On the evolution of genetic incompatibility systems. IV. Modification of response to an existing antigen polymorphism under partial selfing

A 2-locus model of the evolution of self-incompatibility in a population practicing partial selfing is presented. An allele is introduced at a modifier locus which influences the strength of the rejection reaction expressed by the style in response to antigens recognized in pollen. Two causes of inbreeding depression are investigated. First, offspring viability depends solely on the source (self or non-self) of the fertilizing pollen. Second, offspring viability declines with the expression of recessive deleterious alleles, segregating at a third (disease) locus, which exhibit an imperfect association with antigen alleles. Evolutionary changes occurring at the disease locus are not considered in this study. The condition under which a modifier allele that intensifies the incompatibility reaction increases when rare depends upon the number of antigens, the frequency of recessive deleterious alleles at the disease locus, and the level of association between the antigen locus and the disease locus. It is the improvement of viability among offspring derived by outcrossing, rather than the prevention of self-fertilization, that may represent the primary evolutionary function of genetic incompatibility systems.     

On the evolution of genetic incompatibility systems. V. Origin of sporophytic self-incompatibility in response to overdominance in viability

Conditions for the origin of partial sporophytic self-incompatibility (SSI) are obtained from two quantitative models, which differ with respect to the determination of offspring viability. Offspring viability depends solely on the source (self or nonself) of the fertilizing pollen in the first model, which describes changes only at a primitive S-locus itself. Two loci evolve in the second model: overdominant viability selection maintains an arbitrary number of alleles at one locus, with SSI under the control of a separate locus. In both cases, the origin of SSI requires that the relative change in the numbers of offspring derived by the two reproductive modes compensate for the twofold cost of outcrossing. In the first model studied, the viability of inbred offspring fully determines the relative change in the numbers of inbred and outbred offspring produced. In the second model, the relative change in offspring numbers depends in addition on associations between the S-locus and the viability locus. Because these two-locus associations are comparable in magnitude to the differences between the viabilities of inbred and outbred offspring, SSI can arise under less restrictive conditions than expected from the one-locus model. Greater allelic multiplicity at the viability locus facilitates the origin of SSI by reducing the relative viability of inbred offspring. Tight linkage between the S-locus and the viability locus and high rates of receipt of self-pollen promote the generation and maintenance of associations between the S-locus and the viability locus. In populations in which more than two viability alleles are maintained, the active S-allele can invade even in the absence of linkage with the viability locus. The present study establishes that incompatibility systems can arise in response to identity disequilibrium between a modifier of incompatibility and a locus subject to overdominant viability selection; in particular, compensation for the twofold cost of outcrossing does not require preexisting gametic level disequilibria.     

On the evolution of genetic incompatibility systems. III. Introduction of weak gametophytic self-incompatibility under partial inbreeding

I explore the proposition that genetic incompatibility systems serve as a means for parents to evaluate and discriminate among their own offspring. Conditions for the initial increase of gametophytic self-incompatibility in a self-compatible population undergoing selfing, sibmating, and random outcrossing are reported. The adaptive value of reducing the concordance between offspring and maternal genotypes depends upon the relative changes in the numbers of offspring derived by the three modes, parent-offspring relatedness, and the magnitude of distortion of transmission ratios through pollen. Recessivity of stylar expression and low rates of receipt of pollen from related individuals facilitate the evolution of self-incompatibility. Viewed as a means of preferential maternal investment in offspring of high quality, self-incompatibility may be regarded as serving a function in common with diverse phenomena, including sexual selection, brood reduction, and other forms of prezygotic and postzygotic incompatibility. Associations between incompatibility loci and loci expressing inbreeding depression are expected to improve the reliability of the level of concordance at incompatibility loci as a measure of genomic homozygosity and offspring quality.     

Pollen transfer dynamics and the evolution of gametophytic self-incompatibility

Recent studies of mating system evolution have attempted to include aspects of pollination biology in analysis of both theoretical models and experimental systems. In light of this growing trend, we propose a simple population genetic model for the evolution of gametophytic self-incompatibility, incorporating parameters for pollen discounting and pollen export/capture. In this model, we consider several cases that span the spectrum for dominance of the mutant self-incompatibility allele and for the degree of incompatibility conferred by the allele. We confirm earlier results that inbreeding depression is required for successful invasion of the self-incompatibility allele and we demonstrate that, unless pollen discounting is very low, the level of inbreeding depression must be very high for an allele conferring self-incompatibility to become established. Finally, we show that the dominance of the mutant allele has a greater impact on the fate of a newly arisen self-incompatibility allele than the strength of the incompatibility conferred by the allele. In particular, the more recessive the self-incompatibility expression in heterozygote stigmas and the weaker the response induced, the easier it is for a self-incompatibility allele to invade.     

Loss of gametophytic self-incompatibility with evolution of inbreeding depression

Gametophytic self-incompatibility (SI) in plants is a widespread mechanism preventing self-fertilization and the ensuing inbreeding depression, but it often evolves to self-compatibility. We analyze genetic mechanisms for the breakdown of gametophytic SI, incorporating a dynamic model for the evolution of inbreeding depression allowing for partial purging of nearly recessive lethal mutations by selfing, and accounting for pollen limitation and sheltered load linked to the S-locus. We consider two mechanisms for the breakdown of gametophytic SI: a nonfunctional S-allele and an unlinked modifier locus that inactivates the S-locus. We show that, under a wide range of conditions, self-compatible alleles can invade a self-incompatible population. Conditions for invasion are always less stringent for a nonfunctional S-allele than for a modifier locus. The spread of self-compatible genotypes is favored by extremely high or low selfing rates, a small number of S-alleles, and pollen limitation. Observed parameter values suggest that the maintenance of gametophytic SI is caused by a combination of high inbreeding depression in self-incompatible populations coupled with intermediate selfing rates of the self-compatible genotypes and sheltered load linked to the S-locus.     

Coevolution of self-fertilization and inbreeding depression. II. Symmetric overdominance in viability

We describe the evolutionary dynamics of a modifier of selfing coevolving with a locus subject to symmetric overdominance in viability under general levels of reduction in pollination success as a consequence of self-fertilization (pollen discounting). Simple models of the evolution of breeding systems that represent inbreeding depression as a constant parameter do not admit the possibility of stable mixed mating systems involving both inbreeding and random mating. Contrary to this expectation, we find that coevolution between a modifier of selfing and a single overdominant locus situated anywhere in the genome can generate evolutionarily attracting mixed mating systems. Two forms of association between the modifier locus and the viability locus promote the evolution of outcrossing. The favored heterozygous genotype at the viability locus develops positive associations with modifier alleles that enhance outcrossing and with the heterozygous genotype at the modifier locus. Associations between outcrossing and high viability evolve immediately upon the introduction of a rare modifier allele, even in the absence of linkage.     

The effects of the mating system on the evolution of migration in a spatially heterogeneous population

Summary Verbal explanations for the evolution of migration and dispersal often invoke inbreeding depression as an important force. Experimental work on plant populations indicates that while inbreeding depression may favor increased migration rates, adaptation to local environments may reduce the advantage to migrants. We formalize and test this hypothesis using a two-locus genetic model that incorporates lowered fitness in offspring produced by self-fertilization, and habitat differentiation. We also use the model to address questions about the general theory of genetic modifiers and the modifier reduction principle. We find that even under conditions when migration would increase the mean fitness of a population, migration may not be favored. This result is due to the associations that develop between genotypes at a locus subject to overdominant selection and at a neutral locus controlling the migration rate. Thus, it appears that, in this model, the forces of local adaptation, which favor a reduction in the migration rate, overwhelm those of inbreeding depression, which may favor dispersal.     

Heterozygosity at a single locus explains a large proportion of variation in two fitness‐related traits in great tits: a general or a local effect?

In natural populations, mating between relatives can have important fitness consequences due to the negative effects of reduced heterozygosity. Parental level of inbreeding or heterozygosity has been also found to influence the performance of offspring, via direct and indirect parental effects that are independent of the progeny own level of genetic diversity. In this study, we first analysed the effects of parental heterozygosity and relatedness (i.e. an estimate of offspring genetic diversity) on four traits related to offspring viability in great tits (Parus major) using 15 microsatellite markers. Second, we tested whether significant heterozygosity–fitness correlations (HFCs) were due to ‘local’ (i.e. linkage to genes influencing fitness) and/or ‘general’ (genome‐wide heterozygosity) effects. We found a significant negative relationship between parental genetic relatedness and hatching success, and maternal heterozygosity was positively associated with offspring body size. The characteristics of the studied populations (recent admixture, polygynous matings) together with the fact that we found evidence for identity disequilibrium across our set of neutral markers suggest that HFCs may have resulted from genome‐wide inbreeding depression. However, one locus (Ase18) had disproportionately large effects on the observed HFCs: heterozygosity at this locus had significant positive effects on hatching success and offspring size. It suggests that this marker may lie near to a functional locus under selection (i.e. a local effect) or, alternatively, heterozygosity at this locus might be correlated to heterozygosity across the genome due to the extensive ID found in our populations (i.e. a general effect). Collectively, our results lend support to both the general and local effect hypotheses and reinforce the view that HFCs lie on a continuum from inbreeding depression to those strictly due to linkage between marker loci and genes under selection.     

Problems in measuring among-family variation in inbreeding depression

Understanding the sources of variation in inbreeding depression within populations is important for understanding the evolution of selfing rates. At the population level, inbreeding depression is due to decreased heterozygosity caused by inbreeding, which decreases overdominance and increases the frequency of expression of recessive deleterious alleles. However, within individual families inbreeding has two distinct consequences: it reduces heterozygosity and it restricts the alleles present in offspring to those present in the parent. Outcrossing both increases heterozygosity and brings new alleles into a family (compared to the alleles present if the plant is self-pollinated). Both consequences of inbreeding affect offspring fitness, but the most common experimental design used to measure among-family variation in inbreeding depression cannot distinguish them. The result is that variance in inbreeding depression among families is confounded by genetic variation in the traits being measured. Also, correlations (among families) between measures of inbreeding depression or between inbreeding depression and mean trait values are confounded by genetic variation in the traits being measured. I conclude that more complex crossing designs that allow estimation of breeding values for individual families are required to accurately detect and measure among-family variation in inbreeding depression.     

Female mating preferences and offspring survival: testing hypotheses on the genetic basis of mate choice in a wild lekking bird

Indirect benefits of mate choice result from increased offspring genetic quality and may be important drivers of female behaviour. ‘Good‐genes‐for‐viability’ models predict that females prefer mates of high additive genetic value, such that offspring survival should correlate with male attractiveness. Mate choice may also vary with genetic diversity (e.g. heterozygosity) or compatibility (e.g. relatedness), where the female's genotype influences choice. The relative importance of these nonexclusive hypotheses remains unclear. Leks offer an excellent opportunity to test their predictions, because lekking males provide no material benefits and choice is relatively unconstrained by social limitations. Using 12 years of data on lekking lance‐tailed manakins, Chiroxiphia lanceolata, we tested whether offspring survival correlated with patterns of mate choice. Offspring recruitment weakly increased with father attractiveness (measured as reproductive success, RS), suggesting attractive males provide, if anything, only minor benefits via offspring viability. Both male RS and offspring survival until fledging increased with male heterozygosity. However, despite parent–offspring correlation in heterozygosity, offspring survival was unrelated to its own or maternal heterozygosity or to parental relatedness, suggesting survival was not enhanced by heterozygosity per se. Instead, offspring survival benefits may reflect inheritance of specific alleles or nongenetic effects. Although inbreeding depression in male RS should select for inbreeding avoidance, mates were not less related than expected under random mating. Although mate heterozygosity and relatedness were correlated, selection on mate choice for heterozygosity appeared stronger than that for relatedness and may be the primary mechanism maintaining genetic variation in this system despite directional sexual selection.     

Interval Mapping of Viability Loci Causing Heterosis in Arabidopsis

The genetic basis of heterosis has implications for many problems in genetics and evolution. Heterosis and inbreeding depression affect human genetic diseases, maintenance of genetic variation, evolution of breeding systems, agricultural productivity, and conservation biology. Despite decades of theoretical and empirical studies, the genetic basis of heterosis has remained unclear. I mapped viability loci contributing to heterosis in Arabidopsis. An overdominant factor with large effects on viability mapped to a short interval on chromosome I. Homozygotes had 50% lower viability than heterozygotes in this chromosomal region. Statistical analysis of viability data in this cross indicates that observed viability heterosis is better explained by functional overdominance than by pseudo-overdominance. Overdominance sometimes may be an important cause of hybrid vigor, especially in habitually inbreeding species. Finally, I developed a maximum likelihood interval mapping procedure that can be used to examine chromosomal regions showing segregation distortion or viability selection.     

Segregation and the evolution of sex under overdominant selection

The segregation of alleles disrupts genetic associations at overdominant loci, causing a sexual population to experience a lower mean fitness compared to an asexual population. To investigate whether circumstances promoting increased sex exist within a population with heterozygote advantage, a model is constructed that monitors the frequency of alleles at a modifier locus that changes the relative allocation to sexual and asexual reproduction. The frequency of these modifier alleles changes over time as a correlated response to the dynamics at a fitness locus under overdominant selection. Increased sex can be favored in partially sexual populations that inbreed to some extent. This surprising finding results from the fact that inbred populations have an excess of homozygous individuals, for whom sex is always favorable. The conditions promoting increased levels of sex depend on the selection pressure against the homozygotes, the extent of sex and inbreeding in the population, and the dominance of the invading modifier allele.     

Coevolution of self-fertilization and inbreeding depression. III. Homozygous lethal mutations at multiple loci.

We study the evolution of the rate of self-fertilization in response to deleterious mutations at multiple loci. Although partial selfing induces associations among loci even in the absence of linkage, associations among mutations at different loci are of a smaller order of magnitude than the mutation rate. Genotypes that carry homozygous lethal mutations in heterozygous form at i loci occur in frequencies of the order (Ti) mu i, in which T denotes the number of viability loci and mu the mutation rate. While associations between mutations at different loci remain small even under inbreeding, each viability locus develops an association with the modifier of the rate of self-fertilization that substantially affects the evolution of the breeding system. Positive associations between enhancers of selfing and haplotypes carrying multiple wild-type alleles and positive associations in heterozygosity between the modifier locus and the viability loci promote evolutionary increases in the rate of self-fertilization.     

Coevolution of self-fertilization and inbreeding depression. I. Mutation-selection balance at one and two loci

Simple theories for the evolution of breeding systems suggest that the fate of an allele that modifies the rate of self-fertilization hinges only on the degree to which selfing reduces opportunities for outcrossing ("pollen discounting") and the extent of inbreeding depression. These theories predict that outcrossing evolves whenever deleterious mutations have a more severe effect in combination than expected from their individual effects. We study the evolutionary dynamics of a modifier of the rate of self-fertilization in populations subject to complete pollen discounting and recurrent mutations which impair viability at a single locus in diploids and at two loci in haploids. Our analysis indicates that genetic associations arising immediately upon the introduction of a rare modifier allele generate substantial quantitative and qualitative departures from expectation. Higher rates of segregation under selfing in our one-locus diploid model generate positive associations between enhancers of selfing and wild-type viability alleles, which in turn favor the evolution of selfing under a wider range of conditions than expected. Greater opportunities for recombination under outcrossing in our two-locus haploid model generate positive associations between enhancers of outcrossing and wild-type viability alleles. These associations favor the evolution of outcrossing under a wider range of conditions, and introduce the possibility of stable mixed mating systems involving both selfing and outcrossing. Our explicit analysis of genetic associations between loci affecting viability and the rate of self-fertilization indicates that modifiers that enhance the production of offspring with very high (and very low) viability by promoting segregation or recombination develop positive associations with high viability. This advantage of producing extremes can compensate for an initial disadvantage in offspring number.     

On the Origin of Meiotic Reproduction: A Genetic Modifier Model

We study the conditions under which a rare allele that modifies the relative rates of meiotic reproduction and apomixis increases in a population in which meiotic reproduction entails selfing as well as random outcrossing. A distinct locus, at which mutation maintains alleles that are lethal in homozygous form, determines viability. We find that low viability of carriers of the lethal alleles, high rates of selfing, dominance of the introduced modifier allele, and lower rates of recombination promote the evolution of meiosis. Meiotic reproduction can evolve even in the absence of linkage between the modifier and the viability locus. The adaptive value of meiotic reproduction depends on the relative viabilities of offspring derived by meiosis and by apomixis, and on associations between the modifier and the viability locus. Meiotic reproduction, particularly under selfing, generates more diverse offspring, including those with very high and very low viability. Elimination of offspring with low viability generates positive associations between enhancers of meiotic reproduction and high viability. In addition, partial selfing generates positive associations in heterozygosity (identity disequilibrium) between the modifier and the viability locus, even in the absence of linkage. The two kinds of associations together can compensate for initial reductions in mean offspring viability under meiotic reproduction.     

SELECTION ON OVERDOMINANT GENES MAINTAINS HETEROZYGOSITY ALONG MULTIPLE CHROMOSOMES IN A CLONAL LINEAGE OF HONEY BEE

Correlations between fitness and genome‐wide heterozygosity (heterozygosity‐fitness correlations, HFCs) have been reported across a wide range of taxa. The genetic basis of these correlations is controversial: do they arise from genome‐wide inbreeding (“general effects”) or the “local effects” of overdominant loci acting in linkage disequilibrium with neutral loci? In an asexual thelytokous lineage of the Cape honey bee (Apis mellifera capensis), the effects of inbreeding have been homogenized across the population, making this an ideal system in which to detect overdominant loci, and to make inferences about the importance of overdominance on HFCs in general. Here we investigate the pattern of zygosity along two chromosomes in 42 workers from the clonal Cape honey bee population. On chromosome III (which contains the sex‐locus, a gene that is homozygous‐lethal) and chromosome IV we show that the pattern of zygosity is characterized by loss of heterozygosity in short regions followed by the telomeric restoration of heterozygosity. We infer that at least four selectively overdominant genes maintain heterozygosity on chromosome III and three on chromosome IV via local effects acting on neutral markers in linkage disequilibrium. We conclude that heterozygote advantage and local effects may be more common and evolutionarily significant than is generally appreciated.     

Inbreeding depression and the evolution of dispersal rates: a multilocus model

Inbreeding depression is one of the possible reasons organisms disperse. In this article, we present a two-locus model for the evolution of dispersal in the presence of inbreeding depression. The first locus codes for a modifier of the migration rate, while the second locus is a selected locus generating inbreeding depression. We express the change in frequency of the migration modifier as a function of allele frequencies and genetic associations and then use a quasi-equilibrium assumption to express genetic associations as functions of allele frequencies. Our model disentangles two effects of inbreeding depression: it gives an advantage to migrant individuals because their offspring are on average less homozygous, but it also decreases the degree of population structure, thus decreasing the strength of kin selection for dispersal. We then extend our model to include an infinite number of selected loci. When the cost of dispersal is not too high, the model predictions are confirmed by multilocus simulation results and show that inbreeding depression can have a substantial effect on the dispersal rate. For high costs of dispersal, we observe discrepancies between the model and the simulations, probably caused by associations among selected loci, which are neglected in the analysis.     

The Genetic Variance for Viability and Its Components in a Local Population of DROSOPHILA MELANOGASTER

Two hundred and ninety second chromosomes extracted from a natural population of Drosophila melanogaster were analyzed to estimate the genetic variance of viability and its components by means of a partial diallel cross (Design II of Comstock and Robinson 1952). The additive and dominance variances are estimated to be 0.009 and 0.0012. Using the dominance variance and the inbreeding depression, the effective number of overdominant loci contributing to the variance in viability is estimated to be very small, a dozen or less. Either the actual number of loci is small, or the distribution of viabilities is strongly skewed with a large majority of very weakly selected loci. The additive variance in viability appears to be too large to be accounted for by recurrent harmful mutants or by overdominant loci at equilibrium with various genetic parameters estimated independently. The excess might be due to frequency-dependent selection, to negative correlations between viability and fertility, or possibly to the presence of a mutator. The selection for viability and fertility, or possibly to the presence of a mutator. The selection for viability at the average polymorphic locus must be very slight, of the order of 10(-3) or less.     

Inbreeding depression in Campanula rapunculoides L. I. A comparison of inbreeding depression in plants derived from strong and weak self-incompatibility phenotypes

The evolution of selfing taxa from outcrossing ancestors has occurred repeatedly and is the subject of many theoretical models, yet few empirical studies have examined the immediate consequences of inbreeding in a population with variable expression of self-incompatibility. Because self-incompatibility breaks down with floral age in Campanula rapunculoides, we were able to mate outbred and selfed maternal plants in a crossing design which produced progeny with inbreeding coefficients of 0, 0.25, 0.50 and 0.75. Cumulative inbreeding depression in plants that were selfed for one generation was very high in families derived from strongly self-incompatible plants (average δ = 0.98), and somewhat lower in families derived from plants with weaker expression of self-incompatibility (average δ = 0.90). Relative to outbred progeny, inbred progeny produced fewer seeds, had lower rates of germination, less vegetative growth and fewer flowers per plant. Inbred progeny also took longer to germinate, and longer to produce a first leaf and to flower. Interestingly, inbred plants also produced 40% fewer seeds than outcrossed plants (t-test P < 0.001) even when mated to the same, unrelated pollen donor, suggesting that inbreeding can produce profound maternal effects. Most importantly, our results demonstrate that progeny derived from plants with stronger expression of self-incompatibility exhibited greater levels of inbreeding depression than progeny from plants with weaker expression of self-incompatibility. Moreover, the decline in fitness (cumulative, ln-transformed) over the four inbreeding levels was steeper for the progeny of the strongly self-incompatible lineages. These empirical results suggest that inbreeding depression and mating system phenotype have the potential to coevolve.