Genetic Correlations and Maternal Effect Coefficients Obtained from Offspring-Parent Regression

Additive genetic variances and covariances of quantitative characters are necessary to predict the evolutionary response of the mean phenotype vector in a population to natural or artificial selection. Standard formulas for estimating these parameters, from the resemblance between relatives in one or two characters at a time, are biased by natural selection on the parents and by maternal effects. We show how these biases can be removed using a multivariate analysis of offspring-parent regressions. A dynamic model of maternal effects demonstrates that, in addition to the phenotypic variance-covariance matrix of the characters, sufficient parameters for predicting the response of the mean phenotype vector to weak selection are the additive genetic variance-covariance matrix and a set of causal coefficients for maternal effects. These can be simultaneously estimated from offspring-parent regressions alone, in some cases just from the daughter-mother regressions, if all of the important selected and maternal characters have been measured and included in the analysis.     

Genetic and phenotypic correlations among size-related traits, and heritability variation between body parts in Drosophila buzzatii

Recent studies have shown that body size is a heritable trait phenotypically correlated with several fitness components in wild populations of the cactophilic fly Drosophila buzzatii. To obtain further information on size-related variation, heritabilities as well as genetic and phenotypic correlations among size-related traits of several body parts (head, thorax and wings) were estimated. The study was carried out on an Argentinean natural population in which size-related selection was previously detected. The genetic parameters were estimated using offspring-parent regressions (105 families) in the laboratory G₂ generation of a sample of wild flies. The traits were also scored in Wild-Caught Flies (WCF). Laboratory-Reared Flies (LRF) were larger and less variable than WCF. Although heritability estimates were significant for all traits, heritabilities were higher for thorax-wing traits than for head traits. Phenotypic and genetic correlations were all positive. The highest genetic correlations were found between traits which are both functionally and developmentally related. Genetic and phenotypic correlations estimated in the lab show similar correlation patterns (r = 0.49; TP = 0.02, Mantel's test). However, phenotypic correlations were found to be typically larger in WCF than in LRF. The genetic correlation matrix estimated in the relatively homogeneous lab environment is not simply a constant multiplicative factor of the phenotypic correlation matrix estimated in WCF. This revised version was published online in July 2006 with corrections to the Cover Date.     

Quantitative genetic tools for insecticide resistance risk assessment: estimating the heritability of resistance

Quantitative genetic studies of resistance can provide estimates of genetic parameters not available with other types of genetic analyses. Three methods are discussed for estimating the amount of additive genetic variation in resistance to individual insecticides and subsequent estimation of the heritability (h2) of resistance. Sibling analysis and offspring-parent regression permit direct estimates of h2 by comparing the resistance phenotypes of individuals of known relatedness. Threshold trait analyses, performed on data from selection experiments, provide estimates of realized heritability. Procedures are outlined for predicting changes in resistance to insecticides based on h2 estimates. Quantitative genetic theory is examined as it relates to resistance and resistance as a quantitative trait; quantitative genetic methods also are unique in providing estimates of genetic correlations between traits. Comments are included on estimates of genetic correlation between resistance and phenotypic traits (e.g., development time) and how they may be used to predict changes in the genetic aspects of phenology that result from insecticide applications (i.e., to predict how the reproductive capacity of future generations will differ from that of the treated generation).     

HOMOGENEITY OF THE GENETIC VARIANCE-COVARIANCE MATRIX FOR ANTIPREDATOR TRAITS IN TWO NATURAL POPULATIONS OF THE GARTER SNAKE THAMNOPHIS ORDINOIDES

Quantitative genetic models of evolution rely on the genetic variance-covariance matrix to predict the phenotypic response to selection. Both prospective and retrospective studies of phenotypic evolution across generations rely on assumptions about the constancy of patterns of genetic covariance through time. In the absence of robust theoretical predictions about the stability of genetic covariances, this assumption must be tested with empirical comparisons of genetic parameters among populations and species. Genetic variance-covariance matrices were estimated for a suite of antipredator traits in two populations of the northwestern garter snake, Thamnophis ordinoides. The characters studied include color pattern and antipredator behaviors that interact to facilitate escape from predators. Significant heritabilities for all traits were detected in both populations. Genetic correlations and covariances were found among behaviors in both populations and between color pattern and behavior in one of the populations. Phenotypic means differed among populations, but pairwise comparisons revealed no heterogeneity of genetic parameters between the populations. The structure of the genetic variance-covariance matrix has apparently not changed significantly during the divergence of these two populations.     

Genetic,phenotypic, and environmental correlations in black medic,Medicago lupulina L., grown in three different environments

We have investigated the relationship between phenotypic and genetic correlations among a large number of quantitative traits (36) in three different environments in order to determine their degree of disparity and whether phenotypic correlations could be substituted for their genetic counterparts whatever the environment. We also studied the influence of the environment on genetic and phenotypic correlations. Twenty accessions (full-sib families) ofMedicago luPulina were grown in three environments. In two of these two levels of environmental stress were generated by harvesting plants at flowering and by growing plants in competition with barley, respectively. A third environment, with no treatment, was used as a control with no stress. Average values of pod and shoot weight indicate that competition induces the highest level of stress. The genetic and phenotypic correlations among the 36 traits were compared. Significant phenotypic correlations were obtained easily, while there was no genetic variation for 1 or the 2 characters being correlated. The large positive correlation between the genetic and phenotypic correlation matrices indicated a good proportionality between genetic and phenotypic correlations matrices but not their similarity. In a given environment, when only those traits with a significant genetic variance were taken into account, there were still differences between genetic and phenotypic correlations, even when levels of significance for phenotypic correlations were lowered. Consequently, it is dangerous to substitute phenotypic correlations for genetic correlations. The number of traits that showed genetic variability increased with increasing environmental stress, consequently the number of significant genetic correlations also increased with increasing environmental stress. In contrast, the number of significant phenotypic correlations was not influnced by the environment. The structures of both phenotypic and genetic matrices, however, depended on the environment, and not in the same way for both matrices.     

A bivariate quantitative genetic model for a linear Gaussian trait and a survival trait

With the increasing use of survival models in animal breeding to address the genetic aspects of mainly longevity of livestock but also disease traits, the need for methods to infer genetic correlations and to do multivariate evaluations of survival traits and other types of traits has become increasingly important. In this study we derived and implemented a bivariate quantitative genetic model for a linear Gaussian and a survival trait that are genetically and environmentally correlated. For the survival trait, we considered the Weibull log-normal animal frailty model. A Bayesian approach using Gibbs sampling was adopted. Model parameters were inferred from their marginal posterior distributions. The required fully conditional posterior distributions were derived and issues on implementation are discussed. The two Weibull baseline parameters were updated jointly using a Metropolis-Hasting step. The remaining model parameters with non-normalized fully conditional distributions were updated univariately using adaptive rejection sampling. Simulation results showed that the estimated marginal posterior distributions covered well and placed high density to the true parameter values used in the simulation of data. In conclusion, the proposed method allows inferring additive genetic and environmental correlations, and doing multivariate genetic evaluation of a linear Gaussian trait and a survival trait.     

Genetic variance and covariance patterns of larval development in the small white butterflyPieris rapae crucivora Boisduval

Quantitative genetic theory indicates that genetic covariance patterns among life history characters should have played an important role as genetic constraint in life history evolution. Highly positve (and negative) genetic correlations between larval development time (or larval growth rate) and adult size characters were detected by means of sib analysis for the small white butterfly Pieris rapae crucivora. The genetic associations suggested that evolution of developmental characteristics and adult phenotypic traits were constrained by pleiotropy. The positive genetic correlations between development time and adult body size may be compatible with the trade-off between them, but the negative genetic correlations between larval growth rate and adult body size are not predicted from theories of optimal energy allocation. That phenotypic correlations drastically differed from the genetic correlations indicates limitations of evolutionary inferences based only on phenotypic variation.     

The sampling variance of the correlation coefficients estimated from two-fold nested and offspring-parent regression analyses

Summary A formula is presented for the large-sample variance of phenotypic, genetic and environmental correlation coefficients, estimated from two-fold nested genetic analyses of balanced or unbalanced offspring data. Where parents of these offspring are scored, offspring on parent regression estimates of genetic parameters may be obtained for each parental level of the nested model. The large-sample variance of the offspring-parent genetic correlation coefficients, computed from either level or by using mid-parent data, is given. The first formula is a correction and generalisation of an expression given by Grossman (1970), while the second formula is an extension of a relationship derived by Reeve (1955).     

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.     

The genetic architecture of ecological specialization: correlated gene effects on host use and habitat choice in pea aphids

Genetic correlations among phenotypic characters result when two traits are influenced by the same genes or sets of genes. By reducing the degree to which traits in two environments can evolve independently (e.g., Lande 1979; Via and Lande 1985), such correlations are likely to play a central role in both the evolution of ecological specialization and in its link to speciation. For example, negative genetic correlations between fitness traits in different environments (i.e., genetic trade-offs) are thought to influence the evolution of specialization, while positive genetic correlations between performance and characters influencing assortative mating can accelerate the evolution of reproductive isolation between ecologically specialized populations. We first discuss how the genetic architecture of a suite of traits may affect the evolutionary role of genetic correlations among them and review how the mechanisms of correlations can be analyzed using quantitative trait locus (QTL) mapping. We then consider the implications of such data for understanding the evolution of specialization and its link to speciation. We illustrate this approach with a QTL analysis of key characters in two races of pea aphids that are highly specialized on different host plants and partially reproductively isolated. Our results suggest that antagonism among QTL effects on performance in the two environments leads to a genetic trade-off in this system. We also found evidence for parallel QTL effects on host-plant acceptance and fecundity on the accepted host, which could produce assortative mating. These results suggest that the genetic architecture of traits associated with host use may have played a central role in the evolution of specialization and reproductive isolation in pea aphids.     

The place of development in mathematical evolutionary theory

Development plays a critical role in structuring the joint offspring-parent phenotype distribution. It thus must be part of any truly general evolutionary theory. Historically, the offspring-parent distribution has often been treated in such a way as to bury the contribution of development, by distilling from it a single term, either heritability or additive genetic variance, and then working only with this term. I discuss two reasons why this approach is no longer satisfactory. First, the regression of expected offspring phenotype on parent phenotype can easily be nonlinear, and this nonlinearity can have a pronounced impact on the response to selection. Second, even when the offspring-parent regression is linear, it is nearly always a function of the environment, and the precise way that heritability covaries with the environment can have a substantial effect on adaptive evolution. Understanding these complexities of the offspring-parent distribution will require understanding of the developmental processes underlying the traits of interest. I briefly discuss how we can incorporate such complexity into formal evolutionary theory, and why it is likely to be important even for traits that are not traditionally the focus of evo-devo research. Finally, I briefly discuss a topic that is widely seen as being squarely in the domain of evo-devo: novelty. I argue that the same conceptual and mathematical framework that allows us to incorporate developmental complexity into simple models of trait evolution also yields insight into the evolution of novel traits.     

RESPONSES TO SELECTION AMONG LIFE-HISTORY TRAITS IN A NONMIGRATORY POPULATION OF MILKWEED BUGS (ONCOPELTUS FASCIATUS)

Genetic parameters were assessed in the nonmigratory Puerto Rico population of the milkweed bug, Oncopeltus fasciatus, and compared with parameters estimated in a migratory population from Iowa (Palmer and Dingle, 1986). Offspring-parent regression analysis provided initial estimates of heritabilities and phenotypic and genetic correlations among wing length, head-capsule width, female age at first reproduction, fecundity for the first and second five days of reproduction by females, and clutch size for the first and second five days of reproduction by females. Replicated bidirectional selection for wing length was then imposed, with a direct response to selection revealing substantial additive genetic variance for this trait, as was also the case with the Iowa population. Assays for correlated response to selection yielded two further similarities to Iowa: a positive response in head-capsule width and no consistent response in age at first reproduction. In contrast to the results with Iowa bugs, neither regression analysis nor selection revealed statistically significant genetic correlations between fecundity measures and those of other traits. In both populations the potential exists for body-size characters to evolve together independently of age at first reproduction; but in the nonmigratory Puerto Rico bugs, fecundity does not contribute to a life-history syndrome involving genetic correlations among these traits.     

Laboratory Estimates of Heritabilities and Genetic Correlations in Nature

A lower bound on heritability in a natural environment can be determined from the regression of offspring raised in the laboratory on parents raised in nature. An estimate of additive genetic variance in the laboratory is also required. The estimated lower bounds on heritabilities can sometimes be used to demonstrate a significant genetic correlation between two traits in nature, if their genetic and phenotypic correlations in nature have the same sign, and if sample sizes are large, and heritabilities and phenotypic and genetic correlations are high.     

HERITABILITIES OF DOMINANCE-RELATED TRAITS IN MALE BANK VOLES (CLETHRIONOMYS GLAREOLUS)

A number of studies have shown that in several animal species females prefer dominant males as mating partners, but fewer attempts have been made to measure possible indirect benefits of this choice. One reason for this may be that, even though dominance is a widely used concept, the definition of dominance still remains controversial Furthermore, defining and measuring the heritability of social behaviors is problematic because they are not individual traits but, by definition, involve interactions between at least two individuals. In this study we estimated heritabilities and coefficients of additive genetic variances (CV_A) for male traits that are closely associated with dominance and female mating preferences in bank voles (Clethrionomys glareolus). The heritability values were estimated using father-offspring regression. All heritability estimates were relatively high ranging from 0.531 (urine marking) to 0.767 (preputial glands). The CV_A-values indicated high levels of additive genetic variance especially in the characters most closely related to dominance: the weight of preputial glands and urine marking behavior. All phenotypic correlations among the traits measured were significantly positive and the genetic correlations were of similar magnitude as the corresponding phenotypic counterparts. Even though heritabilities may be lower in the natural environment than under controlled laboratory conditions, our results suggest that characters closely related to dominance may be at least partly genetically determined.     

Design of multivariate selection experiments to estimate genetic parameters

Summary The precision of estimates of genetic variances and covariances obtained from multivariate selection experiments of various designs are discussed. The efficiencies of experimental designs are compared using criteria based on a confidence region of the estimated genetic parameters, with estimation using both responses and selection differentials and offspring-parent regression. A good selection criterion is shown to be to select individuals as parents using an index of the sums of squares and crossproducts of the phenotypic measurements. Formulae are given for the optimum selection proportion when the relative numbers of individuals in the parent and progeny generations are fixed or variable. Although the optimum depends on a priori knowledge of the genetic parameters to be estimated, the designs are very robust to poor estimates. For bivariate uncorrelated data, the variance of the estimated genetic parameters can be reduced by approximately 0.4 relative to designs of a more conventional nature when half of the individuals are selected on one trait and half on the other trait. There are larger reductions in variances if the traits are correlated.     

Testing the phenotypic gambit: phenotypic, genetic and environmental correlations of colour

Evolutionary theory is primarily concerned with genetic processes, yet empirical testing of this theory often involves data collected on phenotypes. To make this tenable, the implicit assumption is often made that phenotypic patterns are good predictors of genetic patterns; an assumption that coined the phenotypic gambit. Although this assumption has been validated for traits with high heritability, such as morphology, its generality for traits with low heritabilities, such as life-history and behavioural traits, remains controversial. Using a large-scale cross-fostering experiment, we were able to measure genetic, common environmental and phenotypic correlations between four colour traits and two skeletal traits in a wild population of passerine birds, the blue tit (Parus caeruleus). Colour traits had little heritable variation but common environment effects were found to be important; skeletal traits showed the opposite pattern. Positive correlations because of a shared natal environment were found between all traits, obscuring negative genetic correlations between some colour and skeletal traits. Consequently, phenotypic patterns were poor surrogates for genetic patterns and we suggest that this may be common if trade-offs or substantial parental effects exist. For this group of traits, the phenotypic gambit cannot be made and we suggest caution when inferring genetic patterns from phenotypic data, especially for behavioural and life-history traits.     

Genetic relationship between milk urea nitrogen and reproductive performance in Holstein dairy cows

The objective of this study was to describe the genetic and phenotypic relationship between milk urea nitrogen (MUN) and reproductive traits in Iranian Holstein dairy cows. Test-day MUN data obtained from 57 301 dairy cows on 20 large dairy herds in Iran between January 2005 and June 2009. Genetic parameters for MUN and reproductive traits were estimated with a five-trait model using ASREML program. Random regression test-day models were used to estimate heritabilities separately for MUN from first, second and third lactations. Regression curves were modeled using Legendre polynomials of order 3. Herd-year-season along with age at calving was included as fixed effects in all models for reproductive traits. Heritabilities for MUN and reproductive traits were estimated separately for first lactation, second lactation and third lactation. The estimated heritabilities for MUN varied from 0.18 to 0.22. The heritability estimate was low for reproductive traits, which ranged from 0.02 to 0.06 for different traits and across parities. Except for days open, phenotypic and genetic correlations of MUN with reproductive performance traits were close to zero. Genetic correlations between MUN and days open were 0.23, 0.35 and 0.45 in first, second and third lactation, respectively. However, the phenotypic correlation between MUN at different parities was moderate (0.28 to 0.35), but the genetic correlation between MUN at different parities was high and ranged from 0.84 to 0.97. This study shows a limited application of MUN for use in selection programs to improve reproductive performance.     

Quantitative genetics of skeletal nonmetric traits in the rhesus macaques on Cayo Santiago. II. Phenotypic,genetic, and environmental correlations between traits

The general lack of phenotypic correlation among skeletal nonmetric traits has been interpreted as indicating a lack of genetic correlation among these traits. Nonmetric traits scored on animals in the skeletal collection of rhesus macaques from Cayo Santiago are used to calculate phenotypic, genetic, and environmental correlations between traits. The results show that even when phenotypic correlations are low, there may be large, significant genetic correlations among these traits. The genetic correlation pattern suggests that genes which affect nonmetric trait variation act primarily at a local level in the cranium, even though there are genes with pleiotropic effects on skeletal nonmetric traits throughout the cranium. Environmental and phenotypic correlations do not show this neighborhood pattern of correlation.     

Constraints on evolution and postcopulatory sexual selection: trade-offs among ejaculate characteristics

Ejaculates function as an integrated unit to ensure male fertility and paternity, can have a complex structure, and can experience multiple episodes of selection. Current studies on the evolution of ejaculates typically focus on phenotypic variation in sperm number, size, or related traits such as testes size as adaptations to postcopulatory male-male competition. However, the evolution of the integrated nature of ejaculate structure and function depends on genetic variation in and covariation between the component parts. Here we report a quantitative genetic study of the components of the ejaculate of the cockroach Nauphoeta cinerea, including those we know to experience postcopulatory sexual selection, in the context of functional integration of ejaculate characters. We use the patterns of genetic variation and covariation to infer how the integration of the functions of the ejaculate constrain and shape its evolution. Ejaculate components were highly variable, showed significant additive genetic variance, and moderate to high evolvability. The level of genetic variation in these characters, despite strong directional or truncating selection, may reflect the integration of multiple episodes of selection that occur in N. cinerea. There were few significant phenotypic correlations, but all the genetic correlations among ejaculate characters were significantly different from zero. The patterns of genetic variation and covariation suggest that there are important trade-offs among individual traits of the ejaculate and that evolution of ejaculate characteristics will not proceed unconstrained. Fully describing the genetic relationships among traits that perform as an integrated unit helps us understand how functional relationships constrain or facilitate the evolution of the complex structure that is the ejaculate.     

Four characters in a trade-off: dissecting their phenotypic and genetic relations

Phenotypic characters may covary negatively because they are in a trade-off or positively because they contribute to a single function. Genetic correlations can be used to test the validity and generality of these functional relationships by indicating the level of genetic integration and checking the conditions under which they are expressed. Phenotypic correlations indicate that there is a widespread trade-off between flight capability and early fecundity in insects. Different wing morphs (long and short wing) are thought to have a suite of reproductive and flight capability traits. In a half-sib mating experiment, we estimated phenotypic relationships between two flight-capability-related characters (flight muscle condition, wing morph) and two components of early fecundity (number of eggs in the ovaries, number of eggs laid), as well as genetic correlations relating wing morph and both components of fecundity in the wing-dimorphic cricket, Gryllus firmus. The number of eggs in the ovaries and the number of eggs laid were negatively correlated phenotypically and genetically with wing length morph (i.e., long wings associated with low fecundity). Both fecundity characters differed between wing morphs, but only if flight muscle was present and not histolyzed. The phenotypic and genetic correlations between fecundity characters were not significant. This suggests that the phenotypic relationship between ovary development and eggs laid is complex, they are not genetically integrated, and they may evolve independently. However, both early fecundity characters are functionally and genetically integrated within the trade-off to a similar degree. Finally, the trade-off affects early fecundity of both wing morphs suggesting that the functional relationship depends on flight muscle size. Received: 1 December 1998 / Accepted: 20 May 1999