Author(s):

Barton, Nicholas H; Rouhani, Shahin

Article Title: 
The frequency of shifts between alternative equilibria

Affiliation 

Abstract: 
We derive a formula giving thefrequency with which random drift shifts a population betweenalternativeequilibria. This formula is valid when such shifts are rare (Ns >> 1), and applies over a wide range of mutation rates. When the number of mutations entering the population is low (4Nμ << 1), the rate of stochastic shifts reduces to the product ofthe mutation rate and the probability of fixation of a single mutation. However, when many mutations enter the population in each generation (4Nμ >> 1), the rate is higher than would be expected if mutations were established independently, and converges to that given by a gaussian approximation. We apply recent results on bistable systems to extend this formula to the general multidimensional case. This gives an explicit expression for thefrequencyof stochastic shifts, which depends only on theequilibrium probability distribution near the saddle point separating thealternative stable states. The plausibility of theories of speciation through random drift are discussed in the light of these results.

Keywords: 
Population Dynamics; Models, Genetic; Mutation; Mathematics; Human; Evolution; Adaptation, Biological; evolution; adaptation; human; animal; article; biological model; mathematics; mutation; population dynamics; Animal

Journal Title:

Journal of Theoretical Biology

Volume: 
125

Issue 
4

ISSN:

00225193

Publisher:

Elsevier

Date Published:

19870421

Start Page: 
397

End Page:

418

DOI: 
10.1016/S00225193(87)802102

Open access: 
no 