Journal of Mathematical Biology

, Volume 11, Issue 2, pp 193–205

A continuous migration model with stable demography

  • Stanley Sawyer
  • Joseph Felsenstein

DOI: 10.1007/BF00275442

Cite this article as:
Sawyer, S. & Felsenstein, J. J. Math. Biology (1981) 11: 193. doi:10.1007/BF00275442


A probability model of a population undergoing migration, mutation, and mating in a geographic continuum R is constructed, and an integrodifferential equation is derived for the probability of genetic identity. The equation is solved in one case, and asymptotic analysis done in others. Individuals at x, y ε R in the model mate with probability V(x, y) dt in any time interval (t, t + dt). In two dimensions, if V(x,y) = V(x−y) where V(x) ≈ V(x/β)/β2 approaches a delta function, the equilibrium probability of identity vanishes as β → 0. The asymptotic rate at which this occurs is discussed for mutation rates uuo > 0 and for βCuα, α > 0, and u → 0.

Key words

Migration Population genetics Stepping stone Selective neutrality 

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Stanley Sawyer
    • 1
  • Joseph Felsenstein
    • 2
  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA
  2. 2.Department of GeneticsUniversity of WashingtonSeattleUSA

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