The Clumping Transition in Niche Competition: a Robust Critical Phenomenon

TL;DR

This paper demonstrates a robust phase transition in niche competition models where species distribution lumps form or dissolve depending on niche width, with critical slowing down near the transition point, matching empirical data.

Contribution

It analytically and numerically characterizes a critical clumping transition in niche competition, revealing a universal phenomenon with predictable groupings along the niche axis.

Findings

Lumpy patterns emerge when niche width exceeds a critical threshold.

Number of species lumps follows a power-law distribution.

Predicted lump counts match empirical observations.

Abstract

We show analytically and numerically that the appearance of lumps and gaps in the distribution of n competing species along a niche axis is a robust phenomenon whenever the finiteness of the niche space is taken into account. In this case depending if the niche width of the species $\sigma$ is above or below a threshold $\sigma_c$, which for large n coincides with 2/n, there are two different regimes. For $\sigma > sigma_c$ the lumpy pattern emerges directly from the dominant eigenvector of the competition matrix because its corresponding eigenvalue becomes negative. For $\sigma </- sigma_c$ the lumpy pattern disappears. Furthermore, this clumping transition exhibits critical slowing down as $\sigma$ is approached from above. We also find that the number of lumps of species vs. $\sigma$ displays a stair-step structure. The positions of these steps are distributed according to a power-law. It is thus straightforward to predict the number of groups that can be packed along a niche axis and it coincides with field measurements for a wide range of the model parameters.