The additive genetic variance-covariance matrix (G) summarizes the multivariate genetic relationships among a set of traits. The geometry of G describes the distribution of multivariate genetic variance, and generates genetic constraints that bias the direction of evolution. Determining if and how the multivariate genetic variance evolves has been limited by a number of analytical challenges in comparing G-matrices. Current methods for the comparison of G typically share several drawbacks: metrics that lack a direct relationship to evolutionary theory, the inability to be applied in conjunction with complex experimental designs, difficulties with determining statistical confidence in inferred differences and an inherently pair-wise focus. Here, we present a cohesive and general analytical framework for the comparative analysis of G that addresses these issues, and that incorporates and extends current methods with a strong geometrical basis. We describe the application of random skewers, common subspace analysis, the 4th-order genetic covariance tensor and the decomposition of the multivariate breeders equation, all within a Bayesian framework. We illustrate these methods using data from an artificial selection experiment on eight traits in Drosophila serrata, where a multi-generational pedigree was available to estimate G in each of six populations. One method, the tensor, elegantly captures all of the variation in genetic variance among populations, and allows the identification of the trait combinations that differ most in genetic variance. The tensor approach is likely to be the most generally applicable method to the comparison of G-matrices from any sampling or experimental design.

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Sexually selected traits display substantial genetic variance [1, 2], in conflict with the expectation that sexual selection will deplete it [3-5]. Condition dependence is thought to resolve this paradox [5-7], but experimental tests that relate the direction of sexual selection to the availability of genetic variance are lacking. Here, we show that condition-dependent expression is not sufficient to maintain genetic variance available to sexual selection in multiple male sexually selected traits. We employed an experimental design that simultaneously determined the quantitative genetic basis of nine male cuticular hydrocarbons (CHCs) of Drosophila bunnanda, the extent of condition dependence of these traits, and the strength and direction of sexual selection acting upon them. The CHCs of D. bunnanda are condition dependent, with 18% of the genetic variance in male body size explained by genetic variance in CHCs. Despite the presence of genetic variance in individual male traits, 98% of the genetic variance in CHCs was found to be orientated more than 88 degrees away from the direction of sexual selection and therefore unavailable to selection. A lack of genetic variance in male traits in the direction of sexual selection may represent a general feature of sexually selected systems, even in the presence of condition-dependent trait expression.

Abstract. Fish occupy a range of hydrological habitats that exert different demands on locomotor performance. We examined replicate natural populations of the rainbow fishes Melanotaenia eachamensis and M. duboulayi to determine if colonization of low-velocity (lake) habitats by fish from high-velocity (stream) habitats resulted in adaptation of locomotor morphology and performance. Relative to stream conspecifics, lake fish had more posteriorly positioned first dorsal and pelvic fins, and shorter second dorsal fin bases. Habitat dimorphism observed between wild-caught fish was determined to be heritable as it was retained in M. eachamensis offspring raised in a common garden. Repeated evolution of the same heritable phenotype in independently derived populations indicated body shape divergence was a consequence of natural selection. Morphological divergence between hydrological habitats did not support a priori expectations of deeper bodies and caudal peduncles in lake fish. However, observed divergence in fin positioning was consistent with a family-wide association between habitat and morphology, and with empirical studies on other fish species. As predicted, decreased demand for sustained swimming in lakes resulted in a reduction in caudal red muscle area of lake fish relative to their stream counterparts. Melanotaenia duboulayi lake fish also had slower sustained swimming speeds (U crit ) than stream conspecifics. In M. eachamensis, habitat affected U crit of males and females differently. Specifically, females exhibited the pattern observed in M. duboulayi (lake fish had faster U crit than stream fish), but the opposite association was observed in males (stream males had slower U crit than lake males). Stream M. eachamensis also exhibited a reversed pattern of sexual dimorphism in U crit (males slower than females) relative to all other groups (males faster than females). We suggest that M. eachamensis males from streams responded to factors other than water velocity. Although replication of muscle and U crit phenotypes across same habitat populations within and/or among species was suggestive of adaptation, the common garden experiment did not confirm a genetic basis to these associations. Kinematic studies should consider the effect of the position and base length of dorsal fins.Key words. Burst speed, common garden experiment, Melanotaeniidae, morphology, natural selection, red muscle, U crit .Received April 18, 2002. Accepted September 11, 2002 Locomotion is a complex, whole animal function, crucial for activities that have deterministic effects on fitness. For example, differential locomotor performance has been demonstrated to result in both differential survival (e.g., Beamish 1978; Swain 1993) and feeding efficiency (e.g., Schaefer et al. 1999). There is also mounting evidence that locomotor performance has a genetic basis (van Berkum and Tsuji 1987;Garland 1988Garland , 1994Nicoletto 1995). Therefore, locomotor performance might evolve through natural selection if environments differ in their loco...