A multilocus-multiallele analysis of frequency-dependent selection induced by intraspecific competition

The study of the mechanisms that maintain genetic variation has a long history in population genetics. We analyze a multilocus-multiallele model of frequency- and density-dependent selection in a large randomly mating population. The number of loci and the number of alleles per locus are arbitrary. The n loci are assumed to contribute additively to a quantitative character under stabilizing or directional selection as well as under frequency-dependent selection caused by intraspecific competition. We assume the strength of stabilizing selection to be weak, whereas the strength of frequency dependence may be arbitrary. Density-dependence is induced by population regulation. Our main result is a characterization of the equilibrium structure and its stability properties in terms of all parameters. It turns out that no equilibrium exists with more than two alleles segregating per locus. We give necessary and sufficient conditions on the strength of frequency dependence to ensure the maintenance of multilocus polymorphism. We also give explicit formulas on the number of polymorphic loci maintained at equilibrium. These results are based on the assumption that selection is sufficiently weak compared with recombination, so that linkage equilibrium can be assumed. If additionally the population size is assumed to be constant, we prove that the dynamics of the model form a generalized gradient system. For the model in its general form we are able to derive necessary and sufficient conditions for the stability of the monomorphic equilibria. Furthermore, we briefly analyze a special symmetric two-locus two-allele model for a constant population size but allowing for linkage disequilibrium. Finally, we analyze a single diallelic locus with dominance to illustrate the complications that can occur if the assumption of additivity is relaxed.     

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.     

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.     

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.     

Multilocus genetics and the coevolution of quantitative traits

We develop and analyze an explicit multilocus genetic model of coevolution. We assume that interactions between two species (mutualists, competitors, or victim and exploiter) are mediated by a pair of additive quantitative traits that are also subject to direct stabilizing selection toward intermediate optima. Using a weak-selection approximation, we derive analytical results for a symmetric case with equal locus effects and no mutation, and we complement these results by numerical simulations of more general cases. We show that mutualistic and competitive interactions always result in coevolution toward a stable equilibrium with no more than one polymorphic locus per species. Victim-exploiter interactions can lead to different dynamic regimes including evolution toward stable equilibria, cycles, and chaos. At equilibrium, the victim is often characterized by a very large genetic variance, whereas the exploiter is polymorphic in no more than one locus. Compared to related one-locus or quantitative genetic models, the multilocus model exhibits two major new properties. First, the equilibrium structure is considerably more complex. We derive detailed conditions for the existence and stability of various classes of equilibria and demonstrate the possibility of multiple simultaneously stable states. Second, the genetic variances change dynamically, which in turn significantly affects the dynamics of the mean trait values. In particular, the dynamics tend to be destabilized by an increase in the number of loci.     

Opposing selection on a sexually dimorphic trait through female choice and male competition in a water boatman

Female choice and male-male competition are traditionally considered to act in concert, with male competition facilitating female choice. This situation would enforce the strength of directional selection, which could reduce genetic variation and thus the benefits of choice. Here I show that in a water boatman, Sigara falleni, the direction of selection through female choice and male competition vary among traits under laboratory conditions. The two forces were mutually enforcive in acting on body size but exerted opposing selection on a sexually selected trait, male foreleg pala size. Female choice favored large palae, whereas male competition favored smaller palae, suggesting that large palae are costly in competition. This conflicting selection through female choice and male competition could be one of the forces that contribute to the maintenance of genetic variation in sexually selected traits.     

Spatially and temporally varying selection on intrapopulation quantitative trait loci for a life history trade-off in Mimulus guttatus

Why do populations remain genetically variable despite strong continuous natural selection? Mutation reconstitutes variation eliminated by selection and genetic drift, but theoretical and experimental studies each suggest that mutation‐selection balance insufficient to explain extant genetic variation in most complex traits. The alternative hypothesis of balancing selection, wherein selection maintains genetic variation, is an aggregate of multiple mechanisms (spatial and temporal heterogeneity in selection, frequency‐dependent selection, antagonistic pleiotropy, etc.). Most of these mechanisms have been demonstrated for Mendelian traits, but there is little comparable data for loci affecting quantitative characters. Here, we report a 3‐year field study of selection on intrapopulation quantitative trait loci (QTL) of flower size, a highly polygenic trait in Mimulus guttatus. The QTL exhibit antagonistic pleiotropy: alleles that increase flower size, reduce viability, but increase fecundity. The magnitude and direction of selection fluctuates yearly and on a spatial scale of metres. This study provides direct evidence of balancing selection mechanisms on QTL of an ecologically relevant trait.     

Multivariate stabilizing selection and pleiotropy in the maintenance of quantitative genetic variation

Abstract. We investigate maintenance of quantitative genetic variation at mutation-selection balance for multiple traits. The intrinsic strength of real stabilizing selection on one of these traits denoted the "target trait" and the observed strength of apparent stabilizing selection on the target trait can be quite different: the latter, which is estimable, is much smaller (i.e., implying stronger selection) than the former. Distinguishing them may enable the mutation load to be relaxed when considering multivariate stabilizing selection. It is shown that both correlations among mutational effects and among strengths of real stabilizing selection on the traits are not important unless they are high. The analysis for independent situations thus provides a good approximation to the case where mutant and stabilizing selection effects are correlated. Multivariate stabilizing selection can be regarded as a combination of stabilizing selection on the target trait and the pleiotropic direct selection on fitness that is solely due to the effects of real stabilizing selection on the hidden traits. As the overall fitness approaches a constant value as the number of traits increases, multivariate stabilizing selection can maintain abundant genetic variance only under quite weak selection. The common observations of high polygenic variance and strong stabilizing selection thus imply that if the mutation-selection balance is the true mechanism of maintenance of genetic variation, the apparent stabilizing selection cannot arise solely by real stabilizing selection simultaneously on many metric traits.     

Efficiency of direct selection on quantitative trait loci for a two-trait breeding objective

Selection on known loci affecting quantitative traits (DSQ) was compared to phenotypic selection index for a single and a two-trait selection objective. Two situations were simulated; a single known quantitative locus, and ten identified loci accounting for all the additive genetic variance. Selection efficiency of DSQ relative to traitbased selection was higher for two-trait selection, than was selection on a single trait with the same heritability. The advantage of DSQ was greater when the traits were negatively correlated. Relative selection efficiency (RSE) for a single locus responsible for 0.1 of the genetic variance was 1.11 with heritabilities of 0.45 and 0.2 and zero genetic and phenotypic correlations between the traits. RSE of DSQ for ten known loci was 1.5 to 1.8 in the first 3 generations of selection, but declined in each subsequent generation. With DSQ most loci reached fixation after 7 generations. Response to trait-based selection continued through generation 15 and approached the response obtained with DSQ after 10 generations. The cumulative genetic response after 10 generations of DSQ was only 93% to 97% of the economically optimum genotype because the less favorable allele reached fixation for some loci, generally those with effects in opposite directions on the two traits.     

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.     

A strong quantitative trait locus for wing length on chromosome 2 in a wild population of great reed warblers

Wing length is a key character for essential behaviours related to bird flight such as migration and foraging. In the present study, we initiate the search for the genes underlying wing length in birds by studying a long-distance migrant, the great reed warbler (Acrocephalus arundinaceus). In this species wing length is an evolutionary interesting trait with pronounced latitudinal gradient and sex-specific selection regimes in local populations. We performed a quantitative trait locus (QTL) scan for wing length in great reed warblers using phenotypic, genotypic, pedigree and linkage map data from our long-term study population in Sweden. We applied the linkage analysis mapping method implemented in GridQTL (a new web-based software) and detected a genome-wide significant QTL for wing length on chromosome 2, to our knowledge, the first detected QTL in wild birds. The QTL extended over 25 cM and accounted for a substantial part (37%) of the phenotypic variance of the trait. A genome scan for tarsus length (a body-size-related trait) did not show any signal, implying that the wing-length QTL on chromosome 2 was not associated with body size. Our results provide a first important step into understanding the genetic architecture of avian wing length, and give opportunities to study the evolutionary dynamics of wing length at the locus level.     

Predator-prey relationships and the evolution of colour polymorphism: a comparative analysis in diurnal raptors

Genetically based variation in coloration occurs in populations of many organisms belonging to various taxa, including birds, mammals, frogs, molluscs, insects and plants. Colour polymorphism has evolved in raptors more often than in any other group of birds, suggesting that predator–prey relationships was a driving evolutionary force. Individuals displaying a new invading colour morph may enjoy an initial foraging advantage because prey have difficulties in learning the colour of a rare morph (apostatic selection), or because morphs provide alternative foraging benefits allowing differently coloured individuals to exploit distinct food niches (disruptive selection). Plumage polymorphism should therefore have evolved in species that prey upon animals having the physiological ability to distinguish between differently coloured predators but also to flee once a predator has been detected. From this assumption, we can predict that closely related polymorphic and monomorphic species prey upon different animals. They may also differ in morphology, because foraging upon different prey may require different foraging modes, and in turn different morphological structures. We tested these two predictions in a comparative study of raptors. As expected, polymorphic and monomorphic species had a different diet, and there was a difference in wing length between polymorphic and monomorphic species within two genera ( Buteo and Accipiter ). Across all raptors for which phylogenetic relationships are known, polymorphic species preyed more often upon mammals than did monomorphic ones. These two types of raptor did not differ in the frequency of birds, insects and reptiles in their diets. We discuss these results in the light of the hypothesis that predator–prey relationships played a role in the evolution of colour polymorphism. © 2004 The Linnean Society of London, Biological Journal of the Linnean Society , 2004, 81 , 565–578.     

Natural selection by avian predators on size and colour of a freshwater snail (Pomacea flagellatd)

We identify two avian predators of the Neotropical apple snail, Pomaceaflagellata, and estimate the strength, direction and form of multivariate natural selection by these predators on size and colour of snail shells. Limpkins are tactile predators and act as agents of disruptive selection on snail size, selecting average-sized snails disproportionately more often than small or large snails (y = 0.39, SE = 0.08). In addition, we were able to identify variation in handling behaviours and snail size selection among individual limpkins. Individual limpkins showed preferences for snails of different sizes and punctured the snail shells opposite the aperture mainly when handling large snails. Snail kites are visual predators and seem to be agents of directional selection against lighter coloured snails (β= 0.66, SE = 0.33). The ecological interaction between the apple snail and its predators provides a powerful system to further explore the role of predation in determining evolutionary changes in snail behaviour, morphology and life history.     

A test for negative frequency-dependent mating success as a function of male colour pattern in the bluefin killifish

Rare male mating advantage (a form of negative frequency dependence) is frequently proposed as a mechanism for the maintenance of genetic variation within populations. This hypothesis is attractive for systems with pronounced male colour polymorphism because it can maintain particularly high levels of variation. We tested for negative frequency-dependent mating success between yellow and red male colour patterns in bluefin killifish, Lucania goodei . Lucania goodei populations harbour substantial colour pattern polymorphism, and a large proportion of this variation has a genetic basis. We established outdoor mesocosms with red and yellow males in three different ratios: yellow rare (one yellow ♂ : five red ♂), even (three yellow ♂ : three red ♂), and red rare (five yellow ♂ : one red ♂). We obtained eggs and used microsatellites to determine paternity. By contrast to expectations, we found no support for a rare male mating advantage. Red males had slightly higher spawning success than yellow males, particularly in replicates with large clutches and when red males were rare. However, yellow males did not have higher mating success when rare. We discuss alternative mechanisms for the maintenance of the polymorphism as well as the potential reasons for the lack of a rare male mating advantage.  © 2009 The Linnean Society of London, Biological Journal of the Linnean Society , 2009, 98 , 489–500.     

Stability of the G-matrix in a population experiencing pleiotropic mutation, stabilizing selection, and genetic drift

Abstract. Quantitative genetics theory provides a framework that predicts the effects of selection on a phenotype consisting of a suite of complex traits. However, the ability of existing theory to reconstruct the history of selection or to predict the future trajectory of evolution depends upon the evolutionary dynamics of the genetic variance-covariance matrix (G-matrix). Thus, the central focus of the emerging field of comparative quantitative genetics is the evolution of the G-matrix. Existing analytical theory reveals little about the dynamics of G, because the problem is too complex to be mathematically tractable. As a first step toward a predictive theory of G-matrix evolution, our goal was to use stochastic computer models to investigate factors that might contribute to the stability of G over evolutionary time. We were concerned with the relatively simple case of two quantitative traits in a population experiencing stabilizing selection, pleiotropic mutation, and random genetic drift. Our results show that G-matrix stability is enhanced by strong correlational selection and large effective population size. In addition, the nature of mutations at pleiotropic loci can dramatically influence stability of G. In particular, when a mutation at a single locus simultaneously changes the value of the two traits (due to pleiotropy) and these effects are correlated, mutation can generate extreme stability of G. Thus, the central message of our study is that the empirical question regarding G-matrix stability is not necessarily a general question of whether G is stable across various taxonomic levels. Rather, we should expect the G-matrix to be extremely stable for some suites of characters and unstable for others over similar spans of evolutionary time.     

Contrasting effects of plant inter‐ and intraspecific variation on community trait responses to restoration of a sandy grassland ecosystem

Changes in plant community traits along an environmental gradient are caused by interspecific and intraspecific trait variation. However, little is known about the role of interspecific and intraspecific trait variation in plant community responses to the restoration of a sandy grassland ecosystem. We measured five functional traits of 34 species along a restoration gradient of sandy grassland (mobile dune, semi‐fixed dune, fixed dune, and grassland) in Horqin Sand Land, northern China. We examined how community‐level traits varied with habitat changes and soil gradients using both abundance‐weighted and non‐weighted averages of trait values. We quantified the relative contribution of inter‐ and intraspecific trait variation in specific leaf area (SLA), leaf dry matter content (LDMC), leaf carbon content (LCC), leaf nitrogen content (LNC), and plant height to the community response to habitat changes in the restoration of sandy grassland. We found that five weighted community‐average traits varied significantly with habitat changes. Along the soil gradient in the restoration of sandy grassland, plant height, SLA, LDMC, and LCC increased, while LNC decreased. For all traits, there was a greater contribution of interspecific variation to community response in regard to habitat changes relative to that of intraspecific variation. The relative contribution of the interspecific variation effect of an abundance‐weighted trait was greater than that of a non‐weighted trait with regard to all traits except LDMC. A community‐level trait response to habitat changes was due largely to species turnover. Though the intraspecific shift plays a small role in community trait response to habitat changes, it has an effect on plant coexistence and the maintenance of herbaceous plants in sandy grassland habitats. The context dependency of positive and negative covariation between inter‐ and intraspecific variation further suggests that both effects of inter‐ and intraspecific variation on a community trait should be considered when understanding a plant community response to environmental changes in sandy grassland ecosystems.     

Replication and refinement of a quantitative trait locus influencing milk protein percentage on ovine chromosome 3

A previous genome scan that was conducted in Spanish Churra sheep identified a significant quantitative trait locus (QTL) for milk protein percentage (PP) on chromosome 3 (OAR3), between markers KD103 and OARVH34. The aim of this study was to replicate these results and to refine the mapped position of this QTL. To accomplish this goal, we analysed 14 new half‐sib families of Spanish Churra sheep including 1661 ewes from 29 different flocks. These animals were genotyped for 21 microsatellite markers mapping to OAR3. In addition to a classical linkage analysis (LA), a combined linkage disequilibrium and linkage analysis (LDLA) was performed with the aim of enhancing the resolution of the QTL mapping. The LA that was performed in this sheep population identified the presence of a highly significant QTL for PP near marker KD103 (P_c < 0.001; P_exp < 0.001). The phenotypic variance that was owing to the QTL was 2.74%. Two segregating families for the target QTL were identified in this population with QTL effect estimates of 0.47 and 0.95 SD. The LDLA identified the same QTL as the previous analyses with a high level of statistical significance (P = 9.184 E‐11) and narrowed the confidence interval (CI) to a 13 cM region. These results confirm the segregation of the previously identified OAR3 QTL that influences PP in Spanish Churra sheep. Future research will aim to increase the marker density across the refined CI and to analyse the corresponding candidate genes to identify the allelic variant or variants that underlie this genetic effect.     

Spatial and temporal patterns of nest distribution influence sexual selection in a marine fish

In many species, the natural distribution of material resources important for reproduction can profoundly impact reproductive success among individuals and, hence, the opportunity and intensity of sexual selection. Here, we report on a field‐based experiment investigating the effects of nest aggregation on sexual selection in a fish, the sand goby Pomatoschistus minutus. We found that the distribution of potential nests (sparse versus aggregated nest treatments) affected patterns of nest colonization and reproductive success. Specifically, in the treatment with aggregated nesting resources, a greater proportion of nests remained unoccupied by sand goby males. Although the size of nesting males did not differ between treatments, eggs accumulated more rapidly when nests were sparsely distributed. We found that the opportunity for selection decreased over time with the accumulation of eggs in the nests in both the aggregated and sparse treatments. Moreover, the effect of male size on reproductive success was influenced by an interaction between nest distribution and time, with the selection gradient being highest right after nest colonization when nests were aggregated, while the opposite pattern was observed in the sparse nest treatment. Such findings highlight the vital role that environmental and social factors can play in determining the importance of male phenotypic traits (in this case, male size). More broadly, our results also underscore how the natural distribution of resources, both in space and time, can impact the strength of sexual selection acting on wild animal populations.     

Disentangling the effects of recombination,selection, and demography on the genetic variation at a major histocompatibility complex class II gene in the alpine chamois

The major histocompatibility complex (MHC) harbours some of the most polymorphic loci in vertebrate genomes. MHC genes are thought to be subject to some form of balancing selection, most likely pathogen‐mediated selection. Hence, MHC genes are excellent candidates for exploring adaptive processes. In this study, we investigated the genetic variation at exon 2 of the DRB class II MHC locus in 191 alpine chamois (Rupicapra rupicapra) from 10 populations in the eastern Alps of Italy. In particular, we were interested in distinguishing and estimating the relative impact of selective and demographic factors, while taking into account the confounding effect of recombination. The extremely high d_n/d_s ratio and the presence of trans‐species polymorphisms suggest that a strong long‐term balancing selection effect has been operating at this locus throughout the evolutionary history of this species. We analysed patterns of genetic variation within and between populations, and the mitochondrial D‐loop polymorphism patterns were analysed to provide a baseline indicator of the effects of demographic processes. These analyses showed that (i) the chamois experienced a demographic decline in the last 5000–30 000 years, most likely related to the postglacial elevation in temperature; (ii) this demographic process can explain the results of neutrality tests applied to MHC variation within populations, but cannot justify the much weaker divergence between populations implied by MHC as opposed to mitochondrial DNA; (iii) similar sets of divergent alleles are probably maintained with similar frequencies by balancing selection in different populations, and this mechanism is also operating in small isolated populations, which are strongly affected by drift.     

Non-linear selection response in Drosophila: a strategy for testing the rare-alleles model of quantitative genetic variability

Quantitative genetic theory predicts that variation due to rare alleles at many loci will generate a transient acceleration in the response to directional selection. We have tested this prediction by constructing experimental lines ofDrosophila melanogaster that carry positively selected ethanol resistance alleles at low frequencies, and then subjecting the lines to directional selection for ethanol resistance. Approximately 468,000 files were subjected to artificial selection over 30 generations. The predicted non-linear selection responses were observed in all experimental lines and replicates, on three genetic backgrounds. In contrast, un-selected controls and lines carrying random alleles at low frequencies on the same genetic backgrounds exhibited linear selection responses. These results demonstrate that non-linearities due to rare alleles are detectable and repeatable, provided that experiments are done on a sufficiently large scale. The results suggest that it may be possible to test for rare-alleles as a component of naturally occurring genetic variation by careful examination of selection response curves.