QUANTITATIVE GENETICS OF GEOMETRIC SHAPE IN THE MOUSE MANDIBLE

Abstract We combine the methods of geometric morphometrics and multivariate quantitative genetics to study the patterns of phenotypic and genetic variation of mandible shape in random‐bred mice. The data are the positions of 11 landmarks on the mandibles of 1241 mice from a parent‐offspring breeding design. We use Procrustes superimposition to extract shape variation and restricted maximum likelihood to estimate the additive genetic and environmental components of variance and covariance. Matrix permutation tests showed that the genetic and phenotypic as well as the genetic and environmental covariance matrices were similar, but not identical. Likewise, principal component analyses revealed correspondence in the patterns of phenotypic and genetic variation. Patterns revealed in these analyses also showed similarities to features previously found in the effects of quantitative trait loci and in the phenotypes generated in gene knockout experiments. We used the multivariate version of the breeder's equation to explore the potential for short‐term response to selection on shape. In general, the correlated response is substantial and regularly exceeds the direct response: Selection applied locally to one landmark usually produces a response in other parts of the mandible as well. Moreover, even selection for shifts of the same landmark in different directions can yield dramatically different responses. These results demonstrate the role of the geometry and anatomical structure of the mandible, which are key determinants of the patterns of the genetic and phenotypic covariance matrices, in molding the potential for adaptive evolution.     

QUANTITATIVE GENETICS OF THE WING COLOR PATTERN IN THE BUCKEYE BUTTERFLY (PRECIS COENIA AND PRECIS EVARETE): EVIDENCE AGAINST THE CONSTANCY OF G

Models for the evolution of continuously varying traits use heritabilities, genetic correlations, and the G -matrix to quantify the genetic variation upon which selection acts. Given estimates of these parameters, it is possible to predict the long-term effects of selection, infer past selective forces responsible for observed differences between populations or species, and distinguish the effects of drift from selection. Application of these methods, however, requires the unproven assumption that the G -matrix remains constant from one generation to the next. This study examines the assumption of constancy for the wing pattern characteristics of two sibling species of butterflies, Precis coenia and P. evarete (Lepidoptera: Nymphalidae). Quantitative genetic parameters were estimated from parent-offspring regression. Two approaches were taken to test the null hypothesis of equality between species. First, pairwise tests between corresponding elements of G and between heritabilities and genetic correlations for the two species were constructed. Second, a modification of Bartlett's modified likelihood-ratio test was used to test for equality between the G -matrices. The matrix test failed to detect any between species differences. In contrast, pairwise comparision revealed significant differences. Thus, it appears that constancy cannot be assumed at the species level in quantitative genetic studies. In particular, the assumption of constancy was violated for the trait with the greatest difference in mean phenotype.     

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 AND COEVOLUTION OF MALE AND FEMALE REPRODUCTIVE TRAITS

Studies of experimental sexual selection have tested the effect of variation in the intensity of sexual selection on male investment in reproduction, particularly sperm. However, in several species, including Drosophila pseudoobscura, no sperm response to experimental evolution has occurred. Here, we take a quantitative genetics approach to examine whether genetic constraints explain the limited evolutionary response. We quantified direct and indirect genetic variation, and genetic correlations within and between the sexes, in experimental populations of D. pseudoobscura. We found that sperm number may be limited by low heritability and evolvability whereas sperm quality (length) has moderate V_A and CV_A but does not evolve. Likewise, the female reproductive tract, suggested to drive the evolution of sperm, did not respond to experimental sexual selection even though there was sufficient genetic variation. The lack of genetic correlations between the sexes supports the opportunity for sexual conflict over investment in sperm by males and their storage by females. Our results suggest no absolute constraint arising from a lack of direct or indirect genetic variation or patterns of genetic covariation. These patterns show why responses to experimental evolution are hard to predict, and why research on genetic variation underlying interacting reproductive traits is needed.     

THE EVOLUTIONARY GENETICS OF MALE LIFE-HISTORY CHARACTERS IN DROSOPHILA MELANOGASTER

Alternative models of the maintenance of genetic variability, theories of life-history evolution, and theories of sexual selection and mate choice can be tested by measuring additive and nonadditive genetic variances of components of fitness. A quantitative genetic breeding design was used to produce estimates of genetic variances for male life-history traits in Drosophila melanogaster. Additive genetic covariances and correlations between traits were also estimated. Flies from a large, outbred, laboratory population were assayed for age-specific competitive mating ability, age-specific survivorship, body mass, and fertility. Variance-component analysis then allowed the decomposition of phenotypic variation into components associated with additive genetic, nonadditive genetic, and environmental variability. A comparison of dominance and additive components of genetic variation provides little support for an important role for balancing selection in maintaining genetic variance in this suite of traits. The results provide support for the mutation-accumulation theory, but not the antagonistic-pleiotropy theory of senescence. No evidence is found for the positive genetic correlations between mating success and offspring quality or quantity that are predicted by “good genes” models of sexual selection. Additive genetic coefficients of variation for life-history characters are larger than those for body weight. Finally, this set of male life-history characters exhibits a very low correspondence between estimates of genetic and phenotypic correlations.     

QUANTITATIVE GENETICS OF SEXUAL SELECTION IN THE FIELD CRICKET,GRYLLUS INTEGER

Major theories of sexual selection predict heritable variation in female preferences and male traits and a positive genetic correlation between preference and trait. Here we show that female Texas field crickets, Gryllus integer, have heritable genetic variation for the male calling song stimulus level that produces the greatest phonotactic response. Approximately 34% of the variation in female preferences was due to additive genetic effects. Female choosiness, that is, the strength of the female response to her most preferred stimulus relative to her average response to all stimuli, did not show significant genetic effects. The male calling song character was not related to male size or age but did show significant genetic effects. Approximately 39% of the variation in the number of pulses per trill was due to additive genetic variation. The genetic correlation estimated for the field population was 0.51 ± 0.17. The number of pulses per trill produced by males is under stabilizing sexual selection.     

MAXIMUM-LIKELIHOOD APPROACHES APPLIED TO QUANTITATIVE GENETICS OF NATURAL POPULATIONS

Growing interest in adaptive evolution in natural populations has spurred efforts to infer genetic components of variance and covariance of quantitative characters. Here, I review difficulties inherent in the usual least-squares methods of estimation. A useful alternative approach is that of maximum likelihood (ML). Its particular advantage over least squares is that estimation and testing procedures are well defined, regardless of the design of the data. A modified version of ML, REML, eliminates the bias of ML estimates of variance components. Expressions for the expected bias and variance of estimates obtained from balanced, fully hierarchical designs are presented for ML and REML. Analyses of data simulated from balanced, hierarchical designs reveal differences in the properties of ML, REML, and F-ratio tests of significance. A second simulation study compares properties of REML estimates obtained from a balanced, fully hierarchical design (within-generation analysis) with those from a sampling design including phenotypic data on parents and multiple progeny. It also illustrates the effects of imposing nonnegativity constraints on the estimates. Finally, it reveals that predictions of the behavior of significance tests based on asymptotic theory are not accurate when sample size is small and that constraining the estimates seriously affects properties of the tests. Because of their great flexibility, likelihood methods can serve as a useful tool for estimation of quantitative-genetic parameters in natural populations. Difficulties involved in hypothesis testing remain to be solved.     

THE DETERMINATION OF GENETIC COVARIANCES AND PREDICTION OF EVOLUTIONARY TRAJECTORIES BASED ON A GENETIC CORRELATION MATRIX

There is much interest in measuring selection, quantifying evolutionary constraints, and predicting evolutionary trajectories in natural populations. For these studies, genetic (co)variances among fitness traits play a central role. We explore the conditions that determine the sign of genetic covariances and demonstrate a critical role of selection in shaping genetic covariances. In addition, we show that genetic covariance matrices rather than genetic correlation matrices should be characterized and studied in order to infer genetic basis of population differentiation and/or to predict evolutionary trajectories.     

THE EVOLUTIONARY GENETICS AND DEVELOPMENTAL BASIS OF WING PATTERN VARIATION IN THE BUTTERFLY BICYCLUS ANYNANA

We have studied interactions between developmental processes and genetic variation for the eyespot color pattern on the adult dorsal forewing of the nymphalid butterfly, Bicyclus anynana. Truncation selection was applied in both an upward and a downward direction to the size of a single eyespot consisting of rings with wing scales of differing color pigments. High heritabilities resulted in rapid responses to selection yielding divergent lines with very large or very small eyespots. Strong correlated responses occurred in most of the other eyespots on each wing surface. The cells at the center of a presumptive eyespot (the “focus”) act in the early pupal stage to establish the adult wing pattern. The developmental fate of the scale cells within an eyespot is specified by the “signaling” properties of the focus and the “response” thresholds of the epidermis. The individual eyespots can be envisaged as developmental homologues. Grafting experiments performed with the eyespot foci of the selected lines showed that additive genetic variance exists for both the response and, in particular, the signaling components of the developmental system. The results are discussed in the context of how constraints on the evolution of this wing pattern may be related to the developmental organization.     

QUANTITATIVE GENETICS AND THE EVOLUTION OF REACTION NORMS

We extend methods of quantitative genetics to studies of the evolution of reaction norms defined over continuous environments. Our models consider both spatial variation (hard and soft selection) and temporal variation (within a generation and between generations). These different forms of environmental variation can produce different evolutionary trajectories even when they favor the same optimal reaction norm. When genetic constraints limit the types of evolutionary changes available to a reaction norm, different forms of environmental variation can also produce different evolutionary equilibria. The methods and models presented here provide a framework in which empiricists may determine whether a reaction norm is optimal and, if it is not, to evaluate hypotheses for why it is not.     

QUANTITATIVE GENETICS OF SHELL FORM OF AN INTERTIDAL SNAIL: CONSTRAINTS ON SHORT-TERM RESPONSE TO SELECTION

We investigated the genetic and environmental determinants of shell form in an intertidal snail (Prosobranchia: Littorina sp.) to identify constraints on the short-term response to selection. Our quantitative genetic parameters were estimated from a half-sib experimental design using 288 broods of snails. Each brood was divided into two treatments differing in snail population density, and therefore in grazing area per snail. Differences in population density induced marked differences in shell form. Snails in the low density treatment grew faster and had lighter shells with narrower whorls and narrower apertures than their siblings at high density. Despite this environmental plasticity in shell shape we found significant additive genetic variance for components of shell shape. We discuss two mechanisms that may maintain additive genetic variance for shell shape in intertidal snail populations: migration between environments with different selective pressures and migration between environments with different mean growth rates. We also estimated a genetic variance-covariance matrix for shell form traits and used the matrix to identify constraints on the short-term response to selection. We predict the rate of response to selection for predator-resistant morphology such as would occur upon invasion of predatory crabs. The large negative genetic correlation between relative spire height and shell weight would facilitate simultaneous selection for a lower spire and a heavier shell, both of which would increase resistance to predatory crabs.     

DEVELOPMENTAL QUANTITATIVE GENETICS AND THE EVOLUTION OF ONTOGENIES

A model is presented which permits integration of developmental information into genetic discussions about evolutionary change in morphology. Development of a trait is described in terms of an ontogenetic trajectory whose properties are defined by a small number of parameters. Some evolutionary aspects of development are examined from the perspective of this quantitative genetic model. Particular attention is given to the developmental origin of pleiotropic effects, developmental constraints, heterochrony, and the growth and morphogenesis of complex morphologies. The role of genetic maternal effects in mammalian development is briefly examined, particularly as it relates to selection on developmental traits.     

QUANTITATIVE GENETICS OF SEXUAL DIMORPHISM IN HUMAN BODY SIZE

A classical data set is used to predict the effect of selection on sexual dimorphism and on the population means of three characters—stature, span, and cubit—in humans. Given selection of equal intensity, the population means of stature and of cubit should respond more than 60 times as fast as dimorphism in these characters. The population mean of span should also respond far more rapidly than dimorphism, but no numerical estimate of the ratio of these rates was possible. These results imply that sexual dimorphism in these characters can evolve only very slowly. Consequently, hypotheses about the causes of sexual dimorphism cannot be tested by comparing the dimorphism of different human societies. It has been suggested that primate sexual dimorphism may be an allometric response to selection for larger body size. We show that such selection can indeed generate sexual dimorphism, but that this effect is too weak to account for the observed relationship between dimorphism and body size in primates.     

EVOLUTIONARY GENETICS OF ALLORECOGNITION IN THE COLONIAL HYDROID HYDRACTINIA SYMBIOLONGICARPUS

Many sedentary, clonal marine invertebrates compete intensively with conspecifics for habitable space. Allorecognition systems mediate the nature and outcome of these intraspecific competitive interactions, such that the initiation of agonistic behavior and the potential for intergenotypic fusion depend strongly on the relatedness of the contestants. The dependence of these behaviors on relatedness, along with the extraordinary precision with which self can be discriminated from nonself, suggest that allorecognition systems are highly polymorphic genetically. However, allotypic specificity of this sort could be produced by any number of genetic scenarios, ranging from relatively few loci with abundant allelic variation to numerous loci with relatively few alleles per locus. At this point, virtually nothing is known of the formal genetics of allorecognition in marine invertebrates; consequently, the evolutionary dynamics of such systems remain poorly understood. In this paper, we characterize the formal genetics of allorecognition in the marine hydrozoan Hydractinia symbiolongicarpus. Hydractinia symbiolongicarpus colonizes gastropod shells occupied by hermit crabs. When two or more individuals grow into contact, one of three outcomes ensues: fusion (compatibility), transitory fusion (a temporary state of compatibility), and rejection (incompatibility, often accompanied by the production of agonistic structures termed hyperplastic stolons). Observed patterns of compatibility between unrelated, half-sib pairs, and full-sib pairs show that unrelated and half-sib pairs under laboratory culture have a very low probability of being fusible, whereas full sibs have a roughly 30% rate of fusion in experimental pairings. The genetic simulations indicate that roughly five loci, with 5–7 alleles per locus, confer specificity in this species. In ecological terms, the reproductive ecology of H. symbiolongicarpus should promote the cosettlement of kin, some of which should be full sibs, and some half sibs. Thus, there is potential for kin selection to play a major role in the evolution of the H. symbiolongicarpus allorecognition system. In genetic terms, this system conforms to theoretical predictions for a recognition system selected to distinguish among classes of kin, in addition to self from nonself.     

QUANTITATIVE GENETICS OF SEXUAL SIZE DIMORPHISM IN THE COLLARED FLYCATCHER,FICEDULA ALBICOLLIS

Quantitative genetic theory predicts that evolution of sexual size dimorphism (SSD) will be a slow process if the genetic correlation in size between the sexes is close to unity, and the heritability of size is similar in both sexes. However, there are very few reliable estimates of genetic correlations and sex-specific heritabilities from natural populations, the reasons for this being that (1) offspring have often been sexed retrospectively, and hence, selection acting differently with respect to body size in the two sexes between measuring and sex identification can bias estimates of SSD; and (2) in many taxa, parents may be incorrectly assigned to offspring either because of assignment errors or because of extrapair paternity. We used molecular sex and paternity identification to overcome these problems and estimated sex-specific heritabilities and the genetic correlation in body size between the two sexes in the collared flycatcher, Ficedula albicollis. After exclusion of the illegitimate offspring, the genetic correlation in body size between the sexes was 1.00 (SE = 0.22), implying a severe constraint on the evolution of SSD in this species. Furthermore, sex-specific heritability estimates were very similar, indicating that neither sex will be able to evolve faster than the other. By using estimated genetic parameters, together with empirically derived estimates of sex-specific selection gradients, we further demonstrated that the predicted selection response in female tarsus length is displaced about 200% in the opposite direction from that to be expected if there were no genetic correlation between the sexes. The correspondence between the biochemically estimated rate of extrapair paternity (about 15 % of the young) and that estimated from the “heritability method” (11%) was good. However, the estimated rate of extrapair paternity with the heritability method after exclusion of the illegitimate young was 22%, adding to increasing evidence that factors other than extrapair paternity (e.g., maternal effects) may be resposible for the commonly observed higher mother-offspring than father-offspring resemblance.     

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.