Untersuchungen zur Wechselwirkung von Selektion und Selbstungsrate auf das genetische Gleichgewicht unter besonderer Berücksichtigung tetraploider Populationen. I

Abstract

In the first part of this paper the interaction of selfing, double reduction, and selection has been investigated with regard to the genetic variability in equilibrium populations. Out of the theoretically infinite number of combinations of factors some typical combinations have been chosen and the effect on these of individual factors or factors acting jointly have been described. The essential results are the following: 1. Under the influence of selection, random mating and chromosome segregation the equilibrium of populations is, according to the selection pattern, characterized by a central point (p=0.5), a side point (p=0.25 or p=0.75) or an end point (p=0 or p=1). Both double reduction and selfing (S<1.0) affect the proportions of gametes so as to cause a diminution of the heterozygotes, without changing the relation of p∶q. The effect of inbreeding and double reduction that reduces the frequencies of heterozygotes decreases with increasing selection pressure. Hereby, in spite of high selfing rate including absolute selfing, the maintenance of heterozygotes in a population is possible. 2. Selfing and double reduction, furthermore, may cause populations to become fixed in an end point instead of reaching a non-trivial equilibrium, or, instead of fixation, reach a stable non-trivial equilibrium. Fitness relations of w2=w4=1.0>w1=w5>w3 lead to equilibrium positions deviating from the standard. 3. In the absence of selection, selfing and double reduction are antagonistic factors, as selfing reduces the rate of approach to the equilibrium and double reduction increases it. In the selection models considered here this antagonism is removed by the effect of selection. Both factors now work in the same direction, and, depending on the model of selection, either both accelerate or both delay the approach to the equilibrium. 4. In all selection models the population fitness is reduced by inbreeding as well as by double reduction with the exception of the conditions: w3=1.0>w1=w5>w2=w4.

Zygotic genotypic frequencies under selection on female or male gamete production in partially self-fertilizing plant populations

“…It has often been analytically combined with viability or sexually symmetrical fertility selection. Recurrence equations and the corresponding conditions for the computation of equilibria may be found in Hayman (1953), Lewontin (1958), Workman and Jam (1966), Jam and Workman (1967), Woehrmann and Lange (1970) and for the multiallelic case in Weir (1970). Several numerical examples for the development of genotypic structures are presented in Huehn (1979).…”