Characterizing Species Distributions by Productivity and Mortality Rates in Multispecies Models

Abstract

The temporal change in species composition is one dimension that may be used to characterize ecosystems. Multispecies interactions and species abundance (or biomass) distributions can be analyzed by an N‐species Lotka–Volterra (LV) system of equations. We derive a statistical approximation to the stationary probability distribution of relative species biomass for a system of interacting species. The distribution is parameterized by the mean and variance of the LV species interaction coefficients and can exhibit a variety of shapes. Given this distribution, one can describe the state of the system, and subsequent perturbations within the system, in terms of shifts in the resulting stable distribution. Theoretical distributions with known properties were compared to distributions estimated from simulations and good agreement was found. Our analytical result could be used to develop “ecosystem indicators” for describing changes in the state of species within an ecosystem.