Allelopathy in Spatially Distributed Populations

Abstract

In a homogeneously mixing population of E. coli, colicin-producing and colicin-sensitive strategies both may be evolutionarily stable for certain parameter ranges, with the outcome of competition determined by initial conditions. In contrast, in a spatially-structured population, there is a unique ESS for any given set of parameters; the outcome is determined by how effective allelopathy is in relation to its costs. Furthermore, in a spatially-structured environment, a dynamic equilibrium may be sustained among a colicin-sensitive type, a high colicin-producing type, and a "cheater" that expends less on colicin production but is resistant. Copyright 1997 Academic Press Limited

Competing associations in bacterial warfare with two toxins

“…Detailed investigations have proven later that the introduction of different invasion rates does not modify the basic conclusions significantly. Namely, the self-organized patterns remain similar while the average frequencies of the strains depend on the ratios of invasion rates (Tainaka, 1993;Durrett and Levin, 1997). Boerlijst and Hogeweg (1991) have shown that the corresponding patterns provide stability against some types of external invaders.…”

“…Recent research on bacteriocins (Chao and Levin, 1981;Durrett and Levin, 1997;Iwasa et al, 1998;Pagie and Hogeweg, 1999;Nakamaru and Iwasa, 2000;Cza´ra´n et al, 2002;Kerr et al, 2002) suggests that competitive cycles are in fact the rule rather than the exception in communities of microorganisms.…”

Bacteriocin-mediated competition in cystic fibrosis lung infections

“…While the 'resistant' strains can be outcompeted by 'sensitive' strains because sensitive strains do not invest in the metabolic production of expressing the immunity protein that neutralizes the toxin. In spatially structured populations this can lead to population dynamic cycling with all three strains coexisting, analogous to the rock-paper-scissors (RPS) game, because each strain can be invaded by another strain-producers outcompete sensitive, resistant outcompete producers and sensitive outcompete resistant [1,4,5].…”

A multitype contact process with frozen sites: a spatial model of allelopathy

“…Our mean field model, however, exhibits the same property as the mean field model introduced in Durrett and Levin (1997). That is, the interior fixed point is not locally stable.…”

“…In our case, type-1s are the individuals of an inhibitory species and type-2s the individuals of a susceptible species. The reader especially interested in this biological process may refer to Durrett and Levin (1997). Their stochastic spatial model also is a generalization of the multitype contact process, but has only three states: 0 ≡ empty site, 1 ≡ inhibitory species, and 2 ≡ susceptible species.…”