Competing associations in bacterial warfare with two toxins

Abstract

Simple combinations of common competitive mechanisms can easily result in cyclic competitive dominance relationships between species. The topological features of such competitive networks allow for complex spatial coexistence patterns. We investigate selforganization and coexistence in a lattice model, describing the spatial population dynamics of competing bacterial strains. With increasing diffusion rate the community of the nine possible toxicity/resistance types undergoes two phase transitions. Below a critical level of diffusion, the system exhibits expanding domains of three different defensive alliances, each consisting of three cyclically dominant species. Due to the neutral relationship between these alliances and the finite system size effect, ultimately only one of them remains. At large diffusion rates the system admits three coexisting domains, each containing mutually neutral species. Because of the cyclical dominance between these domains, a long term stable coexistence of all species is ensured. In the third phase at intermediate diffusion the spatial structure becomes even more complicated with domains of mutually neutral species persisting along the borders of defensive alliances. The study reveals that cyclic competitive relationships may produce a large variety of complex coexistence patterns, exhibiting common features of natural ecosystems, like hierarchical organization, phase transitions and sudden, large-scale fluctuations. r

Conditional strategies and the evolution of cooperation in spatial public goods games

“…In their model, however, a cooperator will necessarily invest somewhere, while in our case cooperators may remain dormant for long periods of time before eventually deciding to contribute to the common pool. In terms of potential implication of our findings, apart from their relevance for the successful evolution of prosocial behavior between selfish and unrelated individuals, from the biological point of view, the way inactive cooperators quarantine defectors and force them into convex isolated "bubbles" bears resemblance to the way the immune system works when trying to contain an infection [57]. We hope that this study will inspire future research aimed at investigating the role of conditional strategies in structured populations.…”

Coarsening with nontrivial in-domain dynamics: Correlations and interface fluctuations

“…Much work has been devoted to cyclic cases as for example the three-species cyclic game [21] or the corresponding game with four species where each species is preying on one other species while being at the same time the prey of another species [22][23][24][25][26][27][28][29]. Whereas some earlier papers have considered spatial and stochastic effects in systems with a larger number of species [30][31][32][33][34][35][36][37][38][39][40][41], it is only in the last few years that systematic theoretical studies of more complicated food networks with five or more species 2 have become available [19,[42][43][44][45][46][47][48][49][50][51][52][53][54]. One of the intriguing results of these studies has been the discovery of a rich variety of space-time patterns, including spirals where each wavefront is formed by a single species, fuzzy spirals due to the mixing of different species inside the waves, coarsening domains where every domain is formed by an alliance of mutually neutral species as well as coarsening processes where inside every domain spirals are formed, thus yielding non-trivial dynamics inside the coarsening domains [19,48,51,55].…”

From pairwise to group interactions in games of cyclic dominance

“…In experiments with Escherichia coli, for example, it has been shown that arranging the bacteria on a Petri dish is crucial for keeping all three competing strains alive [8,36]. Accordingly, simulations of spatial rock-paper-scissors and related games of cyclic dominance have a long and fruitful history [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56], which is firmly rooted in methods of statistical physics. In general, if the mobility in the population is sufficiently small [7], the spatial rock-paper-scissors game leads to the stable coexistence of all three competing strategies, whereby the coexistence is maintained by the spontaneous formation of complex spatial patterns.…”