Selection with Gene-Cytoplasm Interactions. II. Maintenance of Gynodioecy

Gynodioecy is apparently frequently inherited through gene-cytoplasm interactions. General conditions for the protectedness of gene-cytoplasm polymorphisms for a biallelic model with two cytoplasm types were obtained previously, and these are applied to seven special cases of gene-cytoplasm interactions controlling gynodioecy and involving dominance. It is assumed that nuclear polymorphisms cannot be maintained in one cytoplasm type only. It is held that pure cytoplasmic inheritance of gynodioecy without nuclear interactions is unlikely, and it is shown that gynodioecy with gene-cytoplasm interactions is easier to establish than purely nuclear gynodioecy, for monogenic biallelic dominant or recessive inheritance. For three special cases, a resource-allocation model with simple assumptions always leads to conditions for protectedness of gynodioecy.     

Polymorphisms for purely cytoplasmically inherited traits in bisexual plants

It is shown that cytoplasm polymorphisms transmitted only by the ovules can be maintained without gene-cytoplasmic interactions. The necessary prerequisites are asymmetry of the plasmotypes in production of ovules and pollen (sexual asymmetry), incomplete and frequency-dependent fertilization efficiency and differential selfing rates. These factors can generate the negative frequency dependence of cytoplasmic fitnesses required for a stable polymorphism. The model considered allows also for facultative fixation of either of two plasmotypes and, thus, may produce all of the dynamical characteristics known for nuclear selection with two alleles at one locus.

Strong sexual asymmetry, which probably occurs frequently in bisexual plants, may facilitate stable cytoplasmic polymorphisms. However, these polymorphisms may also endanger survival of the whole population in the absence of nuclear interactions. Gene-cytoplasmic interactions avoid this risk and, at the same time, utilize the advantages of sexual asymmetry in maintaining genetic polymorphisms.

     

Approaches to the Hardy-Weinberg manifold

Let fertilities and death rates be additive, let fertilities be positive, and let mating be random in the Nagylaki-Crow continuous model of selection at a multiallelic locus in a monoecious population. Then polymorphisms are in Hardy-Weinberg proportions. If some fertilities vanish, there is an example of a diallelic polymorphism that is not in Hardy-Weinberg proportions. If the fertilities are larger, in one sense or another, than the difference between any two death rates, then convergence to the Hardy-Weinberg manifold is shown. If, in addition, the Malthusian parameters are constant, and only a finite number of equilibria exist, then global convergence to equilibria is proved.     

Selection with two alleles and complete dominance

For a plant selection model with frequency-independent viabilities, fertilities and selfing rates, it is shown that apart from global fixation, for certain parameter combinations a protected polymorphism and facultative fixation (either allele may become fixed according to initial frequencies) may both occur. Facultative fixation requires different selling rates for the dominant and recessive type. Protection of the polymorphism requires resource allocation for male and female function. In this connection the problem of purely genetically caused population extinction is discussed.
For general frequency dependence and regular segregation, the chances for establishment of a completely recessive gene are compared to those of a completely dominant gene. It is proven that the process of establishment of the recessive gene, despite a fitness advantage, may be considerably endangered by drift effects if random mating prevails. The recessive gene may reach the same effectivity in establishment as a dominant gene, only if the recessive homozygote mates exclusively with its own type during the period of establishment.     

The maintenance of nucleocytoplasmic polymorphism in a metapopulation: the case of gynodioecy

In gynodioecious species, gender is generally determined by epistatic interactions between cytoplasmic and nuclear loci. However, theoretical studies suggest that, for a joint polymorphism at both cytoplasmic and nuclear loci to be maintained in a panmictic population, selection must act differently on the various genotypes that determine the same gender. Here we show that, in a metapopulation with local extinction and restricted gene flow, nucleocytoplasmic polymorphism can be maintained without these differences. We use deterministic simulations. We assume that gene flow occurred only at recolonization. Founder effects create genetic variance between populations in the metapopulation, and local population growth is faster when the local frequency of females is high. Group selection phenomena are involved in the maintenance of the joint polymorphism in the metapopulation. The frequency of females in the metapopulation at equilibrium is higher than in a panmictic population with the same genetic system. However, these conclusions hold only if nuclear alleles restoring male fertility are dominant.     

Maintenance of a female-limited polymorphism in Ischnura ramburi (Zygoptera: Coenagrionidae)

Colour polymorphisms can be maintained in a population if all morphs have equal fitness on average, if fitness is frequency dependent or if fitness functions cross for some environmental or social variable. We studied female-limited colour polymorphism in the Rambur's forktail damselfly, Ischnura ramburi, in which one female morph looks like the male. The most commonly cited hypotheses to explain this polymorphism involve an advantage to andromorphs of avoiding costly matings through male mimicry. An alternative hypothesis argues that males learn the most common morph and that the polymorphism is maintained by a rare-morph advantage of mating avoidance, irrespective of male mimicry. We tested predictions of the male mimicry hypothesis, learned mate recognition hypothesis (LMR) and two new hypotheses. We used censuses and a mark-resight study to estimate density, sex ratio, morph frequency and mating frequencies. We observed interactions to test for male mimicry and female competition and to evaluate the frequency of mating attempts. Andromorphs were less likely than gynomorphs to receive mating attempts in encounters with males, but did not mate less frequently, or attack males or interrupt oviposition by other females more frequently. Contrary to the LMR hypothesis, the rarer morph was more likely to receive mating attempts. Andromorph frequency was greater in older females than in younger females, suggesting higher mortality or dispersal of gynomorphs. Our results support a modification of the male mimicry hypothesis, the signal detection hypothesis. Together with past studies, our results suggest that the female morphs may be alternative mating avoidance strategies.     

Microhabitat variation and sexual selection can maintain male color polymorphisms

Male color polymorphism may be an important precursor to sympatric speciation by sexual selection, but the processes maintaining such polymorphisms are not well understood. Here, we develop a formal model of the hypothesis that male color polymorphisms may be maintained by variation in the sensory environment resulting in microhabitat-specific selection pressures. We analyze the evolution of two male color morphs when color perception (by females and predators) is dependent on the microhabitat in which natural and sexual selection occur. We find that an environment of heterogeneous microhabitats can lead to the maintenance of color polymorphism despite asymmetries in the strengths of natural and sexual selection and in microhabitat proportions. We show that sexual selection alone is sufficient for polymorphism maintenance over a wide range of parameter space, even when female preferences are weak. Polymorphisms can also be maintained by natural selection acting alone, but the conditions for polymorphism maintenance by natural selection will usually be unrealistic for the case of microhabitat variation. Microhabitat variation and sexual selection for conspicuous males may thus provide a situation particularly favorable to the maintenance of male color polymorphisms. These results are important both because of the general insight they provide into a little appreciated mechanism for the maintenance of variation in natural populations and because such variation is an important prerequisite for sympatric speciation.     

Selection in plant populations of effectively infinite size II. Protectedness of a biallelic polymorphism

The biologically important problem of protectedness of genetic polymorphisms in monoecious plant populations exhibiting genotypically determined variation in rates of self-fertilization and sexually asymmetrical fertilities has hitherto escaped exact, analytical treatment for the reason that appropriate mathematical techniques relying on allelic frequencies do not seem to exist. For the particular case of one locus and two alleles it was possible to develop such a technique which provides conditions of high precision for protectedness of an allele. A comparison of the results with those already known from models that appear to be specializations of the present model showed that some of the earlier conclusions can be generalized, while others have to be handled with great care or should even be rejected. Above all, this concerns the role of self-fertilization, which is frequently considered to counteract the establishment of genetic polymorphisms. However, it turned out that increasing the heterozygote selfing rate also increases protectedness for both alleles in all situations. Moreover, even if the amount of self-fertilization is the same for all genotypes, asymmetry in the production of ovules and pollen, which is more the rule than an exception, may imply protectedness only for comparatively large selfing rates. The probably most outstanding finding is that, depending on the ovule and pollen fertilities, protectedness may be realized only within small ranges of selfing rates, and these ranges may vary from arbitrarily low to arbitrarily high rates. On the other hand, if the ovule fertilities show strong overdominance for the heterozygote—more precisely, if the heterozygote produces more than twice as many ovules as either of the homozygotes—both alleles are protected irrespective of the pollen fertilities and rates of self-fertilization; this generalizes earlier results obtained for more specific models.     

Selection in plant populations of effectively infinite size: IV. The maintenance of males among hermaphrodites for a biallelic model

Conditions for the maintenance of males in androdioecious populations (populations with both male and hermaphrodite individuals) have been derived for four different one-locus two-allele models of inheritance of androdioecy. The results are not in general accordance with those already known: depending on the mode of inheritance, males can be maintained irrespective of their fertilities. If males are sufficiently fertile, it may happen that they are maintained only for intermediate selfing rates of the hermaphrodites. A result already found for gynodioecy is confirmed for androdioecy, namely, that a 11 sex ratio is immediately established among zygotes if hermaphrodites appear as heterozygotes only.     

Nonrandom mating preserves intrasexual polymorphism and stops population differentiation in sexual conflict

Evolutionary conflict between the sexes is predicted to lead to sexual arms races in which male adaptations for acquiring mates ("offense" traits) are met by female counteradaptations--for example, to reduce mating rate ("defense" traits). Such coevolutionary chases may be perpetual. However, we show here that the coevolutionary process may also lead to a stable state in which multiple offense-defense trait pairs are maintained. This type of polymorphism below the species level is a result of sexual conflict in combination with nonrandom mating. Our results show that if nonrandom mating occurs with respect to male and female conflict traits, genetic correlations will act to stabilize the trait frequencies so that all morphs are maintained. We discuss the results in special relation to the evolution of female polymorphism in diving beetles and argue that the process we describe may be a general force that maintains polymorphism in other taxa as well.     

Establishment of allelic two-locus polymorphisms

An exact analysis of necessary and sufficient conditions for the establishment and protectedness of biallelic two-locus polymorphisms is developed for the classical model with constant, sexually symmetric fitnesses and random association of the successful gametes. To demonstrate application of the results to common model types, the model of symmetric viabilities depending on the degree of heterozygosity only is chosen as a paradigm. It is pointed out that a unique locally stable internal equilibrium may exist even though all marginal equilibria (including the fixation states) are locally attractive. This example is quoted as an indication of the priority that analyses of protectedness deserve over analyses of local stability or instability of internal equilibria. Further applications of broader appeal concern the role that recombination plays in protecting polymorphisms. Probably the most interesting finding is that with increasing recombination frequency the chances for protectedness of a polymorphism generally decline. Yet, if a certain hierarchic ordering of the fitnesses with respect to the degree of heterozygosity is realized, the polymorphism is protected for arbitrary amounts of recombination. If recombination is rare, heterozygote advantage is not a universal precondition for persistence of polymorphisms. This phenomenon is utilized to derive conditions under which deleterious recessive mutants can be maintained in a population.     

Mathematical Study of the Evolution of Gynodioecy with Cytoplasmic Inheritance under the Effect of a Nuclear Restorer Gene

A study is described of the influence of the introduction of a dominant nuclear restorer gene into a cytoplasmic gynodioecious plant population. This study includes the consideration of separate effects on the relative female fertility of nuclear, cytoplasmic and sex (phenotypic) factors. Under these assumptions, the introduction of a dominant nuclear restorer gene into a cytoplasmic gynodioecious population can lead to several different situations: persistence of cytoplasmic gynodioecy, appearance of a nuclear-cytoplasmic gynodioecy, appearance of a nuclear gynodioecy or complete restoration of male fertility. The development of stable nuclear-cytoplasmic gynodioecy in a mathematical model is new and is possible because of the consideration of the separate relative female fertilities. The possibility of a transformation of cytoplasmic gynodioecy into a nuclear one has never been obtained before. It could constitute a route for the appearance of this latter kind of gynodioecy in plant populations. Finally, the possibilities of evolution of gynodioecy from one kind to the other, and towards dioecy, are discussed, as are some theoretical schemes that seem to correspond to observed actual situations.     

Theoretical aspects of sexual selection: A generalized model of mating behaviour

A model of mate selection is described in which females mate preferentially according to their probability of encounter with the males they prefer. In this model, different thresholds of response to the courtship of different male phenotypes determine the female mating preferences. Females with a lower threshold toward particular males require fewer encounters before mating with these males and more encounters before mating with any of the others. Such females mate preferentially if they encounter a male they prefer before they have been stimulated to the level of the higher threshold. At the higher threshold they mate at random. The number of the extra encounters required to raise the females' level of stimulation from the lower to the higher threshold is a parameter of the model. The frequency of the preferred males then determines the probability that a female encounters and mates with one of them before she has been sufficiently stimulated to mate at random. Sexual selection by differences in male courtship can also be described in terms of this model.The preferred characters may be determined either by dominant and recessive alleles or by each different genotype. When only one extra encounter is required before the females mate at random, the preferred males only gain a slight frequency-dependent advantage: Stable polymorphisms can only be maintained if the heterozygotes have the greater preference in their favor. When more than one extra encounter is required before random mating, the males gain a negative frequency-dependent advantage: Stable polymorphisms are generally maintained.The models are fitted to published data on the mating success of male Drosophila at varying frequencies and provide an explanation of the “rare male” effect in which less common males gain a mating advantage.     

The cost of sex in hermaphrodite populations with variation in functional sex

In this paper an analysis is made of a model of selection for asexual reproduction in hermaphrodite (or monoecious) populations in which variation occurs in relative female and male fertilities. It is shown that the advantage of an asexual mutant (the cost of sex) increases with increasing degree of differentiation in functional sex. This effect is very marked at low levels of selfing, but weak with a high selfing rate. In general, the advantage of an asexual mutant in a hermaphrodite population depends on the relative resource allocation to male and female gametes, and increases with increasing bias to femaleness. Thus the cost of sex in gynodioecious populations is (with a low level of selfing) as high as in a dioecious population. This applies, however, to a nuclear genetic determination of gynodioecy, which is presumably rare. In a more realistic model assuming nuclear-cytoplasmic determination of gynodioecy the cost of sex is considerably lower.     

Selection in plant populations of effectively infinite size. V. Biallelic models of trioecy

A one-locus two-allele model of trioecy (presence of hermaphrodites, males and females in one population) is considered, in order to study the conditions for the persistence of this system. All possible assignments of the three sex types to the three genotypes are considered. This leads to three different modes of inheritance of trioecy, namely (a) females heterozygous, (b) males heterozygous and (c) hermaphrodites heterozygous, where in each mode each of the remaining two sex types is homozygous for one of the alleles. For mode (c) trioecy is always persistent, and the dependence of the sex ratio (for the three sex types) on the ovule and pollen fertilities and on the hermaphrodite selfing rate is specified. For the other two modes, (a) and (b), trioecy is not protected, i.e., it may not persist for any fertilities, viabilities or selfing rates. Thus, in this situation it is important to study the conditions under which the "marginal" systems of sexuality of trioecy, i.e., hermaphroditism, dioecy and gynodioecy in mode (a), and hermaphroditism, dioecy and androdioecy in mode (b), may become established. The results show that each marginal system may evolve from each other via trioecy. The evolution of dioecy is easier in mode (a) than in (b), so that female heterogamety would be expected to occur more often than male heterogamety in the present model. Under some conditions the breeding system obtained in equilibrium populations may depend on the initial genotype frequencies.—The necessity of considering modes of inheritance for sexual polymorphisms is demonstrated by comparing our results with those obtained from an evolutionary stable strategy (ESS) analysis of a purely phenotypic model.     

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.     

Fitness effects of X chromosome drive in the stalk-eyed fly, Cyrtodiopsis dalmanni

Sex-ratio (SR) males produce predominantly female progeny because most Y chromosome sperm are rendered nonfunctional. The resulting transmission advantage of XSR chromosomes should eventually cause population extinction unless segregation distortion is masked by suppressors or balanced by selection. By screening male stalk-eyed flies, Cyrtodiopsis dalmanni, for brood sex ratio we found unique SR alleles at three X-linked microsatellite loci and used them to determine if SR persists as a balanced polymorphism. We found that XSR/XST females produced more offspring than other genotypes and that SR males had lower sperm precedence and exhibited lower fertility when mating eight females in 24 h. Adult survival was independent of SR genotype but positively correlated with eye span. We infer that the SR polymorphism is likely maintained by a combination of weak overdominance for female fecundity and frequency dependent selection acting on male fertility. Our discovery of two SR haplotypes in the same population in a 10-year period further suggests that this SR polymorphism may be evolving rapidly.     

Natural Selection with Nuclear and Cytoplasmic Transmission. I. a Deterministic Model

A deterministic model allowing variation at a nuclear genetic locus in a population segregating two cytoplasmic types is formulated. Additive, multiplicative and symmetric viability matrices are analyzed for existence and stability of equilibria. The protectedness of polymorphisms in both nuclear genes and cytoplasmic types is also investigated in the general model. In no case is a complete polymorphism protected with this deterministic model. Results are discussed in light of the extensive variation in mtDNA that has recently been reported.     

Local population structure and sex ratio: evolution in gynodioecious plants

Although the influence of population structure on evolution has been explored previously in a variety of theoretical studies, there are few examples of specific traits whose fitness is likely to be modified by the local structure. Here we focus on a specific trait, sex expression in gynodioecious plants, and derive a model in which the fitness of females and hermaphrodites is a function of the local sex ratio. By using the concept d genes. As a consequence, when local demes vary in sex ratio, a polymorphism for a cytoplasmic male sterility (CMS) allele can be maintained in the absence of nuclear alleles that restore male function. When of subjective frequencies, it is shown that among-deme variance in the local sex ratio reduces the average fitness of females when pollen availability limits fertility. In contrast, sex ratio variance increases the fitness of hermaphrodites from the perspective of maternally inherited genes and lessens the negative impact of pollen limitation on hermaphrodite fitness when it is measured from the perspective of biparentally inheriterestorer alleles are introduced into the model, polymorphism cannot be maintained simultaneously at both the cytoplasmic and nuclear loci. In that case, the CMS allele spreads to fixation, and the equilibrium frequency of females is an inverse function of the equilibrium frequency of the restorer allele, which increases with increased structure. The results exemplify how population structure can greatly alter the fitness and evolution of a frequency-dependent trait.