On the Probability of Fixation of Reciprocal Translocations

Abstract

The chance of fixation of a reciprocal translocation in a population of plants, with exclusive sexual reproduction, is of the order 10-3 if the effective population number (N) is 10. It is of the order of 2 x 10-6 in groups of 20 individuals and of the order 3 x 10-14 in groups of 50 individuals. It is assumed that the heterozygotes are semisterile, and that there is no compensating advantage in semisterility by reduction of competition among the progeny and that the translocation has no advantage per se. These figures may be compared with 1/2N, the chance of fixation of an indifferent mutation. Reciprocal translocations in animals have a slightly better chance of fixation than in plants in populations of the same effective size, even if only the balanced types are viable and fertile. Cases in which the heterozygous unbalanced type are at no disadvantage in viability and in number of gametes produced, only the homozygous deficiencies being eliminated, have considerably better chances of fixation than in the cases above. The chance is roughly 3 x 10-3 in populations of 20, 4 x 10-6 in populations of 50, 3 x 10-10 in populations of 100 and 5 x 10-18 in populations of 200. In all the cases given here, there is an element of uncertainty as a result of which the true chance may be smaller or greater by a small factor (less than 4). A statement in a previous paper gave a somewhat exaggerated impression of the difficulty of fixation of reciprocal translocations. It remains true, nevertheless, that such fixation can hardly occur under exclusive sexual reproduction except in a species in which there are numerous isolated populations that pass through phases of extreme reduction of numbers. The most favorable case would seem to be that in which there is frequent extinction of the populations of small isolated localities, with restoration from the progeny of occasional stray migrants from other localities. If one of the unbalanced homozygotes is viable and fertile (unlikely in a reciprocal translocation but not unlikely in the case of a small insertional translocation), the chance of fixation of the nondeficient modified chromosome may be much greater than in the cases considered above and would even be slightly greater than that of an indifferent mutation if the unbalanced homozygote and the heterozygotes that include it are at no disadvantage compared with the balanced homozygotes.