Individual-based predator-prey model for biological coevolution: Fluctuations, stability, and community structure

Rikvold, Per Arne; Sevi̇m, Volkan

doi:10.1103/physreve.75.051920

Cited by 20 publications

(43 citation statements)

References 83 publications

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“…The limit σ F → 0 corresponds to the model considered in the body of this paper. We briefly show this solution for the sake of completeness and readers' convenience, although it is shown in detail in [18,19]. At the fixed point, the condition |P (R, {n * }) = 1/F is satisfied, where |P is the column vector of the reproduction probabilities.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…In Model B [19], the external resource R is introduced. All the species have positive values of the birth cost b I , which are randomly drawn from [0, 1], and a certain proportion (0.05 is used in this paper) of species can feed on the resource, i.e., the resource couplings η I are positive for primary producers or autotrophs, and zero for consumers or heterotrophs.…”

Section: A Reproduction Probabilitymentioning

confidence: 99%

“…The models considered here are extensions of the tangled-nature model studied in [18][19][20]. The tanglednature model is an individual-based model, originally introduced by Hall and co-workers [17] and later simplified by Rikvold and Zia [20].…”

Section: Modelsmentioning

confidence: 99%

“…The tanglednature model is an individual-based model, originally introduced by Hall and co-workers [17] and later simplified by Rikvold and Zia [20]. In the simplified models [18][19][20][21][22]30], the population evolves stochastically in discrete, non-overlapping generations. In these models, each individual of species I gives rise to F offspring with a reproduction probability P I before it dies.…”

Section: Modelsmentioning

confidence: 99%

“…The nonzero elements of the interaction matrix are randomly chosen from a triangular distribution on [−1, +1]. These parameter ranges were chosen to compare with the corresponding individualbased model [19]. The diagonal elements of M, which represent the intraspecies interactions, are selected randomly from a uniform distribution on [−1, 0] for all the species.…”

Section: A Reproduction Probabilitymentioning

confidence: 99%

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Effects of demographic stochasticity on biological community assembly on evolutionary time scales

et al. 2010

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We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic communities show little dependence on the stochastic population fluctuations, predator-prey models show strong dependence on the stochasticity, indicating the relevance of the finiteness of the populations. For a predator-prey model, the noise causes drastic decreases in diversity and total population size. The communities that emerge under influence of the noise consist of species strongly coupled with each other and have stronger linear stability around the fixed-point populations than the corresponding noiseless model. The dynamics on evolutionary time scales for the predator-prey model are also altered by the noise. Approximate 1/f fluctuations are observed with noise, while 1/f 2 fluctuations are found for the model without demographic noise.

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Section: Summary and Discussionmentioning

confidence: 99%

Section: A Reproduction Probabilitymentioning

confidence: 99%

Section: Modelsmentioning

confidence: 99%

Section: Modelsmentioning

confidence: 99%

Section: A Reproduction Probabilitymentioning

confidence: 99%

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Effects of demographic stochasticity on biological community assembly on evolutionary time scales

et al. 2010

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A Universal Lifetime Distribution for Multi-Species Systems

Murase

Shimada

Ito

et al. 2015

Proceedings of the International Conference on Social Modeling and Simulation, Plus Econophysics Colloquium 2014

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Lifetime distributions of social entities, such as enterprises, products, and media contents, are one of the fundamental statistics characterizing the social dynamics. To investigate the lifetime distribution of mutually interacting systems, simple models having a rule for additions and deletions of entities are investigated. We found a quite universal lifetime distribution for various kinds of inter-entity interactions, and it is well fitted by a stretched-exponential function with an exponent close to 1/2. We propose a "modified Red-Queen" hypothesis to explain this distribution. We also review empirical studies on the lifetime distribution of social entities, and discussed the applicability of the model.

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Self-optimization, community stability, and fluctuations in two individual-based models of biological coevolution

Rikvold

2007

J. Math. Biol.

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We compare and contrast the long-time dynamical properties of two individual-based models of biological coevolution. Selection occurs via multispecies, stochastic population dynamics with reproduction probabilities that depend nonlinearly on the population densities of all species resident in the community. New species are introduced through mutation. Both models are amenable to exact linear stability analysis, and we compare the analytic results with large-scale kinetic Monte Carlo simulations, obtaining the population size as a function of an average interspecies interaction strength. Over time, the models self-optimize through mutation and selection to approximately maximize a community potential function, subject only to constraints internal to the particular model. If the interspecies interactions are randomly distributed on an interval including positive values, the system evolves toward self-sustaining, mutualistic communities. In contrast, for the predator-prey case the matrix of interactions is antisymmetric, and a nonzero population size must be sustained by an external resource. Time series of the diversity and population size for both models show approximate 1/f noise and power-law distributions for the lifetimes of communities and species. For the mutualistic model, these two lifetime distributions have the same exponent, while their exponents are different for the predator-prey model. The difference is probably due to greater resilience toward mass extinctions in the food-web like communities produced by the predator-prey model.

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Individual-based predator-prey model for biological coevolution: Fluctuations, stability, and community structure

Cited by 20 publications

References 83 publications

Effects of demographic stochasticity on biological community assembly on evolutionary time scales

Effects of demographic stochasticity on biological community assembly on evolutionary time scales

A Universal Lifetime Distribution for Multi-Species Systems

Self-optimization, community stability, and fluctuations in two individual-based models of biological coevolution

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