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.     

Evolution of hierarchical cytoplasmic inheritance in the plasmodial slime mold Physarum polycephalum

A striking linear dominance relationship for uniparental mitochondrial transmission is known between many mating types of plasmodial slime mold Physarum polycephalum. We herein examine how such hierarchical cytoplasmic inheritance evolves in isogamous organisms with many self-incompatible mating types. We assume that a nuclear locus determines the mating type of gametes and that another nuclear locus controls the digestion of mitochondria DNAs (mtDNAs) of the recipient gamete after fusion. We then examine the coupled genetic dynamics for the evolution of self-incompatible mating types and biased mitochondrial transmission between them. In Physarum, a multiallelic nuclear locus matA controls both the mating type of the gametes and the selective elimination of the mtDNA in the zygotes. We theoretically examine two potential mechanisms that might be responsible for the preferential digestion of mitochondria in the zygote. In the first model, the preferential digestion of mitochondria is assumed to be the outcome of differential expression levels of a suppressor gene carried by each gamete (suppression-power model). In the second model (site-specific nuclease model), the digestion of mtDNAs is assumed to be due to their cleavage by a site-specific nuclease that cuts the mtDNA at unmethylated recognition sites. Also assumed is that the mtDNAs are methylated at the same recognition site prior to the fusion, thereby being protected against the nuclease of the same gamete, and that the suppressor alleles convey information for the recognition sequences of nuclease and methylase. In both models, we found that a linear dominance hierarchy evolves as a consequence of the buildup of a strong linkage disequilibrium between the mating-type locus and the suppressor locus, though it fails to evolve if the recombination rate between the two loci is larger than a threshold. This threshold recombination rate depends on the number of mating types and the degree of fitness reduction in the heteroplasmic zygotes. If the recombination rate is above the threshold, suppressor alleles are equally distributed in each mating type at evolutionary equilibrium. Based on the theoretical results of the site-specific nuclease model, we propose that a nested subsequence structure in the recognition sequence should underlie the linear dominance hierarchy of mitochondrial transmission.     

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.     

The Evolution of the Y Chromosome with X-Y Recombination

A theoretical population genetic model is developed to explore the consequences of X-Y recombination in the evolution of sex chromosome polymorphism. The model incorporates one sex-determining locus and one locus subject to natural selection. Both loci have two alleles, and the rate of classical meiotic recombination between the loci is r. The alleles at the sex-determining locus specify whether the chromosome is X or Y, and the alleles at the selected locus are arbitrarily labeled A and a. Natural selection is modeled as a process of differential viabilities. The system can be expressed in terms of three recurrence equations, one for the frequency of A on the X-bearing gametes produced by females, one for each of the frequency of A on the X- and Y-bearing gametes produced by males. Several special cases are examined, including X chromosome dominance and symmetric selection. Unusual equilibria are found with the two sexes having very different allele frequencies at the selected locus. A significant finding is that the allowance of recombination results in a much greater opportunity for polymorphism of the Y chromosome. Tighter linkage results in a greater likelihood for equilibria with a large difference between the sex chromosomes in allele frequency.     

Effects of misspecifying genetic parameters in lod score analysis

The lod score method is widely used to test linkage and to estimate the recombination fraction between a disease locus and a marker locus. The parameters (gene frequency, penetrance, and degree of dominance) are assumed to be known at each locus. This condition may not be fulfilled at the disease locus. In this paper, we evaluate the errors due to the use of wrong parameters. The power of the linkage test is sensitive to the degree of dominance, and slightly to the penetrance, but not to the gene frequency. In contrast, the estimation of the recombination fraction may be strongly affected by an error on any genetic parameter.     

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.     

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.     

Genetic basis of stage-specific melanism: a putative role for a cysteine sulfinic acid decarboxylase in insect pigmentation

Melanism, the overall darkening of the body, is a widespread form of animal adaptation to particular environments, and includes bookcase examples of evolution by natural selection, such as industrial melanism in the peppered moth. The major components of the melanin biosynthesis pathway have been characterized in model insects, but little is known about the genetic basis of life-stage specific melanism such as cases described in some lepidopteran species. Here, we investigate two melanic mutations of Bicyclus anynana butterflies, called Chocolate and melanine, that exclusively affect pigmentation of the larval and adult stages, respectively. Our analysis of Mendelian segregation patterns reveals that the larval and adult melanic phenotypes are due to alleles at different, independently segregating loci. Our linkage mapping analysis excludes the pigmentation candidate gene black as the melanine locus, and implicates a gene encoding a putative pyridoxal phosphate-dependant cysteine sulfinic acid decarboxylase as the Chocolate locus. We show variation in coding sequence and in expression levels for this candidate larval melanism locus. This is the first study that suggests a biological function for this gene in insects. Our findings open up exciting opportunities to study the role of this locus in the evolution of adaptive variation in pigmentation, and the uncoupling of regulation of pigment biosynthesis across developmental stages with different ecologies and pressures on body coloration.     

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.     

The consequences of gene flow for local adaptation and differentiation: a two-locus two-deme model

We consider a population subdivided into two demes connected by migration in which selection acts in opposite direction. We explore the effects of recombination and migration on the maintenance of multilocus polymorphism, on local adaptation, and on differentiation by employing a deterministic model with genic selection on two linked diallelic loci (i.e., no dominance or epistasis). For the following cases, we characterize explicitly the possible equilibrium configurations: weak, strong, highly asymmetric, and super-symmetric migration, no or weak recombination, and independent or strongly recombining loci. For independent loci (linkage equilibrium) and for completely linked loci, we derive the possible bifurcation patterns as functions of the total migration rate, assuming all other parameters are fixed but arbitrary. For these and other cases, we determine analytically the maximum migration rate below which a stable fully polymorphic equilibrium exists. In this case, differentiation and local adaptation are maintained. Their degree is quantified by a new multilocus version of $F_\mathrm{ST}$ and by the migration load, respectively. In addition, we investigate the invasion conditions of locally beneficial mutants and show that linkage to a locus that is already in migration-selection balance facilitates invasion. Hence, loci of much smaller effect can invade than predicted by one-locus theory if linkage is sufficiently tight. We study how this minimum amount of linkage admitting invasion depends on the migration pattern. This suggests the emergence of clusters of locally beneficial mutations, which may form ‘genomic islands of divergence’. Finally, the influence of linkage and two-way migration on the effective migration rate at a linked neutral locus is explored. Numerical work complements our analytical results.     

Quantitative trait locus mapping with background control in genetic populations of clonal F1 and double cross

In this study, we considered five categories of molecular markers in clonal F₁ and double cross populations, based on the number of distinguishable alleles and the number of distinguishable genotypes at the marker locus. Using the completed linkage maps, incomplete and missing markers were imputed as fully informative markers in order to simplify the linkage mapping approaches of quantitative trait genes. Under the condition of fully informative markers, we demonstrated that dominance effect between the female and male parents in clonal F₁ and double cross populations can cause the interactions between markers. We then developed an inclusive linear model that includes marker variables and marker interactions so as to completely control additive effects of the female and male parents, as well as the dominance effect between the female and male parents. The linear model was finally used for background control in inclusive composite interval mapping (ICIM) of quantitative trait locus (QTL). The efficiency of ICIM was demonstrated by extensive simulations and by comparisons with simple interval mapping, multiple‐QTL models and composite interval mapping. Finally, ICIM was applied in one actual double cross population to identify QTL on days to silking in maize.     

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.     

Linkage Disequilibrium and Genetic Variances under Mutation-Selection Balance

I determine the contribution of linkage disequilibrium to genetic variances using results for two loci and for induced or marginal systems. The analysis allows epistasis and dominance, but assumes that mutation is weak relative to selection. The linkage disequilibrium component of genetic variance is shown to be unimportant for unlinked loci if the gametic mutation rate divided by the harmonic mean of the pairwise recombination rates is much less than one. For tightly linked loci, linkage disequilibrium is unimportant if the gametic mutation rate divided by the (induced) per locus selection is much less than one.     

A multilocus-multiallele analysis of frequency-dependent selection induced by intraspecific competition

The study of the mechanisms that maintain genetic variation has a long history in population genetics. We analyze a multilocus-multiallele model of frequency- and density-dependent selection in a large randomly mating population. The number of loci and the number of alleles per locus are arbitrary. The n loci are assumed to contribute additively to a quantitative character under stabilizing or directional selection as well as under frequency-dependent selection caused by intraspecific competition. We assume the strength of stabilizing selection to be weak, whereas the strength of frequency dependence may be arbitrary. Density-dependence is induced by population regulation. Our main result is a characterization of the equilibrium structure and its stability properties in terms of all parameters. It turns out that no equilibrium exists with more than two alleles segregating per locus. We give necessary and sufficient conditions on the strength of frequency dependence to ensure the maintenance of multilocus polymorphism. We also give explicit formulas on the number of polymorphic loci maintained at equilibrium. These results are based on the assumption that selection is sufficiently weak compared with recombination, so that linkage equilibrium can be assumed. If additionally the population size is assumed to be constant, we prove that the dynamics of the model form a generalized gradient system. For the model in its general form we are able to derive necessary and sufficient conditions for the stability of the monomorphic equilibria. Furthermore, we briefly analyze a special symmetric two-locus two-allele model for a constant population size but allowing for linkage disequilibrium. Finally, we analyze a single diallelic locus with dominance to illustrate the complications that can occur if the assumption of additivity is relaxed.     

Evolution of migration under kin selection and local adaptation

We present here a stochastic two-locus, two-habitat model for the evolution of migration with local adaptation and kin selection. One locus determines the migration rate while the other causes local adaptation. We show that the opposing forces of kin competition and local adaptation can lead to the existence of one or two convergence stable migration rates, notably depending on the recombination rate between the two loci. We show that linkage between migration and local adaptation loci has two antagonist effects: when linkage is tight, cost of local adaptation increases, leading to smaller equilibrium migration rates. However, when linkage is tighter, the population structure at the migration locus tends to be very high because of the indirect selection, and thus equilibrium migration rates increases. This result, qualitatively different from results obtained with other models of migration evolution, indicates that ignoring drift or the detail of the genetic architecture may lead to incorrect conclusions.     

Change in Genetic Variance under Selection in a Self-Fertilizing Population

In this study we show how the genetic variance of a quantitative trait changes in a self-fertilizing population under repeated cycles of truncation selection, with the analysis based on the infinitesimal model in which it is assumed that the trait is determined by an infinite number of unlinked loci without epistasis. The genetic variance is reduced not as a consequence of the genotypic frequency change but due to the build-up of linkage disequilibrium under truncation selection in this model. We assume that the order of the genotypic contribution from each locus is n(-1/2), where n is the number of loci involved, and investigate the change in linkage disequilibrium resulting from selection and self-fertilization using genotypic frequency dynamics in order to analyze the change in the genetic variance. Our analysis gives recurrence relations of genetic variance among the succeeding generations for the three cases of gene action, i.e., purely additive action, pure dominance without additive effect and the presence of both additive effect and dominance, respectively. Numerical examples are also given as a check on the recurrence formulas.     

The evolution of recombination in permanent translocation heterozygotes

The evolution of a selectively neutral locus that controls the degree to which alleles at a single selected locus are linked with a particular set of chromosomes in a permanent translocation heterozygote is studied. With complete selfing and fitness overdominance a new allele at the modifying locus will increase in frequency if it increases the linkage of all alleles at the selected locus to a particular set of chromosomes. With random mating a new allele at the modifying locus will increase when rare if it increases the linkage of alleles at the selected locus to a particular set of chromosomes. In addition, a parameter analogous to the coefficient of linkage disequilibrium in usual two-locus models with random mating must be nonzero if a new allele at the modifying locus is to increase in frequency at a geometric rate when rare. With mixed selfing and random mating a new allele at the modifying locus will apparently increase when rare only if it increases the linkage of alleles at the selected locus to a particular set of chromosomes.     

On the evolution of dominance modifiers II: a non-equilibrium approach to the evolution of genetic systems

The evolution of dominance is both the simplest and best investigated example of the evolution of genetic systems. Nevertheless, there exists striking empirical material, e.g. industrial melanism, for which no satisfactory explanation could so far be provided. In this paper we take an approach to this classical problem based on a global analysis together with computer simulations. It reveals that during the evolution of dominance one has to distinguish a "nonequilibrium phase" and a "Fisherian phase". The non-equilibrium phase appears to be characterized by the fact that in general the selection intensity at the primary locus does not affect the degree of modifier selection but only the time necessary for passing through this phase. A further essential conclusion is that modifier evolution only obtains a reasonable amount of efficiency if the population reaches the Fisherian phase already with a high modifier frequency. Using these results, predictions on the population genetic prerequisites for the evolution of dominance are derived. From these we conclude that even in populations in which dominance evolution has occurred it cannot be expected that back-crosses into relics of the ancestral population lead to a breakdown of dominance within a few generations. These predictions are in accordance with empirical data on Biston betularia and Odontopera bidentata.