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NATURAL SELECTION FOR WITHIN-GENERATION VARIANCE IN OFFSPRING NUMBER II. DISCRETE HAPLOID MODELS
John H. Gillespie 1
1 Environmental Mutagenesis Branch, National Institute of Environmental
Health Sciences, P. O. Box 12233, Research Triangle Park, N. C. 27709
In the classical model of genetic drift in population genetics
theory, use is made of a hypothetical "infinite-gametic pool". If, instead,
the gametic pool is determined by the random number of offspring per individual,
a new form of natural selection acting on the variance in offspring number
occurs. A diffusion model of this selection process is derived and some of
its properties are explored. It is shown that, independent of the sampling
scheme used, the diffusion equation has the drift coefficient M(
p) = p(1-p) (µ1-µ
2 + 
ee22-
e
e12) and the diffusion coefficient v
(p) = p(1-
) [pee
22 + (1-)ee1
2]. It is also pointed out that the Direct Product Branching process
model of genetic drift introduces a non-biological interaction between individuals
and is thus inappropriate for modeling natural selection.
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