Variance-balanced designs under interference for dependent observations

It is shown that variance-balanced designs can be obtained from Type I orthogonal arrays for many general models with two kinds of treatment effects, including ones for interference, with general dependence structures. These designs can be used to obtain optimal and efficient designs. Some examples and design comparisons are given. (C) 2002 Elsevier B.V. All rights reserved.

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.

Analysis of Melanoma Onset: Assessing Familial Aggregation by Using Estimating Equations and Fitting Variance Components via Bayesian Random Effects Models

We investigate whether relative contributions of genetic and shared environmental factors are associated with an increased risk in melanoma. Data from the Queensland Familial Melanoma Project comprising 15,907 subjects arising from 1912 families were analyzed to estimate the additive genetic, common and unique environmental contributions to variation in the age at onset of melanoma. Two complementary approaches for analyzing correlated time-to-onset family data were considered: the generalized estimating equations (GEE) method in which one can estimate relationship-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modeled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov Chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the free ware package BUGS. In addition, we also used a Bayesian model to investigate the relative contribution of genetic and environmental effects on the expression of naevi and freckles, which are known risk factors for melanoma.

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.

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.

Variance components analyses of multiple asthma traits in a large sample of Australian families ascertained through a twin proband

Background: Intermediate phenotypes are often measured as a proxy for asthma. It is largely unclear to what extent the same set of environmental or genetic factors regulate these traits. Objective: Estimate the environmental and genetic correlations between self-reported and clinical asthma traits. Methods: A total of 3073 subjects from 802 families were ascertained through a twin proband. Traits measured included self-reported asthma, airway histamine responsiveness (AHR), skin prick response to common allergens including house dust mite (Dermatophagoides pteronyssinus [D. pter]), baseline lung function, total serum immunoglobulin E (IgE) and eosinophilia. Bivariate and multivariate analyses of eight traits were performed with adjustment for ascertainment and significant covariates. Results: Overall 2716 participants completed an asthma questionnaire and 2087 were clinically tested, including 1289 self-reported asthmatics (92% previously diagnosed by a doctor). Asthma, AHR, markers of allergic sensitization and eosinophilia had significant environmental correlations with each other (range: 0.23-0.89). Baseline forced expiratory volume in 1 s (FEV1) showed low environmental correlations with most traits. Fewer genetic correlations were significantly different from zero. Phenotypes with greatest genetic similarity were asthma and atopy (0.46), IgE and eosinophilia (0.44), AHR and D. pter (0.43) and AHR and airway obstruction (-0.43). Traits with greatest genetic dissimilarity were FEV1 and atopy (0.05), airway obstruction and IgE (0.07) and FEV1 and D. pter (0.11). Conclusion: These results suggest that the same set of environmental factors regulates the variation of many asthma traits. In addition, although most traits are regulated to great extent by specific genetic factors, there is still some degree of genetic overlap that could be exploited by multivariate linkage approaches.

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.