Diffusive public goods and coexistence of cooperators and cheaters on a 1D lattice.

István Scheuring,Attila Csikász-Nagy

doi:10.1371/journal.pone.0100769

István Scheuring, Attila Csikász-Nagy

Open Access

https://doi.org/10.1371/journal.pone.0100769

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Abstract

Many populations of cells cooperate through the production of extracellular materials. These materials (enzymes, siderophores) spread by diffusion and can be applied by both the cooperator and cheater (non-producer) cells. In this paper the problem of coexistence of cooperator and cheater cells is studied on a 1D lattice where cooperator cells produce a diffusive material which is beneficial to the individuals according to the local concentration of this public good. The reproduction success of a cell increases linearly with the benefit in the first model version and increases non-linearly (saturates) in the second version. Two types of update rules are considered; either the cooperative cell stops producing material before death (death-production-birth, DpB) or it produces the common material before it is selected to die (production-death-birth, pDB). The empty space is occupied by its neighbors according to their replication rates. By using analytical and numerical methods I have shown that coexistence of the cooperator and cheater cells is possible although atypical in the linear version of this 1D model if either DpB or pDB update rule is assumed. While coexistence is impossible in the non-linear model with pDB update rule, it is one of the typical behaviors in case of the non-linear model with DpB update rule.

Highlights

The evolutionary stability of cooperation has been in the focus of theoretical biology for decades [1,2,3,4,5]
By using a wide range of parameters of l and d, I observe that if coexistence between P and NP is possible in the linear model, this state will be realized only if the inner NP block is close to the center of the lattice independently whether DpB or pDB update rule is used, that is if Dn1{n2D is less than a critical value (Fig. 3)
It is shown that independently of the used update rule coexistence of producers and non-producers is impossible in the linear model if initially a producer and a non-producer arrays meet on the lattice

Summary

Introduction

The evolutionary stability of cooperation has been in the focus of theoretical biology for decades [1,2,3,4,5]. I have shown that independently to the used update rule coexistence is possible in the linear model (fitness increases linearly with local concentration of the common material) this behavior is rather atypical.

Results

Conclusion