This menu unites commands for a range of methods specific for analyses of quantitative genetics of shape.
In the current version of MorphoJ, two procedures are available: the analysis of the matrix GP-1 and the prediction of the response to selection on shape using the multivariate breeders' equation. Both these methods are derived from the standard theory of multivariate quantitative genetics as presented by Lande (1979) and were introduced in the context of geometric morphometrics by Klingenberg and Leamy (2001).
These analyses are based on the multivariate breeders' equation: Δμ = GP-1s = Gβ, where Δμ is the response to selection, G is the additive genetic covariance matrix, P is the phenotypic covariance matrix, s is the selection differential and β is the selection gradient (Lande 1979).
The matrix GP-1, the additive genetic covariance matrix multiplied by the inverse of the phenotypic covariance matrix, can be considered as a multivariate analogue of the heritability statistic. The minimal and maximal eigenvalues of this matrix are the minimal and maximal heritabilities for any possible linear combination of the variables. Therefore, the range of these eigenvalues provides information, for instance, about the strength of genetic constraints. If the G and P matrices are proportional, as is assumed by a variety of studies, then all eigenvalues of GP-1 are equal and any linear combination of the variables has a heritability equal to those eigenvalues. An examination of these eigenvalues therefore can indicate whether the assumption of proportionality is justified.
The multivariate breeders' equation can be used to predict the response to directional selection on shape if the G and P matrices and the selection vector (either s or β) are known. Even if the actual selection regime is unknown, simulations using various selection vectors can provide useful information, for instance, on whether parts of a structure would respond independently to selection or whether the entire landmark configuration is completely integrated genetically.
A further routine for estimating selection based on empirical data is in preparation.
Klingenberg, C. P., and L. J. Leamy. 2001. Quantitative genetics of geometric shape in the mouse mandible. Evolution 55:2342–2352.
Lande, R. 1979. Quantitative genetic analysis of multivariate evolution, applied to brain:body size allometry. Evolution 33:402–416.