The frequency of shifts between alternative equilibria

N.H. Barton, S. Rouhani, Journal of Theoretical Biology 125 (1987) 397–418.

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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.
Publishing Year
Date Published
1987-04-21
Journal Title
Journal of Theoretical Biology
Volume
125
Issue
4
Page
397 - 418
IST-REx-ID

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Barton NH, Rouhani S. The frequency of shifts between alternative equilibria. Journal of Theoretical Biology. 1987;125(4):397-418. doi:10.1016/S0022-5193(87)80210-2
Barton, N. H., & Rouhani, S. (1987). The frequency of shifts between alternative equilibria. Journal of Theoretical Biology, 125(4), 397–418. https://doi.org/10.1016/S0022-5193(87)80210-2
Barton, Nicholas H, and Shahin Rouhani. “The Frequency of Shifts between Alternative Equilibria.” Journal of Theoretical Biology 125, no. 4 (1987): 397–418. https://doi.org/10.1016/S0022-5193(87)80210-2.
N. H. Barton and S. Rouhani, “The frequency of shifts between alternative equilibria,” Journal of Theoretical Biology, vol. 125, no. 4, pp. 397–418, 1987.
Barton NH, Rouhani S. 1987. The frequency of shifts between alternative equilibria. Journal of Theoretical Biology. 125(4), 397–418.
Barton, Nicholas H., and Shahin Rouhani. “The Frequency of Shifts between Alternative Equilibria.” Journal of Theoretical Biology, vol. 125, no. 4, Elsevier, 1987, pp. 397–418, doi:10.1016/S0022-5193(87)80210-2.

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