Search

Isoenzymes of adenosine deaminase (ADA) in the eelpout, Zoarces viviparus, are determined by an autosomal locus, Ada. In a population at Hov near Aarhus two common alleles and two rare variant alleles, mutually codominant, were found. Data on the segregation of alleles at locus Ada were obtained from samples of mother-offspring combinations. Free recombination between Ada and previously described enzyme loci was verified.

Inference in fitness in natural populations is discussed emphasizing the key role of the concept of selection components. The applicability of observational designs including different kinds of population samples of mother-offspring combinations is reviewed and analysed. It is shown that complete information about all selection components is obtainable for one-locus polymorphism by using mother-offspring combinations with three or more offspring per mother in organisms where every brood has only one sire.

The eelpout population in Kald Cove has been sampled in five consecutive years, from 1969-1974. Each winter a sample including mother-offspring combinations was procured and analyzed for Est/I/ . The samples in the years 1969-1971 have been published. This paper reports on the samples in 1972, 1973 and 1974. The total data of the five year period analyzed here comprised 12,607 adults (5935 motheroffspring combinations) and 253 adolescents. The adults have been sorted into five age classes, which permits the observation of seven discrete cohorts. The data have been subjected to a refined selection component analysis, introducing analysis of the time stability of the population and the adult zygotic selection component, i.e. the viability of differences between the genotypes during their mature life. The new data support the previously found deficit of heterozygotes among adults and indicate that it arises from juvenile zygotic selection, i.e. selection occurring by differential elimination of the zygotes before maturity. The previous preliminary indications of reproductive selection have not been confirmed in this more extensive analysis.

R.A. Fisher and H.J. Muller argued in the 1930s that a major evolutionary advantage of recombination is that it allows favorable mutations to be combined within an individual even when they first appear in different individuals. This effect is evaluated in a two-locus, two-allele model by calculating the average waiting time until a new genotypic combination first appears in a haploid population. Three approximations are developed and compared with Monte Carlo simulations of the Wright-Fisher process of random genetic drift in a finite population. First, a crude method, based on the deterministic accumulation of single mutants, produces a waiting time of 1/square root of N mu(2) with no recombination and [formula: see text] with recombination between the two loci, where mu is the mutation rate, N is the haploid population size, and R is the recombination rate. Second, the waiting time is calculated as the expected value of a heterogeneous geometric distribution obtained from a branching process approximation. This gives accurate estimates for small values of N mu large. The estimates for small values of N mu are considerably lower than the simulated values. Finally, diffusion analysis of the Wright-Fisher process provides accurate estimates for N mu small, and the time scales of the diffusion process show a difference between R = 0 and for R >> 0 of the same order of magnitude as seen in the deterministic analysis. In the absence of recombination, accurate approximations to the waiting time are obtained by using the branching process for high N mu and the diffusion approximation for low N mu. For low N mu the waiting time is well approximated by 1/the square root of 8N2 mu(3). With R >> 0, the following dependence on N mu is observed: For N mu > 1 the waiting time is virtually independent of recombination and is well described by the branching process approximation. For N mu approximately equal to 1 the waiting time is well described by a simplified diffusion approximation that assumes symmetry in the frequencies of single mutants. For N mu << 1 the waiting time is well described by the diffusion approximation allowing asymmetry in the frequencies of single mutants. Recombination lowers the waiting time until a new genotypic combination first appears, but the effect is small compared to that of the mutation rate and population size. For large N mu, recombination has a negligible effect, and its effect is strongest for small N mu, in which case the waiting time approaches a fixed fraction of the waiting time for R = 0. Free recombination lowers the waiting time to about 45% of the waiting time for absolute linkage for small N mu. Selection has little effect on the importance of recombination in general.

It is not generally realized that genetics has finally solved the age-old problem of the reason for the existence (i.e. the function) of sexuality and sex, and that only geneticists can properly answer the question, “Is sex necessary?” ▪ Abstract Optimality arguments and modifier theory are reviewed as paradigms for the study of the evolution of recombination. Optimality criteria (such as maximization of mean fitness) may agree with results from models developed in terms of the evolution of recombination at modifier loci. Modifier models demonstrate, however, that equilibrium mean fitness can decrease during the evolution of recombination rates and is not always maximized. Therefore, optimality arguments do not successfully predict the conditions under which increased or decreased recombination will evolve. The results from modifier models indicate that decreased recombination rates are usually favored when the population is initially near a polymorphic equilibrium with linkage disequilibrium. When the population is subject to directional selection or to deleterious mutations, increased recombination may be favored under certain conditions, provided that there is negative epistasis among alleles.

The genetic mechanism underlying an ‘Optimal outcrossing distance’ in plants (sensu Price and Waser) is discussed. Monte Carlo simulations of a population subdivided as a one-dimensional stepping-stone are used to evaluate possible genetic mechanisms. A simple genetic model with two types of unlinked loci, underdominant and partially dominant, with multiplicative effects on fitness, is found to create an ‘Optimal outcrossing distance’ under a wide range of parameter values. The results are compared to, and discussed in relation to a two-locus epistatic model, previously investigated by Campbell and Waser, and found to give very similar results.

Familial aggregation of complex diseases may have many causes in addition to and apart from genetic predisposition due to common ancestry. For example, exposure to an environment that induces susceptibility to a disease may produce similar familial aggregations when the environment is shared by family members. In general, according to the principles of (Johannsen 1903), the emergence of a disease phenotype is the result of the combined effects of the genotype of the individual and the environment that it experiences during development. The heritability of a disease is a measure of familial aggregation in terms of the covariances among family members relative to the variance in disease state in the general population. Thus heritability expresses the within-family resemblance, observed by Darwin and inferred by him to reflect inheritance, which formed the core of his (Darwin 1859) theory of evolution. Darwin’s inspiration originated from the practical use of family resemblance in animal breeding. Animal breeders have long known that a major obstacle to progress in genetic improvement is the interaction between familial aggregation of environments and the effects of similar genetics within families. The potential importance of this interaction, recognized in classical studies of the genetic epidemiology of complex diseases and other quantitative characters, has reemerged in studies of the effects of epigenetic modifications, their variation, and their transmission between generations.

The introgression of genes carried by a small group of immigrants is studied. The recipient and the donor populations differ at several autosomal loci subject to weak selection, and two allelic forms of each gene are considered. Fitness variation is determined by additive allelic effects, by dominance effects, and by two-locus additive-by-additive epistatic interaction of the effects of the alleles. The fate of the group of immigrants is quantified by the selection barrier that describes the cumulative mean fitness of the hybrids and hybrid descendants relative to the fitness of the resident population. The monomorphic and the polymorphic loci of the recipient population contribute differently to the selection barrier. If the genetic difference between recipient and donor population is small, then the contribution of the monomorphic loci is dominated by a positive term dependent on the difference in gene frequencies. The contribution of the polymorphic loci depends only on the difference of the leading order in the pairwise linkage disequilibria between the two populations. This contribution may be positive or negative; and, thus, polymorphic loci may either contribute to the barrier or inflate the introgression.

We study a population exposed to a lethal infectious disease. Host response is carried at one locus with two alleles while the pathogen occurs in two variants. Based on an Si-type epidemic model we derive explicit equations for the dynamics of each genotype. By assuming small variations in both host and disease, we obtain a separation in time scales between epidemic and evolutionary processes. This allows us to describe explicitly the changes in host and disease gene frequencies. The resulting model has a rich behaviour including multiple stable states and oscillations. However, in the oscillatory situation the model is degenerate excluding the possibility of limit cycles. We show that the degeneracy can only be removed by frequency dependent selection in the pathogen, for example by including direct interaction of virus in a free-living stage. The qualitative conclusions extend to an SIR-type epidemic model, where recovery with immunity from the disease is possible.

We survey the distribution of haplotypes at the self-incompatibility (SI) locus of Arabidopsis lyrata (Brassicaceae) at 12 locations spread over the species' natural distribution in Iceland. Previous investigations of the system have identified 34 functionally different S haplotypes maintained by frequency-dependent selection and arranged them into four classes of dominance in their phenotypic expression. On the basis of this model of dominance and the island model of population subdivision, we compare the distribution of S haplotypes with that expected from population genetic theory. We observe 18 different S haplotypes, recessive haplotypes being more common than dominant ones, and dominant ones being shared by fewer populations. As expected, differentiation, although significant, is very low at the S locus even over distances of up to 300 km. The frequency of the most recessive haplotype is slightly larger than expected for a panmictic population, but consistent with a subdivided population with the observed differentiation. Frequencies in nature reflect effects of segregation distortion previously observed in controlled crosses. The dynamics of the S-locus variation are, however, well represented by a 12-island model and our simplified model of dominance interactions.

Identification and characterization of the self-incompatibility genes in Brassicaceae species now allow typing of self-incompatibility haplotypes in natural populations. In this study we sampled and mapped all 88 individuals in a small population of Arabidopsis lyrata from Iceland. The self-incompatibility haplotypes at the SRK gene were typed for all the plants and some of their progeny and used to investigate the realized mating patterns in the population. The observed frequencies of haplotypes were found to change considerably from the parent generation to the offspring generation around their deterministic equilibria as determined from the known dominance relations among haplotypes. We provide direct evidence that the incompatibility system discriminates against matings among adjacent individuals. Multiple paternity is very common, causing mate availability among progeny of a single mother to be much larger than expected for single paternity.

Influenza in humans is characterised by strongly annual dynamics and antigenic evolution leading to partial escape from prior host immunity. The variability of new epidemic strains depends on the amount of virus currently circulating. In this paper, the amount of antigenic variation produced each year is dependent on the epidemic size. Our model reduces to a one-dimensional map and a full mathematical analysis is presented. This simple system suggests some basic principles which may be more generally applicable. In particular, for diseases with antigenic drift, vaccination may be doubly beneficial. Not only does it protect the population through classical herd immunity, but the overall case reduction reduces the chance of new variants being produced; hence, subsequent epidemics may be milder as a result of this positive feedback. Also, a disease with a high innate rate of antigenic variation will always be able to invade a susceptible population, whereas a disease with less potential for variation may require several introduction events to become endemic.

Evolutionary games have been applied as simple mathematical models of populations where interactions between individuals control the dynamics. Recently, it has been proposed to use this type of model to describe the evolution of tumour cell populations with interactions between cells. We extent the analysis to allow for synergistic effects between cells. A mathematical model of a tumour cell population is presented in which population-level synergy is assumed to originate through the interaction of triplets of cells. A threshold of two cooperating cells is assumed to be required to produce a proliferative advantage. The mathematical behaviour of this model is explored. Even this simple synergism (minor clustering effect) is sufficient to generate qualitatively different cell-population dynamics from the models published previously. The most notable feature of the model is the existence of an unstable internal equilibrium separating two stable equilibria. Thus, cells of a malignant phenotype can exist in a stable polymorphism, but may be driven to extinction by relatively modest perturbations of their relative frequency. The proposed model has some features that may be of interest to biological interpretations of gene therapy. Two prototypical strategies for gene therapy are suggested, both of them leading to extinction of the malignant phenotype: one approach would be to reduce the relative proportion of the cooperating malignant cell type below a certain critical value. Another approach would be to increase the critical threshold value without reducing the relative frequency of cells of the malignant phenotype.

Recombination, including chromosomal segregation, shuffles together the genetic material carried by different members of a sexual species. This genetic mixing unties the evolutionary fate of alleles at one locus from the fate of alleles at neighboring loci and can increase the amount of genetic variation found within a population. In the process, however, recombination separates advantageous gene combinations, the very gene combinations that enabled the parents to survive and reproduce. Whether or not the adaptation of a population to an environment is more rapid in the presence of recombination, that is, whether or not recombination speeds up the evolutionary process, depends critically on the ways in which this process is modelled. As we shall see, the effect of recombination depends on the population size, the initial population composition, and the selection regime under consideration.

The two conditions for stability of an evolutionary equilibrium, the m-stability and the δ-stability conditions, are discussed. The m-stability condition is a condition for the convergence of the population toward the equilibrium, and the δ-stability condition coresponds to a local version of the classic evolutionarily stable strategy (ESS) condition. Together the two conditions provide the condition for a continuous stable strategy. The convergence stability condition corresponds to the requirement for convergence due to initial increase of rare alleles in a monomorphic population, and the local ESS stability condition corresponds to the stability of a monomorphic population at the evolutionary equilibrium against the increase of rare alleles. In this way, an evolutionary equilibrium that is convergence stable, but not local ESS stable, will tend to become polymorphic. The local ESS stability condition therefore contributes more to a description of the dynamics of variation at an evolutionary equilibrium...

The lectures focus on the development of selection component analyses based on population samples including mother-offspring combinations. The need for separation of selection into components is discussed and exemplified by experimental data. The genetic analysis of samples of both simple and complete mother-offspring combinations is developed for one-locus polymorphisms. This is subsequently used to develop an analysis of selection components using population samples including mother-offspring combinations, and this analysis is exemplified by data on natural populations of Zoarces viviparus (simple mother-offspring data) and Gammarus oceanicus (complete mother-offspring data). Finally, the mother- offspring analyses are generalized to cover polymorphisms at multiple loci, and as an introduction to this some population theory for multiple loci is discussed. Index set notation for multi-locus gamete types is introduced and applied to problems concerning population mixing. In addition, the effects of recurrent immigration into a population are investigated in a generalization of Wright’s island model and in the stepping-stone cline model.

The study of very simple selection models has formed a basis to advance our knowledge of simultaneous evolution at two or more loci. Detailed theoretical investigations of the dynamical properties of these models have elucidated many phenomena concerning fitness interactions among loci and the interplay between selection and recombination. The approach commenced with the analysis of the two-locus symmetric viability model by Lewontin and Kojima (1960) and expanded to analyses of models with an additive or a multiplicative structure in fitness. These simplified models posess a unique equilibrium where every locus is polymorphic and where the alleles at the various loci occur independently in the gametes of the population. This equilibrium is a totally polymorphic Robbins equilibrium, and in general, its existence places strict requirements on the fitness matrix (Bodmer and Felsenstein, 1967) because it must be an equilibrium of the corresponding multiple allele model obtained for absolute linkage of the loci. The Robbins equilibrium point may be viewed as representing an equilibrium descending from a totally polymorphic equilibrium for absolute linkage as long as the property of linkage equilibrium is not emphasized. The symmetric viability models have been generalized to three loci by Feldman, Franklin, and Thomson (1974) and to multiple loci by Karlin (1977) and Karlin and Avni (1981). Multi-locus versions of the additive and the multiplicative models of selection have been considered by Roux (1974) and Karlin and Liberman (1978b). Karlin and Liberman (1979a, b) suggested and analyzed selection models with a general combination of additive and multiplicative structures. These models are formulated and analyzed as multiple allele models, but the analysis simplifies considerably when each locus is assumed to posess only two alleles. The description of genotypes and gamete types in two allele models is aided by a set indexation (Christiansen, 1987, 1989a) which retains much of the simplicity of arguments that is characteristic of classical one-locus population genetics.

Single gene models for the evolution of rates of selfing and sib mating in the presence of an inbreeding depression of fitness are treated. In models in which the genetic constitution of the male gamete pool available for random mating is not affected by prior inbreeding, an allele which increases the rate of inbreeding will succeed, provided the inbreeding depression is not too large. The opposite result holds when the proportion of male genotypes available for random mating are reduced according to their rate of prior inbreeding.

The transmission dynamics of a communicable disease in a subdivided population where the spread among groups follows the proportionate mixing model while the within-group transmission can correspond to prefered mixing, proportionate mixing among subgroups, or mixing between social and nonsocial subgroups, is analyzed. It is shown that the threshold condition for the disease to persist is that either (i) the disease can persist within at least one group through intragroup contacts, or—if (i) does not hold—(ii) the intergroup transmission is sufficiently high. The among-group transmission is computed as an average where each subgroup's reproductive number is weighted according to its intragroup activity level squared and the total number of cases that one infectious individual will cause through intragroup contacts. The model thus allows for a study of the relative importance of communitywide disease transmission and of disease transmission within geographically or socially separate groups.

Sufficient conditions for protected polymorphism at an autosomal locus in a diploid organism are developed for a Levene model with explicit modeling of the population dynamics. Levene's condition for protected polymorphism, formulated in terms of weighted harmonic means of relative genotypic fitnesses, is only strictly valid for components of selection that are not immediately relevant for the regulation of the population size in the subpopulations. Global regulation of the population size produces Dempster's condition for protected polymorphism in terms of weighted arithmetic means of absolute genotypic fitnesses. The general condition for protection of an allele may be written in the same form as Levene's condition, but then the weights of the subpopulations depend on the fitnesses in the various habitats. The model allows for marginal habitats that cannot sustain a population if left isolated.

The deterministic properties of a two-locus model with mutation and selection have been investigated. The mutation process is unidirectional, and the model is so constructed that the genetic variation at one locus is selectively neutral in the absence of a mutant allele at the other locus. All genotypes with three or four mutant alleles are deleterious, while the double heterozygotes may have the same fitness as the standard genotype. If one of the mutant alleles becomes fixed in the population, then the other locus will show a regular one-locus mutation-selection balance. Such a boundary equilibrium may be unstable or stable in the full two-locus setting. In the symmetric case, which is analyzed in details, the population will either go to one of the two boundary equilibria, or to a fully polymorphic equilibrium at which both the mutant alleles are rare. The origin of reproductive separation between two populations via the fixation of complementary deleterious mutants at different loci, and the fixation of nonfunctional alleles at duplicated loci, are two biological processes which both can be studied with the present model. In the last part of the paper we show how the results from the deterministic analysis can be used to predict how different factors will influence the rates of evolution in these systems.

Population samples including mother-offspring combinations provide information on the selection components: zygotic selection, sexual selection, gametic seletion and fecundity selection, on the mating pattern, and on the deviation from linkage equilibrium among the loci studied. The theory for the analysis of a sample consisting of adult individuals including combinations of a mother and one randomly chosen offspring in the case of n polymorphic autosomal loci with ma alleles at the ath locus, a = 1, 2,…, n, is developed for an organism with discrete non-overlapping generations. In this general analysis complete determination of the genotypes is assumed. The modifications in the analysis for the case n = 2 and m1 = m2 = 2 when the two double heterozygotes cannot be separated are discussed, and the analysis is illustrated by data from a population of Zoarces viviparus (a marine teleost).

A symmetric viability model for two loci with two alleles at one locus and m alleles at the other is suggested and analyzed. The analysis of the equilibria is complete if the two loci are absolutely linked, while if recombination is allowed the analysis is incomplete. The dynamics of the mode! resemble those of the two locus two allele model, namely that for loose linkage there will be no correlation between the loci and for tight linkage there may be strong correlation. The major caveats to this are: 1. The equilibria stable for tight linkage may belong to an array of different structures dependent on the selection and the number of alleles. 2. If both loci are overdominant in viability, the stable equilibria always contain all alleles segregating in the population; otherwise, the stable equilibria may only be two locus two allele high complementarity equilibria for tight linkage. 3. For intermediate linkage values and special selection values the boundary two locus two allele high complementarity equilibria may be stable simultaneously with the totally polymorphic central point at which there is no association between the loci.

SUMMARYThis paper is devoted to the study of the effects of population subdivision on the evolution of two linked loci. Two simple deterministic models of population subdivision without selection are investigated. One is a finite linear ‘stepping stone’ model and the other is a finite linear stepping stone chain of populations stretching between two large populations of constant genetic constitution. At equilibrium in the first model the gene frequencies in each population are equal and there is linkage equilibrium in each population. The rate of decay to zero of the linkage disequilibrium functions is the larger of (1 –c) and, where λ1is the rate of convergence of the gene frequencies to equilibrium and c is the recombination frequency. In the second model at equilibrium there will be a linear cline in gene frequencies connecting the two large constant populations. This cline will be accompanied by a ‘cline’ of linkage disequilibria. The rate of convergence to this equilibrium cline is independent of the recombination frequency, and, in fact, the gene frequencies and the linkage disequilibria converge to equilibrium at the same rate.

Using the model of exploitative competition of R. H. MacArthur and R. Levins (1967, Amer. Natur. 101, 377–385), evolution at a gene locus which influences the niche position is considered. The locus has multiple alleles, and the contributions of the alleles to the genotypic value are additive. The resource spectrum and the utilization functions of the genotypes are assumed to be Gaussian. Evolution will make the mode of the niche converge to the resource optimum, as long as the allele contributions are small compared to the distance between the mode of the niche and the resource optimum. When this distance is of the same order of magnitude as the allele contributions, then the globally stable equilibrium will maintain at most two alleles in the population, unless the allele contributions are large. Classical overdominance is not needed to maintain polymorphism. This result predicts high linkage disequilibrium in similar multilocus models. It is concluded that intraspecific competition can be a powerful force in maintaining two-allele polymorphisms, and that it can maintain high linkage disequilibrium among closely linked loci.

A two-locus model with three alleles at one locus and two at the other is studied. The viability system is such that all double heterozygotes have fitness unity, all single heterozygotes have fitness w < 1 and all double homozygotes have fitness w2. The following are the major findings: 1. There are more stable equilibria for tight linkage than in the corresponding three-locus model, even though the number of chromosomes is lower. 2. The equilibria stable for tight linkage do not belong to a unique high complementarity class, as is the case for two alleles at each locus. Instead the strength of selection determines the structure of the equilibrium. 3. The increase in number of alleles seems to reduce the possible extent of assocation between the loci. 4. The measure of this association is not well defined, although we have suggested a statistically standard way of getting over this. 5. A mutation introduced while a population is in linkage disequilibrium may, per medium only of the change in number of alleles, destroy the linkage disequilibrium.

Laboratory populations of Drosophila melanogaster bearing the Curly and Plum marked second chromosome inversions were observed in selection experiments for ten discrete generations. Maximum likelihood estimates of the relative fitnesses of Curly, Plum, Curly-Plum, and wild phenotypes were obtained from selection trajectories. Using these estimates, measures of multiplicative and additive epistasis were calculated. These were partitioned into pre-sampling and post-sampling components, and both were found to be significant. In several cases the sign of the epistasis of the two components was reversed, and the direction of net epistasis depended on the particular inversion. The significance of partitioning epistasis into components is discussed in the light of two locus population genetic theory.

Intraspecific competition implies interaction among the individuals of a population, so natural selection on genotypic variation in characters related to the competition will necessarily be frequency dependent. Intraspecific antagonistic competition exhibits properties similar to other behavioural interactions between individuals. In exploitative intraspecific competition the interactions among individuals are less direct. Exploitation modifies the abundance of the various limiting resources according to the use of these resources by the individual members of the population. The amount of resource available to an individual is therefore a function of the phenotypes present in the population, through their density and frequency.

Hard and soft selection are compared in a population subdivided into random mating subpopulations. The possibility for protected polymorphism is greater with soft than with hard selection. Protected polymorphism is more readily achieved with increasing isolation, an effect that is more pronounced with hard selection. The results are discussed in relation to selection components.

Many studies of selection have been based on theoretical population models involving a number of restrictive assumptions concerning the biology of the organism under study. These assumptions may simplify analyses of the system, but a violation of one or more of them may cause a serious bias in the evaluation of the selection operating. In attempts to estimate selection pressures in single locus systems, the model generally applied has been one where the only nonrandom phenomenon is differential survival of the zygotes from birth to the time of observation at maturity. Then for a locus with two alleles, the fitnesses of the three genotypes are estimated from the genotypic frequencies determined at the same stage of development in two successive generations. Provided the assumption is valid that selection has been completed at the time of observation in each of the two generations, the estimated fitnesses are the total or net fitness values determining the dynamics of the population. But when this basic assumption is not correct, these same estimates may become seriously biased indicating apparent frequency-dependent selection (Prout, 1965, 1969; Bundgaard and Christiansen, 1972). Prout (1965) showed for the case of sex-independent fitnesses at an autosomal locus, that unless very special and unlikely conditions hold when selection is not complete at the time of observation, the estimated fitnesses will not equal the true fitnesses. Our objective was to investigate

Sufficient conditions for protected polymorphism at an autosomal locus are developed for a diploid dioecious population subdivided into randomly mating subpopulations. Conditions are formulated in principle as simple algebraic relations between selection and migration under the restriction that migration is independent of the genotype in the considered locus and that selection does not influence the relative size of the subpopulations. Migration models with random outbreeding and homing are analyzed in detail. Homing toward the neighborhood of the birthplace enhances the possibility for polymorphism.

The total dynamics of a fourth chromosome polymorphism in Drosophila melanogaster is studied in an experimental population in which it is possible to measure various selection components simultaneously in each generation. It is demonstrated that although zygotic selection operates in the system, the component of major importance for the dynamics is sexual selection, and it is this component that is responsible for the stability of the polymorphism. Fecundity selection is of very minor importance. Both zygotic and sexual selection components behave in a frequency-dependent way. The results are discussed in relation to genetic load and the detection of selection in natural and experimental populations.

We investigate mate availability in different models of multiallelic self-incompatibility systems in mutation- selection-drift balance in finite populations. Substantial differences among self-incompatibility systems occur in average mate availability, and in variances of mate availability among individual plants. These differences are most pronounced in small populations in which low mate availability may reduce seed set in some types of sporophytic self-incom- patibility. In cases where the pollination system causes a restriction in the number of pollen genotypes available to an individual plant, the fecundity of that plant depends on the availability of compatible pollen, which is determined by its genotype at the incompatibility locus. This leads to an additional component of selection acting on self- incompatibility systems, which we term "fecundity selection." Fecundity selection increases the number of alleles maintained in finite populations and increases mate availability in small populations. The strength of fecundity selection is dependent on the type of self-incompatibility. In some cases, fecundity selection markedly alters the equilibrium dynamics of self-incompatibility alleles. We discuss the population genetic consequences of mate availability and fecundity selection in the contexts of conservation management of self-incompatible plant species and experimental investigations on self-incompatibility in natural populations.

The stationary frequency distribution and allelic dynamics in finite populations are analyzed through stochastic simulations in three models of single-locus, multi-allelic sporophytic self-incompatibility. The models differ in the dominance relationships among alleles. In one model, alleles act codominantly in both pollen and style (SSIcod), in the second, alleles form a dominance hierarchy in pollen and style (SSIdom). In the third model, alleles interact codominantly in the style and form a dominance hierarchy in the pollen (SSIdomcod). The SSIcod model behaves similarly to the model of gametophytic self-incompatibility, but the selection intensity is stronger. With dominance, dominant alleles invade the population more easily than recessive alleles and have a lower frequency at equilibrium. In the SSIdom model, recessive alleles have both a higher allele frequency and higher expected life span. In the SSIdomcod model, however, loss due to drift occurs more easily for pollen-recessive than for pollen-dominant alleles, and therefore, dominant alleles have a higher expected life span than the more recessive alleles. The process of allelic turnover in the SSIdomcod and SSIdom models is closely approximated by a random walk on a dominance ladder. Implications of the results for experimental studies of sporophytic self-incompatibility in natural populations are discussed. Udgivelsesdato: 1997-Oct