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

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.Comment: 20 pages RevTex. Minor revisions consistent with published versio

Genetic rescue of an insular population of large mammals

Natural populations worldwide are increasingly fragmented by habitat loss. Isolation at small population size is thought to reduce individual and population fitness via inbreeding depression. However, little is known about the time-scale over which adverse genetic effects may develop in natural populations or the number and types of traits likely to be affected. The benefits of restoring gene flow to isolates are therefore also largely unknown. In contrast, the potential costs of migration (e.g. disease spread) are readily apparent. Management for ecological connectivity has therefore been controversial and sometimes avoided. Using pedigree and life-history data collected during 25 years of study, we evaluated genetic decline and rescue in a population of bighorn sheep founded by 12 individuals in 1922 and isolated at an average size of 42 animals for 10–12 generations. Immigration was restored experimentally, beginning in 1985. We detected marked improvements in reproduction, survival and five fitness-related traits among descendants of the 15 recent migrants. Trait values were increased by 23–257% in maximally outbred individuals. This is the first demonstration, to our knowledge, of increased male and female fitness attributable to outbreeding realized in a fully competitive natural setting. Our findings suggest that genetic principles deserve broader recognition as practical management tools with near-term consequences for large-mammal conservation