Lattice Model for the Lotka-Volterra System

Czárán

Journal of Theoretical Biology

2007

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

Section: Introductionmentioning

confidence: 99%

Competing associations in bacterial warfare with two toxins

Czárán

Journal of Theoretical Biology

2007

“…The basic Equation (5) well predicts the population dynamics of lattice model. This feature is not common, because the results of lattice models usually differ from those of lattice gas model [13] [14] [20]- [22]. Such differences come from spatial structures: distribution of each species is not random.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Simulation procedures are described. First, we explain the update rule for lattice model (local interaction) [13]. 1) Two body reactions: Choose one cell randomly, and then specify one of four neighboring cells.…”

Section: The Modelmentioning

confidence: 99%

“…It should be necessary to build a refined model. We apply lattice and lattice gas models [13]- [15]. The former interactions occur between a pair of adjacent cells, while in the latter they occur between any pair of cells.…”

Section: Introductionmentioning

confidence: 99%

“…Such equations are served for multiple uses. For examples, the lattice gas models for a single-species system lead the logistic equation [19], and those for prey-predator systems induce LVEs [13] [14] [20] [21]. For this reason, our commensalism model may be effective not only for S. virgatus and C. mitella but also for many pair of species.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Lattice and Lattice Gas Models for Commensalism: Two Shellfishes in Intertidal Zone

Yokoi¹,

Uehara²,

Kawai³

et al. 2014

OJE

Self Cite

The study of mutual interactions in an intertidal zone is important. We are interested in two sessile shellfishes, mussel (Septifer virgatus: species X) and goose barnacle (Capitulum mitella: species Y). Both species X and Y have similar body sizes, and live in an intertidal zone. Their relation is known to be a kind of commensalism: the survival rate of X increases near the location of Y. In contrast, Y receives no gain from X. In the present paper, we present lattice and lattice gas models for commensalism. The latter is mean-field theory of the former. It is found that the relation of commensalism is not stable. Under certain conditions, the competition prevails between both species; if the density of Y is high, the species X receives a damage originated in the limiting space. Moreover, we find that the basic equation derived by lattice gas model well explains the population dynamics for lattice model.

Evolution in spatial predator–prey models and the “prudent predator”: The inadequacy of steady‐state organism fitness and the concept of individual and group selection

et al. 2008

We review recent research which reveals: (1) how spatially distributed populations avoid overexploiting resources due to the local extinction of over-exploitative variants, and (2) how the conventional understanding of evolutionary processes is violated by spatial populations so that basic concepts, including fitness assignment to individual organisms, are not applicable, and even kin and group selection are unable to describe the mechanism by which exploitative behavior is bounded. To understand these evolutionary processes, a broader view is needed of the properties of multiscale spatiotemporal patterns in organism-environment interactions. We discuss measures that quantify the effects of these interactions on the evolution of a population, including multigenerational fitness and the heritability of the environment.2008 Wiley Periodicals, Inc. Complexity 13: 2008