# Homogeneous and Heterogeneous Response of Quorum-Sensing Bacteria in an Evolutionary Context

## TL;DR

This paper models quorum sensing bacteria's cooperative behavior, revealing how cost and benefit functions influence whether bacteria respond uniformly or heterogeneously, challenging traditional views of synchronized responses.

## Contribution

It introduces a theoretical framework linking cost-benefit functions to homogeneous or heterogeneous quorum sensing responses in bacteria.

## Key findings

- Optimal public good production depends on benefit shape.
- Homogeneous responses occur with convex costs.
- Heterogeneous ON/OFF responses occur with concave costs.

## Abstract

To explain the stability of cooperation is a central task of evolutionary theory. We investigate this question in the case of quorum sensing (QS) bacteria, which regulate cooperative traits in response to population density. Cooperation is modeled by the prisoner's dilemma, where individuals produce a costly public good (PG) that equally benefits all members of a community divided into multiple, distinct patches (multilevel selection). Cost and benefit are non-linear functions of the PG production. The analysis of evolutionary stability yields an optimization problem for the expression of PG in dependency on the number of QS individuals within a colony. We find that the optimal total PG production of the QS population mainly depends on the shape of the benefit. A graded and a switch-like response is possible, in accordance with earlier results. Interestingly, at the level of the individual cell, the QS response is determined by the shape of the costs. All QS individuals respond either homogeneously if cost are a convex function of the PG production rate, or they respond heterogeneously with distinct ON/OFF responses if the costs are concave. The latter finding is consistent with recent experimental findings, and contradicts the usual interpretation of QS as a mechanism to establish a uniform, synchronized response of a bacterial population.