  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.
