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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 Biom├ętrie 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.


Differentiation in molar shape among populations, according to three different multivariate analyses.A. Principal Component Analysis (PCA); note that this analysis is performed on all specimens (grey dots). Group means are highlighted (large colored symbols). B. Between-group PCA. C and D. Canonical Variate Analysis (CVA), in C first vs. second axes, in D third vs. fourth axes.
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pone.0132801.g004: Differentiation in molar shape among populations, according to three different multivariate analyses.A. Principal Component Analysis (PCA); note that this analysis is performed on all specimens (grey dots). Group means are highlighted (large colored symbols). B. Between-group PCA. C and D. Canonical Variate Analysis (CVA), in C first vs. second axes, in D third vs. fourth axes.

Mentions: All continental localities from Western Europe cluster together. Insular groups scatter around this continental cluster (Fig 4A). The first axis (37.2% of the total variance) is characterized by the strong divergence of Piana, and to a lesser extent of Corsica, Papa Westray (Orkney) on one side, and from Faray and Eday (Orkney) on the other side. The second axis (24.7% of variance) mostly isolates samples from Guillou. No clear pattern emerges on axes 3 and 4 (PC3 = 10.5%, PC4 = 7.6%; data not shown).


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)

Differentiation in molar shape among populations, according to three different multivariate analyses.A. Principal Component Analysis (PCA); note that this analysis is performed on all specimens (grey dots). Group means are highlighted (large colored symbols). B. Between-group PCA. C and D. Canonical Variate Analysis (CVA), in C first vs. second axes, in D third vs. fourth axes.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0132801.g004: Differentiation in molar shape among populations, according to three different multivariate analyses.A. Principal Component Analysis (PCA); note that this analysis is performed on all specimens (grey dots). Group means are highlighted (large colored symbols). B. Between-group PCA. C and D. Canonical Variate Analysis (CVA), in C first vs. second axes, in D third vs. fourth axes.
Mentions: All continental localities from Western Europe cluster together. Insular groups scatter around this continental cluster (Fig 4A). The first axis (37.2% of the total variance) is characterized by the strong divergence of Piana, and to a lesser extent of Corsica, Papa Westray (Orkney) on one side, and from Faray and Eday (Orkney) on the other side. The second axis (24.7% of variance) mostly isolates samples from Guillou. No clear pattern emerges on axes 3 and 4 (PC3 = 10.5%, PC4 = 7.6%; data not shown).

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 Biom├ętrie 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.