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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.


Location of the studied populations.A. General map, with dots showing sampling localities: Western European mainland areas (in grey) and archipelagos (Orkney, in green; Corsica, in orange; Marion, in dark blue; Kerguelen, light blue). B. Close-up on Orkney archipelago, with the four islands sampled. Colored shapes correspond to reconstruction of the mean outline per population or area is represented (for Guillou, year 2009).
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pone.0132801.g002: Location of the studied populations.A. General map, with dots showing sampling localities: Western European mainland areas (in grey) and archipelagos (Orkney, in green; Corsica, in orange; Marion, in dark blue; Kerguelen, light blue). B. Close-up on Orkney archipelago, with the four islands sampled. Colored shapes correspond to reconstruction of the mean outline per population or area is represented (for Guillou, year 2009).

Mentions: The house mouse (Mus musculus domesticus) is a highly successful colonizer because it accompanied human travels since archaeological times [28, 29]. This has led to a complex phylogeographic pattern across worldwide populations of mice (e.g. [30–32]). This genetic structure is mirrored by differences in molar shape among continental stocks [33, 34]. The house mouse also successfully colonized many islands [29]. Insular conditions are known to promote fast and pronounced morphological differentiation because of peculiar ecological conditions triggering adaptations, as well as due to random processes such as founder effect and subsequent drift in small and isolated populations [35, 36]. As in other rodents, house mice are sensitive to such factors and cases of marked morphological differentiation have been reported for several islands [29, 37–39]. Our data set included continental and insular populations from various environmental contexts (Fig 2). Phylogenetic relationships were assessed based on data from the literature, and compared to the pattern of morphological differentiation, as provided by the different multivariate methods (PCA, bgPCA, and CVA) applied to the same morphometric dataset.


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)

Location of the studied populations.A. General map, with dots showing sampling localities: Western European mainland areas (in grey) and archipelagos (Orkney, in green; Corsica, in orange; Marion, in dark blue; Kerguelen, light blue). B. Close-up on Orkney archipelago, with the four islands sampled. Colored shapes correspond to reconstruction of the mean outline per population or area is represented (for Guillou, year 2009).
© Copyright Policy
Related In: Results  -  Collection

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

pone.0132801.g002: Location of the studied populations.A. General map, with dots showing sampling localities: Western European mainland areas (in grey) and archipelagos (Orkney, in green; Corsica, in orange; Marion, in dark blue; Kerguelen, light blue). B. Close-up on Orkney archipelago, with the four islands sampled. Colored shapes correspond to reconstruction of the mean outline per population or area is represented (for Guillou, year 2009).
Mentions: The house mouse (Mus musculus domesticus) is a highly successful colonizer because it accompanied human travels since archaeological times [28, 29]. This has led to a complex phylogeographic pattern across worldwide populations of mice (e.g. [30–32]). This genetic structure is mirrored by differences in molar shape among continental stocks [33, 34]. The house mouse also successfully colonized many islands [29]. Insular conditions are known to promote fast and pronounced morphological differentiation because of peculiar ecological conditions triggering adaptations, as well as due to random processes such as founder effect and subsequent drift in small and isolated populations [35, 36]. As in other rodents, house mice are sensitive to such factors and cases of marked morphological differentiation have been reported for several islands [29, 37–39]. Our data set included continental and insular populations from various environmental contexts (Fig 2). Phylogenetic relationships were assessed based on data from the literature, and compared to the pattern of morphological differentiation, as provided by the different multivariate methods (PCA, bgPCA, and CVA) applied to the same morphometric dataset.

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.