The Build-Up of Diversity in Complex Ecosystems

TL;DR

This paper proposes a probabilistic model based on a maximally entropic tripartite network with scale-free distributions to explain the emergence of diversity and nestedness in complex ecosystems and other interaction networks.

Contribution

It introduces a minimal model using a random tripartite network with scale-free distributions to reproduce key stylized facts of diversity and nestedness across systems.

Findings

Reproduces diversity explosion patterns accurately

Explains nestedness as a consequence of heterogeneity in building blocks

Shows that scale-free distributions lead to rich, diverse behaviors

Abstract

Diversity is a fundamental feature of ecosystems, even when the concept of ecosystem is extended to sociology or economics. Diversity can be intended as the count of different items, animals, or, more generally, interactions. There are two classes of stylized facts that emerge when diversity is taken into account. The first are Diversity explosions: evolutionary radiations in biology, or the process of escaping 'Poverty Traps' in economics are two well known examples. The second is nestedness: entities with a very diverse set of interactions are the only ones that interact with more specialized ones. In a single sentence: specialists interact with generalists. Nestedness is observed in a variety of bipartite networks of interactions: Biogeographic, macroeconomic and mutualistic to name a few. This indicates that entities diversify following a pattern. Since they appear in such very different systems, these two stylized facts point out that the build up of diversity is driven by a fundamental probabilistic mechanism, and here we sketch its minimal features. We show how the contraction of a random tripartite network, which is maximally entropic in all its degree distributions but one, can reproduce stylized facts of real data with great accuracy which is qualitatively lost when that degree distribution is changed. We base our reasoning on the combinatoric picture that the nodes on one layer of these bipartite networks can be described as combinations of a number of fundamental building blocks. The stylized facts of diversity that we observe in real systems can be explained with an extreme heterogeneity (a scale-free distribution) in the number of meaningful combinations in which each building block is involved. We show that if the usefulness of the building blocks has a scale-free distribution, then maximally entropic baskets of building blocks will give rise to very rich behaviors.