Math @ Duke

Publications [#243500] of Richard T. Durrett
Papers Published
 Cox, JT; Durrett, R, The stepping stone model: New formulas expose old myths,
The Annals of Applied Probability, vol. 12 no. 4
(November, 2002),
pp. 13481377, Institute of Mathematical Statistics [doi]
(last updated on 2019/04/26)
Abstract: We study the stepping stone model on the twodimensional torus. We prove several new hitting time results for random walks from which we derive some simple approximation formulas for the homozygosity in the stepping stone model as a function of the separation of the colonies and for Wright's genetic distance FST. These results confirm a result of Crow and Aoki (1984) found by simulation: in the usual biological range of parameters FST grows like the log of the number of colonies. In the other direction, our formulas show that there is significant spatial structure in parts of parameter space where Maruyama and Nei (1971) and Slatkin and Barton (1989) have called the stepping model "effectively panmictic".


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

