Consistent scaling and parameter choice for linear and Generalized Lotka-Volterra models used in community ecology

Abstract

Many variants of linear and Generalized Lotka-Volterra (GLV) models have been employed in theoretical community ecology. In order to assess what has been learned from these, this paper proposes standard representations and presents results that facilitate comparison of alternative formulations and evaluation of choice of parameter values. Wigner's “semi-circle law” for large random matrices as adapted by May for ecological models is revised and extended using interactance as a measure of system complexity. Diagonal dominance and May's proposed complexity limit for stability are shown to be too conservative for moderate size systems. Biological arguments for choice of parameter values in GLV models are also found to be difficult to sustain. Exploration of linear and GLV models as mathematical systems does, however, suggest questions about the construction and turnover of ecological communities.