The evolution of genetic architectures underlying quantitative traits

In the classic view introduced by R. A. Fisher, a quantitative trait is encoded by many loci with small, additive effects. Recent advances in quantitative trait loci mapping have begun to elucidate the genetic architectures underlying vast numbers of phenotypes across diverse taxa, producing observations that sometimes contrast with Fisher''s blueprint. Despite these considerable empirical efforts to map the genetic determinants of traits, it remains poorly understood how the genetic architecture of a trait should evolve, or how it depends on the selection pressures on the trait. Here, we develop a simple, population-genetic model for the evolution of genetic architectures. Our model predicts that traits under moderate selection should be encoded by many loci with highly variable effects, whereas traits under either weak or strong selection should be encoded by relatively few loci. We compare these theoretical predictions with qualitative trends in the genetics of human traits, and with systematic data on the genetics of gene expression levels in yeast. Our analysis provides an evolutionary explanation for broad empirical patterns in the genetic basis for traits, and it introduces a single framework that unifies the diversity of observed genetic architectures, ranging from Mendelian to Fisherian.     

Self-fertilization and the evolution of recombination

In this article, we study the effect of self-fertilization on the evolution of a modifier allele that alters the recombination rate between two selected loci. We consider two different life cycles: under gametophytic selfing, a given proportion of fertilizations involves gametes produced by the same haploid individual, while under sporophytic selfing, a proportion of fertilizations involves gametes produced by the same diploid individual. Under both life cycles, we derive approximations for the change in frequency of the recombination modifier when selection is weak relative to recombination, so that the population reaches a state of quasi-linkage equilibrium. We find that gametophytic selfing increases the range of epistasis under which increased recombination is favored; however, this effect is substantial only for high selfing rates. Moreover, gametophytic selfing affects the relative influence of different components of epistasis (additive x additive, additive x dominance, dominance x dominance) on the evolution of the modifier. Sporophytic selfing has much stronger effects: even a small selfing rate greatly increases the parameter range under which recombination is favored, when there is negative dominance x dominance epistasis. This effect is due to the fact that selfing generates a correlation in homozygosity at linked loci, which is reduced by recombination.     

The evolution of female preferences for multiple indicators of quality

In a variety of species, females exhibit preferences for multiple male ornaments. Several hypotheses have been proposed to explain this phenomenon. Which, if any, of these hypotheses is the most plausible in general remains largely unresolved based on the available empirical data. Yet theoretical studies conclude that the evolution of preferences for multiple signals of male quality is unlikely, especially when the use of an additional cue in mate choice strongly increases the overall cost of choice. This would imply that most male courtship characters do not reflect the male's genetic quality but instead evolved through Fisherian sexual selection. However, the existing models focus on ornaments that signal overall genetic quality and do not address the possibility that different ornaments provide information about different aspects of quality. Therefore, we develop a model in which the ornaments act as signals for distinct quality components. When the ornaments provide overlapping information about these quality components, we retrieve the results of earlier models. However, when the ornaments provide independent information, preferences for multiple ornaments may evolve, even when exhibiting multiple preferences is costly. We discuss our results in relation to the multiple-message and redundant-signal hypotheses for ornament diversity and identify parallels between Fisherian and good-genes mechanisms for the evolution of multiple ornaments.     

Feedback selection and the evolution of modifiers

The problem of modifier evolution was examined with regard to the idea that modifier evolution can be considered as a result of selection for adaptation speed in populations far from equilibrium. This kind of selection was called feedback selection in order to emphasize the difference to theories which consider modifier evolution near the equilibrium. The basic principles of this kind of selection are derived for asexual populations and the problem of dominance is discussed in the light of this concept. In general the results support the view, that the genetic properties of a character are selected along with the character itself.This work was supported by the Austrian Fonds zur Förderung der Wissenschaftlichen Forschung (Proj. Nr. 3502).     

The reality and importance of founder speciation in evolution

A founder event occurs when a new population is established from a small number of individuals drawn from a large ancestral population. Mayr proposed that genetic drift in an isolated founder population could alter the selective forces in an epistatic system, an observation supported by recent studies. Carson argued that a period of relaxed selection could occur when a founder population is in an open ecological niche, allowing rapid population growth after the founder event. Selectable genetic variation can actually increase during this founder-flush phase due to recombination, enhanced survival of advantageous mutations, and the conversion of non-additive genetic variance into additive variance in an epistatic system, another empirically confirmed prediction. Templeton combined the theories of Mayr and Carson with population genetic models to predict the conditions under which founder events can contribute to speciation, and these predictions are strongly confirmed by the empirical literature. Much of the criticism of founder speciation is based upon equating founder speciation to an adaptive peak shift opposed by selection. However, Mayr, Carson and Templeton all modeled a positive interaction of selection and drift, and Templeton showed that founder speciation is incompatible with peak-shift conditions. Although rare, founder speciation can have a disproportionate importance in adaptive innovation and radiation, and examples are given to show that "rare" does not mean "unimportant" in evolution. Founder speciation also interacts with other speciation mechanisms such that a speciation event is not a one-dimensional process due to either selection alone or drift alone.     

Meta-analysis suggests choosy females get sexy sons more than "good genes"

Female preferences for specific male phenotypes have been documented across a wide range of animal taxa, including numerous species where males contribute only gametes to offspring production. Yet, selective pressures maintaining such preferences are among the major unknowns of evolutionary biology. Theoretical studies suggest that preferences can evolve if they confer genetic benefits in terms of increased attractiveness of sons ("Fisherian" models) or overall fitness of offspring ("good genes" models). These two types of models predict, respectively, that male attractiveness is heritable and genetically correlated with fitness. In this meta-analysis, we draw general conclusions from over two decades worth of empirical studies testing these predictions (90 studies on 55 species in total). We found evidence for heritability of male attractiveness. However, attractiveness showed no association with traits directly associated with fitness (life-history traits). Interestingly, it did show a positive correlation with physiological traits, which include immunocompetence and condition. In conclusion, our results support "Fisherian" models of preference evolution, while providing equivocal evidence for "good genes." We pinpoint research directions that should stimulate progress in our understanding of the evolution of female choice.     

Segregation and the evolution of sex under overdominant selection

The segregation of alleles disrupts genetic associations at overdominant loci, causing a sexual population to experience a lower mean fitness compared to an asexual population. To investigate whether circumstances promoting increased sex exist within a population with heterozygote advantage, a model is constructed that monitors the frequency of alleles at a modifier locus that changes the relative allocation to sexual and asexual reproduction. The frequency of these modifier alleles changes over time as a correlated response to the dynamics at a fitness locus under overdominant selection. Increased sex can be favored in partially sexual populations that inbreed to some extent. This surprising finding results from the fact that inbred populations have an excess of homozygous individuals, for whom sex is always favorable. The conditions promoting increased levels of sex depend on the selection pressure against the homozygotes, the extent of sex and inbreeding in the population, and the dominance of the invading modifier allele.     

A model of the early evolution of soma-to-germline feedback

The V-genes of the immunoglobulin locus in vertebrates code for a part of the heavy and light chain variable regions of antibodies and are extremely variable. Steele (1979) has developed a theory that explains the evolution of adaptive immune response by a soma-to-germline flow of cDNAs derived from somatically mutated V-genes. Here we model the early evolution of soma-to-germline feedback in a population living in a changing viral environment in terms of the dynamics of an initially rare genetic modifier that controls transfer of V-genes to germ cells' DNA. It is shown that a modifier invades the population and creates a great variety of V-genes if the environment follows stepwise temporal changes, i.e. a soma-to-germline feedback machinery evolves in a population if newly derived V-alleles still play a role in protecting the population against foreign antigens in some following generations. The distribution of the age of V-genes evolves to a bell-shaped curve the width and the maximum of which depend mainly on selection strength. Two phases of modifier evolution are distinguished. In the first phase, the dynamics are slow while the number of different V-genes is small. In the second phase, when a sufficiently large number of different V-genes is created, the modifier increases faster in frequency. Linkage of V-genes and the modifier enhances the rate of evolution.     

Weak selection and protein evolution

The "nearly neutral" theory of molecular evolution proposes that many features of genomes arise from the interaction of three weak evolutionary forces: mutation, genetic drift, and natural selection acting at its limit of efficacy. Such forces generally have little impact on allele frequencies within populations from generation to generation but can have substantial effects on long-term evolution. The evolutionary dynamics of weakly selected mutations are highly sensitive to population size, and near neutrality was initially proposed as an adjustment to the neutral theory to account for general patterns in available protein and DNA variation data. Here, we review the motivation for the nearly neutral theory, discuss the structure of the model and its predictions, and evaluate current empirical support for interactions among weak evolutionary forces in protein evolution. Near neutrality may be a prevalent mode of evolution across a range of functional categories of mutations and taxa. However, multiple evolutionary mechanisms (including adaptive evolution, linked selection, changes in fitness-effect distributions, and weak selection) can often explain the same patterns of genome variation. Strong parameter sensitivity remains a limitation of the nearly neutral model, and we discuss concave fitness functions as a plausible underlying basis for weak selection.     

Selection, Generalized Transmission and the Evolution of Modifier Genes. I. the Reduction Principle

Modifier gene models are used to explore the evolution of features of organisms, such as the genetic system, that are not directly involved in the determination of fitness. Recent work has shown that a general "reduction principle" holds in models of selectively neutral modifiers of recombination, mutation, and migration. Here we present a framework for models of modifier genes that shows these reduction results to be part of a more general theory, for which recombination and mutation are special cases. The deterministic forces that affect the genetic composition of a population can be partitioned into two categories: selection and transmission. Selection includes differential viabilities, fertilities, and mating success. Imperfect transmission occurs as a result of such phenomena as recombination, mutation and migration, meiosis, gene conversion, and meiotic drive. Selectively neutral modifier genes affect transmission, and a neutral modifier gene can evolve only by generating association with selected genes whose transmission it affects. We show that, in randomly mating populations at equilibrium, imperfect transmission of selected genes allows a variance in their marginal fitnesses to be maintained. This variance in the marginal fitnesses of selected genes is what drives the evolution of neutral modifier genes. Populations with a variance in marginal fitnesses at equilibrium are always subject to invasion by modifier genes that bring about perfect transmission of the selected genes. It is also found, within certain constraints, that for modifier genes producing what we call "linear variation" in the transmission processes, a new modifier allele can invade a population at equilibrium if it reduces the level of imperfect transmission acting on the selected genes, and will be expelled if it increases the level of imperfect transmission. Moreover, the strength of the induced selection on the modifier gene is shown to range up to the order of the departure of the genetic system from perfect transmission.     

The evolution of trade-offs under directional and correlational selection

Using quantitative genetic theory, we develop predictions for the evolution of trade-offs in response to directional and correlational selection. We predict that directional selection favoring an increase in one trait in a trade-off will result in change in the intercept but not the slope of the trade-off function, with the mean value of the selected trait increasing and that of the correlated trait decreasing. Natural selection will generally favor an increase in some combination of trait values, which can be represented as directional selection on an index value. Such selection induces both directional and correlational selection on the component traits. Theory predicts that selection on an index value will also change the intercept but not the slope of the trade-off function but because of correlational selection, the direction of change in component traits may be in the same or opposite directions. We test these predictions using artificial selection on the well-established trade-off between fecundity and flight capability in the cricket, Gryllus firmus and compare the empirical results with a priori predictions made using genetic parameters from a separate half-sibling experiment. Our results support the predictions and illustrate the complexity of trade-off evolution when component traits are subject to both directional and correlational selection.     

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.     

Rapid independent trait evolution despite a strong pleiotropic genetic correlation

Genetic correlations are the most commonly studied of all potential constraints on adaptive evolution. We present a comprehensive test of constraints caused by genetic correlation, comparing empirical results to predictions from theory. The additive genetic correlation between the filament and the corolla tube in wild radish flowers is very high in magnitude, is estimated with good precision (0.85 ± 0.06), and is caused by pleiotropy. Thus, evolutionary changes in the relative lengths of these two traits should be constrained. Still, artificial selection produced rapid evolution of these traits in opposite directions, so that in one replicate relative to controls, the difference between them increased by six standard deviations in only nine generations. This would result in a 54% increase in relative fitness on the basis of a previous estimate of natural selection in this population, and it would produce the phenotypes found in the most extreme species in the family Brassicaceae in less than 100 generations. These responses were within theoretical expectations and were much slower than if the genetic correlation was zero; thus, there was evidence for constraint. These results, coupled with comparable results from other species, show that evolution can be rapid despite the constraints caused by genetic correlations.     

Dynamics of the classical genetic model for the evolution of dominance

Using a generalized method of Ljapunov functions, the dynamics of the classical genetic model for the evolution of dominance is studied. The model is treated as a two locus two allele system of a primary and a modifying locus with selection, mutation, and recombination. Its behavior may be described either by a system of four differential equations or by a system of four difference equations. In particular, it is proved that under very general conditiones on the five parameters involved, in both cases the well-known fixed point for the mutation-selection balance at the primary locus when the modifier is completely selected is globally asymptotically stable. If, however, the unmodified heterozygote is completely recessive or underdominant, the modifier is only selected if at the beginning of the evolution its frequency and that of the favorable primary allele is not extremely low. Otherwise, it may happen that the favorable primary allele becomes extinct.     

Mate choice evolution, dominance effects, and the maintenance of genetic variation

Female mate choice influences the maintenance of genetic variation by altering the mating success of males with different genotypes. The evolution of preferences themselves, on the other hand, depends on genetic variation present in the population. Few models have tracked this feedback between a choice gene and its effects on genetic variation, in particular when genes that determine offspring viability and attractiveness have dominance effects. Here we build a population genetic model that allows comparing the evolution of various choice rules in a single framework. We first consider preferences for good genes and show that focused preferences for homozygotes evolve more easily than broad preferences, which allow heterozygous males high mating success too. This occurs despite better maintenance of genetic diversity in the latter scenario, and we discuss why empirical findings of superior mating success of heterozygous males consequently do not immediately lead to a better understanding of the lek paradox. Our results thus suggest that the mechanisms that help maintain genetic diversity also have a flipside of making female choice an inaccurate means of producing the desired kind of offspring. We then consider preferences for heterozygosity per se, and show that these evolve only under very special conditions. Choice for compatible genotypes can evolve but its selective advantage diminishes quickly due to frequency-dependent selection. Finally, we show that our model reproduces earlier results on selfing, when the female choice strategy produces assortative mating. Overall, our model indicates that various forms of heterozygote-favouring (or variable) female choice pose a problem for the theory of sexual ornamentation based on indirect benefits, rather than a solution.     

The resolution of sexual antagonism by gene duplication

Disruptive selection between males and females can generate sexual antagonism, where alleles improving fitness in one sex reduce fitness in the other. This type of genetic conflict arises because males and females carry nearly identical sets of genes: opposing selection, followed by genetic mixing during reproduction, generates a population genetic "tug-of-war" that constrains adaptation in either sex. Recent verbal models suggest that gene duplication and sex-specific cooption of paralogs might resolve sexual antagonism and facilitate evolutionary divergence between the sexes. However, this intuitive proximal solution for sexual dimorphism potentially belies a complex interaction between mutation, genetic drift, and positive selection during duplicate fixation and sex-specific paralog differentiation. The interaction of these processes--within the explicit context of duplication and sexual antagonism--has yet to be formally described by population genetics theory. Here, we develop and analyze models of gene duplication and sex-specific differentiation between paralogs. We show that sexual antagonism can favor the fixation and maintenance of gene duplicates, eventually leading to the evolution of sexually dimorphic genetic architectures for male and female traits. The timescale for these evolutionary transitions is sensitive to a suite of genetic and demographic variables, including allelic dominance, recombination, sex linkage, and population size. Interestingly, we find that female-beneficial duplicates preferentially accumulate on the X chromosome, whereas male-beneficial duplicates are biased toward autosomes, independent of the dominance parameters of sexually antagonistic alleles. Although this result differs from previous models of sexual antagonism, it is consistent with several findings from the empirical genomics literature.     

Genetic perspectives on northern population cycles: bridging the gap between theory and empirical studies

Many key species in northern ecosystems are characterised by high‐amplitude cyclic population demography. In 1924, Charles Elton described the ecology and evolution of cyclic populations in a classic paper and, since then, a major focus has been the underlying causes of population cycles. Elton hypothesised that fluctuations reduced population genetic variation and influenced the direction of selection pressures. In concordance with Elton, present theories concern the direct consequences of population cycles for genetic structure due to the processes of genetic drift and selection, but also include feedback models of genetic composition on population dynamics. Most of these theories gained mathematical support during the 1970s and onwards, but due to methodological drawbacks, difficulties in long‐term sampling and a complex interplay between microevolutionary processes, clear empirical data allowing the testing of these predictions are still scarce. Current genetic tools allow for estimates of genetic variation and identification of adaptive genomic regions, making this an ideal time to revisit this subject. Herein, we attempt to contribute towards a consensus regarding the enigma described by Elton almost 90 years ago. We present nine predictions covering the direct and genetic feedback consequences of population cycles on genetic variation and population structure, and review the empirical evidence. Generally, empirical support for the predictions was low and scattered, with obvious gaps in the understanding of basic population processes. We conclude that genetic variation in northern cyclic populations generally is high and that the geographic distribution and amount of diversity are usually suggested to be determined by various forms of context‐ and density‐dependent dispersal exceeding the impact of genetic drift. Furthermore, we found few clear signatures of selection determining genetic composition in cyclic populations. Dispersal is assumed to have a strong impact on genetic structuring and we suggest that the signatures of other microevolutionary processes such as genetic drift and selection are weaker and have been over‐shadowed by density‐dependent dispersal. We emphasise that basic biological and demographical questions still need to be answered and stress the importance of extensive sampling, appropriate choice of tools and the value of standardised protocols.     

Genetic variation in male attractiveness: It is time to see the forest for the trees

Female choice based on multiple male traits, rather than on any single one, has been reported in many species and may well be a rule rather than an exception. However, the implications this has for selection acting on choosiness itself remain underappreciated. We argue that this constitutes one of the important impediments to our understanding of the evolution of mate choice. We discuss this issue primarily in the context of the Fisherian model of sexual selection. We review theory and empirical data, showing how the crucial parameter of the model—genetic variation in male attractiveness—can be estimated when attractiveness is a function of multiple traits. Based on the reviewed theory, we show how relying on individual male traits, instead of overall attractiveness, can produce biased estimates of Fisherian benefits of female choice. This bias can be substantial, especially when many traits contribute to male attractiveness. We discuss a number of methodological issues that, we hope, will stimulate future studies and help resolving the long‐standing mystery of mate choice.     

The evolution of concerted evolution

Concerted evolution is a consequence of processes that convert copies of a gene in a multigene family into the same copy. Here we ask whether this homogenization may be adaptive. Analysis of a modifier of homogenization reveals (1) that the trait is most likely to spread if interactions between deleterious mutations are not strongly synergistic; (2) that selection on the modifier is of the order of the mutation rate, hence the modifier is most likely to be favoured by selection when the species has a large effective population size and/or if the modifier affects many genes simultaneously; and (3) that linkage between the genes in the family, and between these genes and the modifier, makes invasion of the modifier easier, suggesting that selection may favour multigene families being in clustered arrays. It follows from the first conclusion that genes for which mutations may often be dominant or semi-dominant should undergo concerted evolution more commonly than others. By analysis of the mouse knockout database, we show that mutations affecting growth-related genes are more commonly associated with dominant lethality than expected by chance. We predict then that selection will favour homogenization of such genes, and possibly others that are significantly dosage dependent, more often than it favours homogenization in other genes. The first condition is almost the opposite of that required for the maintenance of sexual reproduction according to the mutation-deterministic theory. The analysis here therefore suggests that sexual organisms can simultaneously minimize both the effects of deleterious, strongly synergistically, interacting mutations and those that interact either weakly synergistically, multiplicatively, or antagonistically, assuming the latter class belong to a multicopy gene family. Recombination and an absence of homogenization are efficient in purging deleterious mutations in the former class, homogenization and an absence of recombination are efficient at minimizing the costs imposed by the latter classes.