An exact form of the breeder's equation for the evolution of a quantitative trait under natural selection

Starting with the Price equation, I show that the total evolutionary change in mean phenotype that occurs in the presence of fitness variation can be partitioned exactly into five components representing logically distinct processes. One component is the linear response to selection, as represented by the breeder's equation of quantitative genetics, but with heritability defined as the linear regression coefficient of mean offspring phenotype on parent phenotype. The other components are identified as constitutive transmission bias, two types of induced transmission bias, and a spurious response to selection caused by a covariance between parental fitness and offspring phenotype that cannot be predicted from parental phenotypes. The partitioning can be accomplished in two ways, one with heritability measured before (in the absence of) selection, and the other with heritability measured after (in the presence of) selection. Measuring heritability after selection, though unconventional, yields a representation for the linear response to selection that is most consistent with Darwinian evolution by natural selection because the response to selection is determined by the reproductive features of the selected group, not of the parent population as a whole. The analysis of an explicitly Mendelian model shows that the relative contributions of the five terms to the total evolutionary change depends on the level of organization (gene, individual, or mated pair) at which the parent population is divided into phenotypes, with each frame of reference providing unique insight. It is shown that all five components of phenotypic evolution will generally have nonzero values as a result of various combinations of the normal features of Mendelian populations, including biparental sex, allelic dominance, inbreeding, epistasis, linkage disequilibrium, and environmental covariances between traits. Additive genetic variance can be a poor predictor of the adaptive response to selection in these models. The narrow-sense heritability sigma2A/sigma2P should be viewed as an approximation to the offspring-parent linear regression rather than the other way around.     

The genetic consequences of selection in natural populations

The selection coefficient, s, quantifies the strength of selection acting on a genetic variant. Despite this parameter's central importance to population genetic models, until recently we have known relatively little about the value of s in natural populations. With the development of molecular genetic techniques in the late 20th century and the sequencing technologies that followed, biologists are now able to identify genetic variants and directly relate them to organismal fitness. We reviewed the literature for published estimates of natural selection acting at the genetic level and found over 3000 estimates of selection coefficients from 79 studies. Selection coefficients were roughly exponentially distributed, suggesting that the impact of selection at the genetic level is generally weak but can occasionally be quite strong. We used both nonparametric statistics and formal random‐effects meta‐analysis to determine how selection varies across biological and methodological categories. Selection was stronger when measured over shorter timescales, with the mean magnitude of s greatest for studies that measured selection within a single generation. Our analyses found conflicting trends when considering how selection varies with the genetic scale (e.g., SNPs or haplotypes) at which it is measured, suggesting a need for further research. Besides these quantitative conclusions, we highlight key issues in the calculation, interpretation, and reporting of selection coefficients and provide recommendations for future research.     

Social traits,social networks and evolutionary biology

The social environment is both an important agent of selection for most organisms, and an emergent property of their interactions. As an aggregation of interactions among members of a population, the social environment is a product of many sets of relationships and so can be represented as a network or matrix. Social network analysis in animals has focused on why these networks possess the structure they do, and whether individuals’ network traits, representing some aspect of their social phenotype, relate to their fitness. Meanwhile, quantitative geneticists have demonstrated that traits expressed in a social context can depend on the phenotypes and genotypes of interacting partners, leading to influences of the social environment on the traits and fitness of individuals and the evolutionary trajectories of populations. Therefore, both fields are investigating similar topics, yet have arrived at these points relatively independently. We review how these approaches are diverged, and yet how they retain clear parallelism and so strong potential for complementarity. This demonstrates that, despite separate bodies of theory, advances in one might inform the other. Techniques in network analysis for quantifying social phenotypes, and for identifying community structure, should be useful for those studying the relationship between individual behaviour and group‐level phenotypes. Entering social association matrices into quantitative genetic models may also reduce bias in heritability estimates, and allow the estimation of the influence of social connectedness on trait expression. Current methods for measuring natural selection in a social context explicitly account for the fact that a trait is not necessarily the property of a single individual, something the network approaches have not yet considered when relating network metrics to individual fitness. Harnessing evolutionary models that consider traits affected by genes in other individuals (i.e. indirect genetic effects) provides the potential to understand how entire networks of social interactions in populations influence phenotypes and predict how these traits may evolve. By theoretical integration of social network analysis and quantitative genetics, we hope to identify areas of compatibility and incompatibility and to direct research efforts towards the most promising areas. Continuing this synthesis could provide important insights into the evolution of traits expressed in a social context and the evolutionary consequences of complex and nuanced social phenotypes.     

The conflict between natural and artificial selection in finite populations

Summary A single locus model of the interaction between natural selection and artificial selection for a quantitative character in a finite population, assuming heterozygote superiority in natural fitness but additive action on the character, has been studied using transition probability matrices.If natural selection is strong enough to create a selection plateau in which genetic variance declines relatively slowly, then the total response to artificial selection prior to the plateau will be much less than that expected in the absence of natural selection, and the half-life of response will be shorter. Such a plateau is likely to have a large proportion, if not all, of the original genetic variance still present. In selection programmes using laboratory animals, it seems likely that the homozygote favoured by artificial selection must be very unfit before such a plateau will occur. A significant decrease in population fitness as a result of artificial selection does not necessarily imply that the metric character is an important adaptive character.These implications of this model of natural selection are very similar to those derived by James (1962) for the optimum model of natural selection. In fact, there seems to be no aspect of the observable response to artificial selection that would enable anyone to distinguish between these two models of natural selection.     

The mutation matrix and the evolution of evolvability

Evolvability is a key characteristic of any evolving system, and the concept of evolvability serves as a unifying theme in a wide range of disciplines related to evolutionary theory. The field of quantitative genetics provides a framework for the exploration of evolvability with the promise to produce insights of global importance. With respect to the quantitative genetics of biological systems, the parameters most relevant to evolvability are the G-matrix, which describes the standing additive genetic variances and covariances for a suite of traits, and the M-matrix, which describes the effects of new mutations on genetic variances and covariances. A population's immediate response to selection is governed by the G-matrix. However, evolvability is also concerned with the ability of mutational processes to produce adaptive variants, and consequently the M-matrix is a crucial quantitative genetic parameter. Here, we explore the evolution of evolvability by using analytical theory and simulation-based models to examine the evolution of the mutational correlation, r(mu), the key parameter determining the nature of genetic constraints imposed by M. The model uses a diploid, sexually reproducing population of finite size experiencing stabilizing selection on a two-trait phenotype. We assume that the mutational correlation is a third quantitative trait determined by multiple additive loci. An individual's value of the mutational correlation trait determines the correlation between pleiotropic effects of new alleles when they arise in that individual. Our results show that the mutational correlation, despite the fact that it is not involved directly in the specification of an individual's fitness, does evolve in response to selection on the bivariate phenotype. The mutational variance exhibits a weak tendency to evolve to produce alignment of the M-matrix with the adaptive landscape, but is prone to erratic fluctuations as a consequence of genetic drift. The interpretation of this result is that the evolvability of the population is capable of a response to selection, and whether this response results in an increase or decrease in evolvability depends on the way in which the bivariate phenotypic optimum is expected to move. Interestingly, both analytical and simulation results show that the mutational correlation experiences disruptive selection, with local fitness maxima at -1 and +1. Genetic drift counteracts the tendency for the mutational correlation to persist at these extreme values, however. Our results also show that an evolving M-matrix tends to increase stability of the G-matrix under most circumstances. Previous studies of G-matrix stability, which assume nonevolving M-matrices, consequently may overestimate the level of instability of G relative to what might be expected in natural systems. Overall, our results indicate that evolvability can evolve in natural systems in a way that tends to result in alignment of the G-matrix, the M-matrix, and the adaptive landscape, and that such evolution tends to stabilize the G-matrix over evolutionary time.     

Primate population studies at Polonnaruwa. II. Heritability of body measurements in a natural population of toque macaques (Macaca sinica)

The heritability of quantitative traits, or the proportion of phenotypic variation due to additive genetic or heritable effects, plays an important role in determining the evolutionary response to natural selection. Most quantitative genetic studies are performed in the laboratory, due to difficulty in obtaining genealogical data in natural populations. Genealogies are known, however, from a unique 20-year study of toque macaques (Macaca sinica) at Polonnaruwa, Sri Lanka. Heritability in this natural population was, therefore, estimated. Twenty-seven body measurements representing the lengths and widths of the head, trunk, extremities, and tail were collected from 270 individuals. The sample included 172 offspring-mother pairs from 39 different matrilineal families. Heritabilities were estimated using traditional mother-offspring regression and maximum likelihood methods which utilize all genealogical relationships in the sample. On the common assumption that environmental (including social) factors affecting morphology were randomly distributed across families, all but two of the traits (25 of 27) were significantly heritable, with an average heritability of 0.51 for the mother-offspring analysis and 0.56 for the maximum likelihood analysis. Heritability estimates obtained from the two analyses were very similar. We conclude that the Polonnaruwa macaques exhibit a comparatively moderate to high level of heritability for body form. © 1992 Wiley-Liss, Inc.     

Introduction. Evolutionary dynamics of wild populations: the use of long-term pedigree data

Studies of populations in the wild can provide unique insights into the forces driving evolutionary dynamics. This themed issue of Proc. R. Soc. B focuses on new developments in long-term analyses of animal populations where pedigree information has been collected. These address fundamental questions in evolutionary biology concerning the genetic basis of phenotypic diversity, patterns of natural and sexual selection, the occurrence of inbreeding and inbreeding depression, and speciation. Contributions include the analysis of evolutionary responses to climate change, exploration of the genetic basis of senescence, the exploitation of advances in molecular genetic technology, and reviews of developments in quantitative genetic methodology. We discuss here common themes, specific problems and pointers for future research.     

The influence of variation and of developmental constraints on the rate of multivariate phenotypic evolution

A model of multivariate phenotypic evolution is analysed under the assumption that all characters have the same variance or at least constant ratios of variance. The rate of evolution is examined as a function of the amount of phenotypic variance in a variety of adaptive landscapes (fitness functions). It is demonstrated that the effect of variation depends on the type of adaptive landscape. In “well behaved” adaptive landscapes the rate of evolution can theoretically increase without limits, depending on the amount of heritable phenotypic variation. However, in other adaptive landscapes there are upper limits to the rate of evolution which cannot be exceeded if phenotypic variation is developmentally unconstrained, i. e. if it is the same for all characters. Further it is shown that the maximal rate of evolution becomes small if the number of characters becomes large. Fitness functions of this type are called malignant. It is argued that malignant fitness functions are more adequate models for the evolution of typical organismic systems, because they are models of functionally interdependent characters. It is concluded that there are upper limits to the rate of phenotypic evolution if the variation of functionally interdependent characters is developmentally unconstrained. The possible role of developmental constraints in adaptive phenotypic evolution is discussed.     

Plant self-incompatibility in natural populations: a critical assessment of recent theoretical and empirical advances

Self-incompatibility systems in plants are genetic systems that prevent self-fertilization in hermaphrodites through recognition and rejection of pollen expressing the same allelic specificity as that expressed in the pistils. The evolutionary properties of these self-recognition systems have been revealed through a fascinating interplay between empirical advances and theoretical developments. In 1939, Wright suggested that the main evolutionary force driving the genetic and molecular properties of these systems was strong negative frequency-dependent selection acting on pollination success. The empirical observation of high allelic diversity at the self-incompatibility locus in several species, followed by the discovery of very high molecular divergence among alleles in all plant families where the locus has been identified, supported Wright's initial theoretical predictions as well as many of its later developments. In the last decade, however, advances in the molecular characterization of the incompatibility reaction and in the analysis of allelic frequencies and allelic divergence from natural populations have stimulated new theoretical investigations that challenged some important assumptions of Wright's model of gametophytic self-incompatibility. We here review some of these recent empirical and theoretical advances that investigated: (i) the hypothesis that S-alleles are selectively equivalent, and the evolutionary consequences of genetic interactions between alleles; (ii) the occurrence of frequency-dependent selection in female fertility; (iii) the evolutionary genetics of self-incompatibility systems in subdivided populations; (iv) the evolutionary implications of the self-incompatibility locus's genetic architecture; and (v) of its interactions with the genomic environment.     

Explaining stasis: microevolutionary studies in natural populations

Microevolution, defined as a change in the genetic constitution of a population over time, is considered to be of commonplace occurrence in nature. Its ubiquity can be inferred from the observation that quantitative genetic divergence among populations usually exceeds that to be expected due to genetic drift alone, and from numerous observations and experiments consistent with local adaptation. Experimental manipulations in natural populations have provided evidence that rapid evolutionary responses may occur in the wild. However, there are remarkably few cases where direct observations of natural populations have revealed microevolutionary changes occurring, despite the frequent demonstration of additive genetic variation and strong directional selection for particular traits. Those few cases where responses congruent with expectation have been demonstrated are restricted to changes over one generation. In this article we focus on possible explanations as to why heritable traits under apparently strong directional selection often fail to show the expected evolutionary response. To date, few of these explanations for apparent stasis have been amenable to empirical testing. We describe new methods, derived from procedures developed by animal breeding scientists, which can be used to address these explanations, and illustrate the approach with examples from long-term studies of collared flycatchers (Ficedula albicollis) and red deer (Cervus elaphus). Understanding why most intensively studied natural populations do not appear to be evolving is an important challenge for evolutionary biology.     

Genetic variation, disequilibrium and natural selection on reproductive traits in Allium vineale

Bulbils and seeds collected from Allium vineale plants from natural populations were grown under uniform conditions. The bulbil-derived offspring represented the parental generation, whereas the seed-derived offspring represented the sexually produced offspring generation. Molecular markers were used to identify maternal genets. Variation in traits determining the allocation to sexual and asexual reproduction was partitioned among genets and ramet families in the parental and offspring generations. From observations of a release of genetic variation and slippage in the mean phenotype in the offspring generation, we inferred that there exists extensive genetic disequilibrium for reproductive traits in A. vineale populations, that most of the genetic variance is because of dominance effects, and that natural selection favours a reduced allocation to sexual reproduction. No genetic correlation between sexual and asexual allocation traits was found. We discuss the implications of these results with respect to the evolution of a mixed reproductive system in A. vineale.     

Predicting the evolution of sexual size dimorphism

11 , Evolution 34 : 292–305) equations for predicting the evolution of sexual size dimorphism (SSD) through frequency‐dependent sexual selection, and frequency‐independent natural selection, were tested against results obtained from a stochastic genetic simulation model. The SSD evolved faster than predicted, due to temporary increases in the genetic variance brought about by directional selection. Predictions for the magnitude of SSD at equilibrium were very accurate for weak sexual selection. With stronger sexual selection the total response was greater than predicted. Large changes in SSD can occur without significant long‐term change in the genetic correlation between the sexes. Our results suggest that genetic correlations constrain both the short‐term and long‐term evolution of SSD less than predicted by the Lande model.     

A framework for power and sensitivity analyses for quantitative genetic studies of natural populations, and case studies in Soay sheep (Ovis aries)

Studies of the quantitative genetics of natural populations have contributed greatly to evolutionary biology in recent years. However, while pedigree data required are often uncertain (i.e. incomplete and partly erroneous) and limited, means to evaluate the effects of such uncertainties have not been developed. We have therefore developed a general framework for power and sensitivity analyses of such studies. We propose that researchers first generate a set of pedigree data that they wish to use in a quantitative genetic study, as well as data regarding errors that occur in that pedigree. This pedigree is then permuted using the data regarding errors to generate hypothetical 'true' and 'assumed' pedigrees that differ so as to mimic pedigree errors that might occur in the study system under consideration. Phenotypic data are then simulated across the true pedigree (according to user-defined genetic and environmental covariance structures), before being analysed with standard quantitative genetic techniques in conjunction with the 'assumed' pedigree data. To illustrate this approach, we conducted power and sensitivity analyses in a well-known study of Soay sheep (Ovis aries). We found that, although the estimation of simple genetic (co)variance structures is fairly robust to pedigree errors, some potentially serious biases were detected under more complex scenarios involving maternal effects. Power analyses also showed that this study system provides high power to detect heritabilities as low as about 0.09. Given this range of results, we suggest that such power and sensitivity analyses could greatly complement empirical studies, and we provide the computer program PEDANTICS to aid in their application.     

Flowering time QTL in natural populations of Arabidopsis thaliana and implications for their adaptive value

The genetic basis of phenotypic traits is of great interest to evolutionary biologists, but their contribution to adaptation in nature is often unknown. To determine the genetic architecture of flowering time in ecologically relevant conditions, we used a recombinant inbred line population created from two locally adapted populations of Arabidopsis thaliana from Sweden and Italy. Using these RILs, we identified flowering time QTL in growth chambers that mimicked the natural temperature and photoperiod variation across the growing season in each native environment. We also compared the genomic locations of flowering time QTL to those of fitness (total fruit number) QTL from a previous three‐year field study. Ten total flowering time QTL were found, and in all cases, the Italy genotype caused early flowering regardless of the conditions. Two QTL were consistent across chamber environments, and these had the largest effects on flowering time. Five of the fitness QTL colocalized with flowering time QTL found in the Italy conditions, and in each case, the local genotype was favoured. In contrast, just two flowering time QTL found in the Sweden conditions colocalized with fitness QTL and in only one case was the local genotype favoured. This implies that flowering time may be more important for adaptation in Italy than Sweden. Two candidate genes (FLC and VIN3) underlying the major flowering time QTL found in the current study are implicated in local adaptation.     

Domestication and fitness in the wild: A multivariate view

Domesticated species continually escaping and interbreeding with wild relatives impose a migration load on wild populations. As domesticated stocks become increasingly different as a result of artificial and natural selection in captivity, fitness of escapees in the wild is expected to decline, reducing the effective rate of migration into wild populations. Recent theory suggest that this may alleviate and eventually eliminate the resulting migration load. I develop a multivariate model of trait and wild fitness evolution resulting from the joint effects of artificial and natural selection in the captive environment. Initially, the evolutionary trajectory is dominated by the effects of artificial selection causing a fast initial decline in fitness of escapees in the wild. In later phases, through the counteracting effects of correlational multivariate natural selection in captivity, the mean phenotype is pushed in directions of weak stabilizing selection, allowing a sustained response in the trait subject to artificial selection. Provided that there is some alignment between the adaptive landscapes in the wild and in captivity, these phases are associated with slower rates of decline in wild fitness of the domesticated stock, suggesting that detrimental effects on wild populations are likely to remain a concern in the foreseeable future.     

Conditional neutrality at two adjacent NBS-LRR disease resistance loci in natural populations of Arabidopsis lyrata

We examined patterns of nucleotide diversity at a genomic region containing two linked candidate disease resistance (NBS-LRR) genes in seven populations of the outcrossing plant Arabidopsis lyrata. In comparison with two adjacent control genes and neutral reference genes across the genome, the NBS-LRR genes exhibited elevated nonsynonymous variation and a large number of major-effect polymorphisms causing early stop codons and/or frameshift mutations. In contrast, analysis of synonymous diversity provided no evidence that the region was subject to long-term balancing selection or recent selective sweeps in any of the seven populations surveyed. Also in contrast with earlier surveys of one of these R genes, there was no evidence that the resistance genes or the major-effect mutations were subject to elevated differentiation between populations. We suggest that conditional neutrality in the absence of the corresponding pathogen, rather than long-term balancing selection or local adaptation, may in some circumstances be a significant cause of elevated functional polymorphism at R genes. In contrast with the R genes, analysis of diversity and differentiation at the flanking FERONIA locus showed high population divergence, suggesting local adaptation on this locus controlling male-female signalling during fertilization.     

Paths to selection on life history loci in different natural environments across the native range of Arabidopsis thaliana

Selection on quantitative trait loci (QTL) may vary among natural environments due to differences in the genetic architecture of traits, environment‐specific allelic effects or changes in the direction and magnitude of selection on specific traits. To dissect the environmental differences in selection on life history QTL across climatic regions, we grew a panel of interconnected recombinant inbred lines (RILs) of Arabidopsis thaliana in four field sites across its native European range. For each environment, we mapped QTL for growth, reproductive timing and development. Several QTL were pleiotropic across environments, three colocalizing with known functional polymorphisms in flowering time genes (CRY2, FRI and MAF2‐5), but major QTL differed across field sites, showing conditional neutrality. We used structural equation models to trace selection paths from QTL to lifetime fitness in each environment. Only three QTL directly affected fruit number, measuring fitness. Most QTL had an indirect effect on fitness through their effect on bolting time or leaf length. Influence of life history traits on fitness differed dramatically across sites, resulting in different patterns of selection on reproductive timing and underlying QTL. In two oceanic field sites with high prereproductive mortality, QTL alleles contributing to early reproduction resulted in greater fruit production, conferring selective advantage, whereas alleles contributing to later reproduction resulted in larger size and higher fitness in a continental site. This demonstrates how environmental variation leads to change in both QTL effect sizes and direction of selection on traits, justifying the persistence of allelic polymorphism at life history QTL across the species range.     

A guide to the genomics of ecological speciation in natural animal populations

Interest in ecological speciation is growing, as evidence accumulates showing that natural selection can lead to rapid divergence between subpopulations. However, whether and how ecological divergence can lead to the buildup of reproductive isolation remains under debate. What is the relative importance of natural selection vs. neutral processes? How does adaptation generate reproductive isolation? Can ecological speciation occur despite homogenizing gene flow? These questions can be addressed using genomic approaches, and with the rapid development of genomic technology, will become more answerable in studies of wild populations than ever before. In this article, we identify open questions in ecological speciation theory and suggest useful genomic methods for addressing these questions in natural animal populations. We aim to provide a practical guide for ecologists interested in incorporating genomic methods into their research programs. An increased integration between ecological research and genomics has the potential to shed novel light on the origin of species.