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A diffusion process with killing: the time to formation of recurrent deleterious mutant genes

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  • Karlin, Samuel
  • Tavaré, Simon

Abstract

We analyze the role of recurrent mutation on the time to formation or detection of particular genotypes in finite populations. The traditional method of approximating Markov chain models by diffusion processes is used. However, the diffusion approximations that arise in this context are governed not only by infinitesimal drift and diffusion coefficients, but also by a state-dependent killing rate that arises from the formation events. The resulting processes are particularly tractable, and allow a comprehensive analysis of the role of mutation in this problem.

Suggested Citation

  • Karlin, Samuel & Tavaré, Simon, 1982. "A diffusion process with killing: the time to formation of recurrent deleterious mutant genes," Stochastic Processes and their Applications, Elsevier, vol. 13(3), pages 249-261, September.
    • Handle: RePEc:eee:spapps:v:13:y:1982:i:3:p:249-261
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