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Abstract:
Geometric morphometrics aims to characterize of the geometry of complex traits. It is therefore
by essence multivariate. The most popular methods to investigate patterns of differentiation
in this context are (1) the Principal Component Analysis (PCA), which is an eigenvalue
decomposition of the total variance-covariance matrix among all specimens; (2) the Canonical
Variate Analysis (CVA, a.k.a. linear discriminant analysis (LDA) for more than two
groups), which aims at separating the groups by maximizing the between-group to withingroup
variance ratio; (3) the between-group PCA (bgPCA) which investigates patterns of
between-group variation, without standardizing by the within-group variance. Standardizing
within-group variance, as performed in the CVA, distorts the relationships among groups,
an effect that is particularly strong if the variance is similarly oriented in a comparable way in
all groups. Such shared direction of main morphological variance may occur and have a biological
meaning, for instance corresponding to the most frequent standing genetic variation
in a population. Here we undertake a case study of the evolution of house mouse molar
shape across various islands, based on the real dataset and simulations.We investigated
how patterns of main variance influence the depiction of among-group differentiation
according to the interpretation of the PCA, bgPCA and CVA. Without arguing about a
method performing ‘better’ than another, it rather emerges that working on the total or
between-group variance (PCA and bgPCA) will tend to put the focus on the role of direction
of main variance as line of least resistance to evolution. Standardizing by the within-group
variance (CVA), by dampening the expression of this line of least resistance, has the potential
to reveal other relevant patterns of differentiation that may otherwise be blurred.
