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Outcrossing and Selfing Evolution in Populations Under Directional Selection

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Outcrossing and Selfing Evolution in Populations Under Directional Selection Heredityll (1993) 642—651 Received 15 June 1993 Genetical Society of Great Britain Outcrossing and selfing evolution in populations under directional selection JACQUES L. DAVID*I, YVAN SAVYl & PHILIPPE BRABANTt tStation de Genétique Vegétale, /NRA -UPS, Ferme du Moulon, F-91 190 Gif sur Yvette, and lnst/tut National Agrono- mique Paris -Grignon, 16 rue Claude Bernard, F-75005 Paris, France Manyplant species have a mixed mating system using self-pollination and cross-pollination. Such behaviour has no simple evolutionary explanation. When inbreeding depression is low the theory predicts that self-pollination should be fixed. A residual crossing habit exists in practically all self- pollinated species that show low inbreeding depression. As recombination is useful to generate new genotypes it can be valuable when the environmental conditions are not stable. We used a simulation model to study the dynamics of adaptation with regard to different mixing mating systems. The evolution of a quantitative trait related to fitness has been related to the mating behaviour. In a first approach, all the individuals of a population outcrossed with the same propor- tion. The comparison between populations differing for their outcrossing rate, their effective size and their initial level of adaptation for new enironments, led us to the conclusion that the smaller the population and the lower its adaptation level, the more valuable outcrossing is. An optimum level of outcrossing has been found for each situation studied. In a second approach, selfing rate was controlled by a polymorphic additional locus. Thus, individuals with different outcrossing behaviours competed within each population. We found that a low level of outcrossing can be maintained and randomly fixed in such conditions, in spite of no inbreeding depression. The outcrossing rate that can be fixed when individuals with different mating behaviour compete is much lower than the optimum outcrossing rate found for the whole population. Keywords:directionalselection, evolution, mixed mating system, outcrossing rate, selfing rate, simulation. Introduction populations preventing this fixation and sampling errors (Schemske & Lande, 1985). Recent models also Incontrast to animals, many plant species can self- deal with the coevolution of selfing and inbreeding fertilize. Some of them have a mixed mating behaviour depression when the genotypes at the mating system and a portion of their zygotes also comes from out- loci are not independent of the depression effect crossing. The existence of such mixed mating systems induced by selfing: selfing purges the populations of has no simple evolutionary explanation. Many authors deleterious alleles making the inbreeding depression have dealt with that issue considering the relationships decrease (Holsinger, 1988; Charlesworth eta!., 1990; between mating system and inbreeding depression Uyenoyama & WaIler, 1991). They describe the evolu- (Fisher, 1941; Nagilaki, 1976; Wells, 1979; Charles- tion of the mating system not only with the relative per- worth, 1980; Lande & Schemske, 1985). Their models formance of inbred and outcrossed offspring but also predict that selfing should be complete when inbreed- with the positive associations between the mating ing depression is low and outcrossing should be com- system and the viability when deleterious mutations plete otherwise. occur at the viability loci. Some mechanisms have then been suggested for the An advantage in recombination for outcrossing in existence of mixed mating: transient situations before predominantly selfers has also been suggested permit- fixation of selfing, balance between ecologically rever- ting new adaptation (Maynard-Smith, 1978; Stebbins, sible conditions favouring selfing, gene flow between 1957 in Lande & Schemske, 1985; Crow, 1992). Lewontin (1974) demonstrated that an optimum of Correspondence. recombination exists for adaptation in a multilocus SELFING EVOLUTION UNDER DIRECTIONAL SELECTION 643 context. However, that advantage in recombination for The model simulates the evolution of a herma- outcrossing could be insufficient to lead to stable phroditic diploid population of N individuals. The equilibria with selfing (Lande & Schemske, 1985). population size is kept to N during all successive Nevertheless, in preferential selfing species, for generations. Eighty independent loci determine the which inbreeding depression is weak, low levels of out- genotypic fitness. At each locus two different alleles are crossing are often found (Allard & Workman, 1963; possible, one favourable and one unfavourable. We Harding & Tucker, 1965; Kahier et al., 1975; Agren & assigned the values 2, 1 and 0 respectively to the Schemske, 1993). This could be grounds for evolu- favourable homozygote, heterozygote and unfavour- tionary mechanisms, and if so, it could be considered able homozygote. The fitness of a genotype is obtained as a particular breeding system in response to variable by summing up the elementary values at its 80 loci so environments. In such conditions, what is the optimum that the worst genotypic value is 0 and the best is 160. mating strategy for the whole population and what is An 81st independent locus determines the outcross- the maximum level of outcrossing that can actually be ing rate 't'. The effective outcrossing rate of an individ- maintained as selfing alleles should become rapidly ual is obtained by summing up the values of its two fixed in the absence of inbreeding depression? To outcrossing alleles. Thus, an individual whose genotype answer these questions, we simulated the evolution of is [0.0 1/0.011 at the mating locus, mates 2 per cent of ill-adapted populations (not yet adapted to a new its ovules with out-pollen and self-fertilizes the remain- environment). We did not try to find stable equilibria ing 98 per cent. Outcrossing is simulated as panmixia. between outcrossing and selfing but to understand the The program generates the next generation with dynamics of adaptation with regard to different mixed the previous one following three steps: selection, mating systems. We supposed that fitness is a quantita- mating and fertilization. For each individual of the old tive trait determined by many loci so that many recom- generation, a relative selective value is computed binations are necessary to get the best adapted according to its genotypic value and the mean value of genotype that does not exist in the initial populations. If the population. N new individuals are then successively the number of loci is too small, the best genotype generated. A random number determines the mother appears too quickly to visualize the recombination according to its relative selective value. According to advantage of outcrossing. The selfing rate is controlled the selfing rate of this female, a second random number by an additional locus that has no direct action on fit- determines if the new individual will proceed from self- ness. This could appear unrealistic but it is actually ing or outcrossing. In the latter case, a last random equivalent to the mating modifiers of the previous number determines the father according to its relative quoted models. Moreover, there is no inbreeding effect selective value. Two gametes are finally created by in the model. simulating meiosis between independent genes and First the selfing rate was fixed for all the individuals are associated to create the new individual. within a population and we compared the evolution of the selective value of different populations with differ- ent selfing rates. This first approach will be later Definitionof the initial populations referred to as 'group selection'. We particularly studied Wecreated starting populations according to three the influence of the size and genetic composition of the parameters: N, the number of individuals in the popu- populations. lation, P the mean frequency of the favourable alleles In a second part we added within-population poly- (all the viability loci have the same frequency expecta- morphism for the selfing rate to verify if partial out- tion for the favourable allele), and t the mean outcross- crossing could be maintained under individual selec- ing rate. The genotypes of the first generation were tion. This second approach will be referred to as generated by randomly drawing favourable alleles with 'individual selection'. the probability P in a uniform distribution. All the initial populations were created by simulating panmixia Materials and methods at the 80 viability loci. We studied two values for N(100 and 1000 individ- uals) and for P (0.5and0.1). This leads to four para- The model meter sets. They will be quoted as: (N= 1000, P 0.5), We developed a computer model very close to those (N=1000, P=0.1), (N=100, P=0.5) and (N=100, described in breeding or in natural selection studies to P= 0.1).In the group selection study, t was fixed for simulate quantitative traits (Mani et al., 1990; Hospital a given population and changed only over simulations. & Chevalet, 1993). The code had been written in We studied the influence of t varying from 0 to 1 on the FORTRAN77 and we used the random number generator evolution of fitness. proposed by Lécuyer (1988). 644 J. L. DAVID ETAL. In the individual selection study, one-half of the (a) starting population was supposed homozygote [0,0] at the mating locus and the other half homozygote [A,A]. The respective outcrossing rates of the two genotypes were then 0 and 2A, the heterozygotes arising in the following generations outcrossed in a proportion A, so that tvariedevery generation with the frequency of the outcrossing allele. A simulation under individual selec- tio. will then be referred to as 0 vs. 2A. Three values b( of A were tested, namely 0.005, 0.015 and 0.025 giving C 60 three situations, (0 vs. 1 per cent), (0 vs. 3 per cent) and SO (0 vs. 5 per cent). To determine the selection influence on the evolution of t, each class of mating competition C has been studied under selective neutrality and under U directional selection. In the neutrality pattern, there U was no selective difference between individuals; their fitness was 1/N.
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