Natural selection for within-generation variance in offspring number II. Discrite haploid models.

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) (mul--mu2 + sigma2e2--sigma2el) and the diffusion coefficient v(p) equals p(1-p) [psigma2e2 + (l--p)sigma2el]. 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.