Long-term evolution of polygenic traits under frequency-dependent intraspecific competition

We analytically investigate the long-term evolution of a continuously varying quantitative character in a diploid population that is determined additively by a finite number of loci. The trait is under a mixture of frequency-dependent disruptive selection induced by intraspecific competition and frequency-independent stabilizing selection. Moreover, the trait is restricted to a finite range by constraints on the particular loci. Our investigations are based on explicit analytical results (provided by Bürger [2005. A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative trait. J. Math. Biol. 50, 355-396]; Schneider [2006. A multilocus-multiallele analysis of frequency-dependent selection induced by intraspecific competition. J. Math. Biol. 52, 483-523]) on the short-term dynamics under the assumption of linkage equilibrium. We show that the population always reaches a long-term equilibrium (LTE), i.e., an equilibrium that is resistant against perturbations of mutations of sufficiently small effect. In general, several LTEs can coexist. They can be calculated explicitly, and we provide necessary and sufficient conditions for their existence. In the case that more than one LTE exists, we exemplify numerically that the evolutionary outcome depends crucially on the initial genetic architecture, on the joint distribution of mutational effects across loci, and on the particular realization of the mutation process. Therefore, long-term evolution cannot be predicted from the ecology alone. We further show that a partial order exists for the LTEs. The set of LTEs has a 'largest' element, an LTE which is reached during long-term evolution if the effects of the occurring mutant alleles are sufficiently large.     

The evolution of genetic architecture under frequency-dependent disruptive selection

We propose a model to analyze a quantitative trait under frequency-dependent disruptive selection. Selection on the trait is a combination of stabilizing selection and intraspecific competition, where competition is maximal between individuals with equal phenotypes. In addition, there is a density-dependent component induced by population regulation. The trait is determined additively by a number of biallelic loci, which can have different effects on the trait value. In contrast to most previous models, we assume that the allelic effects at the loci can evolve due to epistatic interactions with the genetic background. Using a modifier approach, we derive analytical results under the assumption of weak selection and constant population size, and we investigate the full model by numerical simulations. We find that frequency-dependent disruptive selection favors the evolution of a highly asymmetric genetic architecture, where most of the genetic variation is concentrated on a small number of loci. We show that the evolution of genetic architecture can be understood in terms of the ecological niches created by competition. The phenotypic distribution of a population with an adapted genetic architecture closely matches this niche structure. Thus, evolution of the genetic architecture seems to be a plausible way for populations to adapt to regimes of frequency-dependent disruptive selection. As such, it should be seen as a potential evolutionary pathway to discrete polymorphisms and as a potential alternative to other evolutionary responses, such as the evolution of sexual dimorphism or assortative mating.     

Additive genetic variation under intraspecific competition and stabilizing selection: a two-locus study

A diallelic two-locus model is investigated in which the loci determine the genotypic value of a quantitative trait additively. Fitness has two components: stabilizing selection on the trait and a frequency-dependent component, as induced, for instance, if the ability to utilize different food resources depends on this trait. Since intraspecific competition induces disruptive selection, this model leads to a conflict of selective forces. We study how the underlying genetics (recombination rate and allelic effects) interacts with the selective forces, and explore the resulting equilibrium structure. For the special case of equal effects, global stability results are proved. Unless the locus effects are sufficiently different, the genetic variance maintained at equilibrium displays a threshold-like dependence on the strength of competition. For loci with equal effects, the equilibrium fitnesses of genotypic values exhibit disruptive selection if and only if competition is strong enough to maintain a stable two-locus polymorphism. For unequal effects, disruptive selection can be observed for weaker competition and in the absence of a stable polymorphism.     

Harvest-induced disruptive selection increases variance in fitness-related traits

The form of Darwinian selection has important ecological and management implications. Negative effects of harvesting are often ascribed to size truncation (i.e. strictly directional selection against large individuals) and resultant decrease in trait variability, which depresses capacity to buffer environmental change, hinders evolutionary rebound and ultimately impairs population recovery. However, the exact form of harvest-induced selection is generally unknown and the effects of harvest on trait variability remain unexplored. Here we use unique data from the Windermere (UK) long-term ecological experiment to show in a top predator (pike, Esox lucius) that the fishery does not induce size truncation but disruptive (diversifying) selection, and does not decrease but rather increases variability in pike somatic growth rate and size at age. This result is supported by complementary modelling approaches removing the effects of catch selectivity, selection prior to the catch and environmental variation. Therefore, fishing most likely increased genetic variability for somatic growth in pike and presumably favoured an observed rapid evolutionary rebound after fishery relaxation. Inference about the mechanisms through which harvesting negatively affects population numbers and recovery should systematically be based on a measure of the exact form of selection. From a management perspective, disruptive harvesting necessitates combining a preservation of large individuals with moderate exploitation rates, and thus provides a comprehensive tool for sustainable exploitation of natural resources.     

On a genetic model of intraspecific competition and stabilizing selection

A genetic model is investigated in which two recombining loci determine the genotypic value of a quantitative trait additively. Two opposing evolutionary forces are assumed to act: stabilizing selection on the trait, which favors genotypes with an intermediate phenotype, and intraspecific competition mediated by that trait, which favors genotypes whose effect on the trait deviates most from that of the prevailing genotypes. Accordingly, fitnesses of genotypes have a frequency-independent component describing stabilizing selection and a frequency- and density-dependent component modeling competition. We study how the underlying genetics, in particular recombination rate and relative magnitude of allelic effects, interact with the conflicting selective forces and derive the resulting, surprisingly complex equilibrium patterns. We also investigate the conditions under which disruptive selection on the phenotypes can be observed and examine how much genetic variation can be maintained in such a model. We discovered a number of unexpected phenomena. For instance, we found that with little recombination the degree of stably maintained polymorphism and the equilibrium genetic variance can decrease as the strength of competition increases relative to the strength of stabilizing selection. In addition, we found that mean fitness at the stable equilibria is usually much lower than the maximum possible mean fitness and often even lower than the fitness at other, unstable equilibria. Thus, the evolutionary dynamics in this system are almost always nonadaptive.     

Pleiotropic Models of Polygenic Variation, Stabilizing Selection, and Epistasis

We show that in polymorphic populations many polygenic traits pleiotropically related to fitness are expected to be under apparent ``stabilizing selection' independently of the real selection acting on the population. This occurs, for example, if the genetic system is at a stable polymorphic equilibrium determined by selection and the nonadditive contributions of the loci to the trait value either are absent, or are random and independent of those to fitness. Stabilizing selection is also observed if the polygenic system is at an equilibrium determined by a balance between selection and mutation (or migration) when both additive and nonadditive contributions of the loci to the trait value are random and independent of those to fitness. We also compare different viability models that can maintain genetic variability at many loci with respect to their ability to account for the strong stabilizing selection on an additive trait. Let V(m) be the genetic variance supplied by mutation (or migration) each generation, V(g) be the genotypic variance maintained in the population, and n be the number of the loci influencing fitness. We demonstrate that in mutation (migration)-selection balance models the strength of apparent stabilizing selection is order V(m)/V(g). In the overdominant model and in the symmetric viability model the strength of apparent stabilizing selection is approximately 1/(2n) that of total selection on the whole phenotype. We show that a selection system that involves pairwise additive by additive epistasis in maintaining variability can lead to a lower genetic load and genetic variance in fitness (approximately 1/(2n) times) than an equivalent selection system that involves overdominance. We show that, in the epistatic model, the apparent stabilizing selection on an additive trait can be as strong as the total selection on the whole phenotype.     

Revisiting santa rosalia to unfold a degeneracy of classic models of speciation

Abstract Many classic models of speciation incorporate assortative mating based on mating groups, such as plants with different flowering times, and they investigate whether an ecological trait under disruptive natural selection becomes genetically associated with the selectively neutral mating trait. It is well known that this genetic association is potently destroyed by recombination. In this note, we point out a more fundamental difficulty: if a "knife-edge" symmetry assumption of previous models is violated, then the mating trait is no longer neutral and sexual selection eliminates the polymorphism in the mating locus. This result strengthens the growing consensus that magic traits are the more likely route to nonallopatric speciation. We expand the model assuming also ecological selection on the mating trait and investigate the conditions for natural selection to overcome sexual selection and maintain mating polymorphism; we find that the combination of natural and sexual selection can cause also bistability of allele frequencies.     

Rapid differentiation of experimental populations of wheat for heading time in response to local climatic conditions

BACKGROUND AND AIMS: Dynamic management (DM) of genetic resources aims at maintaining genetic variability between different populations evolving under natural selection in contrasting environments. In 1984, this strategy was applied in a pilot experiment on wheat (Triticum aestivum). Spatio-temporal evolution of earliness and its components (partial vernalization sensitivity, daylength sensitivity and earliness per se that determines flowering time independently of environmental stimuli) was investigated in this multisite and long-term experiment. METHODS: Heading time of six populations from the tenth generation was evaluated under different vernalization and photoperiodic conditions. KEY RESULTS: Although temporal evolution during ten generations was not significant, populations of generation 10 were genetically differentiated according to a north-south latitudinal trend for two components out of three: partial vernalization sensitivity and narrow-sense earliness. CONCLUSIONS: It is concluded that local climatic conditions greatly influenced the evolution of population earliness, thus being a major factor of differentiation in the DM system. Accordingly, a substantial proportion (approximately 25 %) of genetic variance was distributed among populations, suggesting that diversity was on average conserved during evolution but was differently distributed by natural selection (and possibly drift). Earliness is a complex trait and each genetic factor is controlled by multiple homeoalleles; the next step will be to look for spatial divergence in allele frequencies.     

The effects of intraspecific competition and stabilizing selection on a polygenic trait

The equilibrium properties of an additive multilocus model of a quantitative trait under frequency- and density-dependent selection are investigated. Two opposing evolutionary forces are assumed to act: (i) stabilizing selection on the trait, which favors genotypes with an intermediate phenotype, and (ii) intraspecific competition mediated by that trait, which favors genotypes whose effect on the trait deviates most from that of the prevailing genotypes. Accordingly, fitnesses of genotypes have a frequency-independent component describing stabilizing selection and a frequency- and density-dependent component modeling competition. We study how the equilibrium structure, in particular, number, degree of polymorphism, and genetic variance of stable equilibria, is affected by the strength of frequency dependence, and what role the number of loci, the amount of recombination, and the demographic parameters play. To this end, we employ a statistical and numerical approach, complemented by analytical results, and explore how the equilibrium properties averaged over a large number of genetic systems with a given number of loci and average amount of recombination depend on the ecological and demographic parameters. We identify two parameter regions with a transitory region in between, in which the equilibrium properties of genetic systems are distinctively different. These regions depend on the strength of frequency dependence relative to pure stabilizing selection and on the demographic parameters, but not on the number of loci or the amount of recombination. We further study the shape of the fitness function observed at equilibrium and the extent to which the dynamics in this model are adaptive, and we present examples of equilibrium distributions of genotypic values under strong frequency dependence. Consequences for the maintenance of genetic variation, the detection of disruptive selection, and models of sympatric speciation are discussed.     

Models of sexual selection on a quantitative genetic trait when preference is acquired by sexual imprinting

The evolution of a quantitative genetic trait under stabilizing viability selection and sexual selection is modeled for a polygynous species in which female mating preferences are acquired by sexual imprinting on the parents and by exposure to the surviving population at large. Stabilizing viability selection acts equally on both sexes in the case of a sexually monomorphic trait and on males only in the case of a dimorphic trait. A genetically fixed sensory or perceptual bias defines the origin of the scale on which the trait is measured, and the possibility is incorporated that female preferences may deviate asymmetrically from the familiar-either toward or away from this origin. When viability selection is strong relative to sexual selection, the models predict that the mean trait value will evolve to the viability optimum. With intermediate ratios of the strength of viability to sexual selection, a stable equilibrium can occur on either side of this viability optimum, depending on the direction of asymmetry in female preferences. When viability selection is relatively weak and certain other conditions are also satisfied, runaway selection is predicted.     

Speciation: more likely through a genetic or through a learned habitat preference?

A problem in understanding sympatric speciation is establishing how reproductive isolation can arise when there is disruptive selection on an ecological trait. One of the solutions that has been proposed is that a habitat preference evolves, and that mates are chosen within the preferred habitat. We present a model where the habitat preference can evolve either by means of a genetic mechanism or by means of learning. Employing an adaptive-dynamical analysis, we show that evolution proceeds either to a single population of specialists with a genetic preference for their optimal habitat, or to a population of generalists without a habitat preference. The generalist population subsequently experiences disruptive selection. Learning promotes speciation because it increases the intensity of disruptive selection. An individual-based version of the model shows that, when loci are completely unlinked and learning confers little cost, the presence of disruptive selection most probably leads to speciation via the simultaneous evolution of a learned habitat preference. For high costs of learning, speciation is most likely to occur via the evolution of a genetic habitat preference. However, the latter only happens when the effect of mutations is large, or when there is linkage between genes coding for the different traits.     

Evolution of dominance under frequency-dependent intraspecific competition

A population-genetic analysis is performed of a two-locus two-allele model, in which the primary locus has a major effect on a quantitative trait that is under frequency-dependent disruptive selection caused by intraspecific competition for a continuum of resources. The modifier locus determines the degree of dominance at the trait level. We establish the conditions when a modifier allele can invade and when it becomes fixed if sufficiently frequent. In general, these are not equivalent because an unstable internal equilibrium may exist and the condition for successful invasion of the modifier is more restrictive than that for eventual fixation from already high frequency. However, successful invasion implies global fixation, i.e., fixation from any initial condition. Modifiers of large effect can become fixed, and also invade, in a wider parameter range than modifiers of small effect. We also study modifiers with a direct, frequency-independent deleterious fitness effect. We show that they can invade if they induce a sufficiently high level of dominance and if disruptive selection on the ecological trait is strong enough. For deleterious modifiers, successful invasion no longer implies global fixation because they can become stuck at an intermediate frequency due to a stable internal equilibrium. Although the conditions for invasion and for fixation if sufficiently frequent are independent of the linkage relation between the two loci, the rate of spread depends strongly on it. The present study provides further support to the view that evolution of dominance may be an efficient mechanism to remove unfit heterozygotes that are maintained by balancing selection. It also demonstrates that an invasion analysis of mutants of very small effect is insufficient to obtain a full understanding of the evolutionary dynamics under frequency-dependent selection.     

Frequency-dependent selection in bacterial populations

There are many situations in which the direction and intensity of natural selection in bacterial populations will depend on the relative frequencies of genotypes. In some cases, this selection will favour rare genotypes and result in the maintenance of genetic variability; this is termed stabilizing frequency-dependent selection. In other cases, selection will only favour genotypes when they are common. Rare types cannot invade and genetic variability will not be maintained; this is known as disruptive frequency-dependent selection. Phage-mediated selection for bacteria with novel restriction-modification systems is frequency-dependent and stabilizing. In mass culture, selection for the production of toxins and allelopathic agents is likely to be frequency-dependent but disruptive. This also occurs in selection favouring genes and transposable elements that cause mutations. Here I review the results of theoretical and experimental studies of stabilizing and disruptive frequency-dependent selection in bacterial populations, and speculate on the importance of this kind of selection in the adaptation and evolution of these organisms and their accessory elements (plasmid, phage and transposons).     

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.     

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.     

Evolutionary responses of Drosophila melanogaster to selection at different larval densities: changes in genetic variation,specialization and phenotypic plasticity

Abstract We studied the evolutionary response to novel environments by applying artificial selection for total progeny biomass in populations of Drosophila melanogaster maintained at three different larval population densities. We found the relative amount of genetic variability for characters related with biomass to be lower and the correlation between them more negative at the intermediate density, and that selection resulted in changes in phenotypic plasticity and in patterns of resource allocation between traits. We found some evidence for tradeoffs between densities, which suggests that populations living at heterogeneous densities might be subject to disruptive selection. Our results show that adaptation to new environments may be a complex process, involving not only changes in trait means, but also in correlations between traits and between environments.     

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.     

Testing the prediction from sexual selection of a positive genetic correlation between human mate preferences and corresponding traits

Sexual selection can cause evolution in traits that affect mating success, and it has thus been implicated in the evolution of human physical and behavioural traits that influence attractiveness. We use a large sample of identical and nonidentical female twins to test the prediction from mate choice models that a trait under sexual selection will be positively genetically correlated with preference for that trait. Six of the eight preferences we investigated, i.e. height, hair colour, intelligence, creativity, exciting personality, and religiosity, exhibited significant positive genetic correlations with the corresponding traits, while the personality measures ‘easy going’ and ‘kind and understanding’ exhibited no phenotypic or genetic correlation between preference and trait. The positive results provide important evidence consistent with the involvement of sexual selection in the evolution of these human traits.     

Pleiotropic Stabilizing Selection Limits the Number of Polymorphic Loci to at Most the Number of Characters

We demonstrate that, in a model incorporating weak Gaussian stabilizing selection on n additively determined characters, at most n loci are polymorphic at a stable equilibrium. The number of characters is defined to be the number of independent components in the Gaussian selection scheme. We also assume linkage equilibrium, and that either the number of loci is large enough that the phenotypic distribution in the population can be approximated as multivariate Gaussian or that selection is weak enough that the mean fitness of the population can be approximated using only the mean and the variance of the characters in the population. Our results appear to rule out antagonistic pleiotropy without epistasis as a major force in maintaining additive genetic variation in a uniform environment. However, they are consistent with the maintenance of variability by genotype-environment interaction if a trait in different environments corresponds to different characters and the number of different environments exceeds the number of polymorphic loci that affect the trait.     

Speciation through competition: a critical review

We examined causes of speciation in asexual populations in both sympatry and parapatry, providing an alternative explanation for the speciation patterns reported by Dieckmann and Doebeli (1999) and Doebeli and Dieckmann (2003). Both in sympatry and parapatry, they find that speciation occurs relatively easily. We reveal that in the sympatric clonal model, the equilibrium distribution is continuous and the disruptive selection driving evolution of discrete clusters is only transient. Hence, if discrete phenotypes are to remain stable in the sympatric sexual model, there should be some source of nontransient disruptive selection that will drive evolution of assortment. We analyze sexually reproducing populations using the Bulmer's infinitesimal model and show that cost-free assortment alone leads to speciation and disruptive selection only arises when the optimal distribution cannot be matched--in this example, because the phenotypic range is limited. In addition, Doebeli and Dieckmann's analyses assumed a high genetic variance and a high mutation rate. Thus, these theoretical models do not support the conclusion that sympatric speciation is a likely outcome of competition for resources. In their parapatric model (Doebeli and Dieckmann 2003), clustering into distinct phenotypes is driven by edge effects, rather than by frequency-dependent competition.