The evolution of dominance: Haldane v Fisher revisited.

Fisher's model for the evolution of dominance indicates that the accumulation of dominance modifiers will be accelerated by (1) an increased frequency of the mutant heterozygote, (2) increased selection for the phenotype of the normal homozygote. The model has been criticised by Haldane on the grounds that point (1) is not fulfilled, that is dominance appears to be more common in populations with a low frequency of mutant heterozygotes (populations of inbreeders). In support of Fisher's model it is argued that intense selection for the wild type phenotype is more common in inbreeders than outbreeders. This situation should promote the accumulation of dominance modifiers (point (2) above).     

Evolution of dominance in polymorphic Batesian mimicry

Models of two simple genetic systems of two alleles segregating at two loci are used to study the evolution of dominance of a Batesian mimic maintained in a population by frequency-dependent selection. The alleles at one locus determine the mimetic patterns, and their dominance is modified by the alleles at the other locus. In the model, the modifiers of dominance may themselves be either fully dominant or have additive effects on the dominance of the mimics. When the modifier is fully dominant in its effect on the dominance of a new mimic, the mimic will evolve dominance irrespective of the initial frequency of the modifier. When the modifiers act additively on the dominance of the mimics, a new mimic will evolve either dominance or recessiveness depending on the initial frequency of the modifiers. Unless the modifier is initially at quite a high frequency dominance will not evolve. And dominance will not evolve fully unless the modifiers are more or less selectively neutral in their effects on all other characters except the mimicry. The significance of these results is discussed with reference to the different dominance relations of the mimics in different races of the butterfly Papilio dardanus.     

EVOLUTION OF DOMINANCE UNDER FREQUENCY-DEPENDENT INTRASPECIFIC COMPETITION IN AN ASSORTATIVELY MATING POPULATION

We study the evolution of higher levels of dominance as a response to negative frequency-dependent selection. In contrast to previous studies, we focus on the effect of assortative mating on the evolution of dominance under frequency-dependent intraspecific competition. We analyze a two-locus two-allele model, in which the primary locus has a major effect on a quantitative trait that is under a mixture of frequency-independent stabilizing selection, density-dependent selection, and frequency-dependent selection caused by intraspecific competition for a continuum of resources. The second (modifier) locus determines the degree of dominance at the trait level. Additionally, the population mates assortatively with respect to similarities in the ecological trait. Our analysis shows that the parameter region in which dominance can be established decreases if small levels of assortment are introduced. In addition, the degree of dominance that can be established also decreases. In contrast, if assortment is intermediate, sexual selection for extreme types can be established, which leads to evolution of higher levels of dominance than under random mating. For modifiers with large effects, intermediate levels of assortative mating are most favorable for the evolution of dominance. For large modifiers, the speed of fixation can even be higher for intermediate levels of assortative mating than for random mating.     

The integrative biology of genetic dominance

Dominance is a basic property of inheritance systems describing the link between a diploid genotype at a single locus and the resulting phenotype. Models for the evolution of dominance have long been framed as an opposition between the irreconcilable views of Fisher in 1928 supporting the role of largely elusive dominance modifiers and Wright in 1929, who viewed dominance as an emerging property of the structure of enzymatic pathways. Recent theoretical and empirical advances however suggest that these opposing views can be reconciled, notably using models investigating the regulation of gene expression and developmental processes. In this more comprehensive framework, phenotypic dominance emerges from departures from linearity between any levels of integration in the genotype-to-phenotype map. Here, we review how these different models illuminate the emergence and evolution of dominance. We then detail recent empirical studies shedding new light on the diversity of molecular and physiological mechanisms underlying dominance and its evolution. By reconciling population genetics and functional biology, we hope our review will facilitate cross-talk among research fields in the integrative study of dominance evolution.     

Evolution of assortative mating in a population expressing dominance

In this article, we study the influence of dominance on the evolution of assortative mating. We perform a population-genetic analysis of a two-locus two-allele model. We consider a quantitative trait that is under a mixture of frequency-independent stabilizing selection and density- and frequency-dependent selection caused by intraspecific competition for a continuum of resources. The trait is determined by a single (ecological) locus and expresses intermediate dominance. The second (modifier) locus determines the degree of assortative mating, which is expressed in females only. Assortative mating is based on similarities in the quantitative trait ('magic trait' model). Analytical conditions for the invasion of assortment modifiers are derived in the limit of weak selection and weak assortment. For the full model, extensive numerical iterations are performed to study the global dynamics. This allows us to gain a better understanding of the interaction of the different selective forces. Remarkably, depending on the size of modifier effects, dominance can have different effects on the evolution of assortment. We show that dominance hinders the evolution of assortment if modifier effects are small, but promotes it if modifier effects are large. These findings differ from those in previous work based on adaptive dynamics.     

Evidence for Fisher's dominance theory: how many 'special cases'?

Dominance, its genetic basis and evolution has been at the heart of one of the most intense controversies in the history of genetics. For more than eighty years the existence of dominance modifiers, genetic elements controlling dominance-recessivity interactions, has been suggested as a theoretical possibility, but the modifier elements themselves have remained elusive. A recent study of the self-incompatibility locus in flowering plants provided the first empirical evidence for such genetic elements: small non-coding RNAs that control dominance-recessivity by mediating methylation of the promoter of the recessive allele. Theory has shown that several biological situations are favorable for the evolution of dominance modifiers. We argue that the elucidation of this mechanism of dominance opens up new research avenues that could lead to uncovering dominance modifiers in other genetic systems, such as genes controlling Batesian and Müllerian mimicry or host-parasite interactions, thereby shedding light on the generality of the proposed mechanism.     

Evolution of dominance under frequency-dependent intraspecific competition

A population-genetic analysis is performed of a two-locus two-allele model, in which the primary locus has a major effect on a quantitative trait that is under frequency-dependent disruptive selection caused by intraspecific competition for a continuum of resources. The modifier locus determines the degree of dominance at the trait level. We establish the conditions when a modifier allele can invade and when it becomes fixed if sufficiently frequent. In general, these are not equivalent because an unstable internal equilibrium may exist and the condition for successful invasion of the modifier is more restrictive than that for eventual fixation from already high frequency. However, successful invasion implies global fixation, i.e., fixation from any initial condition. Modifiers of large effect can become fixed, and also invade, in a wider parameter range than modifiers of small effect. We also study modifiers with a direct, frequency-independent deleterious fitness effect. We show that they can invade if they induce a sufficiently high level of dominance and if disruptive selection on the ecological trait is strong enough. For deleterious modifiers, successful invasion no longer implies global fixation because they can become stuck at an intermediate frequency due to a stable internal equilibrium. Although the conditions for invasion and for fixation if sufficiently frequent are independent of the linkage relation between the two loci, the rate of spread depends strongly on it. The present study provides further support to the view that evolution of dominance may be an efficient mechanism to remove unfit heterozygotes that are maintained by balancing selection. It also demonstrates that an invasion analysis of mutants of very small effect is insufficient to obtain a full understanding of the evolutionary dynamics under frequency-dependent selection.     

Molecular mechanisms of dominance evolution in Müllerian mimicry

Natural selection acting on dominance between adaptive alleles at polymorphic loci can be sufficiently strong for dominance to evolve. However, the molecular mechanisms underlying such evolution are generally unknown. Here, using Müllerian mimicry as a case‐study for adaptive morphological variation, we present a theoretical analysis of the invasion of dominance modifiers altering gene expression through different molecular mechanisms. Toxic species involved in Müllerian mimicry exhibit warning coloration, and converge morphologically with other toxic species of the local community, due to positive frequency‐dependent selection acting on these colorations. Polymorphism in warning coloration may be maintained by migration–selection balance with fine scale spatial heterogeneity. We modeled a dominance modifier locus altering the expression of the warning coloration locus, targeting one or several alleles, acting in cis or trans, and either enhancing or repressing expression. We confirmed that dominance could evolve when balanced polymorphism was maintained at the color locus. Dominance evolution could result from modifiers enhancing one allele specifically, irrespective of their linkage with the targeted locus. Nonspecific enhancers could also persist in populations, at frequencies tightly depending on their linkage with the targeted locus. Altogether, our results identify which mechanisms of expression alteration could lead to dominance evolution in polymorphic mimicry.     

Sporophytic self-incompatibility in Senecio squalidus (Asteraceae): S allele dominance interactions and modifiers of cross-compatibility and selfing rates

Understanding genetic mechanisms of self-incompatibility (SI) and how they evolve is central to understanding the mating behaviour of most outbreeding angiosperms. Sporophytic SI (SSI) is controlled by a single multi-allelic locus, S, which is expressed in the diploid (sporophyte) plant to determine the SI phenotype of its haploid (gametophyte) pollen. This allows complex patterns of independent S allele dominance interactions in male (pollen) and female (pistil) reproductive tissues. Senecio squalidus is a useful model for studying the genetic regulation and evolution of SSI because of its population history as an alien invasive species in the UK. S. squalidus maintains a small number of S alleles (7–11) with a high frequency of dominance interactions. Some S. squalidus individuals also show partial selfing and/or greater levels of cross-compatibility than expected under SSI. We previously speculated that these might be adaptations to invasiveness. Here we describe a detailed characterization of the regulation of SSI in S. squalidus. Controlled crosses were used to determine the S allele dominance hierarchy of six S alleles and effects of modifiers on cross-compatibility and partial selfing. Complex dominance interactions among S alleles were found with at least three levels of dominance and tissue-specific codominance. Evidence for S gene modifiers that increase selfing and/or cross-compatibility was also found. These empirical findings are discussed in the context of theoretical predictions for maintenance of S allele dominance interactions, and the role of modifier loci in the evolution of SI.     

On the evolution of dominance modifiers I. A nonlinear analysis

A well known mathematical model of evolution of dominance is subjected to a nonlinear analysis. For the case where the primary locus and the modifying locus are completely linked (r = 0) a global Ljapunov function is given. This proves that selection of dominance modifiers entirely due to their modifying effect is possible. This result is also extended to small recombination fractions r by using the method of Ljapunov functions in a more sophisticated way. For r = 0 and μ = 0 a lower bound for the success of selection of the modifier is given. Furthermore, the influence of the dominance relations between the alleles (measured by the parameters h and k) is investigated. Finally it is shown that differential and difference equations lead to the same results (which need not be the case in general). As a by-product we obtain a new equilibrium point in the classical one locus selection-mutation model.     

THE EVOLUTION OF DOMINANCE IN SPOROPHYTIC SELF-INCOMPATIBILITY SYSTEMS. II. MATE AVAILABILITY AND RECOMBINATION

Sporophytic self-incompatibility (SSI) is a self-pollen recognition system that enforces outcrossing in plants. Recognition in SSI systems is typically controlled by a complex locus ( S -locus) with separate genes that determine pollen and stigma specificity. Experimental studies show that S -alleles can be dominant, recessive, or codominant, and that the dominance level of a given S -allele can depend upon whether pollen or stigma specificity is examined. Here and in the companion paper by Llaurens and colleagues, the evolution of dominance in single-locus SSI is explored using numerical models and simulation. Particular attention is directed at factors that can cause S -allele dominance to differ in pollen versus stigma. The effect of recombination between the S -locus and modifier locus is also examined. The models predict that limitation in the number of compatible mates is required for the evolution of S -allele dominance in the stigma but not in the pollen. Tight linkage between the S -locus and modifier promotes the evolution of S -allele dominance hierarchies. Model results are interpreted with respect to published information on the molecular basis of dominance in SSI systems, and reported S -allele dominance relationships in a variety of species. These studies show that dominant S -alleles are more common in the pollen than in the stigma, a pattern that when interpreted in light of model predictions, suggests that mate limitation may be relatively infrequent in natural populations with SSI.     

Evolutionarily stable transition rates in a stage-structured model. An application to the analysis of size distributions of badges of social status

This paper deals with the adaptive dynamics associated to a hierarchical non-linear discrete population model with a general transition matrix. In the model, individuals are categorized into n dominance classes, newborns lie in the subordinate class, and it is considered as evolutionary trait a vector eta of probabilities of transition among classes. For this trait, we obtain the evolutionary singular strategy and prove its neutral evolutionary stability. Finally, we obtain conditions for the invading potential of such a strategy, which is sufficient for the convergence stability of the latter. With the help of the previous results, we provide an explanation for the bimodal distribution of badges of status observed in the Siskin (Carduelis spinus). In the Siskin, as in several bird species, patches of pigmented plumage signal the dominance status of the bearer to opponents, and central to the discussion on the evolution of status signalling is the understanding of which should be the frequency distribution of badge sizes. Though some simple verbal models predicted a bimodal distribution, up to now most species display normal distributions and bimodality has only been described for the Siskin. In this paper, we give conditions leading to one of these two distributions in terms of the survival, fecundity and aggression rates in each dominance class.     

Towards a theory of the evolution of modifier genes

The main findings of a study of the evolution of modifier gene frequencies in models of deterministic population genetics are presented. A wide variety of random mating systems are subject to selection with modifiers operating, in different cases, on mutation rates, migration between subpopulations, and linkage between other loci. In all these instances, the modifier frequencies evolve in such a way as to maximize the mean fitness of the population at equilibrium. This is remarkable since, the modifier genes are selectively neutral in the sense that they do not affect the fitness of their individual carriers. In nonrandom mating systems, the mean fitness concept is not well-defined, and there does not appear to be such a simple principle governing the evolution of modifier frequencies. In assortative mating systems, modifiers favoring reduced assortment propensities tend to increase. In contrast, for selfing-outcrossing systems, modifiers favoring increased selfing tend to increase.     

Dominance Modifiers in NEUROSPORA CRASSA: Phenocopy Selection and Influence on Certain Ascus Mutants

When homozygous in zygotes, mutant alleles at the peak locus in linkage group V of Neurospora crassa initiate aberrant asci that are nonlinear, in contrast to the linear asci characteristic of wild type. Most mutant alleles are recessive, inasmuch as crosses of the mutant strains with wild type give linear asci. However, five different mutant alleles, when heterozygous with the wild-type allele, act in varying degrees as zygote dominants, initiating both linear and nonlinear asci, the relative proportions depending on the allele. Five modifiers that act on the dominance relationships of at least one of the five possible heterozygotes of a dominant peak and its wild-type allele have been characterized, four of them having been obtained by selection directed against a phenocopy of these mutants induced by treatment of wild type with l-sorbose. The pattern of modifier specificity observed among the various dominant peak heterozygotes indicates that the phenotypic effects are produced by a complex relationship between the modifiers and the dominant peak alleles in relation to their wild-type allele. In all but two cases the direction of modification, where present, is towards decreasing the dominance of the mutant allele in the heterozygote, evidenced by an increase in the percentage of linear asci when compared with control data. The modifiers exert their maximum modification when they themselves are heterozygous with their wild-type alleles and when the dominant peak allele is heterozygous with its wild-type allele. No modification occurs when heterozygous modifiers are included in zygotes homozygous for a dominant peak allele, reinforcing the notion that the modifiers act on the dominance relationship existent between a dominant peak allele and its wild-type allele, rather than influencing some activity of the mutant allele itself. The modifiers have no detectable effect of their own on ascus morphology, since homozygous modifier zygotes initiate entirely linear asci when only wild-type alleles of peak are present in the zygotes. Their only detectable effect, other than dominance modification, appears to be in conferring sorbose resistance to the mycelium. The modifiers are unlinked to the peak locus, and, except for two of them, they are nonallelic.     

A general model to explore complex dominance patterns in plant sporophytic self-incompatibility systems

We developed a general model of sporophytic self-incompatibility under negative frequency-dependent selection allowing complex patterns of dominance among alleles. We used this model deterministically to investigate the effects on equilibrium allelic frequencies of the number of dominance classes, the number of alleles per dominance class, the asymmetry in dominance expression between pollen and pistil, and whether selection acts on male fitness only or both on male and on female fitnesses. We show that the so-called "recessive effect" occurs under a wide variety of situations. We found emerging properties of finite population models with several alleles per dominance class such as that higher numbers of alleles are maintained in more dominant classes and that the number of dominance classes can evolve. We also investigated the occurrence of homozygous genotypes and found that substantial proportions of those can occur for the most recessive alleles. We used the model for two species with complex dominance patterns to test whether allelic frequencies in natural populations are in agreement with the distribution predicted by our model. We suggest that the model can be used to test explicitly for additional, allele-specific, selective forces.     

Evolution of the individual

This article studies the transition in evolution from single cells to multicellular organisms as a case study in the origin of individuality. The issues considered are applicable to all major transitions in the units of selection that involve the emergence of cooperation and the regulation of conflict. Explicit genetic models of mutation and selection both within and between organisms are studied. Cooperation among cells increases when the fitness covariance at the level of the organism overcomes within-organism change toward defection. Selection and mutation during development generate significant levels of within-organism variation and lead to variation in organism fitness at equilibrium. This variation selects for gem-line modifiers and other mediators of within-organism conflict, increasing the heritability of fitness at the organism level. The evolution of these modifiers is the first new function at the emerging organism level and a necessary component of the evolution of individuality.     

Comparative analysis of position-effect variegation mutations in Drosophila melanogaster delineates the targets of modifiers.

In Drosophila melanogaster, heterochromatin-induced silencing or position-effect variegation (PEV) of a reporter gene has provided insights into the properties of heterochromatin. Class I modifiers suppress PEV, and class II modifiers enhance PEV when the modifier gene is present in fewer than two doses. We have examined the effects of both class I and class II modifiers on four PEV mutations. These mutations include the inversions In(1)w(m4) and In(2R)bw(VDe2), which are classical chromosomal rearrangements that typify PEV mutations. The other mutations are a derivative of brown(Dominant), in which brown+ reporters are inactivated by a large block of heterochromatin, and a P[white+] transposon insertion associated with second chromosome heterochromatin. In general, we find that class I modifiers affect both classical and nonclassical PEV mutations, whereas class II modifiers affect only classical PEV mutations. We suggest that class II modifiers affect chromatin architecture in the vicinity of reporter genes, and only class I modifiers identify proteins that are potentially involved in heterochromatin formation or maintenance. In addition, our observations support a model in which there are different constraints on the process of heterochromatin-induced silencing in classical vs. nonclassical PEV mutations.     

Contribution of genetic effects to genetic variance components with epistasis and linkage disequilibrium

Background

Cockerham genetic models are commonly used in quantitative trait loci (QTL) analysis with a special feature of partitioning genotypic variances into various genetic variance components, while the F_∞ genetic models are widely used in genetic association studies. Over years, there have been some confusion about the relationship between these two type of models. A link between the additive, dominance and epistatic effects in an F_∞ model and the additive, dominance and epistatic variance components in a Cockerham model has not been well established, especially when there are multiple QTL in presence of epistasis and linkage disequilibrium (LD).

Results

In this paper, we further explore the differences and links between the F_∞ and Cockerham models. First, we show that the Cockerham type models are allelic based models with a special modification to correct a confounding problem. Several important moment functions, which are useful for partition of variance components in Cockerham models, are also derived. Next, we discuss properties of the F_∞ models in partition of genotypic variances. Its difference from that of the Cockerham models is addressed. Finally, for a two-locus biallelic QTL model with epistasis and LD between the loci, we present detailed formulas for calculation of the genetic variance components in terms of the additive, dominant and epistatic effects in an F_∞ model. A new way of linking the Cockerham and F_∞ model parameters through their coding variables of genotypes is also proposed, which is especially useful when reduced F_∞ models are applied.

Conclusion

The Cockerham type models are allele-based models with a focus on partition of genotypic variances into various genetic variance components, which are contributed by allelic effects and their interactions. By contrast, the F_∞ regression models are genotype-based models focusing on modeling and testing of within-locus genotypic effects and locus-by-locus genotypic interactions. When there is no need to distinguish the paternal and maternal allelic effects, these two types of models are transferable. Transformation between an F_∞ model's parameters and its corresponding Cockerham model's parameters can be established through a relationship between their coding variables of genotypes. Genetic variance components in terms of the additive, dominance and epistatic genetic effects in an F_∞ model can then be calculated by translating formulas derived for the Cockerham models.

     

Anecdotal,Historical and Critical Commentaries on Genetics: Wright and Fisher on Inbreeding and Random Drift

Sewall Wright and R. A. Fisher often differed, including on the meaning of inbreeding and random gene frequency drift. Fisher regarded them as quite distinct processes, whereas Wright thought that because his inbreeding coefficient measured both they should be regarded as the same. Since the effective population numbers for inbreeding and random drift are different, this would argue for the Fisher view.SEWALL Wright and R. A. Fisher were central figures in mathematical population genetics; along with J. B. S. Haldane they effectively invented the field and dominated it for many years. On most issues the three were in agreement. In particular, all favored a neo-Darwinian gradualist approach and believed in the importance of a mathematical theory for understanding the evolutionary process. Yet on a few questions Fisher and Wright differed profoundly and argued vehemently. Fisher was contentious and was often involved in controversy, frequently attacking his opponents mercilessly. Wright, in contrast, was very gentle to most people. But there were a few exceptions and Fisher was one. Haldane mostly stayed out of the arguments between them.One question on which the two disagreed was the importance of random gene frequency drift and its role in Wright''s shifting-balance theory of evolution. Wright thought that a structured population with many partially isolated subpopulations, within which there was random drift and among which there was an appropriate amount of migration, offered the greatest chance for evolutionary novelty and could greatly increase the speed of evolution. Fisher thought that a large panmictic population offered the best chance for advantageous genes and gene combinations to spread through the population, unimpeded by random processes. They also disagreed on dominance, Fisher believing that it evolved by selection of dominance modifiers and Wright that it was a consequence of the nature of gene action. These differences were widely argued by population geneticists in the middle third of the twentieth century, and the interested community divided into two camps. Although the issues are not settled, Wright''s shifting-balance theory has less support than it formerly had. As for dominance, there is general quantitative disagreement with Fisher''s explanation of modifiers, but other mechanisms (e.g., selection for more active alleles) have to some extent replaced it. Wright''s theory remains popular and has been generalized and extended (Kacser and Burns 1973).     

DYNAMICS OF SEXUAL SELECTION IN DIPLOID POPULATIONS

We describe results for a diploid, two-locus model for the evolution of a female mating preference directed at an attractive male trait that is subject to viability and/or fertility selection. Using computer simulation, we studied a large, random sample of parameter values, assuming additivity of alleles at the preference locus and partial dominance at the trait locus. Simulation results were classifiable into nine types of parameter sets, each differing in equilibria, evolutionary trajectories, and rates of evolution. For many parameters, evolutionary trajectories converged on curves within the allelic frequency plane and subsequently evolved along the curves toward fixation. Neutrally stable curves of equilibria did not occur in Fisherian models that assume only viability and sexual selection unless there is complete dominance at the trait locus. The Fisherian models also exhibited oscillation of allelic frequencies and unique polymorphic equilibria. “Sexy son” models in which attractive males had reduced fertility were much less likely to lead to increase in traits and preferences than were the Fisherian models. However, if less fertile males had increased viability, trait polymorphisms and fixation of rare “sexy” alleles occurred. In general, the behavior of the diploid model was much more complex than that of analogous haploid or polygenic models.