# The role of metabolic trade-offs in the establishment of biodiversity

**Date:**

This talk has been held during the conference Stochastic Models in Ecology and Evolutionary Biology.

After a brief introduction on two of the most important problems in theoretical ecology (May’s stability criterion and the Competitive Exclusion Principle) I have illustrated the latest results of my research work, including my Master’s thesis and all the findings I have made from the beginning of my PhD.

You can find here the slides I have shown during the talk.

## Abstract

Since the famous article written by May in 1972, one of the most important subjects in the study of ecosystems has always been the relationship between stability and biodiversity. In particular, one of the most intriguing theoretical problems in ecology is the so-called “paradox of the plankton”: according to the “competitive exclusion principle” one would expect that the number of species competing for a common pool of resources in an ecosystem cannot be greater than the number of resources themselves, but there are many known cases in nature where this is not true. A recent theoretical result inspired by the paradox of the plankton has suggested that metabolic trade-offs could play a major role in the establishment of biodiversity. In particular, the model considered by Posfai et al. describes $m$ microbial species competing for $p$ resources, and the metabolic strategy of species is described by a vector containing the rates at which that species absorbs all the resources. Posfai et al. have shown that under the trade-off $\sum_i \alpha_{\sigma i} = \text{const.}$ there are very simple conditions under which the system achieves coexistence for any value of $m$, particularly for $m > p$. In this talk I will present the latest advancements of my work, which is based on this result by Posfai et al. In particular, I will show what happens if the metabolic strategies $\vec{\alpha}_\sigma$ are no longer kept fixed but are allowed to evolve in time following an appropriately defined differential equation. Furthermore, inspired by some recent experimental results I have also considered a slightly modified version of the model, which can attain survival of a community of species even when there is no external supply of resources.