Paradoxical effect in a three-candidate voter model

Tainaka, Kei–ichi

doi:10.1016/0375-9601(93)90923-n

Cited by 102 publications

(81 citation statements)

References 11 publications

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“…74 In our model, this "externally supported" species is species C, since it is not resource-limited in contrast to the other two species. Thus, species C kills more of its prey (species A), whose population decreases.…”

Section: B Population Dynamicsmentioning

confidence: 99%

The impact of resource dependence of the mechanisms of life on the spatial population dynamics of an in silico microbial community

Daly

Baetens

Baets

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Biodiversity has a critical impact on ecosystem functionality and stability, and thus the current biodiversity crisis has motivated many studies of the mechanisms that sustain biodiversity, a notable example being non-transitive or cyclic competition. We therefore extend existing microscopic models of communities with cyclic competition by incorporating resource dependence in demographic processes, characteristics of natural systems often oversimplified or overlooked by modellers. The spatially explicit nature of our individual-based model of three interacting species results in the formation of stable spatial structures, which have significant effects on community functioning, in agreement with experimental observations of pattern formation in microbial communities. Published by AIP Publishing.[http://dx.doi.org/10.1063/1.4972788]Biodiversity plays a crucial role in promoting and preserving the proper functioning of ecosystems.1 As a result, significant attention has been devoted to understanding the mechanisms that maintain biodiversity, 2 in particular, the role of cyclic competition. Existing microscopic models of communities with cyclic competition often significantly oversimplify or even neglect the resource-dependent nature of demographic processes. 3-6We therefore extend existing models by considering this key factor in a spatially heterogeneous landscape, to align them more closely with real-world microbial ecosystems, and to investigate how this more realistic approach affects community productivity and biodiversity. We demonstrate the consequent dramatic effects on the population dynamics of this community of three species, consistent with other modelling and experimental studies. These results have implications for the maintenance and development of natural ecosystems, as well as for pattern formation in microbial communities.

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Section: B Population Dynamicsmentioning

confidence: 99%

The impact of resource dependence of the mechanisms of life on the spatial population dynamics of an in silico microbial community

Daly

Baetens

Baets

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…In an ironic twist, the improved Rock* decreases in abundance because of the expansion of its victim's victim. This form of negative feedback ensures that a higher displacement rate results in decreased abundance (21)(22)(23)(24). Thus, more restrained players may be less prone to extinction, a phenomenon termed "survival of the weakest" (21).…”

Section: William Shakespearementioning

confidence: 99%

Evolution of restraint in a structured rock–paper–scissors community

Nahum

Harding

Kerr

2011

Proc. Natl. Acad. Sci. U.S.A.

107

117

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It is not immediately clear how costly behavior that benefits others evolves by natural selection. By saving on inherent costs, individuals that do not contribute socially have a selective advantage over altruists if both types receive equal benefits. Restrained consumption of a common resource is a form of altruism. The cost of this kind of prudent behavior is that restrained individuals give up resources to less-restrained individuals. The benefit of restraint is that better resource management may prolong the persistence of the group. One way to dodge the problem of defection is for altruists to interact disproportionately with other altruists. With limited dispersal, restrained individuals persist because of interaction with like types, whereas it is the unrestrained individuals that must face the negative long-term consequences of their rapacity. Here, we study the evolution of restraint in a community of three competitors exhibiting a nontransitive (rock-paper-scissors) relationship. The nontransitivity ensures a form of negative feedback, whereby improvement in growth of one competitor has the counterintuitive consequence of lowering the density of that improved player. This negative feedback generates detrimental long-term consequences for unrestrained growth. Using both computer simulations and evolution experiments with a nontransitive community of Escherichia coli, we find that restrained growth can evolve under conditions of limited dispersal in which negative feedback is present. This research, thus, highlights a set of ecological conditions sufficient for the evolution of one form of altruism.survival of the weakest | experimental evolution | positive assortment | ecological feedback | bacteriocin Wisely and slow; they stumble that run fast. William ShakespeareT he conflict between individual and group interests is a common element in many social dilemmas. Consider the rate at which an organism consumes shared resources. Prudent use of common resources promotes the longevity or fecundity of the group; however, any individual that exhibits restraint suffers in competition with those using resources rapidly. Rapacity is selectively favored and the displacement of prudent types by their unrestrained contemporaries occurs despite harmful consequences for the group (1, 2). Restraint in the use of common resources is a form of altruism: behavior that is self-sacrificial and prosocial. Like other types of altruistic behavior, restraint faces a fundamental problem of subversion (3, 4). How can restrained types persist in the midst of would-be cheaters-individuals that have a competitive edge because they are unrestrained? In this article, we address this question directly by outlining ecological conditions sufficient to favor the evolution of restraint.One ingredient found in most explanations for the evolution of altruism, and thus relevant to the evolution of restraint, is positive assortment. Altruism stands a better chance when altruistic individuals disproportionately help those possessing the genes f...

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“…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.…”

Section: Introductionmentioning

confidence: 99%

“…Boerlijst and Hogeweg (1991) have shown that the corresponding patterns provide stability against some types of external invaders. The unusual response to external effects is discussed by Tainaka (1993) and Frean and Abraham (2001). The main results in lattice systems remain qualitatively unaffected if we assume mutations from S to K, from K to R, and from R to S (mutations in the opposite directions are ineffective, because the mutant is immediately outcompeted by the resident type, cf.…”

Section: Introductionmentioning

confidence: 99%

Competing associations in bacterial warfare with two toxins

Szabó

Czárán

Szabó

2007

Journal of Theoretical Biology

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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

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Paradoxical effect in a three-candidate voter model

Cited by 102 publications

References 11 publications

The impact of resource dependence of the mechanisms of life on the spatial population dynamics of an in silico microbial community

The impact of resource dependence of the mechanisms of life on the spatial population dynamics of an in silico microbial community

Evolution of restraint in a structured rock–paper–scissors community

Competing associations in bacterial warfare with two toxins

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