A continuous migration model with stable demography Article DOI:
Cite this article as: Sawyer, S. & Felsenstein, J. J. Math. Biology (1981) 11: 193. doi:10.1007/BF00275442 Abstract
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)/ β 2 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 u ≡ u o > 0 and for β ≈ Cu α, α > 0, and u → 0. Key words Migration Population genetics Stepping stone Selective neutrality
Partially supported by NSF grant MCS79-03472
Research was partially supported by Task Agreement No. DE-AT06-76EV71005 under Contract No. DE-AM06-76RL02225 between the U.S. Dept. Energy and the University of Washington
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