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Once upon Multivariate Analyses: When They Tell Several Stories about Biological Evolution.

Renaud S, Dufour AB, Hardouin EA, Ledevin R, Auffray JC - PLoS ONE (2015)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire de Biométrie et Biologie Evolutive, UMR5558, CNRS, University Lyon 1, 69622 Villeurbanne, France.

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 within-group 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.

No MeSH data available.


Diagrams showing how Pmax impacts the patterns of differentiation provided by a PCA and a CVA.Symbols represent group means, lines are phylogenetic relationships; full lines are ‘ancient’ branches representing differentiations of clades, dotted lines represent recent diversification in an archipelago. Dotted ellipses represent the ellipse of variance of some groups; the vector inside Pmax. Dotted vector: first axis of the multivariate analysis. Above: the first axis of a PCA is aligned with Pmax; recent diversification events occurring along this line of least resistance are highlighted. Below: the standardization of the within-group variance in a CVA compresses the differentiation along Pmax up to make the variance per group circular; this dampens the representation of diversification along Pmax and promotes patterns of phylogenetic differentiation along other axes. To the right, reconstructed outlines (using an inverse Fourier transform) exemplifying the corresponding interpretation in the cases of molar shape. Pmax corresponds to a variance from thin to broad molars; so does the first axis of the PCA. The first axis of the CVA is oblique to this direction and corresponds to more localized, detailed features on the tooth.
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pone.0132801.g006: Diagrams showing how Pmax impacts the patterns of differentiation provided by a PCA and a CVA.Symbols represent group means, lines are phylogenetic relationships; full lines are ‘ancient’ branches representing differentiations of clades, dotted lines represent recent diversification in an archipelago. Dotted ellipses represent the ellipse of variance of some groups; the vector inside Pmax. Dotted vector: first axis of the multivariate analysis. Above: the first axis of a PCA is aligned with Pmax; recent diversification events occurring along this line of least resistance are highlighted. Below: the standardization of the within-group variance in a CVA compresses the differentiation along Pmax up to make the variance per group circular; this dampens the representation of diversification along Pmax and promotes patterns of phylogenetic differentiation along other axes. To the right, reconstructed outlines (using an inverse Fourier transform) exemplifying the corresponding interpretation in the cases of molar shape. Pmax corresponds to a variance from thin to broad molars; so does the first axis of the PCA. The first axis of the CVA is oblique to this direction and corresponds to more localized, detailed features on the tooth.

Mentions: Considering the present case study, the PCA and the CVA highlight different evolutionary patterns in the evolution of molar shape in insular populations of house mice (Fig 4; schematic representation Fig 6). The PCA, be it on the total variance or on between-group variance, tended to promote a picture of evolution favored along lines of least resistance along the direction of main variance existing within any population (Pmax). The important divergence within the Orkney archipelago particularly exemplifies this trend, as well as the divergence of molar shape on the small islet of Piana off Corsica. In contrast, the CVA provided a pattern of evolution enhancing more basal phylogenetic divergence, such as shape features shared by all Orkney Islands. The shape changes involved (Fig 6) are a trend from slender to broad molars, when considering Pmax as divergence along the first axis of the PCA. This trend has repeatedly been shown to be a major direction of within-population variation and between-population divergence in recent and fossil murine rodents [26, 27, 62]. By standardizing by the within-group variance, the CVA puts to the front more subtle shape changes, such as a broader forepart or a backward more prominent labial cusp (Fig 6).


Once upon Multivariate Analyses: When They Tell Several Stories about Biological Evolution.

Renaud S, Dufour AB, Hardouin EA, Ledevin R, Auffray JC - PLoS ONE (2015)

Diagrams showing how Pmax impacts the patterns of differentiation provided by a PCA and a CVA.Symbols represent group means, lines are phylogenetic relationships; full lines are ‘ancient’ branches representing differentiations of clades, dotted lines represent recent diversification in an archipelago. Dotted ellipses represent the ellipse of variance of some groups; the vector inside Pmax. Dotted vector: first axis of the multivariate analysis. Above: the first axis of a PCA is aligned with Pmax; recent diversification events occurring along this line of least resistance are highlighted. Below: the standardization of the within-group variance in a CVA compresses the differentiation along Pmax up to make the variance per group circular; this dampens the representation of diversification along Pmax and promotes patterns of phylogenetic differentiation along other axes. To the right, reconstructed outlines (using an inverse Fourier transform) exemplifying the corresponding interpretation in the cases of molar shape. Pmax corresponds to a variance from thin to broad molars; so does the first axis of the PCA. The first axis of the CVA is oblique to this direction and corresponds to more localized, detailed features on the tooth.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4507858&req=5

pone.0132801.g006: Diagrams showing how Pmax impacts the patterns of differentiation provided by a PCA and a CVA.Symbols represent group means, lines are phylogenetic relationships; full lines are ‘ancient’ branches representing differentiations of clades, dotted lines represent recent diversification in an archipelago. Dotted ellipses represent the ellipse of variance of some groups; the vector inside Pmax. Dotted vector: first axis of the multivariate analysis. Above: the first axis of a PCA is aligned with Pmax; recent diversification events occurring along this line of least resistance are highlighted. Below: the standardization of the within-group variance in a CVA compresses the differentiation along Pmax up to make the variance per group circular; this dampens the representation of diversification along Pmax and promotes patterns of phylogenetic differentiation along other axes. To the right, reconstructed outlines (using an inverse Fourier transform) exemplifying the corresponding interpretation in the cases of molar shape. Pmax corresponds to a variance from thin to broad molars; so does the first axis of the PCA. The first axis of the CVA is oblique to this direction and corresponds to more localized, detailed features on the tooth.
Mentions: Considering the present case study, the PCA and the CVA highlight different evolutionary patterns in the evolution of molar shape in insular populations of house mice (Fig 4; schematic representation Fig 6). The PCA, be it on the total variance or on between-group variance, tended to promote a picture of evolution favored along lines of least resistance along the direction of main variance existing within any population (Pmax). The important divergence within the Orkney archipelago particularly exemplifies this trend, as well as the divergence of molar shape on the small islet of Piana off Corsica. In contrast, the CVA provided a pattern of evolution enhancing more basal phylogenetic divergence, such as shape features shared by all Orkney Islands. The shape changes involved (Fig 6) are a trend from slender to broad molars, when considering Pmax as divergence along the first axis of the PCA. This trend has repeatedly been shown to be a major direction of within-population variation and between-population divergence in recent and fossil murine rodents [26, 27, 62]. By standardizing by the within-group variance, the CVA puts to the front more subtle shape changes, such as a broader forepart or a backward more prominent labial cusp (Fig 6).

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire de Biométrie et Biologie Evolutive, UMR5558, CNRS, University Lyon 1, 69622 Villeurbanne, France.

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 within-group 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.

No MeSH data available.