THE MIXED-MODEL ANALYSIS OF VARIANCE APPLIED TO QUANTITATIVE GENETICS: BIOLOGICAL MEANING OF THE PARAMETERS

The mixed-model factorial analysis of variance has been used in many recent studies in evolutionary quantitative genetics. Two competing formulations of the mixed-model ANOVA are commonly used, the “Scheffe” model and the “SAS” model; these models differ in both their assumptions and in the way in which variance components due to the main effect of random factors are defined. The biological meanings of the two variance component definitions have often been unappreciated, however. A full understanding of these meanings leads to the conclusion that the mixed-model ANOVA could have been used to much greater effect by many recent authors. The variance component due to the random main effect under the two-way SAS model is the covariance in true means associated with a level of the random factor (e.g., families) across levels of the fixed factor (e.g., environments). Therefore the SAS model has a natural application for estimating the genetic correlation between a character expressed in different environments and testing whether it differs from zero. The variance component due to the random main effect under the two-way Scheffe model is the variance in marginal means (i.e., means over levels of the fixed factor) among levels of the random factor. Therefore the Scheffe model has a natural application for estimating genetic variances and heritabilities in populations using a defined mixture of environments. Procedures and assumptions necessary for these applications of the models are discussed. While exact significance tests under the SAS model require balanced data and the assumptions that family effects are normally distributed with equal variances in the different environments, the model can be useful even when these conditions are not met (e.g., for providing an unbiased estimate of the across-environment genetic covariance). Contrary to statements in a recent paper, exact significance tests regarding the variance in marginal means as well as unbiased estimates can be readily obtained from unbalanced designs with no restrictive assumptions about the distributions or variance-covariance structure of family effects.     

THE QUANTITATIVE GENETICS OF SEXUAL DIMORPHISM IN SILENE LATIFOLIA (CARYOPHYLLACEAE). II. RESPONSE TO SEX-SPECIFIC SELECTION

A well-established theoretical relationship exists between genetic correlations between the sexes and the dynamics of response to sex-specific selection. The present study investigates the response to sex-specific selection for two sexually dimorphic traits that have been documented to be genetically variable, calyx diameter and flower number, in Silene latifolia. Following the establishment of a base generation with a known genetic background, selection lines were established and two generations of sex-specific selection were imposed. Calyx diameter responded directly to sex-specific selection, and the positive genetic correlation between the sexes was reflected in correlated responses in the sex that was not the basis for selection within a particular line. Flower number showed a more erratic response to sex-specific selection in that selection in some lines was initially in the wrong direction, that is, selection for a decrease in flower number resulted in an increase. These erratic responses were attributable to genotype-environment interaction as reflected in significant heteroscedasticity in variance among families. Correlated responses to selection in the sex that was not the immediate basis for selection indicated the possible existence of a negative genetic correlation between the sexes for this trait. These results test for the first time the impact of genetic correlations between the sexes on the evolutionary dynamics of sexually dimorphic traits in a plant species.     

THE CONTRIBUTION OF MATERNAL EFFECTS TO SELECTION RESPONSE: AN EMPIRICAL TEST OF COMPETING MODELS

Maternal effects can dramatically influence the evolutionary process, in some cases facilitating and in others hindering adaptive evolution. Maternal effects have been incorporated into quantitative genetic models using two theoretical frameworks: the variance‐components approach, which partitions variance into direct and maternal components, and the trait‐based approach, which assumes that maternal effects are mediated by specific maternal traits. Here, we demonstrate parallels between these models and test their ability to predict evolutionary change. First, we show that the two approaches predict equivalent responses to selection in the absence of maternal effects mediated by traits that are themselves maternally influenced. We also introduce a correction factor that may be applied when such cascading maternal effects are present. Second, we use several maternal effect models, as well as the standard breeder's equation, to predict evolution in response to artificial selection on flowering time in American bellflower, Campanulastrum americanum. Models that included maternal effects made much more accurate predictions of selection response than the breeder's equation. Maternal effect models differed somewhat in their fit, with a version of the trait‐based model providing the best fit. We recommend fitting such trait‐based models when possible and appropriate to make the most accurate evolutionary predictions.     

THE ACTION OF STABILIZING SELECTION,MUTATION, AND DRIFT ON EPISTATIC QUANTITATIVE TRAITS

For a quantitative trait under stabilizing selection, the effect of epistasis on its genetic architecture and on the changes of genetic variance caused by bottlenecking were investigated using theory and simulation. Assuming empirical estimates of the rate and effects of mutations and the intensity of selection, we assessed the impact of two‐locus epistasis (synergistic/antagonistic) among linked or unlinked loci on the distribution of effects and frequencies of segregating loci in populations at the mutation‐selection‐drift balance. Strong pervasive epistasis did not modify substantially the genetic properties of the trait and, therefore, the most likely explanation for the low amount of variation usually accounted by the loci detected in genome‐wide association analyses is that many causal loci will pass undetected. We investigated the impact of epistasis on the changes in genetic variance components when large populations were subjected to successive bottlenecks of different sizes, considering the action of genetic drift, operating singly (D), or jointly with mutation (MD) and selection (MSD). An initial increase of the different components of the genetic variance, as well as a dramatic acceleration of the between‐line divergence, were always associated with synergistic epistasis but were strongly constrained by selection.     

DENSITY-DEPENDENT SELECTION ON CONTINUOUS CHARACTERS: A QUANTITATIVE GENETIC MODEL

A quantitative genetic model of density-dependent selection is presented and analysed with parameter values obtained from laboratory selection experiments conducted by Mueller and his coworkers. The ecological concept of r- and K-selection is formulated in terms of selection gradients on underlying phenotypic characters that influence the density-dependent measure of fitness. Hence the selection gradients on traits are decomposed into two components, one that changes in the direction to increase r, and one that changes in the direction to increase K. The relative importance of the two components is determined by temporal fluctuations in population density. The evolutionary rate of r and K (per-generation changes in r and K due to the genetic responses of the underlying traits) is also formulated. Numerical simulation has shown that with moderate genetic variances of the underlying characters, r and K can evolve rapidly and the evolutionary rate is influenced by synergistic interaction between characters that contribute to r and K. But strong r-selection can occur only with severe and continuous disturbances of populations so that the population density is kept low enough to prevent K-selection.     

QUANTITATIVE GENETICS OF BRYOZOAN PHENOTYPIC EVOLUTION. II. ANALYSIS OF SELECTION AND RANDOM CHANGE IN FOSSIL SPECIES USING RECONSTRUCTED GENETIC PARAMETERS

The roles of natural selection and random genetic change in the punctuated phenotypic evolution of eight Miocene-Pliocene tropical American species of the cheilostome bryozoan Metrarabdotos are analyzed by quantitative genetic methods. Trait heritabilities and genetic covariances reconstructed by partitioning within- and among-colony phenotypic variance are similar to those previously obtained for living species of the cheilostome Stylopoma using breeding data. The hypothesis that differences in skeletal morphology between species of Metrarabdotos are entirely due to mutation and genetic drift cannot be rejected for reasonable rates of mutation maintained for periods brief enough to account for the geologically abrupt appearances of these species in the fossil record. Except for one pair of species, separated by the largest morphologic distance, directional selection acting alone would require unrealistically high rates of selective mortality to be maintained for these periods. Thus, directional selection is not strongly implicated in the divergence of Metrarabdotos species. Within species, rates of net phenotypic change are slow enough to require stabilizing selection, but mask large, relatively rapid fluctuations, all of which, however, can be attributed to chance departures from the mean phenotype by mutation and genetic drift, rather than to tracking environmental fluctuation by directional selection. The results are consistent with genetic models involving shifts between multiple adaptive peaks on which phenotypes remain more or less static through long-term stabilizing selection. Regardless of the degree to which directional selection may be involved in peak shifts, phenotypic differentiation is thus related to processes different than the pervasive stabilizing selection acting within species.     

QUANTITATIVE GENETICS OF RESPONSE TO COMPETITORS IN NEMOPHILA MENZIESII: A GREENHOUSE STUDY

To determine the potential for adaptation to a local biotic environment, we examined the magnitude and nature of genetic variation in response to neighboring plants within a natural population of the native California annual, Nemophila menziesii. A total of 22 plants from a natural population were crossed in three reciprocal factorials. The progeny were grown in a greenhouse in nine treatments that varied in conspecific density and in the density of a naturally co-occurring grass species, Bromus diandrus. Increasing the density of each species significantly reduced individual survival, fruit number, and dry weight. Among survivors, we found small to moderate heritability of dry weight within treatments. Additive genetic correlations (r_A) of dry weight between competitive regimes were generally large and positive. In no case were they significantly different from 1, as expected under the null hypothesis that the relative performance of the genotypes under consideration is the same in all environments. On the basis of these results, we cannot conclude that the structure of genetic covariation within this population would promote genetic differentiation in response to locally varying conditions of density of these two species. Aspects of the experiment that may have compromised our ability to detect r_A differing from 1 are discussed.     

SEXUAL SIZE DIMORPHISM AS A CORRELATED RESPONSE TO SELECTION ON BODY SIZE: AN EMPIRICAL TEST OF THE QUANTITATIVE GENETIC MODEL

We artificially selected for body size in Drosophila melanogaster to test Lande's quantitative genetic model for the evolution of sexual size dimorphism. Thorax width was used as an estimator of body size. Selection was maintained for 21 generations in both directions on males only, females only, or both sexes simultaneously. The correlated response of sexual size dimorphism in each selection regime was compared to the response predicted by four variants of the model, each of which differed only in assumptions about input parameters. Body size responded well to selection, but the correlated response of sexual size dimorphism was weaker than that predicted by any of the variants. Dimorphism decreased in most selection lines, contrary to the model predictions. We suggest that selection on body size acts primarily on growth trajectories. Changes in dimorphism are caused by the fact that male and female growth trajectories are not parallel and termination of growth at different points along the curves results in dimorphism levels that are difficult to predict without detailed knowledge of growth parameters. This may also explain many of the inconsistent results in dimorphism changes seen in earlier selection experiments.     

UNPREDICTABILITY OF CORRELATED RESPONSE TO SELECTION: PLEIOTROPY AND SAMPLING INTERACT

Given a set of loci that contribute additive genetic variation for a trait being selected, the pleiotropic effects of these loci on a second trait may vary. I simulated selection on genetic systems having different combinations of pleiotropic effects to investigate the variability of correlated responses to selection. The simulation shows that there are many possible combinations of pleiotropic effects that are characterized by the same value of the genetic correlation; the genetic correlation does not uniquely determine a set of pleiotropic effects. Furthermore, for a given value of the genetic correlation, differences in pleiotropic effects have a substantial impact on the variation in correlated responses. Some combinations of pleiotropic effects constrain correlated response to a narrow range of possible values; others allow a wide range, including some correlated responses in a direction opposite the sign of the genetic correlation. The genetic correlation is not a reliable predictor of pleiotropic constraint. Whereas it has been previously established that genetic correlations are not necessarily constraints, the alternative is also true: correlated response can be strictly constrained despite a genetic correlation of zero. Given the frequency of correlated responses in a direction opposite to the one predicted by the genetic correlation, it follows that correlated response is not a reliable predictor of genetic correlation in the base population.     

LIMITS TO BEHAVIORAL EVOLUTION: THE QUANTITATIVE GENETICS OF A COMPLEX TRAIT UNDER DIRECTIONAL SELECTION

Replicated selection experiments provide a powerful way to study how “multiple adaptive solutions” may lead to differences in the quantitative–genetic architecture of selected traits and whether this may translate into differences in the timing at which evolutionary limits are reached. We analyze data from 31 generations (n = 17,988) of selection on voluntary wheel running in house mice. The rate of initial response, timing of selection limit, and height of the plateau varied significantly between sexes and among the four selected lines. Analyses of litter size and realized selection differentials seem to rule out counterposing natural selection as a cause of the selection limits. Animal‐model analyses showed that although the additive genetic variance was significantly lower in selected than control lines, both before and after the limits, the decrease was not sufficient to explain the limits. Moreover, directional selection promoted a negative covariance between additive and maternal genetic variance over the first 10 generations. These results stress the importance of replication in selection studies of higher‐level traits and highlight the fact that long‐term predictions of response to selection are not necessarily expected to be linear because of the variable effects of selection on additive genetic variance and maternal effects.     

THE MEASUREMENT OF SELECTION ON QUANTITATIVE TRAITS: BIASES DUE TO ENVIRONMENTAL COVARIANCES BETWEEN TRAITS AND FITNESS

The use of regression techniques for estimating the direction and magnitude of selection from measurements on phenotypes has become widespread in field studies. A potential problem with these techniques is that environmental correlations between fitness and the traits examined may produce biased estimates of selection gradients. This report demonstrates that the phenotypic covariance between fitness and a trait, used as an estimate of the selection differential in estimating selection gradients, has two components: a component induced by selection itself and a component due to the effect of environmental factors on fitness. The second component is shown to be responsible for biases in estimates of selection gradients. The use of regressions involving genotypic and breeding values instead of phenotypic values can yield estimates of selection gradients that are not biased by environmental covariances. Statistical methods for estimating the coefficients of such regressions, and for testing for biases in regressions involving phenotypic values, are described.     

QUANTITATIVE GENETICS IN PLANTS: THE EFFECT OF THE BREEDING SYSTEM ON GENETIC VARIABILITY

The expected effects of breeding system on quantitative genetic variation under various models for the maintenance of such variation are examined, with particular emphasis on the contrast between randomly mating and highly self-fertilizing populations. Estimates of quantitative genetic parameters from plant populations are reviewed. There is some evidence for reduced within-population genetic variance in highly inbreeding populations, compared with outbreeders, but more empirical work appears necessary. Although the estimate of the magnitude of the effect of breeding system is subject to considerable error, the reduction in genetic variance in inbreeding populations appears greater than expected if the variation were maintained by overdominance, or if it were due to neutral mutations. It is more consistent with models involving mutation-selection balance, although a rather larger reduction in genetic variance is estimated than is expected theoretically. We discuss some possible reasons for the lower level of genetic variance in selfers than is predicted by such models.     

SEASONALLY VARYING DIET QUALITY AND THE QUANTITATIVE GENETICS OF DEVELOPMENT TIME AND BODY SIZE IN BIRCH FEEDING INSECTS

Abstract Genetic variance‐covariance structures (G), describing genetic constraints on microevolutionary changes of populations, have a central role in the current theories of life‐history evolution. However, the evolution of Gs in natural environments has been poorly documented. Resource quality and quantity for many animals and plants vary seasonally, which may shape genetic architectures of their life histories. In the mountain birch‐insect herbivore community, leaf quality of birch for insect herbivores declines profoundly during both leaf growth and senescence, but remains stable during midsummer. Using six sawfly species specialized on the mountain birch foliage, we tested the ways in which the seasonal variation in foliage quality of birch is related to the genetic architectures of larval development time and body size. In the species consuming mature birch leaves of stable quality, that is, without diet‐imposed time constraints for development time, long development led to high body mass. This was revealed by the strongly positive phenotypic and genetic correlations between the traits. In the species consuming growing or senescing leaves, on the other hand, the rapidly deteriorating leaf quality prevented the larvae from gaining high body mass after long development. In these species, the phenotypic and genetic correlations between development time and final mass were negative or zero. In the early‐summer species with strong selection for rapid development, genetic variation in development time was low. These results show that the intuitively obvious positive genetic relationship between development time and final body mass is a probable outcome only when the constraints for long development are relaxed. Our study provides the first example of a modification in guild‐wide patterns in the genetic architectures brought about by seasonal variation in resource quality.     

EVOLUTION OF RESISTANCE TO A MULTIPLE‐HERBIVORE COMMUNITY: GENETIC CORRELATIONS,DIFFUSE COEVOLUTION,AND CONSTRAINTS ON THE PLANT'S RESPONSE TO SELECTION

Although plants are generally attacked by a community of several species of herbivores, relatively little is known about the strength of natural selection for resistance in multiple‐herbivore communities—particularly how the strength of selection differs among herbivores that feed on different plant organs or how strongly genetic correlations in resistance affect the evolutionary responses of the plant. Here, we report on a field study measuring natural selection for resistance in a diverse community of herbivores of Solanum carolinense. Using linear phenotypic‐selection analyses, we found that directional selection acted to increase resistance to seven species. Selection was strongest to increase resistance to fruit feeders, followed by flower feeders, then leaf feeders. Selection favored a decrease in resistance to a stem borer. Bootstrapping analyses showed that the plant population contained significant genetic variation for each of 14 measured resistance traits and significant covariances in one‐third of the pairwise combinations of resistance traits. These genetic covariances reduced the plant's overall predicted evolutionary response for resistance against the herbivore community by about 60%. Diffuse (co)evolution was widespread in this community, and the diffuse interactions had an overwhelmingly constraining (rather than facilitative) effect on the plant's evolution of resistance.     

QUANTIFYING EVOLUTIONARY POTENTIAL OF MARINE FISH LARVAE: HERITABILITY,SELECTION, AND EVOLUTIONARY CONSTRAINTS

For many marine fish, intense larval mortality may provide considerable opportunity for selection, yet much less is known about the evolutionary potential of larval traits. We combined field demographic studies and manipulative experiments to estimate quantitative genetic parameters for both larval size and swimming performance for a natural population of a common coral‐reef fish, the bicolor damselfish (Stegastes partitus). We also examined selection on larval size by synthesizing information from published estimates of selective mortality. We introduce a method that uses the Lande–Arnold framework for examining selection on quantitative traits to empirically reconstruct adaptive landscapes. This method allows the relationship between phenotypic value and fitness components to be described across a broad range of trait values. Our results suggested that despite strong viability selection for large larvae and moderate heritability (h²= 0.29), evolutionary responses of larvae would likely be balanced by reproductive selection favoring mothers that produce more, smaller offspring. Although long‐term evolutionary responses of larval traits may be constrained by size‐number trade‐offs, our results suggest that phenotypic variation in larval size may be an ecologically important source of variability in population dynamics through effects on larval survival and recruitment to benthic populations.     

THE RESPONSE TO SELECTION FOR FAST LARVAL DEVELOPMENT IN DROSOPHILA MELANOGASTER AND ITS EFFECT ON ADULT WEIGHT: AN EXAMPLE OF A FITNESS TRADE-OFF

A selection experiment using Drosophila melanogaster revealed a strong trade-off between adult weight and larval development time (LDT), supporting the view that antagonistic pleiotropy for these two fitness traits determines mean adult size. Two experimental lines of flies were selected for a shorter LDT (measured from egg laying to pupation). After 15 generations LDT was reduced by an average of 7.9%. The response appeared to be controlled primarily by autosomal loci. A correlated response to the selection was a reduction in adult dry weight: individuals from the selected populations were on average 15.1% lighter than the controls. The lighter females of the selected lines showed a 35% drop in fecundity, but no change in longevity. Thus, there is no direct relationship between LDT and adult longevity. The genetic correlation between weight and LDT, as measured from their joint response to selection, was 0.86. Although there was weak evidence for dominance in LDT, there was none for weight, making it unlikely that selection acting on this antagonistic pleiotropy could lead to a stable polymorphism. In all lines, sex differences in weight violated expectations based on intrasex genetic correlations: Females, being larger than males, ought to require a longer LDT, whereas there was a slight trend in the opposite direction. Because the sexual dimorphism in size was not significantly altered by selection, it appears that the controlling loci are either invariant or have very limited pleiotropic effect on developmental time. It is suggested that they probably control some intrinsic, energy-intensive developmental process in males.     

THE RESPONSE TO DIFFERING SELECTION ON PLANT PHYSIOLOGICAL TRAITS: EVIDENCE FOR LOCAL ADAPTATION

Understanding adaptive evolution to differing environments requires studies of genetic variances, of natural selection, and of the genetic differentiation between populations. Plant physiological traits such as leaf size and water-use efficiency (the ratio of carbon gained per water lost) have been suggested by physiological plant ecologists to be important in local adaptation to environments differing in water availability. In this study, I raised families of Cakile edentula var lacustris derived from a wet-site population and a dry-site population in a common greenhouse environment to determine the degree of genetic differentiation between the two populations and the genetic architecture of the traits. The dry-site population had significantly smaller leaf size and significantly greater water-use efficiency than the wet-site population. I used a retrospective selection analysis to compare long-term selection inferred from these results to measures of phenotypic selection from a field experiment. Both direct measures in the field and the retrospective selection gradients were consistent with the hypothesis that greater water-use efficiency and smaller leaves were adaptive in drier environments. Though the correlation between population means for water-use efficiency and leaf size was negative, the genetic correlation within populations between water-use efficiency and leaf size was positive and thus would be expected to constrain the evolutionary response to selection.     

GENE FLOW FROM DOMESTICATED SPECIES TO WILD RELATIVES: MIGRATION LOAD IN A MODEL OF MULTIVARIATE SELECTION

Domesticated species frequently spread their genes into populations of wild relatives through interbreeding. The domestication process often involves artificial selection for economically desirable traits. This can lead to an indirect response in unknown correlated traits and a reduction in fitness of domesticated individuals in the wild. Previous models for the effect of gene flow from domesticated species to wild relatives have assumed that evolution occurs in one dimension. Here, I develop a quantitative genetic model for the balance between migration and multivariate stabilizing selection. Different forms of correlational selection consistent with a given observed ratio between average fitness of domesticated and wild individuals offsets the phenotypic means at migration–selection balance away from predictions based on simpler one-dimensional models. For almost all parameter values, correlational selection leads to a reduction in the migration load. For ridge selection, this reduction arises because the distance the immigrants deviates from the local optimum in effect is reduced. For realistic parameter values, however, the effect of correlational selection on the load is small, suggesting that simpler one-dimensional models may still be adequate in terms of predicting mean population fitness and viability.