A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative trait

The equilibrium structure of an additive, diallelic multilocus model of a quantitative trait under frequency- and density-dependent selection is derived. The trait is under stabilizing selection and mediates intraspecific competition as induced, for instance, by differential resource utilization. It is assumed that stabilizing selection is weak, but the strength of competition may be arbitrary relative to it. Density dependence is caused by population regulation, which may be of a very general kind. The number and effects of loci are arbitrary, and stabilizing selection is not necessarily symmetric with respect to the range of phenotypic values. All previously studied models of intraspecific competition for a continuum of resources known to the author reduce to a special case of the present model if overall selection is weak. Therefore, in this case our results are applicable as approximations to all these models. Our central result is the (nearly) complete characterization of the equilibrium and stability structure in terms of all parameters. It is derived under the sole assumption that selection is weak enough relative to recombination to ignore linkage disequilibrium. In particular, necessary and sufficient conditions on the strength of competition relative to stabilizing selection are found that ensure the maintenance of multilocus polymorphism and the occurrence of disruptive selection. In this case, explicit formulas for the number of polymorphic loci at equilibrium, the allele frequencies, the genetic variance, and the strength of disruptive selection are obtained. For two loci, the effects of linkage are investigated analytically; for several loci, they are studied numerically.     

The conditions for speciation through intraspecific competition

Abstract It has been shown theoretically that sympatric speciation can occur if intraspecific competition is strong enough to induce disruptive selection. However, the plausibility of the involved processes is under debate, and many questions on the conditions for speciation remain unresolved. For instance, is strong disruptive selection sufficient for speciation? Which roles do genetic architecture and initial composition of the population play? How strong must assortative mating be before a population can split in two? These are some of the issues we address here. We investigate a diploid multilocus model of a quantitative trait that is under frequency‐dependent selection caused by a balance of intraspecific competition and frequency‐independent stabilizing selection. This trait also acts as mating character for assortment. It has been established previously that speciation can occur only if competition is strong enough to induce disruptive selection. We find that speciation becomes more difficult for very strong competition, because then extremely strong assortment is required. Thus, speciation is most likely for intermediate strengths of competition, where it requires strong, but not extremely strong, assortment. For this range of parameters, however, it is not obvious how assortment can evolve from low to high levels, because with moderately strong assortment less genetic variation is maintained than under weak or strong assortment sometimes none at all. In addition to the strength of frequency‐dependent competition and assortative mating, the roles of the number of loci, the distribution of allelic effects, the initial conditions, costs to being choosy, the strength of stabilizing selection, and the particular choice of the fitness function are explored. A multitude of possible evolutionary outcomes is observed, including loss of all genetic variation, splitting in two to five species, as well as very short and extremely long stable limit cycles. On the methodological side, we propose quantitative measures for deciding whether a given distribution reflects two (or more) reproductively isolated clusters.     

Host–parasite coevolution: genetic variation in a virus population and the interaction with a host gene

Host–parasite coevolution is considered to be an important factor in maintaining genetic variation in resistance to pathogens. Drosophila melanogaster is naturally infected by the sigma virus, a vertically transmitted and host‐specific pathogen. In fly populations, there is a large amount of genetic variation in the transmission rate from parent to offspring, much of which is caused by major‐effect resistance polymorphisms. We have found that there are similarly high levels of genetic variation in the rate of paternal transmission among 95 different isolates of the virus as in the host. However, when we examined a transmission‐blocking gene in the host, we found that it was effective across virus isolates. Therefore, the high levels of genetic variation observed in this system do not appear to be maintained because of coevolution resulting from interactions between this host gene and parasite genes.     

The maintenance of genetic diversity under host–parasite coevolution in finite,structured populations

As a corollary to the Red Queen hypothesis, host–parasite coevolution has been hypothesized to maintain genetic variation in both species. Recent theoretical work, however, suggests that reciprocal natural selection alone is insufficient to maintain variation at individual loci. As highlighted by our brief review of the theoretical literature, models of host–parasite coevolution often vary along multiple axes (e.g. inclusion of ecological feedbacks or abiotic selection mosaics), complicating a comprehensive understanding of the effects of interacting evolutionary processes on diversity. Here we develop a series of comparable models to explore the effect of interactions between spatial structures and antagonistic coevolution on genetic diversity. Using a matching alleles model in finite populations connected by migration, we find that, in contrast to panmictic populations, coevolution in a spatially structured environment can maintain genetic variation relative to neutral expectations with migration alone. These results demonstrate that geographic structure is essential for understanding the effect of coevolution on biological diversity.     

Antagonistic coevolution with parasites maintains host genetic diversity: an experimental test

Genetic variation in natural populations is a prime prerequisite allowing populations to respond to selection, but is under constant threat from forces that tend to reduce it, such as genetic drift and many types of selection. Haldane emphasized the potential importance of parasites as a driving force of genetic diversity. His theory has been taken for granted ever since, but despite numerous studies showing correlations between genetic diversity and parasitism, Haldane''s hypothesis has rarely been tested experimentally for unambiguous support. We experimentally staged antagonistic coevolution between the host Tribolium castaneum and its natural microsporidian parasite, Nosema whitei, to test for the relative importance of two separate evolutionary forces (drift and parasite-induced selection) on the maintenance of genetic variation. Our results demonstrate that coevolution with parasites indeed counteracts drift as coevolving populations had significantly higher levels of heterozygosity and allelic diversity. Genetic drift remained a strong force, strongly reducing genetic variation and increasing genetic differentiation in small populations. To our surprise, differentiation between the evolving populations was smaller when they coevolved with parasites, suggesting parallel balancing selection. Hence, our results experimentally vindicate Haldane''s original hypothesis 60 years after its conception.     

The quantitative genetics of fluctuating asymmetry

Fluctuating asymmetry (subtle departures from identical expression of a trait across an axis of symmetry) in many taxa is under stabilizing selection for reduced asymmetry. However, lack of reliable estimates of genetic parameters for asymmetry variation hampers our ability to predict the evolutionary outcome of this selection. Here we report on a study, based on analysis of variation within and between isofemale lines and of generation means (line-cross analysis), designed to dissect in detail the quantitative genetics of positional fluctuating asymmetry (PFA) in bristle number in natural populations of Drosophila falleni. PFA is defined as the difference between the two sides of the body in the placement or position of components of a meristic trait. Heritability (measured at 25 degrees C) of two related measures of PFA were 13% and 21%, both of which differed significantly from zero. In contrast, heritability estimates for fluctuating asymmetry in the total number of anterior (0.7%) and transverse (2.4%) sternopleural bristles were smaller, not significant, and in quantitative agreement with previously published estimates. Heritabilities for bristle number (trait size) were considerably greater than that for any asymmetry measure. The experimental design controlled for the potentially confounding effects of common familial environment, and repeated testing revealed that PFA differences between lines were genetically stable for up to 16 generations in the laboratory at 25 degrees C. We performed line cross analysis between strains at the extremes of the PFA distribution (highest and lowest values); parental strains, F1, F1r (reciprocal), F2, backcross, and backcross reciprocal generations were represented. The inheritance of PFA was described best by additive and dominance effects localized to the X-chromosomes, whereas autosomal dominance effects were also detected. Epistatic, maternal, and cytoplasmic effects were not detected. The inheritance of trait size was notably more complex and involved significant autosomal additive, dominance, and epistatic effects; maternal dominance effects; and additive and dominance effects localized to the X-chromosomes. The additive genetic correlation between PFA and its associated measure of trait size was negative (-0.049), but not statistically significant, indicating that the loci contributing additive genetic effects to these traits are probably different. It is suggested that PFA may be a sensitive measure of developmental instability because PFA taps the ability of an organism to integrate interconnected developmental pathways.     

Bower-building: coevolution of display traits in response to the costs of female choice?

Bower-building is peculiar to polygynous species in the family Ptilonorhynchidae (Bowerbirds). Here we summarize past and current theories regarding the evolution of bower-building, evaluate the evidence that can be used to differentiate between them and suggest future areas for research.     

Genetic variation in a host-parasite association: potential for coevolution and frequency-dependent selection

Abstract.— Models of host‐parasite coevolution assume the presence of genetic variation for host resistance and parasite infectivity, as well as genotype‐specific interactions. We used the freshwater crustacean Daphnia magna and its bacterial microparasite Pasteuria ramosa to study genetic variation for host susceptibility and parasite infectivity within each of two populations. We sought to answer the following questions: Do host clones differ in their susceptibility to parasite isolates? Do parasite isolates differ in their ability to infect different host clones? Are there host clone‐parasite isolate interactions? The analysis revealed considerable variation in both host resistance and parasite infectivity. There were significant host clone‐parasite isolate interactions, such that there was no single host clone that was superior to all other clones in the resistance to every parasite isolate. Likewise, there was no parasite isolate that was superior to all other isolates in infectivity to every host clone. This form of host clone‐parasite isolate interaction indicates the potential for coevolution based on frequency‐dependent selection. Infection success of original host clone‐parasite isolate combinations (i.e., those combinations that were isolated together) was significantly higher than infection success of novel host clone‐parasite isolate combinations (i.e., those combinations that were created in the laboratory). This finding is consistent with the idea that parasites track specific host genotypes under natural conditions. In addition, correspondence analysis revealed that some host clones, although distinguishable with neutral genetic markers, were susceptible to the same set of parasite isolates and thus probably shared resistance genes.     

The evolution of quantitative traits in complex environments

Species inhabit complex environments and respond to selection imposed by numerous abiotic and biotic conditions that vary in both space and time. Environmental heterogeneity strongly influences trait evolution and patterns of adaptive population differentiation. For example, heterogeneity can favor local adaptation, or can promote the evolution of plastic genotypes that alter their phenotypes based on the conditions they encounter. Different abiotic and biotic agents of selection can act synergistically to either accelerate or constrain trait evolution. The environmental context has profound effects on quantitative genetic parameters. For instance, heritabilities measured in controlled conditions often exceed those measured in the field; thus, laboratory experiments could overestimate the potential for a population to respond to selection. Nevertheless, most studies of the genetic basis of ecologically relevant traits are conducted in simplified laboratory environments, which do not reflect the complexity of nature. Here, we advocate for manipulative field experiments in the native ranges of plant species that differ in mating system, life-history strategy and growth form. Field studies are vital to evaluate the roles of disparate agents of selection, to elucidate the targets of selection and to develop a nuanced perspective on the evolution of quantitative traits. Quantitative genetics field studies will also shed light on the potential for natural populations to adapt to novel climates in highly fragmented landscapes. Drawing from our experience with the ecological model system Boechera (Brassicaceae), we discuss advancements possible through dedicated field studies, highlight future research directions and examine the challenges associated with field studies.     

Antagonistic coevolution between multiple quantitative traits: Matching dynamics can arise from difference interactions

Coevolution is one of the major drivers of complex dynamics in population ecology. Historically, antagonistic coevolution in victim-exploiter systems has been a topic of special interest, and involves traits with various genetic architectures (e.g., the number of genes involved) and effects on interactions. For example, exploiters may need to have traits that “match” those of victims for successful exploitation (i.e., a matching interaction), or traits that exceed those of victims (i.e., a difference interaction). Different models exist which are appropriate for different types of traits, including Mendelian (discrete) and quantitative (continuous) traits. For models with multiple Mendelian traits, recent studies have shown that antagonistic coevolutionary patterns that appear as matching interactions can arise due to multiple difference interactions with costs of having large trait values. Here we generalize their findings to quantitative traits and show, analogously, that the multidimensional difference interactions with costs sometimes behave qualitatively the same as matching interactions. While previous studies in quantitative genetics have used the dichotomy between matching and difference frameworks to explore coevolutionary dynamics, we suggest that exploring multidimensional trait space is important to examine the generality of results obtained from one-dimensional traits.     

Evolutionary quantitative genetics of nonlinear developmental systems

In quantitative genetics, the effects of developmental relationships among traits on microevolution are generally represented by the contribution of pleiotropy to additive genetic covariances. Pleiotropic additive genetic covariances arise only from the average effects of alleles on multiple traits, and therefore the evolutionary importance of nonlinearities in development is generally neglected in quantitative genetic views on evolution. However, nonlinearities in relationships among traits at the level of whole organisms are undeniably important to biology in general, and therefore critical to understanding evolution. I outline a system for characterizing key quantitative parameters in nonlinear developmental systems, which yields expressions for quantities such as trait means and phenotypic and genetic covariance matrices. I then develop a system for quantitative prediction of evolution in nonlinear developmental systems. I apply the system to generating a new hypothesis for why direct stabilizing selection is rarely observed. Other uses will include separation of purely correlative from direct and indirect causal effects in studying mechanisms of selection, generation of predictions of medium‐term evolutionary trajectories rather than immediate predictions of evolutionary change over single generation time‐steps, and the development of efficient and biologically motivated models for separating additive from epistatic genetic variances and covariances.     

Natural selection and quantitative genetics of life-history traits in Western women: a twin study

Whether contemporary human populations are still evolving as a result of natural selection has been hotly debated. For natural selection to cause evolutionary change in a trait, variation in the trait must be correlated with fitness and be genetically heritable and there must be no genetic constraints to evolution. These conditions have rarely been tested in human populations. In this study, data from a large twin cohort were used to assess whether selection will cause a change among women in a contemporary Western population for three life-history traits: age at menarche, age at first reproduction, and age at menopause. We control for temporal variation in fecundity (the "baby boom" phenomenon) and differences between women in educational background and religious affiliation. University-educated women have 35% lower fitness than those with less than seven years education, and Roman Catholic women have about 20% higher fitness than those of other religions. Although these differences were significant, education and religion only accounted for 2% and 1% of variance in fitness, respectively. Using structural equation modeling, we reveal significant genetic influences for all three life-history traits, with heritability estimates of 0.50, 0.23, and 0.45, respectively. However, strong genetic covariation with reproductive fitness could only be demonstrated for age at first reproduction, with much weaker covariation for age at menopause and no significant covariation for age at menarche. Selection may, therefore, lead to the evolution of earlier age at first reproduction in this population. We also estimate substantial heritable variation in fitness itself, with approximately 39% of the variance attributable to additive genetic effects, the remainder consisting of unique environmental effects and small effects from education and religion. We discuss mechanisms that could be maintaining such a high heritability for fitness. Most likely is that selection is now acting on different traits from which it did in pre-industrial human populations.     

Coevolutionary genetics of hosts and parasites with quantitative inheritance

Summary A model of host—parasite coevolution is analysed. A host resistance trait and a parasite virulence trait interact to determine the outcome of a parasitic attack, where each trait is determined by quantitative genetic variation. The resistance and virulence traits are assumed to have a fitness cost. Each host and parasite genotype is treated as a separate species in a multidimensional Lotka—Volterra system in which the numerical abundance of each genotype is free to change. Thus, the epidemiological effects of fluctuating population sizes are analysed jointly with changes in genotype frequencies. Population sizes fluctuate increasingly as the parasites' reproductive capacity increases and as resistance and virulence benefits per unit cost decline. The patterns of genetic variability depend mainly on the stability of population sizes and on the shape of the relationship between the costs and benefits of a trait.     

Determinants of the strength of disruptive and/or divergent selection arising from resource competition

We investigate how the intensity of competition for resources affects the strength of disruptive selection on a resource acquisition trait. This is done by analyzing several consumer–resource models in which consumers use a linear array of resources. We show that disruptive selection can be diminished under both strong and weak competition, making disruptive selection a unimodal function of the strength of competition. Weak selection under strong competition arises when competition causes the extinction (for self-reproducing resources) or depletion (for abiotic resources) of the most rapidly caught resources. Weak selection under weak competition is a consequence of minimal effects of consumers on resources. The precise relationship between intensity of competition and strength of disruptive selection is sensitive to the shape of the consumer's resource utilization curve and the nature of resource growth. The most strongly unimodal competition–selection relationships result from utilization curves with long tails. Our results show that a simple comparison of the width of the resource abundance distribution and the consumer's utilization function is not sufficient to determine whether selection is disruptive. The results may explain some contradictory experimental findings regarding the effect of consumer mortality on the strength of disruptive selection.     

Multivariate quantitative genetics and the lek paradox: genetic variance in male sexually selected traits of Drosophila serrata under field conditions

Single male sexually selected traits have been found to exhibit substantial genetic variance, even though natural and sexual selection are predicted to deplete genetic variance in these traits. We tested whether genetic variance in multiple male display traits of Drosophila serrata was maintained under field conditions. A breeding design involving 300 field-reared males and their laboratory-reared offspring allowed the estimation of the genetic variance-covariance matrix for six male cuticular hydrocarbons (CHCs) under field conditions. Despite individual CHCs displaying substantial genetic variance under field conditions, the vast majority of genetic variance in CHCs was not closely associated with the direction of sexual selection measured on field phenotypes. Relative concentrations of three CHCs correlated positively with body size in the field, but not under laboratory conditions, suggesting condition-dependent expression of CHCs under field conditions. Therefore condition dependence may not maintain genetic variance in preferred combinations of male CHCs under field conditions, suggesting that the large mutational target supplied by the evolution of condition dependence may not provide a solution to the lek paradox in this species. Sustained sexual selection may be adequate to deplete genetic variance in the direction of selection, perhaps as a consequence of the low rate of favorable mutations expected in multiple trait systems.     

Genome divergence and diversification within a geographic mosaic of coevolution

Despite substantial interest in coevolution's role in diversification, examples of coevolution contributing to speciation have been elusive. Here, we build upon past studies that have shown both coevolution between South Hills crossbills and lodgepole pine (Pinus contorta), and high levels of reproductive isolation between South Hills crossbills and other ecotypes in the North American red crossbill (Loxia curvirostra) complex. We used genotyping by sequencing to generate population genomic data and applied phylogenetic and population genetic analyses to characterize the genetic structure within and among nine of the ecotypes. Although genome‐wide divergence was slight between ecotypes (F_ST = 0.011–0.035), we found evidence of relative genetic differentiation (as measured by F_ST) between and genetic cohesiveness within many of them. As expected for nomadic and opportunistic breeders, we detected no evidence of isolation by distance. The one sedentary ecotype, the South Hills crossbill, was genetically most distinct because of elevated divergence at a small number of loci rather than pronounced overall genome‐wide divergence. These findings suggest that mechanisms related to recent local coevolution between South Hills crossbills and lodgepole pine (e.g. strong resource‐based density dependence limiting gene flow) have been associated with genome divergence in the face of gene flow. Our results further characterize a striking example of coevolution driving speciation within perhaps as little as 6000 years.     

The long-term evolution of multilocus traits under frequency-dependent disruptive selection

Frequency-dependent disruptive selection is widely recognized as an important source of genetic variation. Its evolutionary consequences have been extensively studied using phenotypic evolutionary models, based on quantitative genetics, game theory, or adaptive dynamics. However, the genetic assumptions underlying these approaches are highly idealized and, even worse, predict different consequences of frequency-dependent disruptive selection. Population genetic models, by contrast, enable genotypic evolutionary models, but traditionally assume constant fitness values. Only a minority of these models thus addresses frequency-dependent selection, and only a few of these do so in a multilocus context. An inherent limitation of these remaining studies is that they only investigate the short-term maintenance of genetic variation. Consequently, the long-term evolution of multilocus characters under frequency-dependent disruptive selection remains poorly understood. We aim to bridge this gap between phenotypic and genotypic models by studying a multilocus version of Levene's soft-selection model. Individual-based simulations and deterministic approximations based on adaptive dynamics theory provide insights into the underlying evolutionary dynamics. Our analysis uncovers a general pattern of polymorphism formation and collapse, likely to apply to a wide variety of genetic systems: after convergence to a fitness minimum and the subsequent establishment of genetic polymorphism at multiple loci, genetic variation becomes increasingly concentrated on a few loci, until eventually only a single polymorphic locus remains. This evolutionary process combines features observed in quantitative genetics and adaptive dynamics models, and it can be explained as a consequence of changes in the selection regime that are inherent to frequency-dependent disruptive selection. Our findings demonstrate that the potential of frequency-dependent disruptive selection to maintain polygenic variation is considerably smaller than previously expected.     

Comparison of genetic differentiation at marker loci and quantitative traits

The comparison of the degree of differentiation in neutral marker loci and genes coding quantitative traits with standardized and equivalent measures of genetic differentiation (F_ST and Q_ST, respectively) can provide insights into two important but seldom explored questions in evolutionary genetics: (i) what is the relative importance of random genetic drift and directional natural selection as causes of population differentiation in quantitative traits, and (ii) does the degree of divergence in neutral marker loci predict the degree of divergence in genes coding quantitative traits? Examination of data from 18 independent studies of plants and animals using both standard statistical and meta‐analytical methods revealed a number of interesting points. First, the degree of differentiation in quantitative traits (Q_ST) typically exceeds that observed in neutral marker genes (F_ST), suggesting a prominent role for natural selection in accounting for patterns of quantitative trait differentiation among contemporary populations. Second, the F_ST – Q_ST difference is more pronounced for allozyme markers and morphological traits, than for other kinds of molecular markers and life‐history traits. Third, very few studies reveal situations were Q_ST < F_ST, suggesting that selection pressures, and hence optimal phenotypes, in different populations of the same species are unlikely to be often similar. Fourth, there is a strong correlation between Q_ST and F_ST indices across the different studies for allozyme (r=0.81), microsatellite (r=0.87) and combined (r=0.75) marker data, suggesting that the degree of genetic differentiation in neutral marker loci is closely predictive of the degree of differentiation in loci coding quantitative traits. However, these interpretations are subject to a number of assumptions about the data and methods used to derive the estimates of population differentiation in the two sets of traits.     

The maintenance of phenotypic and genetic variation in threshold traits by frequency-dependent selection

Many traits are phenotypically dimorphic but determined by the action of many loci, the phenotype being a result of a threshold of sensitivity. Quantitative genetic analysis has shown that generally there is considerable additive genetic variation for the trait, the average heritability being 0.52. In numerous cases threshold traits have been shown, or are assumed, to be under frequency-dependent selection; examples include satellite-territorial behaviour, sex-determination, wing dimorphism and trophic dimorphism. In this paper I investigate the potential for frequency-dependent selection to maintain both phenotypic and additive genetic variation in threshold traits. The qualitative results are robust to the particular form of the frequency-dependent selection function. The equilibrium proportion is more or less independent of population size but the heritability increases with population size, typically approaching its maximal value at a population size of 5000, when the mutation rate is 10^?4. A tenfold decrease in the mutation rate requires an approximate doubling of the population size before an asymptotic value is approached. Thus frequency-dependent selection can account for both the existence of two morphs in a population and the observed levels of heritability. It is also shown, both via simulation and theory, that the quantitative genetic model and a simple phenotypic analysis predict the same equilibrium morph proportion.