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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.


Related in: MedlinePlus

Mouse teeth exemplifying the morphological variation within and between populations.From left to right: Western European mainland populations (Gardouch, South France; Reggiolo, Northern Italy); insular populations: Corsica (Fango, Corsica mainland; Piana islet); Orkney (Eday and Papa Westray islands); sub-antarctic islands (Guillou, island part of the Kerguelen archipelago and Marion, part of Prince Edward islands). Anterior part to the top, lingual side to the right.
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pone.0132801.g001: Mouse teeth exemplifying the morphological variation within and between populations.From left to right: Western European mainland populations (Gardouch, South France; Reggiolo, Northern Italy); insular populations: Corsica (Fango, Corsica mainland; Piana islet); Orkney (Eday and Papa Westray islands); sub-antarctic islands (Guillou, island part of the Kerguelen archipelago and Marion, part of Prince Edward islands). Anterior part to the top, lingual side to the right.

Mentions: In this context, one can wonder how much a multivariate method will be sensitive to such biologically-relevant patterns of main variance, and how much this will influence the depiction of among-group differentiation offered to interpretation. We address here these issues using a case study: the evolution of house mouse molar shape across various islands. The mouse molar (Fig 1) has been shown to display directions of main variance shared among populations [26] that seems to constitute preferential directions of among-group differentiation [27]. In this case study, we (1) compared the pattern of among-group differentiation provided by three popular multivariate analyses in geometric morphometrics: PCA, bgPCA and CVA; (2) tested on real and simulated data sets how far these patterns were influenced by directions of main variance shared among groups; and (3) questioned the biological relevance of interpretations based on the among-group patterns provided by the various methods. Without arguing about one 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 evidence other relevant patterns of differentiation that may otherwise be blurred.


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)

Mouse teeth exemplifying the morphological variation within and between populations.From left to right: Western European mainland populations (Gardouch, South France; Reggiolo, Northern Italy); insular populations: Corsica (Fango, Corsica mainland; Piana islet); Orkney (Eday and Papa Westray islands); sub-antarctic islands (Guillou, island part of the Kerguelen archipelago and Marion, part of Prince Edward islands). Anterior part to the top, lingual side to the right.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0132801.g001: Mouse teeth exemplifying the morphological variation within and between populations.From left to right: Western European mainland populations (Gardouch, South France; Reggiolo, Northern Italy); insular populations: Corsica (Fango, Corsica mainland; Piana islet); Orkney (Eday and Papa Westray islands); sub-antarctic islands (Guillou, island part of the Kerguelen archipelago and Marion, part of Prince Edward islands). Anterior part to the top, lingual side to the right.
Mentions: In this context, one can wonder how much a multivariate method will be sensitive to such biologically-relevant patterns of main variance, and how much this will influence the depiction of among-group differentiation offered to interpretation. We address here these issues using a case study: the evolution of house mouse molar shape across various islands. The mouse molar (Fig 1) has been shown to display directions of main variance shared among populations [26] that seems to constitute preferential directions of among-group differentiation [27]. In this case study, we (1) compared the pattern of among-group differentiation provided by three popular multivariate analyses in geometric morphometrics: PCA, bgPCA and CVA; (2) tested on real and simulated data sets how far these patterns were influenced by directions of main variance shared among groups; and (3) questioned the biological relevance of interpretations based on the among-group patterns provided by the various methods. Without arguing about one 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 evidence other relevant patterns of differentiation that may otherwise be blurred.

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.


Related in: MedlinePlus