The interaction between effective population size and linkage intensity under artificial selection

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Abstract
The effects of tight linkage on the total response due to pairs of identical additive loci, segregating in a population initially in linkage equilibrium, have been studied both algebraically and by means of computer simulation. Particular attention has been given to the effects of finite population size on the probabilities of (a) the elimination from the population of the gamete carrying both ‘plus’ alleles; (b) the joint preservation of the two types of repulsion gametes; (c) the recovery of the desired combination of plus alleles through crossing-over; and (d) the fixation of the gamete in the population following its recovery.The study is restricted to situations in which linkage is known to have an appreciable effect on total selection response, i.e. to the case of genes of large effect initially at low frequency. A comparison of regimes with the same expected response under free recombination has shown the probability of (a) to be high, and the probability of (b) to be very nearly the same for all regimes tested. Provided that the recovery of the gamete carrying both plus alleles is an unlikely event at any given point in time, the probability of the fixation of the gamete, once reconstituted, is expected to be independent of population size for genes of large effect. In this context, approximate algebraic expressions have been derived for the probability of effective recovery of the required gamete, and for the mean waiting time involved.