On the proportional abundance of species: Integrating population genetics and community ecology

Pablo A Marquet,Angela Ganz,Sebastian R Abades,Guillermo Espinoza,Rolando Rebolledo

doi:10.1038/s41598-017-17070-1

Abstract

The frequency of genes in interconnected populations and of species in interconnected communities are affected by similar processes, such as birth, death and immigration. The equilibrium distribution of gene frequencies in structured populations is known since the 1930s, under Wright’s metapopulation model known as the island model. The equivalent distribution for the species frequency (i.e. the species proportional abundance distribution (SPAD)), at the metacommunity level, however, is unknown. In this contribution, we develop a stochastic model to analytically account for this distribution (SPAD). We show that the same as for genes SPAD follows a beta distribution, which provides a good description of empirical data and applies across a continuum of scales. This stochastic model, based upon a diffusion approximation, provides an alternative to neutral models for the species abundance distribution (SAD), which focus on number of individuals instead of proportions, and demonstrate that the relative frequency of genes in local populations and of species within communities follow the same probability law. We hope our contribution will help stimulate the mathematical and conceptual integration of theories in genetics and ecology.

Highlights

Ever since the evolutionary synthesis, population genetics theory has been integrated, to different extents, into different disciplines within biology including systematics and ecology
There is a major barrier to this integration, while population geneticists pioneered the use of diffusion approximations to the understanding of processes affecting gene frequencies[20], ecologists have favored to work with the distribution of the number of individuals across species or SAD8,21–23
We show that if one assumes that birth and death rates follow the functional form used in neutral theory[8,28] the stationary distribution for the species proportional abundance distribution (SPAD), the same as for genes, is a beta distribution with parameters α and β that quantify the relative importance of immigration and speciation, respectively, in relation to stochastic fluctuations

Summary

Introduction

Ever since the evolutionary synthesis, population genetics theory has been integrated, to different extents, into different disciplines within biology including systematics and ecology. We show that if one assumes that birth and death rates follow the functional form used in neutral theory[8,28] the stationary distribution for the species proportional abundance distribution (SPAD), the same as for genes, is a beta distribution with parameters α and β that quantify the relative importance of immigration and speciation, respectively, in relation to stochastic fluctuations.

Results

Conclusion