Effects of Differential Selection in the Sexes on Cytonuclear Polymorphism and Disequilibria

We develop a series of models that examine the effects of differential selection between the sexes on cytonuclear polymorphism and disequilibria. A detailed analysis is provided for populations under constant fertility or viability selection censused at life stages without frequency differences in the sexes. We show analytically that cytonuclear disequilibria can be generated de novo if the cytoplasmic and nuclear loci each affect female fitness and there is a nonmultiplicative fitness interaction between them. While computer simulations demonstrate that the majority of disequilibria produced by random selection are transient and small in magnitude, measurable permanent disequilibria can result from selective differences both within and between the two sexes. We derive analytic conditions for a protected cytonuclear polymorphism and use numerical simulations to quantitate the likelihood of obtaining permanent nuclear, cytoplasmic, and cytonuclear variation under various patterns of selection. The numerical analysis identifies special selection regimes more likely to generate disequilibria and maintain cytonuclear polymorphism and reveals a direct correlation to the strength of selection. As a byproduct, our models also provide the first decomposition of the different parental contributions to cytonuclear dynamics and the analytic conditions under which selection can cause cytoplasmic frequency changes or a cytonuclear hitchhiking effect.     

The spatial structure of sexual and cytonuclear polymorphism in the gynodioecious Beta vulgaris ssp. maritima: I/ at a local scale

We have analyzed the spatial distribution of the sex phenotypes and of mitochondrial, chloroplast, and nuclear markers within two gynodioecious populations of Beta vulgaris ssp. maritima. Within both populations, sexual phenotype variation is controlled mainly by the cytoplasmic genotype, although in one study population a joint polymorphism of cytonuclear factors is clearly involved. In spite of contrasts in the ecology (mainly due to different habitats), a clear common feature in both populations is the highly patchy distribution of cytoplasmic haplotypes, contrasting with the wide distribution of nuclear diversity. This high contrast between cytoplasmic vs. nuclear spatial structure may have important consequences for the maintenance of gynodioecy. It provides opportunities for differential selection since nuclear restorer alleles are expected to be selected for in the presence of their specific cytoplasmic male sterile (CMS) type, but to be neutral (or selected against if there is a cost of restoration) in the absence of their CMS type. Selective processes in such a cytonuclear landscape may explain the polymorphism we observed at restorer loci for two CMS types.     

Intergenomic epistasis for fitness: within-population interactions between cytoplasmic and nuclear genes in Drosophila melanogaster

The symbiotic relationship between the mitochondrial and nuclear genomes coordinates metabolic energy production and is fundamental to life among eukaryotes. Consequently, there is potential for strong selection to shape interactions between these two genomes. Substantial research attention has focused on the possibility that within-population sequence polymorphism in mitochondrial DNA (mtDNA) is maintained by mitonuclear fitness interactions. Early theory predicted that selection will often eliminate mitochondrial polymorphisms. However, recent models demonstrate that intergenomic interactions can promote the maintenance of polymorphism, especially if the nuclear genes involved are linked to the X chromosome. Most empirical studies to date that have assessed cytonuclear fitness interactions have studied variation across populations and it is still unclear how general and strong such interactions are within populations. We experimentally tested for cytonuclear interactions within a laboratory population of Drosophila melanogaster using 25 randomly sampled cytoplasmic genomes, expressed in three different haploid nuclear genetic backgrounds, while eliminating confounding effects of intracellular bacteria (e.g., Wolbachia). We found sizable cytonuclear fitness interactions within this population and present limited evidence suggesting that these effects were sex specific. Moreover, the relative fitness of cytonuclear genotypes was environment specific. Sequencing of mtDNA (2752 bp) revealed polymorphism within the population, suggesting that the observed cytoplasmic genetic effects may be mitochondrial in origin.     

Sexually antagonistic cytonuclear fitness interactions in Drosophila melanogaster

Theoretical and empirical studies have shown that selection cannot maintain a joint nuclear-cytoplasmic polymorphism within a population except under restrictive conditions of frequency-dependent or sex-specific selection. These conclusions are based on fitness interactions between a diploid autosomal locus and a haploid cytoplasmic locus. We develop a model of joint transmission of X chromosomes and cytoplasms and through simulation show that nuclear-cytoplasmic polymorphisms can be maintained by selection on X-cytoplasm interactions. We test aspects of the model with a "diallel" experiment analyzing fitness interactions between pairwise combinations of X chromosomes and cytoplasms from wild strains of Drosophila melanogaster. Contrary to earlier autosomal studies, significant fitness interactions between X chromosomes and cytoplasms are detected among strains from within populations. The experiment further demonstrates significant sex-by-genotype interactions for mtDNA haplotype, cytoplasms, and X chromosomes. These interactions are sexually antagonistic--i.e., the "good" cytoplasms in females are "bad" in males--analogous to crossing reaction norms. The presence or absence of Wolbachia did not alter the significance of the fitness effects involving X chromosomes and cytoplasms but tended to reduce the significance of mtDNA fitness effects. The negative fitness correlations between the sexes demonstrated in our empirical study are consistent with the conditions that maintain cytoplasmic polymorphism in simulations. Our results suggest that fitness interactions with the sex chromosomes may account for some proportion of cytoplasmic variation in natural populations. Sexually antagonistic selection or reciprocally matched fitness effects of nuclear-cytoplasmic genotypes may be important components of cytonuclear fitness variation and have implications for mitochondrial disease phenotypes that differ between the sexes.     

Paternal leakage sustains the cytoplasmic polymorphism underlying gynodioecy but remains invasible by nuclear restorers

Cytoplasmic male sterility (CMS) in plants often results in gynodioecious populations, composed of hermaphrodites and male-sterile females. All models of gynodioecy assume maternal inheritance of the cytoplasmic alleles and postulate a variety of negatively frequency-dependent mechanisms to maintain the cytoplasmic polymorphisms observed in many natural populations. However, in some plant species, mitochondria are transmitted at least occasionally by pollen, a process called paternal leakage. We show that even a small amount of paternal leakage is sufficient to sustain a permanent, stable cytoplasmic polymorphism. Because only hermaphrodites provide pollen in gynodioecious species, the effects of paternal leakage are biased and occur more often from the non-CMS male-fertile haplotype to the CMS male-sterile haplotype. We also show that a nuclear restorer disrupts the polymorphic cytoplasmic equilibrium, leading to fixation of both the CMS allele and the restorer. Although a dominant nuclear restorer fixes, it fixes much more slowly than in the standard CMS models. Although a stable cytonuclear polymorphism is possible with "matching alleles" nuclear restoration, oscillations to low frequencies present a risk of loss by drift. Paternal leakage enhances the stability of joint cytonuclear polymorphism by reducing the chance that a CMS allele is lost by drift.     

Cytonuclear disequilibria in a spatially structured hybrid zone

A hybrid zone model was developed that uses a stepping-stone model of population structure along with both nuclear and cytoplasmic genotypes to evaluate the effect that migration has on random mating organisms when no selection is present. Numerical simulations indicate that a number of different allele frequency and cytonuclear disequilibrium patterns can be found across the hybrid zone when it has reached equilibrium, and these results are discussed in the context of relative migration rates of the two sexes and the two source populations. The importance of numbers of subpopulations sampled, census time, and the persistence of pure species individuals into the hybrid zone are also discussed. Although this model does not consider selection or assortative mating in the hybrid zone, it should provide a useful baseline for evaluating joint cytonuclear genetic data from a structurally complex hybrid zone.     

Associations between cytoplasmic and nuclear Loci in hybridizing populations

We extend current multilocus models to describe the effects of migration, recombination, selection, and nonrandom mating on sets of genes in diploids with varied modes of inheritance, allowing us to consider the patterns of nuclear and cytonuclear associations (disequilibria) under various models of migration. We show the relationship between the multilocus notation recently presented by Kirkpatrick, Johnson, and Barton (developed from previous work by Barton and Turelli) and the cytonuclear parameterization of Asmussen, Arnold, and Avise and extend this notation to describe associations between cytoplasmic elements and multiple nuclear genes. Under models with sexual symmetry, both nuclear-nuclear and cytonuclear disequilibria are equivalent. They differ, however, in cases involving some type of sexual asymmetry, which is then reflected in the asymmetric inheritance of cytoplasmic markers. An example given is the case of different migration rates in males and females; simulations using 2, 3, 4, or 5 unlinked autosomal markers with a maternally inherited cytoplasmic marker illustrate how nuclear-nuclear and cytonuclear associations can be used to separately estimate female and male migration rates. The general framework developed here allows us to investigate conditions where associations between loci with different modes of inheritance are not equivalent and to use this nonequivalence to test for deviations from simple models of admixture.     

Cytonuclear genetic signatures of hybridization phenomena: Rationale,utility, and empirical examples from fishes and other aquatic animals

By definition, organisms of hybrid ancestry carry amalgamations of divergent genomes. Thus, exaggerated effects of genomic interactions might be anticipated in hybrid populations, thereby magnifying the impact of natural selection and making this and other evolutionary forces easier to document. Mating biases and other gender-based asymmetries also frequently characterize hybrid populations. Thus, maternally inherited cytoplasmic polymorphisms assayed jointly with those at biparentally inherited nuclear loci provide powerful genetic markers to dissect ethological, ecological, and evolutionary processes in hybrid settings. Population-level topics that can be addressed using cytonuclear markers include the frequency of hybridization and introgression in nature, behavioral and ecological factors (such as mating preferences and hybrid fitnesses) influencing the genetic architectures of hybrid zones, the degree of consistency in genetic outcomes across multiple hybrid contact regions, and environmental impacts (including the introduction of alien species) on hybridization processes. Several empirical studies on fish populations in hybrid settings illustrate the application of cytonuclear appraisals in such contexts.     

Cytonuclear Theory for Haplodiploid Species and X-Linked Genes. I. Hardy-Weinberg Dynamics and Continent-Island, Hybrid Zone Models

We develop models that describe the cytonuclear structure for either a cytoplasmic and nuclear marker in a haplodiploid species or a cytoplasmic and X-linked marker in a diploid species. Sex-specific disequilibrium statistics that summarize nonrandom cytonuclear associations in such systems are defined, and their basic Hardy-Weinberg dynamics and admixture formulae are delimited. We focus on the context of hybrid zones and develop continent-island models whereby individuals from two genetically differentiated source populations migrate into and mate within a single zone of admixture. We examine the effects of differential migration of the sexes, assortative mating by pure type females, and census time (relative to mating and migration), as well as special cases of random mating and migration subsumed under the general models. We show that pure type individuals and nonzero cytonuclear disequilibria can be maintained within a hybrid zone if there is continued migration from both source populations, and that females generally have a greater influence over these cytonuclear variables than males. The resulting theoretical framework can be used to estimate the rates of assortative mating and sex-specific gene flow in hybrid zones and other zones of admixture involving haplodiploid or sex-linked cytonuclear data.     

Seed and pollen flow and cline discordance among genes with different modes of inheritance

The relationships between seed and pollen flow and cline discordance/concordance between cytoplasmic and nuclear genes, with the incorporation of the effects of natural selection, are formulated for one locus with two alleles, under assumptions of random mating, no drift and no mutation. Results show that under certain conditions, the relative roles of seed and pollen flow in shaping cline discordance/ concordance are very similar to their roles in influencing population differentiation for selectively neutral markers with different modes of inheritance. Where the disequilibria between cytoplasmic and nuclear genes are of the order similar to selection coefficient, cline discordance/concordance can be predicted from the relative values of the ratio of pollen to seed flow and the ratio of selection coefficients. Where the disequilibria attained by seed and pollen flow are significant, the integrated cytonuclear data are recommended for cline analysis. In both cases, the relative rates of selection coefficients between cytoplasmic and nuclear genes can be roughly estimated according to their characteristic length.     

Cytonuclear models of epistatic mating with backcrossing and selection

We develop hybrid zone models that explore the combined effects of mating system and either backcrossing or viability selection on the disequilibria between nuclear and cytoplasmic genes. In the epistatic mating plus backcrossing model, we find patterns of permanent cytonuclear disequilibria like those found when epistatic mating is the only factor, as well as a novel combination of significant cytonuclear disequilibria sign patterns. The second group of models evaluates the potential of epistatic mating and postzygotic viability selection to maintain cytonuclear disequilibria. Simulations are used to evaluate nine patterns of selection, each of which represent differing forms of selection against hybrids, and show that while all disequilibria usually decay to zero, under certain circumstances a number of different patterns of significant cytonuclear disequilibria are possible at equilibrium. The results from these models are compared to the observed cytonuclear disequilibria previously found in a hybrid population of Hyla treefrogs.     

The effects of unidirectional incompatibility on cytonuclear disequilibria in a hybrid zone

Unidirectional incompatibility selection is examined as an alternate mechanism of natural selection to cytoplasmic male sterility (CMS) for generating cytonuclear disequilibria. Differences in the dynamics and equilibrium behavior of cytonuclear disequilibria between these two cytonuclear selection models may allow for statistical tests of CMS vs. unidirectional incompatibility between mating cytotypes. Unlike CMS without migration, unidirectional incompatibility causes the cytoplasmic allele frequency to change over time rather than remain constant, and the nuclear allele frequencies hitchhike on the cytoplasmic frequencies. The decay of disequilibria is also distinctive in the absence of migration. Furthermore, in comparing both models with migration it is seen that the opportunity for internal equilibrium can be two or three times higher in a unidirectional incompatibility vs. CMS model. An example is presented that shows how unidirectional incompatibility can be statistically eliminated as a possible mechanism of cytonuclear selection. This revised version was published online in July 2006 with corrections to the Cover Date.     

Comparative Effects of Pollen and Seed Migration on the Cytonuclear Structure of Plant Populations. II. Paternal Cytoplasmic Inheritance

We continue our study of the effects of pollen and seed migration on the cytonuclear structure of mixed-mating plant populations by analyzing two deterministic continent-island models under the critical assumption of paternal cytoplasmic inheritance. The major results of this study that contrast with our previous conclusions based on maternal cytoplasmic inheritance are (i) pollen gene flow can significantly affect the cytonuclear structure of the island population, and in particular can help to generate cytonuclear disequilibria that greatly exceed the magnitude of those that would be produced by seed migration or mixed mating alone; (ii) with simultaneous pollen and seed migration, nonzero cytonuclear disequilibria will be maintained not only when there is disequilibrium in the immigrant pollen or seeds, but also through a variety of intermigrant admixture effects when the two pools of immigrants differ appropriately in their cytonuclear compositions; (iii) either immigrant pollen or immigrant seeds can generate disequilibria de novo in populations with initially random cytonuclear associations, but pollen migration alone generally produces lower levels of disequilibrium than does comparable seed migration, especially at high levels of self-fertilization when the overall fraction of immigrant pollen is low; (iv) the equilibrium state of the island population will be influenced by the rate of pollen gene flow whenever there is either allelic disequilibrium in the immigrant pollen or simultaneous seed migration coupled with different cytoplasmic or nuclear allele frequencies in immigrant pollen and seeds or nonzero allelic disequilibrium in either immigrant pool. The estimation of pollen migration should therefore be facilitated with paternal cytoplasmic inheritance relative to the case of maternal cytoplasmic inheritance. These basic conclusions hold whether the population is censused as seeds or as adults, but with simultaneous pollen and seed migration, the relationship between census time and the ability to detect nonrandom cytonuclear associations is complex. When migration is through pollen alone, however, the cytonuclear structure of the island population is independent of the life stage censused.     

The effects of admixture and population subdivision on cytonuclear disequilibria

We examine the generation of cytonuclear disequilibria by admixture and continued gene flow. General formulas analogous to the nuclear case are first derived showing that the allelic and genotypic disequilibria from admixture or population subdivision equal their expected value across the contributing (sub) populations plus the covariance across these sources between the cytoplasmic gene frequency and the relevant nuclear frequency. A detailed study is then presented of the cytonuclear dynamics, in a random-mating population under two different migration scenarios. In both cases closed-form solutions are given for all variables as a function of the initial conditions and relevant migration parameters. The dynamics of the gene frequencies and allelic disequilibria, which dominate each system, are the same as those involving two unlinked nuclear loci, while the dynamics of the genotypic disequilibria and cytonuclear frequencies have no nuclear counterpart. The continent-island formulation focuses on a population receiving continued immigration from a large source of constant composition. A major discovery is that cytonuclear disequilibria can transiently build up on the "island" to levels far exceeding those found at equilibrium. In contrast, the admixture formulation focuses on the dynamics within two populations undergoing continued intermigration. Although in this case all cytonuclear associations must ultimately decay to zero, long-term transient disequilibria can develop which are many times their initial admixture values. For both migration scenarios it is shown that the time of population censusing relative to migration and reproduction dramatically affects both the amount and pattern of the nonrandom associations produced. The empirical relevance of these models is discussed in light of nuclear-mitochondrial data from a hybrid zone between European and North American eels and from a zone of racial admixture in humans.     

CYTONUCLEAR INTERACTIONS CAN FAVOR THE EVOLUTION OF GENOMIC IMPRINTING

Interactions between cytoplasmic (generally organelle) and nuclear genomes may be relatively common and could potentially have major fitness consequences. As in the case of within-genome epistasis, this cytonuclear epistasis can favor the evolutionary coadaptation of high-fitness combinations of nuclear and cytoplasmic alleles. Because cytoplasmic factors are generally uniparentally inherited, the cytoplasmic genome is inherited along with only one of the nuclear haplotypes, and therefore, coadaptation is expected to evolve through the interaction of these coinherited (usually maternally inherited) genomes. Here I show that, as a result of this coinheritance of the two genomes, cytonuclear epistasis can favor the evolution of genomic imprinting such that, when the cytoplasmic factor is maternally inherited, selection favors maternal expression of the nuclear locus and when the factor is paternally inherited selection favors paternal expression. Genomic imprinting evolves in this model because it leads to a pattern of gene expression in the nuclear haplotype that is coadapted with (i.e., adaptively coordinated with) gene expression in the coinherited cytoplasmic genome.     

The cytonuclear effects of facultative apomixis. II. Definitions and dynamics of disequilibria in tetraploid populations

We develop a cytonuclear framework for tetraploid populations in which a diallelic nuclear marker exhibits tetrasomic inheritance. This system requires two separate parameterizations, with six cytonuclear disequilibria (nonrandom associations) in tetraploid individuals and four in their diploid gametes. Double reduction during meiosis adds further complexity by causing gametic output to vary with the distance of the nuclear locus from the centromere. We derive and analyze dynamical solutions for the disequilibria under generalized mixed mating, with any combination of apomixis, selfing, and outcrossing, with and without double reduction. As in comparable diploid systems, all disequilibria ultimately decay to zero, unless nuclear and cytoplasmic alleles are nonrandomly associated and outcrossing is absent, in which case permanent associations result. Selfing and apomixis retard the decay of disequilibria (or approach to equilibrium), and often to the same extent. In contrast, double reduction can accelerate the loss of tetraploid cytonuclear associations, but only negligibly in hybrid zones, and this loss is never faster than in diploids. Only in the absence of allelic associations or outcrossing is the asymptotic approach to equilibrium differentially affected by apomixis and selfing or slower under tetrasomic than disomic inheritance. To facilitate empirical applications, we also examine tetraploid hybrid zone dynamics and offer practical guidelines for experimental design and data analysis, showing how the consequences of the mating system alone provide a valuable baseline for drawing evolutionary inferences from the observed patterns of cytonuclear associations.     

DO RECENT FINDINGS IN PLANT MITOCHONDRIAL MOLECULAR AND POPULATION GENETICS HAVE IMPLICATIONS FOR THE STUDY OF GYNODIOECY AND CYTONUCLEAR CONFLICT?

The coexistence of females and hermaphrodites in plant populations, or gynodioecy, is a puzzle recognized by Darwin. Correns identified cytoplasmic inheritance of one component of sex expression, now known as cytoplasmic male sterility (CMS). Lewis established cytonuclear inheritance of gynodioecy as an example of genetic conflict. Although biologists have since developed an understanding of the mechanisms allowing the joint maintenance of CMS and nuclear male fertility restorer genes, puzzles remain concerning the inheritance of sex expression and mechanisms governing the origination of CMS. Much of the theory of gynodioecy rests on the assumption of maternal inheritance of the mitochondrial genome. Here we review recent studies of the genetics of plant mitochondria, and their implications for the evolution and transmission of CMS. New studies of intragenomic recombination provide a plausible origin for the chimeric ORFs that characterize CMS. Moreover, evidence suggests that nonmaternal inheritance of mitochondria may be more common than once believed. These findings may have consequences for the maintenance of cytonuclear polymorphism, mitochondrial recombination, generation of gynomonoecious phenotypes, and interpretation of experimental crosses. Finally we point out that CMS can alter the nature of the cytonuclear conflict that may have originally selected for uniparental inheritance.     

POPULATION CAGE EXPERIMENTS WITH A VERTEBRATE: THE TEMPORAL DEMOGRAPHY AND CYTONUCLEAR GENETICS OF HYBRIDIZATION IN GAMBUSIA FISHES

The dynamics of mitochondrial and multilocus nuclear genotypic frequencies were monitored for 2 yr in experimental populations established with equal numbers of two poeciliid fishes (Gambusia affinis and Gambusia holbrooki) that hybridize naturally in the southeastern United States. In replicated “small-pool” populations (experiment I), 1018 sampled individuals at six time periods revealed an initial flush of hybridization, followed by a rapid decline in frequencies of G. affinis nuclear and mitochondrial alleles over 64 wk. Decay of gametic and cytonuclear disequilibria differed from expectations under random mating as well as under a model of assortative mating involving empirically estimated mating propensities. In two replicate “large-pond” populations (experiment II), 841 sampled individuals across four reproductive cohorts revealed lower initial frequencies of F₁ hybrids than in experiment I, but again G. holbrooki alleles achieved high frequencies over four generations (72 wk). Thus, evolution within experimental Gambusia hybrid populations can be extremely rapid, resulting in consistent loss of G. affinis nuclear and cytoplasmic alleles. Concordance in results between experiments and across genetic markers suggests strong directional selection favoring G. holbrooki genotypes. Results are interpreted in light of previous reports of genotype-specific differences in life-history traits, reproductive ecology, patterns of recruitment, and size-specific mortality, and in the context of patterns of introgression previously studied indirectly from spatial observations on cytonuclear genotypes in natural Gambusia populations.     

The cytonuclear effects of facultative apomixis. I. Disequilibrium dynamics in diploid populations

We comprehensively analyze the cytonuclear effects of generalized mixed mating, including all combinations of selfing, outcrossing, and apomixis, the asexual production of seeds. After first deriving the time-dependent solutions for nonrandom associations (disequilibria) between a diallelic cytoplasmic marker and the alleles and genotypes at a diploid nuclear locus, we delimit all possible dynamical behaviors and the conditions under which each occurs. As in standard mixed mating systems, all disequilibria ultimately decay to zero except when outcrossing is absent, in which case permanent disequilibria result if the allelic association is initially nonzero. When at least some outcrossing is present, any initial allelic association decays at a constant geometric rate, whereas genotypic disequilibria may first increase in magnitude or change sign. Although selfing and apomixis tend to retard the decay of disequilibria (or approach to equilibrium) and often to the same extent, apomixis can have a stronger effect under some conditions. We also determine the dynamics of cytonuclear disequilibria in specific examples that may be of particular interest for empirical studies of hybrid zones. The results suggest several practical guidelines for experimental design and data analysis and show how the cytonuclear disequilibrium dynamics under mating system alone furnish a quantitative baseline for null hypotheses against which to test for the presence of other evolutionary forces.     

Sampling Theory for Cytonuclear Disequilibria

We examine the statistical properties of cytonuclear disequilibria within a system including one diploid nuclear locus and one haploid cytoplasmic locus, each with two alleles. The results provide practical guidelines for the design and interpretation of cytonuclear surveys seeking to utilize the novel evolutionary information recorded in the observed pattern of cytonuclear associations. Important applications include population studies of nuclear allozymes in conjunction with genes from mitochondria, chloroplasts, or cytoplasmically inherited microorganisms. Our attention focuses on the allelic and genotypic disequilibria, which respectively measure the nonrandom associations between the cytotypes and the nuclear alleles and genotypes. We first derive the maximum likelihood estimators and their approximate large sample variances for each disequilibrium measure. These are each in turn used to set up an asymptotic test of the null hypothesis of no disequilibrium. We then calculate the minimum sample sizes required to detect the disequilibria under specified alternate hypotheses. The work also incorporates the deviation from Hardy-Weinberg equilibrium at the nuclear locus, which can significantly affect the results. The practical utility of this new sampling theory is illustrated through applications to two nuclear-mitochondrial data sets.