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The frequency of shifts between alternative equilibria
1Department of Genetics and Biometry, University College London, U.K.
Journal of Theoretical Biology
|April 21, 1987
Summary
Random drift can shift populations between stable states, with the frequency depending on mutation rates. This study provides a formula for these shifts, applicable across various mutation levels and dimensions.
Area of Science:
- Evolutionary biology
- Population genetics
- Theoretical biology
Background:
- Stochastic processes, like random drift, play a crucial role in evolutionary dynamics.
- Understanding population shifts between alternative stable states is key to evolutionary theory.
Purpose of the Study:
- To derive a general formula for the frequency of population shifts between alternative equilibria due to random drift.
- To analyze how mutation rates and population size influence the rate of these stochastic shifts.
Main Methods:
- Derivation of a formula for rare shifts (N*S >> 1) across a range of mutation rates (4*N*mu).
- Application of results from bistable systems to generalize the formula to multidimensional cases.
- Analysis of the dependence on the equilibrium probability distribution near saddle points.
Main Results:
- The rate of stochastic shifts is influenced by mutation rates, reducing to mutation rate times fixation probability at low rates (4*N*mu << 1).
- At high mutation rates (4*N*mu >> 1), the shift rate increases beyond independent mutation establishment, approaching a Gaussian approximation.
- An explicit expression for shift frequency in multidimensional systems was derived, dependent on saddle point distributions.
Conclusions:
- The derived formula provides a quantitative understanding of population shifts driven by random drift.
- Results offer insights into the mechanisms of speciation, particularly concerning the role of random drift in population divergence.