# Coevolution Maintains Diversity in the Stochastic "Kill the Winner" Model

## TL;DR

This paper introduces a stochastic coevolutionary model for the 'Kill the Winner' hypothesis, showing that demographic stochasticity disrupts stable coexistence but coevolution promotes persistent diversity through ongoing species flux.

## Contribution

It develops a novel stochastic coevolutionary model demonstrating how predator-prey dynamics sustain diversity despite stochastic extinction risks.

## Key findings

- Demographic stochasticity destroys stable coexistence in the deterministic model.
- Predator-prey coevolution induces persistent species flux and high diversity.
- Stochastic effects lead to ongoing extinction and recolonization cycles.

## Abstract

The "Kill the Winner" hypothesis is an attempt to address the problem of diversity in biology. It argues that host-specific predators control the population of each prey, preventing a winner from emerging and thus maintaining the coexistence of all species in the system. We develop a stochastic model for the "Kill the Winner" paradigm and show that the stable coexistence state of the deterministic "Kill the Winner" model is destroyed by demographic stochasticity, through a cascade of extinction events. We formulate an individual-level stochastic model in which predator-prey coevolution promotes high diversity of the ecosystem by generating a persistent population flux of species.