Complex Behavior in Simple Models of Biological Coevolution

Rikvold, Per Arne

doi:10.1142/s012918310901445x

Cited by 3 publications

(5 citation statements)

References 21 publications

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“…They are therefore not highly realistic. However, the fact that the results of numerical simulations can be compared with exact analytical results make these simplified models ideal as benchmarks for simulations of more realistic coevolution models in the future [48].…”

Section: Discussionmentioning

confidence: 99%

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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Section: Discussionmentioning

confidence: 99%

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

Rikvold

2007

J. Math. Biol.

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“…5, dotted lines). This is a widespread property of systems with complex dynamics, and its significance is discussed elsewhere (Bak et al 1987;Halley 1996;Rikvold 2009). However, adaptive behavior produced marked departures from this statistical pattern.…”

Section: Resultsmentioning

confidence: 99%

“…1/ f noise can be created by very different physical processes: fractal renewal processes, interrupted and perennial aging processes, nonlinear stochastic differential equations, and superposition of many relaxation processes (Eliazar and Klafter 2010). In the context of evolutionary ecology, power laws have been observed with species-based and individual-based models of coevolution (e.g., Caldarelli et al 1998;Laird et al 2008;Rikvold and Zia 2003;Rikvold 2009) and have been interpreted as the presence of self-organized criticality (Bak et al 1987). In our results, there is a direct interpretation in the time domain: The 1/ f decay indicates that there is a long-time correlation of the abundances of across several decades of generations.…”

Section: Discussionmentioning

confidence: 99%

Evolutionary ecology of movement by predators and prey

2011

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An essential key to explaining the mechanistic basis of ecological patterns lies in understanding the consequences of adaptive behavior for distributions and abundances of organisms. We developed a model that simultaneously incorporates (a) ecological dynamics across three trophic levels and (b) evolution of behaviors via the processes of mutation, selection, and drift in populations of variable, unique individuals. Using this model to study adaptive movements of predators and prey in a spatially explicit environment produced a number of unexpected results. First, even though predators and prey had limited information and sometimes moved in the "wrong" direction, evolved movement mechanisms allowed them to achieve average spatial distributions approximating optimal, ideal free distributions. Second, predators' demographic parameters had marked, nonlinear effects on the evolution of movement mechanisms in the prey: As the predator mortality rate was increased past a critical point, prey abruptly shifted from making very frequent movements away from predators to making infrequent movements mainly in response to resources.Third, time series analyses revealed that adaptive, conditional movements coupled ecological dynamics across species and space. Our results provide general predictions, heretofore lacking, about how predators and prey should respond to one another on both ecological and evolutionary time scales.

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“…We use an individual-based model inspired by the Tangled-Nature model Hall et al, 2002;di Collobiano and al., 2003;Jensen, 2004) and a similar model by Rikvold and co-authors (Rikvold and Zia, 2003;Zia and Rikvold, 2004;Sevim and Rikvold, 2005;Rikvold, 2006Rikvold, , 2007Rikvold and Sevim, 2007), which are both non-spatial models of biological coevolution. In these models, the individuals of the community are identified by their species genotype and interact via a set of fixed species-species interactions.…”

Section: Definition Of the Modelmentioning

confidence: 99%

“…Conversely, when f i is large, species i is suited to the local community and its reproduction probability is consequently high. The fitness of a species i is given by (Rikvold, 2006(Rikvold, , 2007Rikvold and Sevim, 2007)…”

Section: The Fitnessmentioning

confidence: 99%

Community-driven dispersal in an individual-based predator–prey model

Filotas

Grant

Parrott

et al. 2008

Ecological Complexity

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We present a spatial, individual-based predator-prey model in which dispersal is dependent on the local community. We determine species suitability to the biotic conditions of their local environment through a time and space varying fitness measure.Dispersal of individuals to nearby communities occurs whenever their fitness falls below a predefined tolerance threshold. The spatiotemporal dynamics of the model is described in terms of this threshold. We compare this dynamics with the one obtained through densityindependent dispersal and find marked differences. In the community-driven scenario, the spatial correlations in the population density do not vary in a linear fashion as we increase 2 the tolerance threshold. Instead we find the system to cross different dynamical regimes as the threshold is raised. Spatial patterns evolve from disordered, to scale-free complex patterns, to finally becoming well-organized domains. This model therefore predicts that natural populations, the dispersal strategies of which are likely to be influenced by their local environment, might be subject to complex spatiotemporal dynamics.

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Complex Behavior in Simple Models of Biological Coevolution

Cited by 3 publications

References 21 publications

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

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

Evolutionary ecology of movement by predators and prey

Community-driven dispersal in an individual-based predator–prey model

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