Selection in plant populations of effectively infinite size VI. Overlapping generations

A selection model for iteroparous, monoecious, or hermaphroditic plant populations is considered which encompasses viabilities, pollen fertilities, ovule fertilities, and rates of self-fertilization which may arbitrarily depend on both age and genotype. The general conditions for establishment (which are also those for protectedness) of an allele are derived. The classical conjecture that the conditions of protectedness are the same for separated and overlapping generations if the intrinsic rates of increase are applied is discussed. For this purpose it is necessary to introduce two new intrinsic values: the intrinsic rate of self-fertilization and the intrinsic pollen-to-ovule ratio. The significance of the intrinsic values is demonstrated for complete self-fertilization, selection restricted to differential, partial self-fertilization, and sexual asymmetry (absence of proportionality between pollen and ovule production), including selection restricted to one sex. With the exception of asymmetric selection in both sexes, it turns out that the intrinsic values suffice to state the conditions for protectedness, but more information about the life histories is required to determine the exact speed of establishment. For asymmetric selection in both sexes, the concept of intrinsic value is inadequate for investigating the problem of establishment and thus the evolution of life histories. Since sexual asymmetry is rather the rule than the exception and selfing is common in plants, the consequences for finding optimal life histories are outlined.     

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 with gene-cytoplasm interactions. I. Maintenance of cytoplasm polymorphisms

General conditions for the protectedness of gene-cytoplasm polymorphisms are considered for a biallelic model with two cytoplasm types and under the assumption that nuclear polymorphisms cannot be maintained in the presence of only one cytoplasm type. Analytical results involving male fertilities, female fertilities, viabilities and selfing rates are obtained, and numerical results show spiral and cyclic behavior of population trajectories. It is shown that a maternally inherited cytoplasmic polymorphism cannot be maintained in the absence of a nuclear polymorphism, and that a gene-cytoplasm polymorphism can only be maintained if the population shows sexual asymmetry, i.e. , if the ratio of male to female fertility varies among genotypes. Thus, the classical viability selection model does not allow gene-cytoplasm polymorphisms.     

The significance of over- and underdominance for the maintenance of genetic polymorphisms. I. Underdominance and stability

It is pointed out that the standard selection models in population genetics all require some form of heterozygote advantage in fitness in order to guarantee the maintenance or stability of genetic polymorphisms. Even more recent results demonstrating the existence of stable two-locus polymorphisms with marginal underdominance at both loci are based on certain epistatically acting heterosis assumptions. This raises the question as to whether heterozygote advantage in fitness is indeed a generally valid principle of maintaining polymorphisms. To avoid ambiguity in definition of heterozygote advantage (overdominance) as it appears in multiallele or multilocus systems, a one-locus-two-allele model is considered. This model allows for sexually asymmetric selection and random mating. It is shown that the model produces globally stable polymorphisms exhibiting underdominance in fitness for a considerable and biologically reasonable range of selection values. Having thus properly refuted the general validity of the common overdominance principle, a modified version is suggested which covers the classical viability selection model and its extension to arbitrary, sexually asymmetric viability and fertility selection. This modified overdominance principle is based on the notion of fractional fitnesses and relates protectedness of biallelic polymorphisms to the extent to which each genotype reproduces its own type. The fact that the model treated displays frequency dependent fitnesses which may change in ranking while approaching equilibrium is discussed in relation to problems of the evolution of overdominance and underdominance.     

Genetic Variation in Heterogeneous Environments

A model of population structure in heterogeneous environments is described and conditions sufficient for maintaining a polymorphism are derived.

The absolute fitness of any genotype is regarded as a function of location in the niche space and the population density at that location. Two modes of habitat selection are examined: (1) organisms are distributed uniformly over the environment; and (2) each organism selects to occupy that habitat in which it is most fit ("optimal habitant selection").—Sufficient conditions for maintenance of genetic polymorphisms are derived for both models. In populations which do not practice habitat selection heterozygote superiority averaged over the environment is sufficient to guarantee the existence of polymorphisms. Comparable conditions for populations which practice optimal habitat selection are much less restrictive. If the heterozygotes are superior to one homozygote in any one part of the niche and to the other homozygote in any other part of the niche then a polymorphism will be defined.—A positive correlation between genetic and environmental variation follows from the model with habitat selection, but not from the other. The adaptive significance of polymorphisms thus depends on how animals behave.

     

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.     

Male versus female mate choice: sexual selection and the evolution of species recognition via reinforcement

Male mate choice, expressed through courtship preferences, sometime occurs even under the mating system of polygyny, when the operational sex ratio is skewed toward males. The conditions under which male mate choice may be expected during polygyny are not well established. Servedio and Lande (2006, Evolution 60:674-685), assuming strict polygyny where all females have equal mating success, show that when having a preference does not increase the amount of energy that a male can put into courtship, male preferences for "arbitrary" female ornaments should not be expected to evolve; direct selection acts against them because they place males that carry them into situations in which there is high competition for mates. Here I explore in detail two situations under which logic dictates that this effect may be overcome or reversed. First I determine the contributions that direct and indirect selection place on male versus female preferences for traits that increase viability, using notation that allows the exact expression of these measures of selection. I find that direct selection against male preferences still predominates in the male mate choice model, causing less evolution by male than female preferences under these conditions. Second I address whether male mate choice is likely to evolve as a mechanism of premating isolation leading to species recognition, driven by the process of reinforcement. Reinforcement is compared under male and female mate choice, using a variety of models analyzed by both analytical techniques assuming weak selection and numerical techniques under broader selective conditions. I demonstrate that although under many conditions stronger premating isolation evolves under female mate choice, reinforcement may indeed occur via male mate choice alone.     

Sex‐specific recombination rates and allele frequencies affect the invasion of sexually antagonistic variation on autosomes

The introduction and persistence of novel, sexually antagonistic alleles can depend upon factors that differ between males and females. Understanding the conditions for invasion in a two‐locus model can elucidate these processes. For instance, selection can act differently upon the sexes, or sex linkage can facilitate the invasion of genetic variation with opposing fitness effects between the sexes. Two factors that deserve further attention are recombination rates and allele frequencies – both of which can vary substantially between the sexes. We find that sex‐specific recombination rates in a two‐locus diploid model can affect the invasion outcome of sexually antagonistic alleles and that the sex‐averaged recombination rate is not necessarily sufficient to predict invasion. We confirm that the range of permissible recombination rates is smaller in the sex benefitting from invasion and larger in the sex harmed by invasion. However, within the invasion space, male recombination rate can be greater than, equal to or less than female recombination rate in order for a male‐benefit, female‐detriment allele to invade (and similarly for a female‐benefit, male‐detriment allele). We further show that a novel, sexually antagonistic allele that is also associated with a lowered recombination rate can invade more easily when present in the double heterozygote genotype. Finally, we find that sexual dimorphism in resident allele frequencies can impact the invasion of new sexually antagonistic alleles at a second locus. Our results suggest that accounting for sex‐specific recombination rates and allele frequencies can determine the difference between invasion and non‐invasion of novel, sexually antagonistic alleles in a two‐locus model.     

Biased sex‐ratio and sex‐biased heterozygote disadvantage affect the maintenance of a genetic polymorphism and the properties of hybrid zones

The evolution of biodiversity is a major issue of modern biology, and it is becoming increasingly topical as the ongoing erosion of diversity puts serious threats on human well‐being. An elementary mechanism that allows maintaining diversity is the interplay between dispersal and heterozygote selective disadvantage, which can lead to self‐sustainable spatial genetic structures and is central to the stability of hybrid zones. Theoretical studies supporting the importance of this mechanism assume a balanced sex‐ratio and a heterozygote disadvantage equally affecting both sexes, despite the multiplicity of empirical evidence that (i) adult sex‐ratio is usually biased towards either male or female and that (ii) heterozygote disadvantage often affects a single sex. We expanded the existing theory by weighting the strength of selection against heterozygote according to the biased in sex‐ratio and in heterozygote disadvantage. The range of conditions allowing for the maintenance of polymorphism can then either double or vanish. We discuss the implications of such finding for birds, mammals and insects diversity. Finally, we provide simple analytical predictions about the effect of those biased on the width and speed of hybrid zones and on the time for the spread of beneficial mutations through such zones.     

Why are heterozygotes often superior in fitness?

Author opposes the usual explanaation of allelic polymorphisms as the consequence of heterozygote superiority. Polymorphism and average heterozygote superiority in fitness are shown to be joint consequences of natural selection rather than the cause of each other.     

Anisogamy,sexual selection,and the evolution and maintenance of sex

Summary In the present paper we distinguish between two aspects of sexual reproduction. Genetic recombination is a universal features of the sexual process. It is a primitive condition found in simple, single-celled organisms, as well as in higher plants and animals. Its function is primarily to repair genetic damage and eliminate deleterious mutations. Recombination also produces new variation, however, and this can provide the basis for adaptive evolutionary change in spatially and temporally variable environments.The other feature usually associated with sexual reproduction, differentiated male and female roles, is a derived condition, largely restricted to complex, diploid, multicellular organisms. The evolution of anisogamous gametes (small, mobile male gametes containing only genetic material, and large, relatively immobile female gametes containing both genetic material and resources for the developing offspring) not only established the fundamental basis for maleness and femaleness, it also led to an asymmetry between the sexes in the allocation of resources to mating and offspring. Whereas females allocate their resources primarily to offspring, the existence of many male gametes for each female one results in sexual selection on males to allocate their resources to traits that enhance success in competition for fertilizations. A consequence of this reproductive competition, higher variance in male than female reproductive success, results in more intense selection on males.The greater response of males to both stabilizing and directional selection constitutes an evolutionary advantage of males that partially compensates for the cost of producing them. The increased fitness contributed by sexual selection on males will complement the advantages of genetic recombination for DNA repair and elimination of deleterious mutations in any outcrossing breeding system in which males contribute only genetic material to their offspring. Higher plants and animals tend to maintain sexual reproduction in part because of the enhanced fitness of offspring resulting from sexual selection at the level of individual organisms, and in part because of the superiority of sexual populations in competition with asexual clones.     

Insecticide resistance enhances male reproductive success in a beetle

Abstract.— Malathion-specific resistance in the red flour beetle, Tribolium castaneum , is widespread and stable in natural populations even in the absence of pesticide exposure. To understand this stability, both resistant and susceptible males were placed in competition for susceptible female fertilization. Females were then isolated and their progeny was tested for malathion susceptibility. Male reproductive success was estimated for populations originating from different geographic areas and for isogenic strains. In most cases, resistant males had a greater reproductive success rate than susceptibles. The results suggest that male reproductive success is not traded against the selection for malathion resistance, even resistant individuals are at an advantage for this fitness trait. This absence of fitness cost may be the result of postselection of (1) modifier gene which ameliorate the fitness of resistant individuals or (2) nondeleterious resistance gene. Resistant phenotype superiority could be due to increased male mating success, improved ability of resistant males in sperm competition, female mate choice, and/or cryptic female choice of resistance gene(s). The effect of male phenotypic frequency on male reproductive success was also examined. We observed that male fertilization success is frequency dependent and inversely related to their frequency. However, this "rare male" advantage did not counteract the superiority of the resistant males.     

The exact values of the probability of fixation of underdominant chromosomal rearrangements.

A numerical analysis of the probability of fixation of a chromosomal mutation with partial sterility of the heterozygote in a single population is performed. Three different genetic models are considered: the first model entails constant selection against the heterozygote and is the model almost universally used in previous works; in the other two models selection against the heterozygote depends on its frequency. The exact values of the fixation probability are found by iterating transition matrices with genotype specification. Differences in results among models are small. The exact values found in the first model are compared to estimates obtained from approximations. Solutions based on diffusion models give good approximations when selection against the heterozygote is low, especially if the population is very small. For the higher values of the selection coefficient against the heterozygote, the estimates are rather imprecise, especially when the populations are not very small.     

Major histocompatibility complex (MHC) heterozygote superiority to natural multi-parasite infections in the water vole (Arvicola terrestris)

The fundamental role of the major histocompatibility complex (MHC) in immune recognition has led to a general consensus that the characteristically high levels of functional polymorphism at MHC genes is maintained by balancing selection operating through host–parasite coevolution. However, the actual mechanism by which selection operates is unclear. Two hypotheses have been proposed: overdominance (or heterozygote superiority) and negative frequency-dependent selection. Evidence for these hypotheses was evaluated by examining MHC–parasite relationships in an island population of water voles (Arvicola terrestris). Generalized linear mixed models were used to examine whether individual variation at an MHC class II DRB locus explained variation in the individual burdens of five different parasites. MHC genotype explained a significant amount of variation in the burden of gamasid mites, fleas (Megabothris walkeri) and nymphs of sheep ticks (Ixodes ricinus). Additionally, MHC heterozygotes were simultaneously co-infected by fewer parasite types than homozygotes. In each case where an MHC-dependent effect on parasite burden was resolved, the heterozygote genotype was associated with fewer parasites, and the heterozygote outperformed each homozygote in two of three cases, suggesting an overall superiority against parasitism for MHC heterozygote genotypes. This is the first demonstration of MHC heterozygote superiority against multiple parasites in a natural population, a mechanism that could help maintain high levels of functional MHC genetic diversity in natural populations.     

Maximum-likelihood estimation of gene location by linkage disequilibrium.

Linkage disequilibrium, D, between a polymorphic disease and mapped markers can, in principle, be used to help find the map position of the disease gene. Likelihoods are therefore derived for the value of D conditional on the observed number of haplotypes in the sample and on the population parameter Nc, where N is the effective population size and c the recombination fraction between the disease and marker loci. The likelihood is computed explicitly for the case of two loci with heterozygote superiority and, more generally, by computer simulations assuming a steady state of constant population size and selective pressures or neutrality. It is found that the likelihood is, in general, not very dependent on the degree of selection at the loci and is very flat. This suggests that precise information on map position will not be obtained from estimates of linkage disequilibrium.     

Sympatric speciation by sexual selection alone is unlikely

According to Darwin, sympatric speciation is driven by disruptive, frequency-dependent natural selection caused by competition for diverse resources. Recently, several authors have argued that disruptive sexual selection can also cause sympatric speciation. Here, we use hypergeometric phenotypic and individual-based genotypic models to explore sympatric speciation by sexual selection under a broad range of conditions. If variabilities of preference and display traits are each caused by more than one or two polymorphic loci, sympatric speciation requires rather strong sexual selection when females exert preferences for extreme male phenotypes. Under this kind of mate choice, speciation can occur only if initial distributions of preference and display are close to symmetric. Otherwise, the population rapidly loses variability. Thus, unless allele replacements at very few loci are enough for reproductive isolation, female preferences for extreme male displays are unlikely to drive sympatric speciation. By contrast, similarity-based female preferences that do not cause sexual selection are less destabilizing to the maintenance of genetic variability and may result in sympatric speciation across a broader range of initial conditions. Certain groups of African cichlids have served as the exclusive motivation for the hypothesis of sympatric speciation by sexual selection. Mate choice in these fishes appears to be driven by female preferences for extreme male phenotypes rather than similarity-based preferences, and the evolution of premating reproductive isolation commonly involves at least several genes. Therefore, differences in female preferences and male display in cichlids and other species of sympatric origin are more likely to have evolved as isolating mechanisms under disruptive natural selection.     

The evolutionary significance of sexual selection

A model for the joint evolution of a secondary sexual male trait Z and a female mating preference Y is discussed. Recurrence relations for the moments of (Z, Y) are given under the assumption that the traits are binormally distributed. It is shown that female preference for a male character can lead to an equilibrium distribution of the male trait with non-zero variances. The conditions under which the distribution is stable, are given. Unstable situations, in which a continued exaggeration of the male trait occurs, are described. It is demonstrated that the effect of sexual selection on the evolution of the male trait depends on the intensity of natural selection, i.e. the effect of the sexual selection increases when the intensity of natural selection is reduced. The effect of the female preference on the male trait also increases with increasing availability of males. This provides a link to several ecological conditions which have generally been known to be correlated with the degree of sexual selection. Furthermore, it is demonstrated that perturbations away from the equilibrium may cause rapid evolution of the male character, eventually leading to speciation.     

Partial male sterility and the evolution of nuclear gynodioecy in plants

Gynodioecy, a genetic dimorphism of females and hermaphrodites, is pertinent to an understanding of the evolution of plant gender, mating and genetic variability. Classical models of nuclear gynodioecy attribute the maintenance of the dimorphism to frequency-dependent selection in which the female phenotype has a fitness advantage at low frequency owing to a doubled ovule fertility. Here, I analyse explicit genetic models of nuclear gynodioecy that expand on previous work by allowing partial male sterility in combination with either fixed or dynamically evolving mutational inbreeding depression. These models demonstrate that partial male sterility causes fitness underdominance at the mating locus, which can prevent the spread of females. However, if partial male sterility is compensated by a change in selfing rate, overdominance at the mating locus can cause the spread of females. Overdominance at introduction of the male sterility allele can be caused by high inbreeding depression and a lower selfing rate in the heterozygote, by purging of mutations by a higher selfing rate in the heterozygote, and by low inbreeding depression and a higher selfing rate in the heterozygote. These processes might be of general importance in the maintenance of mating polymorphisms in plants.     

Quantitative dermatoglyphic markers in fra-X-syndrome

Quantitative dermatoglyphic characters of fingers and palms of 61 male patients with fra-X-syndrome and 20 female heterozygote carriers were analysed and compared with the data from 84 male and 90 female normal individuals. Univariate and multivariate analysis of the data led to the following conclusions: 1. The fra-X-syndrome patients show higher ridge count and higher MLI value (increased transversality of the main lines), and lower a-b ridge counts than the controls. In addition to this, differences are observed also for the diversity and asymmetry measures. 2. Discriminant analysis as applied to the sexes separately, showed that 75% of males can be correctly classified in their group. However, the percent of correctly classified females is lower than the males; it is 70% (fra-X female) ad 64.4% (control female). 3. D2-matrix and the comparison of TFR C values support the hypothesis of X-chromosomal doses effect on the dermatoglyphics.     

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.