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15 results for “G matrix”
G-matrix stability of clinally diverging populations of an annual weed
<p>How phenotypic and genetic divergence among populations is influenced by the genetic architecture of those traits, and how microevolutionary changes in turn affect the within-population patterns of genetic variation, are of major interest to evolutionary biology. Work on <em>Ipomoea hederacea</em>, an annual vine, has found genetic clines in the means of a suite of ecologically important traits, including flowering time, growth rate, seed mass, and corolla width. Here we investigate the genetic (co)variances of these clinally varying traits in two northern range-edge and two central populations of <em>Ipomoea hederacea </em>to evaluate the influence of the genetic architecture on divergence across the range. We find 1) limited evidence for clear differentiation between Northern and Southern populations in the structure of <strong>G</strong>, suggesting overall stability of <strong>G</strong> across the range despite mean trait divergence and 2) that the axes of greatest variation (g<sub>max</sub>) were unaligned with the axis of greatest multivariate divergence. Together these results indicate the role of the quantitative genetic architecture in constraining evolutionary response and divergence among populations across the geographic range.</p>
G-matrix stability of clinally diverging populations of an annual weed
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Evolutionary and ecological processes determining properties of the $\bm G$-matrix
<p>The $\bm G$-matrix is the matrix of additive genetic variances and covariances for a vector of phenotypes. Here we apply the classical theory for the balance between selection drift and mutations to find the contributions to $\bm G$ from each locus. The fitness is approximated by a linear function of phenotypes. Fluctuations in the environment generate variation in the coefficients of the fitness function. We show that the $\bm G$-matrix can be decomposed into 4 additive components generated by selection, drift, mutations and environmental fluctuations. Selection is on average counteracted by the other three processes included in Fisher's concept of the deterioration of the environment, in accordance with Frank's approximate conservation law proposing that the response to selection at stasis on average is canceled by effects of drift and mutations. The theory illustrates that Fisher's fundamental theorem cannot be used to accumulate selection through time to describe adaption unless the other effects are corrected for. Another implication of the analyses is that the factor loadings to the eigenvector of the $\bm G$-matrix with the least eigenvalue are likely to indicate which characters contributing the most to the fitness function. This is information notoriously difficult to obtain in natural populations. </p>
Evolutionary and ecological processes determining properties of the $\bm G$-matrix
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Data from: Similarity in G matrix structure among natural populations of Arabidopsis lyrata
Understanding the stability of the G matrix in natural populations is fundamental for predicting evolutionary trajectories, yet, the extent of its spatial variation and how this impacts responses to selection remain open questions. With a nested paternal half-sib crossing design and plants grown in a field experiment, we examined differences in the genetic architecture of flowering time, floral display and plant size among four Scandinavian populations of Arabidopsis lyrata. Using a multivariate Bayesian framework, we compared the size, shape and orientation of G matrices and assessed their potential to facilitate or constrain trait evolution. Flowering time, floral display and rosette size varied among populations and significant additive genetic variation within populations indicated potential to evolve in response to selection. Yet, some characters, including flowering start and number of flowers, may not evolve independently because of genetic correlations. Using a multivariate framework, we found few differences in the genetic architecture of traits among populations. G matrices varied mostly in size rather than shape or orientation. Differences in multivariate responses to selection predicted from differences in G were small, suggesting overall matrix similarity and shared constraints to trait evolution among populations.
FIGURES 22–24. Figures 22–23. Plectrocnemia g. geniculata McLachlan 1871, 5 in The larva of Plectrocnemia renetta Malicky 1975 (Trichoptera, Polycentropodidae), including a discriminatory matrix to the larvae of Plectrocnemia Stephens 1836 species of Greece
FIGURES 22–24. Figures 22–23. Plectrocnemia g. geniculata McLachlan 1871, 5th instar larva: 22, head, dorsal (dotted lines = half-trapezoidal pattern of spots on posterior frontoclypeus, about 100°); 23, labrum, dorsal. Figure 24. P. c. conspersa (Curtis 1834), 5th instar larva, labrum, dorsal (arrow = posterior mark). Scale bars: 0.5 mm.
FIGURES 22–24. Figures 22–23. Plectrocnemia g. geniculata McLachlan 1871, 5 in The larva of Plectrocnemia renetta Malicky 1975 (Trichoptera, Polycentropodidae), including a discriminatory matrix to the larvae of Plectrocnemia Stephens 1836 species of Greece
FIGURES 22–24. Figures 22–23. Plectrocnemia g. geniculata McLachlan 1871, 5th instar larva: 22, head, dorsal (dotted lines = half-trapezoidal pattern of spots on posterior frontoclypeus, about 100°); 23, labrum, dorsal. Figure 24. P. c. conspersa (Curtis 1834), 5th instar larva, labrum, dorsal (arrow = posterior mark). Scale bars: 0.5 mm.
Data from: Similarity in G matrix structure among natural populations of Arabidopsis lyrata
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Data from: What affects the predictability of evolutionary constraints using a G-matrix? The relative effects of modular pleiotropy and mutational correlation
Phenotypic traits do not always respond to selection independently from each other and often show correlated responses to selection. The structure of a genotype-phenotype map (GP map) determines trait covariation, which involves variation in the degree and strength of the pleiotropic effects of the underlying genes. It is still unclear, and debated, how much of that structure can be deduced from variational properties of quantitative traits that are inferred from their genetic (co)variance matrix (G-matrix). Here we aim to clarify how the extent of pleiotropy and the correlation among the pleiotropic effects of mutations differentially affect the structure of a G-matrix and our ability to detect genetic constraints from its eigen decomposition. We show that the eigenvectors of a G-matrix can be predictive of evolutionary constraints when they map to underlying pleiotropic modules with correlated mutational effects. Without mutational correlation, evolutionary constraints caused by the fitness costs associated with increased pleiotropy are harder to infer from evolutionary metrics based on a G-matrix's geometric properties because uncorrelated pleiotropic effects do not affect traits' genetic correlations. Correlational selection induces much weaker modular partitioning of traits' genetic correlations in absence then in presence of underlying modular pleiotropy.
Data from: Environmental effects on the structure of the G-matrix
Genetic correlations between traits determine the multivariate response to selection in the short term, and thereby play a causal role in evolutionary change. While individual studies have documented environmentally induced changes in genetic correlations, the nature and extent of environmental effects on multivariate genetic architecture across species and environments remain largely uncharacterized. We reviewed the literature for estimates of the genetic variance-covariance (G) matrix in multiple environments, and compared differences in G between environments to the divergence in G between conspecific populations (measured in a common garden). We found that the predicted evolutionary trajectory differed as strongly between environments as it did between populations. Between-environment differences in the underlying structure of G (total genetic variance and the relative magnitude and orientation of genetic correlations) were equal to or greater than between-population differences. Neither environmental novelty nor the difference in mean phenotype predicted these differences in G. Our results suggest that environmental effects on multivariate genetic architecture may be comparable to the divergence that accumulates over dozens or hundreds of generations between populations. We outline avenues of future research to address the limitations of existing data and characterize the extent to which lability in genetic correlations shapes evolution in changing environments.
Data from: What affects the predictability of evolutionary constraints using a G-matrix? The relative effects of modular pleiotropy and mutational correlation
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Data from: Environmental effects on the structure of the G-matrix
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Data from: There is more than one way to skin a G matrix
Because of its importance in directing evolutionary trajectories there has been considerable interest in comparing variation among genetic variance-covariance ( G) matrices. Numerous statistical approaches have been suggested but no general analysis of the relationship among these methods has previously been published. In this paper we used data from a half-sib experiment and simulations to explore the results of applying eight tests (T method, modified Mantel test, Bartlett's test, Flury hierarchy, Jackknife-MANOVA, Jackknife-eigenvalue test, random skewers, selection skewers). Whereas a randomization approach produced acceptable estimates those from a bootstrap were typically unacceptable and we recommend randomization as the preferred method. All methods except the Jackknife-eigenvalue test gave similar results although a fine scale analysis suggested that the former group can be subdivided into two or possibly three groups, hierarchical tests, skewers, and the rest (Jackknife-MANOVA, Modified Mantel, T method, probably Bartlett's). An advantage of the jackknife methods is that they permit tests of association with other factors, such as in this case, temperature and sex. We recommend applying all the tests described in this paper, with the exception of the T method, and provide R functions for this purpose.
Data from: There is more than one way to skin a G matrix
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Data from: Rapid and unpredictable changes of the G-matrix in a natural bird population over 25 years
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