Reconciling cooperation, biodiversity and stability in complex ecological communities      
Chengyi Tu, Samir Suweis, Jacopo Grilli, Marco Formentin & Amos Maritan

Empirical evidences show that ecosystems with high biodiversity can persist in time even in the presence of few types of resources and are more stable than low biodiverse communities. This evidence is contrasted by the conventional mathematical modeling, which predicts that the presence of many species and/or cooperative interactions are detrimental for ecological stability and persistence. Here we propose a modelling framework for population dynamics, which also include indirect cooperative interactions mediated by other species (e.g. habitat modification). We show that in the large system size limit, any number of species can coexist and stability increases as the number of species grows, if mediated cooperation is present, even in presence of exploitative or harmful interactions (e.g. antibiotics). Our theoretical approach thus shows that appropriate models of mediated cooperation naturally lead to a solution of the long-standing question about complexity-stability paradox and on how highly biodiverse communities can coexist.

Graphical representation of the model. (A,B) The population dynamics is stochastic: at each time step a randomly chosen individual of a given species (denoted by the color) die and it is replaced by another species that is also picked at random and give birth to an offspring. The species birth rate depends on the species population abundance and on the species interaction matrix (C).

The results of the mean field predictions. (A) Species interaction network for 7 species where each species i has one mutualistic partner j. (B) Time evolution of the populations of the 7 species as predicted by the mean field dynamics. (C) Species interaction network for 7 species where one species is not helped by any species and the iterative pruning process, as described in the main text, leads to a cascade of extinctions. (D) As the time evolution of the mean field Eq. , only one species dominates the community. (E) Nested structure for fruit eating birds community in Mexico^. (F) All species coexist, as predicted by our theoretical framework. In the ordinate axis use the notation 𝜂¯ and not η.

https://go.nature.com/2IWFFtG