TALK BY Riccardo DI Clemente: The build-up of diversity in complex ecosystems.

CCS’15 Conference on Complex Systems. (Phoenix, AZ, USA)

Diversity is a fundamental feature of ecosystems, even when the concept of ecosystem is ex- tended 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. Di- versity explosions are the first stylized fact: evolutionary radiations in biology, or the process of escaping "Poverty Traps" in economics are two well known examples. The second stylized fact 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 (Islands-Animals), macroeconomic (countries-products) and mutualistic (e.g. Pollinators-Plants) to name a few. This indicates that entities diversify following a pattern.

For the fact that they appear in such very different systems, these two stylized facts seem to point out that the build up of diversity might be driven by a fundamental mechanism of probabilistic nature, and in this chapter we try to sketch its minimal features. Namely 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 (e.g. animals, or products) can be described as combinations of a number of fundamental building blocks. We propose the idea that the stylized facts of diversity that we observe in real systems can be explained with an extreme heterogeneity (a scale-free distri- bution) in the number of meaningful combinations (usefulness) 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 behaviours in accordance with what is observed in real systems.