An analysis of G matrix variation in two closely related cricket species, Gryllus firmus and G. pennsylvanicus

Abstract

An important issue in evolutionary biology is understanding the pattern of G matrix variation in natural populations. We estimated four G matrices based on the morphological traits of two cricket species, Gryllus firmus and G. pennsylvanicus, each reared in two environments. We used three matrix comparison approaches, including the Flury hierarchy, to improve our ability to perceive all aspects of matrix variation. Our results demonstrate that different methods perceive different aspects of the matrices, which suggests that, until more is known about these methods, future studies should use several different statistical approaches. We also found that the differences in G matrices within a species can be larger than the differences between species. We conclude that the expression of the genetic architecture can vary with the environment and that future studies should compare G matrices across several environments. We also conclude that G matrices can be conserved at the level of closely related species.

Comparing Gmatrices: A Manova Approach

“…The pairwise comparisons suggest that the difference between rearing conditions (further experiments have shown no differences between morphs in the case of G. firmus) may be as great as the difference between species (Table 2; Begin and Roff 2001). Because rearing conditions also differed between species, the species effect may also be a rearing effect.…”

“…The two methods reached the same statistical verdict in four of the comparisons (except that the T method only addresses the test of equal vs. not equal) but differed in two ( Table 2). As noted by Begin and Roff (2001), the Flury and T methods appear to be sensitive to different aspects of the data distribution. The MANOVA method reaches the same statistical conclusions as the Flury method.…”

“…Variation among the G matrices was previously analyzed using the Flury method and the T method (Begin and Roff 2001). The Flury method is based on a comparison of principal components and steps through a hierarchical analysis testing for equality of matrices, proportionality of matrices, and common principal components .…”

“…In both methods significance is tested by randomization under the null hypothesis of no difference. Begin and Roff (2001) restricted their analysis to pairwise comparisons and used only females. The two methods reached the same statistical verdict in four of the comparisons (except that the T method only addresses the test of equal vs. not equal) but differed in two ( Table 2).…”

“…The probability of obtaining such a value under the null hypothesis of no difference between the two matrices is estimated by a randomization procedure. Although this method does show promise (Begin and Roff 2001), it cannot readily be implemented on standard computer statistical packages. Maximum-likelihood methods have been used (Shaw 1991(Shaw , 1992 but like the preceding method are difficult to implement, require specialized programming skills, and can be exceedingly computer-intensive.…”