2005/08/31 by Per Arne Rikvold · 36 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Physics and Astronomy · Social Sciences · #Biology #Coevolution #Computer science #Ecology #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Physics #Population #Population model #Stability (learning theory) #Statistical physics #cond-mat.stat-mech #nlin.AO #q-bio.PE
paper · pdf · doi:10.1007/s00285-007-0101-y
published in Journal of Mathematical Biology 55(5-6), 653-677 (Springer Science+Business Media) · 26 pages, 12 figures. Discussion of early-time dynamics added. J. Math. Biol., in press
arxiv created 2007/05/03 · openalex publication_date 2007/05/29 · arxiv updated 2011/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 fitness 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.