How Gaussian competition leads to lumpy or uniform species distributions

TL;DR

This paper investigates how the shape of the competition kernel, especially Gaussian versus non-Gaussian, influences whether species distributions are uniform or lumped, revealing the non-robustness of Gaussian assumptions in ecological models.

Contribution

The study demonstrates that Gaussian competition kernels are a border case and small deviations can lead to different species distribution patterns, highlighting the sensitivity of ecological models.

Findings

Gaussian kernels are a border case for species distribution outcomes.

Small deviations from Gaussian shape can cause lumped or uniform distributions.

Model implementation details can influence the emergence of species distribution patterns.

Abstract

A central model in theoretical ecology considers the competition of a range of species for a broad spectrum of resources. Recent studies have shown that essentially two different outcomes are possible. Either the species surviving competition are more or less uniformly distributed over the resource spectrum, or their distribution is 'lumped' (or 'clumped'), consisting of clusters of species with similar resource use that are separated by gaps in resource space. Which of these outcomes will occur crucially depends on the competition kernel, which reflects the shape of the resource utilization pattern of the competing species. Most models considered in the literature assume a Gaussian competition kernel. This is unfortunate, since predictions based on such a Gaussian assumption are not robust. In fact, Gaussian kernels are a border case scenario, and slight deviations from this function can lead to either uniform or lumped species distributions. Here we illustrate the non-robustness of the Gaussian assumption by simulating different implementations of the standard competition model with constant carrying capacity. In this scenario, lumped species distributions can come about by secondary ecological or evolutionary mechanisms or by details of the numerical implementation of the model. We analyze the origin of this sensitivity and discuss it in the context of recent applications of the model.