Permanence and Stability of a Kill the Winner Model in Marine Ecology

TL;DR

This paper investigates the long-term behavior of 'kill the winner' models in marine ecology, demonstrating conditions for stable coexistence and permanence of bacteria, viruses, and zooplankton populations.

Contribution

It provides a rigorous analysis showing the existence of a unique stable equilibrium and permanence in the model, advancing understanding of marine microbial community dynamics.

Findings

Existence of a unique stable equilibrium with all populations present

System is permanent under certain conditions

Long-term solutions are strongly constrained by the model

Abstract

We focus on the long term dynamics of "killing the winner" Lotka-Volterra models of marine communities consisting of bacteria, virus, and zooplankton. Under suitable conditions, it is shown that there is a unique equilibrium with all populations present which is stable, the system is permanent, and the limiting behavior of its solutions is strongly constrained.