INBREEDING WITH SELECTION and LINKAGE

SUMMARY General formulae are given for calculating the rate of progress towards fixation, and the equilibrium frequencies, at a locus (A, B) under selfing, when different selection intensities act against the two alternative homozygotes, and the selection intensities acting within and between lines are also different. It is shown that selection between lines is much more powerful than selection within lines in slowing down progress or preventing fixation. Formulae are given for calculating the rate of progress towards fixation of a pair of alleles (a, b) which are not directly affected by selection but are linked to the pair (A, B) subject to within line ami between line selection against homozygosis. The effects of different selection intensities are examined. Very strong selection, sufficient to keep most of the population heterozygous for A/B , leads to a loss of heterozygosity at the (a, b) locus of 2y(l – y) per generation, where y is the recombination frequency. With selection just preventing fixation at the {A, B) locus, the rate of loss of (a/6) heterozygotes is at first more rapid, but approaches asymptotically the rate of 2y(l – y). Selection acting only within lines has a much milder effect on the rate of progress at the (a, b) locus. The effects on inbreeding progress of linkage of the {a, b) locus, not itself under selection, to one and to two pairs of lethals, are compared (Table 8). It appears that severe selection against homozygosis at a few points on a chromosome could reduce considerably the rate of progress towards fixation by inbreeding; and it is suggested that, as inbreeding progresses, the severity of this type of selection, and the number of loci at which it acts, will generally increase, so that the average progress towards fixation will fall more and more behind that expected on the classical theory, as the coefficient of inbreeding increases.