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G Matrices (g + matrix)
Selected AbstractsCONSTANCY OF THE G MATRIX IN ECOLOGICAL TIMEEVOLUTION, Issue 6 2004Mats BjÖrklund Abstract The constancy of the genetic variance-covariance matrix (G matrix) across environments and populations has been discussed and tested empirically over the years but no consensus has so far been reached. In this paper, I present a model in which morphological traits develop hierarchically, and individuals differ in their resource allocation and acquisition patterns. If the variance in resource acquisition is many times larger than the variance in resource allocation then strong genetic correlations are expected, and with almost isometric relations among traits. As the variation in resource acquisition decreases below a certain threshold, the correlations decrease overall and the relations among traits become a function of the allocation patterns, and in particular reflecting the basal division of allocation. A strong bottleneck can break a pattern of strong genetic correlation, but this effect diminishes rapidly with increasing bottleneck size. This model helps to understand why some populations change their genetic correlations in different environments, whereas others do not, since the key factor is the relation between the variances in resource acquisition and allocation. If a change in environment does not lead to a change in this ratio, no change can be expected, whereas if the ratio is changed substantially then major changes can be expected. This model can also help to understand the constancy of morphological patterns within larger taxa as a function of constancy in resource acquisition patterns over time and environments. When this pattern breaks, for example on islands, larger changes can be expected. [source] EMPIRICAL COMPARISON OF G MATRIX TEST STATISTICS: FINDING BIOLOGICALLY RELEVANT CHANGEEVOLUTION, Issue 10 2009Brittny Calsbeek A central assumption of quantitative genetic theory is that the breeder's equation (R=GP,1S) accurately predicts the evolutionary response to selection. Recent studies highlight the fact that the additive genetic variance,covariance matrix (G) may change over time, rendering the breeder's equation incapable of predicting evolutionary change over more than a few generations. Although some consensus on whether G changes over time has been reached, multiple, often-incompatible methods for comparing G matrices are currently used. A major challenge of G matrix comparison is determining the biological relevance of observed change. Here, we develop a "selection skewers"G matrix comparison statistic that uses the breeder's equation to compare the response to selection given two G matrices while holding selection intensity constant. We present a bootstrap algorithm that determines the significance of G matrix differences using the selection skewers method, random skewers, Mantel's and Bartlett's tests, and eigenanalysis. We then compare these methods by applying the bootstrap to a dataset of laboratory populations of Tribolium castaneum. We find that the results of matrix comparison statistics are inconsistent based on differing a priori goals of each test, and that the selection skewers method is useful for identifying biologically relevant G matrix differences. [source] FROM MICRO- TO MACROEVOLUTION THROUGH QUANTITATIVE GENETIC VARIATION: POSITIVE EVIDENCE FROM FIELD CRICKETSEVOLUTION, Issue 10 2004Mattieu Bégin Abstract . -Quantitative genetics has been introduced to evolutionary biologists with the suggestion that microevolution could be directly linked to macroevolutionary patterns using, among other parameters, the additive genetic variance/ covariance matrix (G) which is a statistical representation of genetic constraints to evolution. However, little is known concerning the rate and pattern of evolution of G in nature, and it is uncertain whether the constraining effect of G is important over evolutionary time scales. To address these issues, seven species of field crickets from the genera Gryllus and Teleogryllus were reared in the laboratory, and quantitative genetic parameters for morphological traits were estimated from each of them using a nested full-sibling family design. We used three statistical approaches (T method, Flury hierarchy, and Mantel test) to compare G matrices or genetic correlation matrices in a phylogenetic framework. Results showed that G matrices were generally similar across species, with occasional differences between some species. We suggest that G has evolved at a low rate, a conclusion strengthened by the consideration that part of the observed across-species variation in G can be explained by the effect of a genotype by environment interaction. The observed pattern of G matrix variation between species could not be predicted by either morphological trait values or phylogeny. The constraint hypothesis was tested by comparing the multivariate orientation of the reconstructed ancestral G matrix to the orientation of the across-species divergence matrix (D matrix, based on mean trait values). The D matrix mainly revealed divergence in size and, to a much smaller extent, in a shape component related to the ovipositor length. This pattern of species divergence was found to be predictable from the ancestral G matrix in agreement with the expectation of the constraint hypothesis. Overall, these results suggest that the G matrix seems to have an influence on species divergence, and that macroevolution can be predicted, at least qualitatively, from quantitative genetic theory. Alternative explanations are discussed. [source] A tale of two matrices: multivariate approaches in evolutionary biologyJOURNAL OF EVOLUTIONARY BIOLOGY, Issue 1 2007M. W. BLOWS Abstract Two symmetric matrices underlie our understanding of microevolutionary change. The first is the matrix of nonlinear selection gradients (,) which describes the individual fitness surface. The second is the genetic variance,covariance matrix (G) that influences the multivariate response to selection. A common approach to the empirical analysis of these matrices is the element-by-element testing of significance, and subsequent biological interpretation of pattern based on these univariate and bivariate parameters. Here, I show why this approach is likely to misrepresent the genetic basis of quantitative traits, and the selection acting on them in many cases. Diagonalization of square matrices is a fundamental aspect of many of the multivariate statistical techniques used by biologists. Applying this, and other related approaches, to the analysis of the structure of , and G matrices, gives greater insight into the form and strength of nonlinear selection, and the availability of genetic variance for multiple traits. [source] An analysis of G matrix variation in two closely related cricket species, Gryllus firmus and G. pennsylvanicusJOURNAL OF EVOLUTIONARY BIOLOGY, Issue 1 2001M. Bégin 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. [source] FROM MICRO- TO MACROEVOLUTION THROUGH QUANTITATIVE GENETIC VARIATION: POSITIVE EVIDENCE FROM FIELD CRICKETSEVOLUTION, Issue 10 2004Mattieu Bégin Abstract . -Quantitative genetics has been introduced to evolutionary biologists with the suggestion that microevolution could be directly linked to macroevolutionary patterns using, among other parameters, the additive genetic variance/ covariance matrix (G) which is a statistical representation of genetic constraints to evolution. However, little is known concerning the rate and pattern of evolution of G in nature, and it is uncertain whether the constraining effect of G is important over evolutionary time scales. To address these issues, seven species of field crickets from the genera Gryllus and Teleogryllus were reared in the laboratory, and quantitative genetic parameters for morphological traits were estimated from each of them using a nested full-sibling family design. We used three statistical approaches (T method, Flury hierarchy, and Mantel test) to compare G matrices or genetic correlation matrices in a phylogenetic framework. Results showed that G matrices were generally similar across species, with occasional differences between some species. We suggest that G has evolved at a low rate, a conclusion strengthened by the consideration that part of the observed across-species variation in G can be explained by the effect of a genotype by environment interaction. The observed pattern of G matrix variation between species could not be predicted by either morphological trait values or phylogeny. The constraint hypothesis was tested by comparing the multivariate orientation of the reconstructed ancestral G matrix to the orientation of the across-species divergence matrix (D matrix, based on mean trait values). The D matrix mainly revealed divergence in size and, to a much smaller extent, in a shape component related to the ovipositor length. This pattern of species divergence was found to be predictable from the ancestral G matrix in agreement with the expectation of the constraint hypothesis. Overall, these results suggest that the G matrix seems to have an influence on species divergence, and that macroevolution can be predicted, at least qualitatively, from quantitative genetic theory. Alternative explanations are discussed. [source] CONSTANCY OF THE G MATRIX IN ECOLOGICAL TIMEEVOLUTION, Issue 6 2004Mats BjÖrklund Abstract The constancy of the genetic variance-covariance matrix (G matrix) across environments and populations has been discussed and tested empirically over the years but no consensus has so far been reached. In this paper, I present a model in which morphological traits develop hierarchically, and individuals differ in their resource allocation and acquisition patterns. If the variance in resource acquisition is many times larger than the variance in resource allocation then strong genetic correlations are expected, and with almost isometric relations among traits. As the variation in resource acquisition decreases below a certain threshold, the correlations decrease overall and the relations among traits become a function of the allocation patterns, and in particular reflecting the basal division of allocation. A strong bottleneck can break a pattern of strong genetic correlation, but this effect diminishes rapidly with increasing bottleneck size. This model helps to understand why some populations change their genetic correlations in different environments, whereas others do not, since the key factor is the relation between the variances in resource acquisition and allocation. If a change in environment does not lead to a change in this ratio, no change can be expected, whereas if the ratio is changed substantially then major changes can be expected. This model can also help to understand the constancy of morphological patterns within larger taxa as a function of constancy in resource acquisition patterns over time and environments. When this pattern breaks, for example on islands, larger changes can be expected. [source] | ||||||||||