&lt;title&gt;Fluctuations in models of biological macroevolution (Invited Paper)&lt;/title&gt;

Rikvold, Per Arne

doi:10.1117/12.609762

Cited by 6 publications

(8 citation statements)

References 27 publications

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“…The correlations further increase the proportion of very long QSS (figure 5b), but curiously they also lead to an increase of intermediate-lifetime species (figure 4). These effects do not seem very easy to reconcile, but we speculate that they may be due to a decoupling of the species lifetimes and the QSS durations that has been observed in an uncorrelated predator-prey version of this model [9]. The increased activity in the intermediate-time regime results in increased intensity in the higher-frequency half of the PSD (figure 6b).…”

Section: Simulation Resultsmentioning

confidence: 88%

“…In this paper we have considered the effects of introducing correlations between the elements of the interaction matrix M that determines the interspecies interactions in an individual-based coevolution model [7,8,9], in which individuals are represented by a genome in the form of a bitstring of length L. The correlations were introduced by replacing each element M 0 ij in an uncorrelated interaction matrix with the average over all the elements M 0 kl such that the Hamming distance between the concatenated bitstrings ij and kl is less than or equal to n, and then reweighting the resulting matrix element M ij such as to maintain the standard deviation of its probability density unchanged.…”

Section: Discussionmentioning

confidence: 99%

“…We note that the population dynamics used in the model is somewhat unrealistic, due to the absence of external energy resources and conservation of energy (or biomass) [7,8,9, 10, 11, 12]. (The distributions are not averaged over independent runs.)…”

Section: Modelmentioning

confidence: 99%

“…Although this means that individual-based models of macroevolution must span a dauntingly large range of timescales, this is now becoming possible with the aid of modern computers and algorithms. We therefore recently studied an individual-based biological coevolution model [7,8,9] with random interspecies interactions. This model is a simplified version of the tangled-nature model introduced by Jensen, et al [10,11,12].…”

Section: Introductionmentioning

confidence: 99%

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Effects of correlated interactions in a biological coevolution model with individual-based dynamics

Sevi̇m

Rikvold

2005

J. Phys. A: Math. Gen.

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Abstract. Models of biological coevolution have recently been proposed and studied, in which a species is defined by a genome in the form of a finite bitstring, and the interactions between species i and j are given by a fixed matrix with independent, randomly distributed elements M ij . A consequence of the stochastic independence is that species whose genotypes differ even by a single bit may have completely different phenotypes, as defined by their interactions with the other species. This is clearly unrealistic, as closely related species should be similar in their interactions with the rest of the ecosystem. Here we therefore study a model, in which the M ij are correlated to a controllable degree by means of a local averaging scheme. We calculate, both analytically and numerically, the correlation function for matrix elements M ij and M kl versus the Hamming distance between the bitstrings representing the species. The agreement between the analytical and numerical calculations is excellent for correlations of limited range, but explainable differences arise for correlation ranges that are a significant fraction of the length of the bitstring. We compare long kinetic Monte Carlo simulations of coevolution models with uncorrelated and correlated interactions, respectively. In particular, we consider the probability density for the lifetimes of individual species. The species-lifetime distribution is close to a power law with an exponent near −2 over eight decades in time in both uncorrelated and correlated cases. The durations of quasi-steady states and power spectral densities for the diversity indices display noticeable differences. However, some qualitative features, like 1/f behaviour in power spectral densities for the diversity indices, are not affected by the correlations in the interaction matrix.

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Section: Simulation Resultsmentioning

confidence: 88%

Section: Discussionmentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effects of correlated interactions in a biological coevolution model with individual-based dynamics

Sevi̇m

Rikvold

2005

J. Phys. A: Math. Gen.

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“…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%

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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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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<title>Fluctuations in models of biological macroevolution (Invited Paper)</title>

Cited by 6 publications

References 27 publications

Effects of correlated interactions in a biological coevolution model with individual-based dynamics

Effects of correlated interactions in a biological coevolution model with individual-based dynamics

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

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

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