Evolutionary Stability of Ecological Hierarchy

TL;DR

This paper presents a self-similar, evolutionarily stable hierarchical solution to the multi-dimensional Lotka-Volterra equations, explaining key features of ecosystems like pyramidal populations and trophic structures.

Contribution

It introduces a novel stable hierarchical solution to Lotka-Volterra models, elucidating ecological hierarchy features through self-similarity and stability analysis.

Findings

Hierarchical ecosystems exhibit self-similarity and stability.

The model explains pyramidal population distributions.

Higher trophic levels show increased aggressiveness.

Abstract

A self-similar hierarchical solution that is both dynamically and evolutionarily stable is found to the multi dimensional Lotka-Volterra equation with a single chain of prey-predator relations. This gives a simple and natural explanation to the key features of hierarchical ecosystems, such as its ubiquity, pyramidal population distribution, and higher aggressiveness among higher trophic levels. pacs{87.23.Kg, 89.75.Da, 05.45.-a} keywords{Lotka-Volterra equation, Trophic pyramid, Self-similarity}