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. VI. a Three-Locus Modifier Model for the Origin of Gametophytic Self-Incompatibility

Recent genetic analyses have demonstrated that self-incompatibility in flowering plants derives from the coordinated expression of a system of loci. To address the selective mechanisms through which a genetic system of this kind evolves, I present a three-locus model for the origin of gametophytic self-incompatibility. Conventional models assume that a single locus encodes all physiological effects associated with self-incompatibility and that the viability of offspring depends only on whether they were derived by selfing or outcrossing. My model explicitly represents the genetic determination of offspring viability by a locus subject to symmetrically overdominant selection. Initially, the level of expression of the proto-S locus is insufficient to induce self-incompatibility. Weak gametophytic self-incompatibility arises upon the introduction of a rare allele at an unlinked modifier locus which enhances the expression of the proto-S locus. While conventional models predict that the origin of self-incompatibility requires at least two- to threefold levels of inbreeding depression, I find that the comparatively low levels of inbreeding depression generated by a single overdominant locus can ensure the invasion of an enhancer of self-incompatibility under sufficiently high rates of receipt of self-pollen. Associations among components of the incompatibility system promote the origin of self-incompatibility. Enhancement of heterozygosity at the initially neutral proto-S locus improves offspring viability through associative overdominance. Further, the modifier that enhances the expression of self-incompatibility develops a direct association with heterozygosity at the overdominant viability locus. These results suggest that the evolutionary processes by which incompatibility systems originate may differ significantly from those associated with their breakdown. The genetic mechanism explored here may apply to the evolution of other systems that restrict reproduction, including maternal-fetal incompatibility in mammals.     

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.     

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.     

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.     

Modifiers of mutation rate: a general reduction principle

A deterministic two-locus population genetic model with random mating is studied. The first locus, with two alleles, is subject to mutation and arbitrary viability selection. The second locus, with an arbitrary number of alleles, controls the mutation at the first locus. A class of viability-analogous Hardy-Weinberg equilibria is analyzed in which the selected gene and the modifier locus are in linkage equilibrium. It is shown that at these equilibria a reduction principle for the success of new mutation-modifying alleles is valid. A new allele at the modifier locus succeeds if its marginal average mutation rate is less than the mean mutation rate of the resident modifier allele evaluated at the equilibrium. Internal stability properties of these equilibria are also described.     

Allelic Negative Complementation at the Abruptex Locus of DROSOPHILA MELANOGASTER

The mutations of the Abruptex locus in Drosophila melanogaster fall into three categories. There are recessive lethal alleles and viable alleles. The latter can be divided into suppressors and nonsuppressors of Notch mutations. The recessive lethals are lethal in heterozygous combination with Notch. As a rule the recessive lethals are lethal also in heterozygous combination with the viable alleles. Heterozygous combinations of certain viable alleles are also lethal. In such heterozygotes, one heteroallele is a suppressor of Notch and the other is a nonsuppressor. Other heterozygous combinations of viable alleles are viable and have an Abruptex phenotype. The insertion of the wild allele of the Abruptex locus as an extra dose (carried by a duplication) into the chromosomal complement of the fly fully restores the viability of the otherwise lethal heterozygotes if two viable alleles are involved. The extra wild allele also restores the viability of heterozygotes in which a lethal and a suppressor allele are present. If, however, a lethal and a nonsuppressor are involved, the wild allele only partly restores the viability, and the effect of the wild allele is weakest if two lethal alleles are involved. It seems likely that of the viable alleles the suppressors of Notch are hypermorphic and the nonsuppressors are hypomorphic. The lethal alleles share properties of both types, and are possibly antimorphic mutations. It is suggested that the locus is responsible for a single function which, however, consists of two components. The hypermorphic mutations are defects of the one component and the hypomorphic mutations of the other. In heterozygotes their cumulative action leads to decreased viability. The lethal alleles are supposed to be defects of the function as a whole. The function controlled by the locus might be a regulative function.     

Natural variation for a hybrid incompatibility between two species of Mimulus

Understanding the process by which hybrid incompatibility alleles become established in natural populations remains a major challenge to evolutionary biology. Previously, we discovered a two-locus Dobzhansky-Muller incompatibility that causes severe hybrid male sterility between two inbred lines of the incompletely isolated wildflower species, Mimulus guttatus and M. nasutus. An interspecific cross between these two inbred lines revealed that the M. guttatus (IM62) allele at hybrid male sterility 1 (hms1) acts dominantly in combination with recessive M. nasutus (SF5) alleles at hybrid male sterility 2 (hms2) to cause nearly complete hybrid male sterility. In this report, we extend these genetic analyses to investigate intraspecific variation for the hms1-hms2 incompatibility in natural populations of M. nasutus and M. guttatus, performing a series of interspecific crosses between individuals collected from a variety of geographic locales. Our results suggest that hms2 incompatibility alleles are common and geographically widespread within M. nasutus, but absent or rare in M. guttatus. In contrast, the hms1 locus is polymorphic within M. guttatus and the incompatibility allele appears to be extremely geographically restricted. We found evidence for the presence of the hms1 incompatibility allele in only two M. guttatus populations that exist within a few kilometers of each other. The restricted distribution of the hms1 incompatibility allele might currently limit the potential for the hms1-hms2 incompatibility to act as a species barrier between sympatric populations of M. guttatus and M. nasutus. Extensive sampling within a single M. guttatus population revealed that the hms1 locus is polymorphic and that the incompatibility allele appears to segregate at intermediate frequency, a pattern that is consistent with either genetic drift or natural selection.     

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.     

The genetics of self-incompatibility in Brassica campestris L. ssp. Oleifera Metzg. I. Characteristics of S-locus. Control of self-incompatibility

Self-incompatibility in Brassica campestris c.v. Arlo is controlled by a single locus sporophytic system. The identity and expression of the S alleles were determined in eight inbred and two hybrid families. It was found that co-dominance of alleles is more frequent in the stigma, whereas dominance relations between pairs of alleles predominate in the pollen. A linear order of dominance was established between six S alleles and alleles high, intermediate and low in the dominance series were recognized.In considering the variation in the expression of compatibility and the segregation ratios in inbred, F₁, F₂ and backcross progenies, the presence of a specific S allele conditioning self-fertility, or a single dominant self-compatibility factor independent of the S locus could not be established. Instead, self-compatibility in this cultivar was ascribed to the segregation of a polygenic complex which is capable of modifying the incompatibility reaction to the point of self-fertility, or to a reduction in the strength of the reaction due to the presence of S alleles low in the dominance series.     

Control of mating type heterokaryon incompatibility by the tol gene in Neurospora crassa and N. tetrasperma.

The mating-type of Neurospora crassa (A and a) have a dual function: A and a individuals are required for sexual reproduction, but only strains of the same mating type will form a stable vegetative heterokaryon. Neurospora tetrasperma, in contrast, is a naturally occurring A+a heterokaryon. It was shown previously that the mating-type genes of both species are functionally the same and are not responsible for this difference in heterokaryon incompatibility. This suggests that a separate genetic system determines the heterokaryon incompatibility function of mating type. The mutant tolerant (tol) in N. crassa, unlinked to mating type, acts as a specific suppressor of A+a heterokaryon incompatibility. In the present study, the wild-type alleles at the tol locus were introgressed reciprocally, from N. crassa into N. tetrasperma and from N. tetrasperma into N. crassa, to investigate the action of these alleles in the A+a heterokaryon incompatibility systems of these species. The wild-type allele from N. tetrasperma (tolT) acts as a recessive suppressor of A+a heterokaryon incompatibility in N. crassa. Furthermore, the wild-type allele from N. crassa (tolC) causes A and a to become heterokaryon incompatible in N. tetrasperma, while having no effect on the sexual reproduction. Therefore, the tol gene plays a major role in determining the heterokaryon compatibility of mating type in these species: tolC is an active allele that causes incompatibility and tolT an inactive allele that suppresses incompatibility by its inactivity.     

Population genetics of modifiers of meiotic drive. I. The solution of a special case and some general implications

This is a study of the formal population genetics of a two locus model where the alleles at one locus are subject to meiotic drive and zygotic selection and the only effect of the other locus is the modification of drive intensity. A complete analytic solution is obtained for a biologically reasonable special case. It is then argued, partially with the aid of computer analysis, that with moderate relaxation of assumptions of the special case, the conclusions derived from that case still hold. These conclusions are that if there is linkage a stable two locus polymorphism can result. There is permanent linkage disequilibrium with the loosing allele at the drive locus in coupling with the suppressor allele at the modifier locus, and the driven allele coupled with the modifier allele which enhances drive. It is suggested that this result explains how the SD system in Drosophila maintains its integrity in natural populations.     

Genetic regulation of self‐incompatibility

Self‐incompatibility is a cell‐cell recognition system in higher plants that is based on the ability of the pistil to discriminate “self‐pollen from “non‐self"‐pollen. In the simplest systems, this recognition response is controlled by a single locus — the S‐locus — with multiple alleles. Pollination of a pistil with pollen bearing an S‐allele recognition factor identical to that expressed in the host plant stigma or style results in rejection of the “self"‐pollen. Most of the studies on the molecular genetics of self‐incompatibility that are summarized in this review have had as their goal the identification and characterization of the gene product(s) associated with the self‐incompatibility response. These studies have provided a great deal of new and important information about self‐incompatibility — despite the fact that many critical questions remain unresolved. Taken together, the present evidence from these studies indicates that the self‐incompatibility response is likely to be far more complex than suggested by historical models.     

Fewer S‐alleles are maintained in plant populations with sporophytic as opposed to gametophytic self‐incompatibility

Plants use self‐incompatibility to reject pollen bearing alleles in common at the S‐locus. These systems are classified as gametophytic (GSI) if recognition involves haploid pollen or sporophytic (SSI) if recognition involves diploid paternal genotypes. Dominance in SSI systems reduces the number of S‐alleles, but it has not been clear which system should maintain greater diversity when all else is equal. We simulated finite populations to compare the equilibrium number of S‐alleles in populations with either GSI or a co‐dominant SSI system. When population size was constant, SSI systems maintained more S‐alleles than GSI systems. When populations fluctuated in response to an S‐Allee effect, fewer S‐alleles were observed in SSI systems when S‐allele diversity was low, and SSI populations were vulnerable to extinction over a broader range of parameters. Turnover rates at the S‐locus were also faster in SSI populations experiencing strong S‐Allee effects. Given the variable expectations concerning S‐allele diversity in these systems, we reviewed published estimates of S‐allele diversity. GSI populations have significantly more S‐alleles on average than SSI populations (GSI = 25.70 and SSI = 16.80). Dominance likely contributes to this pattern, although the demographic consequences of the S‐Allee effect may be important in populations with fewer than 10 S‐alleles.     

THE EVOLUTION OF STRONG REPRODUCTIVE ISOLATION

Felsenstein distinguished two ways by which selection can directly strengthen isolation. First, a modifier that strengthens prezygotic isolation can be favored everywhere. This fits with the traditional view of reinforcement as an adaptation to reduce deleterious hybridization by strengthening assortative mating. Second, selection can favor association between different incompatibilities, despite recombination. We generalize this "two allele" model to follow associations among any number of incompatibilities, which may include both assortment and hybrid inviability. Our key argument is that this process, of coupling between incompatibilities, may be quite different from the usual view of reinforcement: strong isolation can evolve through the coupling of any kind of incompatibility, whether prezygotic or postzygotic. Single locus incompatibilities become coupled because associations between them increase the variance in compatibility, which in turn increases mean fitness if there is positive epistasis. Multiple incompatibilities, each maintained by epistasis, can become coupled in the same way. In contrast, a single-locus incompatibility can become coupled with loci that reduce the viability of haploid hybrids because this reduces harmful recombination. We obtain simple approximations for the limits of tight linkage, and strong assortment, and show how assortment alleles can invade through associations with other components of reproductive isolation.     

INTERSPECIFIC INCOMPATIBILITY IN SOLANUM SPECIES

Pandey , K.K. (Crop Res. Div., D.S. & I.R., Lincoln, Christchurch, New Zealand.) Interspecific incompatibility in Solanum species. Amer. Jour. Bot. 49(8): 874–882. Illus. 1962.—A diallel cross involving 11 self-incompatible and 3 self-compatible species of Solanum was made to study the genetic basis of interspecific incompatibility. Interspecific incompatibility was not limited to crosses in which a self-compatible species was used as the male parent onto a self-incompatible species (unilateral incompatibility). A number of crosses between self-incompatible species were incompatible. In one cross, Q vernei X verrucosum, a self-compatible species was successful as a pollen parent with a self-incompatible species. Unlike other hybrids between self-compatible and self-incompatible species, which are self-incompatible, these F₁ hybrids were self-fertile, and cross-fertile among themselves and with both parents. The self-fertile S. polyadenium was cross-incompatible as a female as well as a male parent with all other species. It is suggested that the unilateral incompatibility is a property of the allele S_C which originated as a consequence of one kind of breakdown of the S_I gene; the S_C allele produces “bare” pollen growth substances which are inactivated in an incompatible style. It is proposed that the failure of the principle of unilateral interspecific incompatibility in solanaceous species may be due to the action of alleles at the second incompatibility locus revealed in certain Mexican species. It is assumed that the South American species are selected intraspecifically only for the action of S alleles but that in certain interspecific crosses and rarely in intraspecific crosses the alleles at the second locus may be expressed, thus interfering with the usual action of S alleles. The F₁ hybrids Q verrucosum (self-fertile) X simplicifolium (self-sterile) were self-incompatible at the tetraploid as well as the diploid level, and their cross-compatibility behavior was consistent with the expected activity of the S_C and S_I alleles of the 2 parents respectively.     

On the evolutionary stability of Mendelian segregation

We present a model of a primary locus subject to viability selection and an unlinked locus that causes sex-specific modification of the segregation ratio at the primary locus. If there is a balanced polymorphism at the primary locus, a population undergoing Mendelian segregation can be invaded by modifier alleles that cause sex-specific biases in the segregation ratio. Even though this effect is particularly strong if reciprocal heterozygotes at the primary locus have distinct viabilities, as might occur with genomic imprinting, it also applies if reciprocal heterozygotes have equal viabilities. The expected outcome of the evolution of sex-specific segregation distorters is all-and-none segregation schemes in which one allele at the primary locus undergoes complete drive in spermatogenesis and the other allele undergoes complete drive in oogenesis. All-and-none segregation results in a population in which all individuals are maximally fit heterozygotes. Unlinked modifiers that alter the segregation ratio are unable to invade such a population. These results raise questions about the reasons for the ubiquity of Mendelian segregation.     

Selection in complex genetic systems IV. Multiple alleles and interactions between two loci

Summary 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.Dedicated to the memory of Ove Frydenberg.Research supported in part by a grant from the Danish Natural Science Research Council, a grant from National Science Foundation, U.S.A., and by USPHS grant NIH 10452-09-11.     

The genetics of self-incompatibility inLeavenworthia crassa rollins (Cruciferae)

Six plants of a self-incompatible population ofLeavenworthia çrassa were grown from seed collected in nature and cross-pollinated in all combinations. The incompatibility relationships between sibs were determined in eleven of the F₁ families. A one-locus sporophytic incompatibility system was established. None of the parents was homozygous at the S locus. At least five, and possibly all six, of the parents did not share an S allele. Only one pair of alleles was shown to have different interactions in the pollen and stigmata. The identity and expression of the S alleles were determined in six families. Eight pairs of alleles were independently expressed in both the pollen grains and the stigmata. Sixteen pairs of alleles showed dominance of one allele over the other in the pollen grains or the stigmata or both.F₁ plants of two crosses between different self-incompatible races were self-incompatible. F₁ plants of six crosses between self-incompatible and self-compatible races were self-incompatible; in five of the families, the frequency of pseudo-compatibility was higher than in the self-incompatible parent. Self-incompatible hybrids from a cross between a self-incompatible and a self-compatible population provide a method for rapidly determining allelic interactions in plants with a sporophytic incompatibility system.The research was carried out at the Biological Laboratories, Harvard University, Cambridge, Massachusetts, U.S.A.     

A model of migration modification

Two subpopulations whose different sizes are in a constant ratio interact via migration. The fitness of the diploid organisms is determined by two alleles at a single locus and by the niche the organism is in. The rates of migration depend upon two neutral modifier genes at a second locus. The second modifying allele is introduced into an equilibrium where the first modifying allele is fixed, and where the other two alleles are already polymorphic. It is shown that the new migration modifier is selected for when it reduces migration. The similarity between this result and some recombination modifier models is noted.