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

  • Per Arne RikvoldEmail author
Article

Abstract

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.

Keywords

Evolution Self-optimization Community stability Predator–prey model Mutualism 

Mathematics Subject Classification (2000)

92D15 92D25 60K35 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.School of Computational Science, Center for Materials Research and Technology, National High Magnetic Field Laboratory, and Department of PhysicsFlorida State UniversityTallahasseeUSA
  2. 2.Department of Fundamental Sciences, Faculty of Integrated Human StudiesKyoto UniversityKyotoJapan

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