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A major obstacle, however, to studying multivariate trait selection and evolution is the accurate estimation of G[ 23].
The aforementioned results generalize naturally to multivariate trait selection where the alternative Lande's equation is R ′ = (Ω + E ) Ω − 1 S ′ (2 where R′ and S′ are the vectorial phenotype lag, and Ω and E are the covariance matrices of the fitness function and the environment respectively.
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Studies of Drosophila have shown that sexual selection can erode genetic variance along the axes of variation in multivariate trait space that are under selection, and yet maintain considerable additive genetic variance along axes orthoganol to those under selection [ 11, 21].
However, univariate analyses of complex traits like cuticular hydrocarbon blends can significantly underestimate nonlinear selection operating in multivariate trait space [ 32].
Selection coefficients can be estimated both for individual traits and for the multivariate trait combinations that have been established here to be affected by pleiotropic mutations.
In both the bivariate and the multivariate analyses (outlined below), traits are assigned to their bi- or multivariate trait set completely randomly, without reference to their biological function.
Such R-gene markers would be valuable in marker-assisted selection programs for trait selection.
Thus multivariate trait analysis in the literature did not address the issue to be studied here.
Quantitative genetics often deals with selection on multivariate traits, and this theory has been placed in the rescue setting (Gomulkiewicz and Houle 2009).
Regressions were carried out both with individual traits and with multivariate traits as determined by principal components (PCs).
Principal component analysis (PCA) was carried out to reduce the number of traits to fewer uncorrelated multivariate traits.
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