Orientation of the genetic variance-covariance matrix and the fitness surface for multiple male sexually selected traits

Stabilizing selection has been predicted to change genetic variances and covariances so that the orientation of the genetic variance-covariance matrix (G) becomes aligned with the orientation of the fitness surface, but it is less clear how directional selection may change G. Here we develop statistical approaches to the comparison of G with vectors of linear and nonlinear selection. We apply these approaches to a set of male sexually selected cuticular hydrocarbons (CHCs) of Drosophila serrata. Even though male CHCs displayed substantial additive genetic variance, more than 99% of the genetic variance was orientated 74.9degrees away from the vector of linear sexual selection, suggesting that open-ended female preferences may greatly reduce genetic variation in male display traits. Although the orientation of G and the fitness surface were found to differ significantly, the similarity present in eigenstructure was a consequence of traits under weak linear selection and strong nonlinear ( convex) selection. Associating the eigenstructure of G with vectors of linear and nonlinear selection may provide a way of determining what long-term changes in G may be generated by the processes of natural and sexual selection.

Determining the effective dimensionality of the genetic variance-covariance matrix

Determining the dimensionality of G provides an important perspective on the genetic basis of a multivariate suite of traits. Since the introduction of Fisher's geometric model, the number of genetically independent traits underlying a set of functionally related phenotypic traits has been recognized as an important factor influencing the response to selection. Here, we show how the effective dimensionality of G can be established, using a method for the determination of the dimensionality of the effect space from a multivariate general linear model introduced by AMEMIYA (1985). We compare this approach with two other available methods, factor-analytic modeling and bootstrapping, using a half-sib experiment that estimated G for eight cuticular hydrocarbons of Drosophila serrata. In our example, eight pheromone traits were shown to be adequately represented by only two underlying genetic dimensions by Amemiya's approach and factor-analytic modeling of the covariance structure at the sire level. In, contrast, bootstrapping identified four dimensions with significant genetic variance. A simulation study indicated that while the performance of Amemiya's method was more sensitive to power constraints, it performed as well or better than factor-analytic modeling in correctly identifying the original genetic dimensions at moderate to high levels of heritability. The bootstrap approach consistently overestimated the number of dimensions in all cases and performed less well than Amemiya's method at subspace recovery.

Multivariate quantitative genetics and the Lek Paradox: Genetic variance in male sexually selected traits of Drosophila serrata under field control

Single male sexually selected traits have been found to exhibit substantial genetic variance, even though natural and sexual selection are predicted to deplete genetic variance in these traits. We tested whether genetic variance in multiple male display traits of Drosophila serrata was maintained under field conditions. A breeding design involving 300 field-reared males and their laboratory-reared offspring allowed the estimation of the genetic variance-covariance matrix for six male cuticular hydrocarbons (CHCs) under field conditions. Despite individual CHCs displaying substantial genetic variance under field conditions, the vast majority of genetic variance in CHCs was not closely associated with the direction of sexual selection measured on field phenotypes. Relative concentrations of three CHCs correlated positively with body size in the field, but not under laboratory conditions, suggesting condition-dependent expression of CHCs under field conditions. Therefore condition dependence may not maintain genetic variance in preferred combinations of male CHCs under field conditions, suggesting that the large mutational target supplied by the evolution of condition dependence may not provide a solution to the lek paradox in this species. Sustained sexual selection may be adequate to deplete genetic variance in the direction of selection, perhaps as a consequence of the low rate of favorable mutations expected in multiple trait systems.

Phenotypic divergence along lines of genetic variance

Natural populations inhabiting the same environment often independently evolve the same phenotype. Is this replicated evolution a result of genetic constraints imposed by patterns of genetic covariation? We looked for associations between directions of morphological divergence and the orientation of the genetic variance-covariance matrix (G) by using an experimental system of morphological evolution in two allopatric nonsister species of rainbow fish. Replicate populations of both Melanotaenia eachamensis and Melanotaenia duboulayi have independently adapted to lake versus stream hydrodynamic environments. The major axis of divergence (z) among all eight study populations was closely associated with the direction of greatest genetic variance (g(max)), suggesting directional genetic constraint on evolution. However, the direction of hydrodynamic adaptation was strongly associated with vectors of G describing relatively small proportions of the total genetic variance, and was only weakly associated with g(max). In contrast, divergence between replicate populations within each habitat was approximately proportional to the level of genetic variance, a result consistent with theoretical predictions for neutral phenotypic divergence. Divergence between the two species was also primarily along major eigenvectors of G. Our results therefore suggest that hydrodynamic adaptation in rainbow fish was not directionally constrained by the dominant eigenvector of G. Without partitioning divergence as a consequence of the adaptation of interest (here, hydrodynamic adaptation) from divergence due to other processes, empirical studies are likely to overestimate the potential for the major eigenvectors of G to directionally constrain adaptive evolution.

Genetic constraints on the evolution of mate recognition under natural selection

Field populations of Drosophila serrata display reproductive character displacement in cuticular hydrocarbons (CHCs) when sympatric with Drosophila birchii. We have previously shown that the naturally occurring pattern of reproductive character displacement can be experimentally replicated by exposing field allopatric populations of D. serrata to experimental sympatry with D. birchii. Here, we tested whether the repeated evolution of reproductive character displacement in natural and experimental populations was a consequence of genetic constraints on the evolution of CHCs. The genetic variance-covariance (G) matrices for CHCs were determined for populations of D. serrata that had evolved in either the presence or absence of D. birchii under field and experimental conditions. Natural selection on mate recognition under both field and experimental sympatric conditions increased the genetic variance in CHCs consistent with a response to selection based on rare alleles. A close association between G eigenstructure and the eigenstructure of the phenotypic divergence (D) matrix in natural and experimental populations suggested that G matrix eigenstructure may have determined the direction in which reproductive character displacement evolved during the reinforcement of mate recognition.

The genetic basis of academic achievement on the Queensland Core Skills Test and its shared genetic variance with IQ

First, this study examined genetic and environmental sources of variation in performance on a standardised test of academic achievement, the Queensland Core Skills Test (QCST) (Queensland Studies Authority, 2003a). Second, it assessed the genetic correlation among the QCST score and Verbal and Performance IQ measures using the Multidimensional Aptitude Battery (MAB), [Jackson, D. N. (1984) Multidimensional Aptitude Battery manual. Port Huron, MI:Research Psychologist Press, Inc.]. Participants were 256 monozygotic twin pairs and 326 dizygotic twin pairs aged from 15 to 18 years (mean 17 years +/- 0.4 [SD]) when achievement tested, and from 15 to 22 years (mean 16 years +/- 0.4 [SD]) when IQ tested. Univariate analysis indicated a heritability for the QCST of 0.72. Adjustment to this estimate due to truncate selection (downward adjustment) and positive phenotypic assortative mating (upward adjustment) suggested a heritability of 0.76 The phenotypic (0.81) and genetic (0.91) correlations between the QCST and Verbal IQ (VIQ) were significantly stronger than the phenotypic (0.57) and genetic (0.64) correlations between the QCST and Performance IQ (PIQ). The findings suggest that individual variation in QCST performance is largely due to genetic factors and that common environmental effects may be substantially accounted for by phenotypic assortative mating. Covariance between academic achievement on the QCST and psychometric IQ (particularly VIQ) is to a large extent due to common genetic influences.

Dissecting the complex genetic basis of mate choice

The genetic analysis of mate choice is fraught with difficulties. Males produce complex signals and displays that can consist of a combination of acoustic, visual, chemical and behavioural phenotypes. Furthermore, female preferences for these male traits are notoriously difficult to quantify. During mate choice, genes not only affect the phenotypes of the individual they are in, but can influence the expression of traits in other individuals. How can genetic analyses be conducted to encompass this complexity? Tighter integration of classical quantitative genetic approaches with modern genomic technologies promises to advance our understanding of the complex genetic basis of mate choice.

Evolution of additive and nonadditive genetic variance in development time along a cline in Drosophila serrata

Latitudinal clines provide natural systems that may allow the effect of natural selection on the genetic variance to be determined. Ten clinal populations of Drosophila serrata collected from the eastern coast of Australia were used to examine clinal patterns in the trait mean and genetic variance of the life-history trait egg-to-adult development time. Development time significantly lengthened from tropical areas to temperate areas. The additive genetic variance for development time in each population was not associated with latitude but was associated with the population mean development time. Additive genetic variance tended to be larger in populations with more extreme development times and appeared to be consistent with allele frequency change. In contrast, the nonadditive genetic variance was not associated with the population mean but was associated with latitude. Levels of nonadditive genetic variance were greatest in the region of the cline where the gradient in the change in mean was greatest, consistent with Barton's (1999) conjecture that the generation of linkage disequilibrium may become an important component of the genetic variance in systems with a spatially varying optimum.

Analysis of population pharmacokinetic data using NONMEM and WinBUGS

The aim of this report is to describe the use of WinBUGS for two datasets that arise from typical population pharmacokinetic studies. The first dataset relates to gentamicin concentration-time data that arose as part of routine clinical care of 55 neonates. The second dataset incorporated data from 96 patients receiving enoxaparin. Both datasets were originally analyzed by using NONMEM. In the first instance, although NONMEM provided reasonable estimates of the fixed effects parameters it was unable to provide satisfactory estimates of the between-subject variance. In the second instance, the use of NONMEM resulted in the development of a successful model, albeit with limited available information on the between-subject variability of the pharmacokinetic parameters. WinBUGS was used to develop a model for both of these datasets. Model comparison for the enoxaparin dataset was performed by using the posterior distribution of the log-likelihood and a posterior predictive check. The use of WinBUGS supported the same structural models tried in NONMEM. For the gentamicin dataset a one-compartment model with intravenous infusion was developed, and the population parameters including the full between-subject variance-covariance matrix were available. Analysis of the enoxaparin dataset supported a two compartment model as superior to the one-compartment model, based on the posterior predictive check. Again, the full between-subject variance-covariance matrix parameters were available. Fully Bayesian approaches using MCMC methods, via WinBUGS, can offer added value for analysis of population pharmacokinetic data.

Genetic covariance between indices of body condition and immunocompetence in a passerine bird

Background: Condition-dependence is a ubiquitous feature of animal life histories and has important implications for both natural and sexual selection. Mate choice, for instance, is typically based on condition-dependent signals. Theory predicts that one reason why condition-dependent signals may be special is that they allow females to scan for genes that confer high parasite resistance. Such explanations require a genetic link between immunocompetence and body condition, but existing evidence is limited to phenotypic associations. It remains unknown, therefore, whether females selecting males with good body condition simply obtain a healthy mate, or if they acquire genes for their offspring that confer high immunocompetence. Results: Here we use a cross-foster experimental design to partition the phenotypic covariance in indices of body condition and immunocompetence into genetic, maternal and environmental effects in a passerine bird, the zebra finch Taeniopygia guttata. We show that there is significant positive additive genetic covariance between an index of body condition and an index of cell-mediated immune response. In this case, genetic variance in the index of immune response explained 56% of the additive genetic variance in the index of body condition. Conclusion: Our results suggest that, in the context of sexual selection, females that assess males on the basis of condition-dependent signals may gain genes that confer high immunocompetence for their offspring. More generally, a genetic correlation between indices of body condition and imuunocompetence supports the hypothesis that parasite resistance may be an important target of natural selection. Additional work is now required to test whether genetic covariance exists among other aspects of both condition and immunocompetence.

Genetic covariance among measures of information processing speed, working memory, and IQ

The genetic relationship between lower (information processing speed), intermediate (working memory), and higher levels (complex cognitive processes as indexed by IQ) of mental ability was studied in a classical twin design comprising 166 monozygotic and 190 dizygotic twin pairs. Processing speed was measured by a choice reaction time (RT) task (2-, 4-, and 8-choice), working memory by a visual-spatial delayed response task, and IQ by the Multidimensional Aptitude Battery. Multivariate analysis, adjusted for test-retest reliability, showed the presence of a genetic factor influencing all variables and a genetic factor influencing 4- and 8-choice RTs, working memory, and IQ. There were also genetic factors specific to 8-choice RT, working memory, and IQ. The results confirmed a strong relationship between choice RT and IQ (phenotypic correlations: -0.31 to -0.53 in females, -0.32 to -0.56 in males; genotypic correlations: -0.45 to -0.70) and a weaker but significant association between working memory and IQ (phenotypic: 0.26 in females, 0.13 in males; genotypic: 0.34). A significant part of the genetic variance (43%) in IQ was not related to either choice RT or delayed response performance, and may represent higher order cognitive processes.

The genetic covariance among clinal environments after adaptation to an environmental gradient in Drosophila serrata

We examined the genetic basis of clinal adaptation by determining the evolutionary response of life-history traits to laboratory natural selection along a gradient of thermal stress in Drosophila serrata. A gradient of heat stress was created by exposing larvae to a heat stress of 36degrees for 4 hr for 0, 1, 2, 3, 4, or 5 days of larval development, with the remainder of development taking place at 25degrees. Replicated lines were exposed to each level of this stress every second generation for 30 generations. At the end of selection, we conducted a complete reciprocal transfer experiment where all populations were raised in all environments, to estimate the realized additive genetic covariance matrix among clinal environments in three life-history traits. Visualization of the genetic covariance functions of the life-history traits revealed that the genetic correlation between environments generally declined as environments became more different and even became negative between the most different environments in some cases. One exception to this general pattern was a life-history trait representing the classic trade-off between development time and body size, which responded to selection in a similar genetic fashion across all environments. Adaptation to clinal environments may involve a number of distinct genetic effects along the length of the cline, the complexity of which may not be fully revealed by focusing primarily on populations at the ends of the cline.

On the heritability of inspection time and its covariance with IQ: A twin study

Using the classical twin design, this study investigates the influence of genetic factors on the large phenotypic variance in inspection time (IT), and whether the well established IT-IQ association can be explained by a common genetic factor. Three hundred ninety pairs of twins (184 monozygotic, MZ; 206 dizygotic, DZ) with a mean age of 16 years participated, and 49 pairs returned approximately 3 months, later for retesting. As in many IT studies, the pi figure stimulus was used and IT was estimated from the cumulative normal ogive. IT ranged from 39.4 to 774.1 ms (159 +/- 110.1 ms) with faster ITs (by an average of 26.9 ms) found in the retest session from which a reliability of .69 was estimated. Full-scale IQ (FIQ) was assessed by the Multidimensional Aptitude Battery (MAB) and ranged from 79 to 145 (111 +/- 13). The phenotypic association between IT and FIQ was confirmed (- .35) and bivariate results showed that a common genetic factor accounted for 36% of the variance in IT and 32% of the variance in FIQ. The maximum likelihood estimate of the genetic correlation was - .63. When performance and verbal IQ (PIQ & VIQ) were analysed with IT, a stronger phenotypic and genetic relationship was found between PIQ and IT than with VIQ. A large part of the IT variance (64%) was accounted for by a unique environmental factor. Further genetic factors were needed to explain the remaining variance in IQ with a small component of unique environmental variance present. The separability of a shared genetic factor influencing IT and IQ from the total genetic variance in IQ suggests that IT affects a specific subcomponent of intelligence rather than a generalised efficiency. (C) 2001 Elsevier Science Inc. All rights reserved.

A reassessment of genetic limits to evolutionary change

An absence of genetic variance in traits under selection is perhaps the oldest explanation for a limit to evolutionary change, but has also been the most easily dismissed. We review a range of theoretical and empirical results covering single traits to more complex multivariate systems, and show that an absence of genetic variance may be more common than is currently appreciated. From a single-trait perspective, we highlight that it is becoming clear that some trait types do not display significant levels of genetic variation, and we raise the possibility that species with restricted ranges may differ qualitatively from more widespread species in levels of genetic variance in ecologically important traits. A common misconception in many life-history studies is that a lack of genetic variance in single traits, and genetic constraints as a consequence of bivariate genetic correlations, are different causes of selection limits. We detail how interpretations of bivariate patterns are unlikely to demonstrate genetic limits to selection in many cases. We advocate a multivariate definition of genetic constraints that emphasizes the presence (or otherwise) of genetic variance in the multivariate direction of selection. For multitrait systems, recent results using longer term studies of organisms, in which more is understood concerning what traits may be under selection, have indicated that selection may exhaust genetic variance, resulting in a limit to the selection response.