# Biodiversity, extinctions and evolution of ecosystems with shared resources

## TL;DR

This paper analyzes how stable ecological networks with shared resources form through extinctions, deriving relations for species coexistence, extinction impacts, and trait concentration, with a focus on a stress parameter influencing biodiversity.

## Contribution

It introduces a novel analytical framework linking species traits, resource characteristics, and environmental stress to ecosystem stability and biodiversity outcomes.

## Key findings

- Stable ecosystems emerge via extinctions driven by environmental stress.
- Derived analytical relations for species coexistence and extinction impacts.
- Identified a key parameter predicting trait concentration and biodiversity levels.

## Abstract

We investigate the formation of stable ecological networks where many species share the same resource. We show that such stable ecosystem naturally occurs as a result of extinctions. We obtain an analytical relation for the number of coexisting species and find a relation describing how many species that may go extinct as a result of a sharp environmental change. We introduce a special parameter that is a combination of species traits and resource characteristics used in the model formulation. This parameter describes the pressure on system to converge, by extinctions. When that stress parameter is large we obtain that the species traits concentrate at some values. This stress parameter is thereby a parameter that determines the level of final biodiversity of the system. Moreover, we show that dynamics of this limit system can be described by simple differential equations.