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Punctuated equilibria and 1/f noise in a biological coevolution model with individual-based dynamics

Per Arne Rikvold·R. K. P. Zia
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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 (quasi-steady 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 3.4x10^7 generations.

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Per Arne Rikvold, R. K. P. Zia. 2003-10-18. Punctuated equilibria and 1/f noise in a biological coevolution model with individual-based dynamics. https://doi.org/10.1103/physreve.68.031913

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