

Abstract

Analysis of species abundance patterns in assemblages with relatively large number of species has been an important issue in community ecology for several decades. Following Preston's pioneering work, Sugihara proposed a model to account for such patterns in a diverse range of communities, which has been given further support from analyses of recent data that are considered to be of particularly high quality. This paper re-examines Sugihara's approach and points out that there has been confusion and misunderstanding among workers as to the exact nature of his widely-publicised hypothesis. In particular, the 'fixed ratio' division cannot be considered as an expected (average) pattern of the triangular assumption; they represent fundamentally different entities. Further, Tokeshi's Random fraction model should not be treated as synonymous with Sugihara's fixed division model. The RF model has its own identity as a niche apportionment model and can account for patterns in some species-rich assemblages. With this background, this paper proposes a new niche apportionment model to explain relative abundance patterns in ecological communities, termed the Power fraction model. The PF model envisages that the probability (p) of selection for a subsequent division is positively but weakly related to niche sizes/abundances (x) of species as a power function (pαx k where 0 ≤ k ≤ 1.0; i.e. niche division/invasion is more likely in species with high abundance/large niche) and that division occurs with any ratio (i.e. a barrier to split a species' population may occur anywhere in the species' range), with the RF model representing an extreme case on the spectrum of the PF model. The Power fraction model with k ∼ 0.05 or k ∼ 0-0.2 demonstrates a good fit to a miscellany of data from species-rich assemblages. The PF model is not restrictive in terms of division ratios, and can be framed as either a community-specific or a global explanation of patterns. Thus, the new model is more flexible and realistic from ecological and evolutionary points of view and offers a possibility of cross-community comparisons within a uniform, integrative framework.