title: Punctuated equilibria and 1/f noise in a biological coevolution model with individual-based dynamics.
abstract: We present a study by linear stability analysis and large-scale Monte Carlo simulations of a simple model of biological coevolution. Selection is provided through a reproduction probability that contains quenched, random interspecies interactions, while genetic variation is provided through a low mutation rate. Both selection and mutation act on individual organisms. Consistent with some current theories of macroevolutionary dynamics, the model displays intermittent, statistically self-similar behavior with punctuated equilibria. The probability density for the lifetimes of ecological communities is well approximated by a power law with exponent near -2, and the corresponding power spectral densities show 1/f noise (flicker noise) over several decades. The long-lived communities (quasisteady states) consist of a relatively small number of mutualistically interacting species, and they are surrounded by a "protection zone" of closely related genotypes that have a very low probability of invading the resident community. The extent of the protection zone affects the stability of the community in a way analogous to the height of the free-energy barrier surrounding a metastable state in a physical system. Measures of biological diversity are on average stationary with no discernible trends, even over our very long simulation runs of approximately 3.4 x 10(7) generations.
authors.affiliation: School of Computational Science and Information Technology, Center for Materials Research and Technology, Florida State University, Tallahassee, Florida 32306-4120, USA. rikvold@csit.fsu.edu
authors.forename: Per Arne
authors.initials: PA
authors.lastname: Rikvold
authors.forename: R K P
authors.initials: RK
authors.lastname: Zia