Size correction in biology: How reliable are approaches based on (common) principal component analysis?

Zoological Institute, University of Basel, Basel, Switzerland.
Oecologia (Impact Factor: 3.09). 02/2011; 166(4):961-71. DOI: 10.1007/s00442-011-1934-z
Source: PubMed


Morphological traits typically scale with the overall body size of an organism. A meaningful comparison of trait values among individuals or populations that differ in size therefore requires size correction. A frequently applied size correction method involves subjecting the set of n morphological traits of interest to (common) principal component analysis [(C)PCA], and treating the first principal component [(C)PC1] as a latent size variable. The remaining variation (PC2-PCn) is considered size-independent and interpreted biologically. I here analyze simulated data and natural datasets to demonstrate that this (C)PCA-based size correction generates systematic statistical artifacts. Artifacts arise even when all traits are tightly correlated with overall size, and they are particularly strong when the magnitude of variance is heterogeneous among the traits, and when the traits under study are few. (C)PCA-based approaches are therefore inappropriate for size correction and should be abandoned in favor of methods using univariate general linear models with an adequate independent body size metric as covariate. As I demonstrate, (C)PC1 extracted from a subset of traits, not themselves subjected to size correction, can provide such a size metric.

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    • "Cranial variation in the European snow vole high proportion of variance in the original dataset, which allows a reduction of the dimensionality of a multivariate dataset. The first PC (PC1) is responsible for the largest possible variance and acts in morphometrics as a size vector (Berner, 2011). Because PCs are mutually orthogonal, the remaining components account for size-out (shape) variance. "
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    ABSTRACT: Fragmented landscapes entail important consequences for the evolution of the species confined to them. Isolation of population fragments accelerates selection for narrow local conditions and facilitates morphological divergence. Throughout its range, the European snow vole Chionomys nivalis is restricted to fractured, rocky substrate in mountain regions, which is naturally fragmented into ‘continental archipelagos’. Consequently, its extensive morphological and genetic diversity was categorized into about 20 traditional subspecies and at least eight allopatric phylogenetic lineages. In this study, we aimed toward an integrative understanding of cranial variation throughout the European snow vole range. We analyzed seven linear cranial variables on 326 adult skulls from 27 populations belonging to eight phylogenetic lineages. We confirmed significant variation among the fragmented populations but retrieved little meaningful patterning in morphometric variability. Phenetic distances among populations were not related to the phylogenetic architecture of the species, and traditional subspecies were at odds with morphologically diagnosable populations. The lack of an association between morphometric and geographic distances argued against isolation by distance. Furthermore, mean size did not correlate with climatic variables. Morphological principal components 2 and 3 (loaded by the interorbital width and length of neurocranium, respectively) correlated significantly with geographic coordinates and climatic variables. Shape variables discriminated between the abulensis and nivalis phylogroups, and the European and Asiatic populations, but the largest phylogroups (nivalis and malyi) showed high interpopulation heterogeneity and classification accuracy was low. We suggest that cranial shape or size do not incorporate a signal that is strong enough to be of reliable use for subspecific taxonomy. Skull is seemingly prone to vary according to narrow local conditions, which distorts the underlying phylogenetic signal. A small-scale approach, with detailed knowledge of environmental parameters within each habitat fragment, might be more appropriate for a species whose range is actually a continental archipelago.
    Journal of zoology 09/2015; DOI:10.1111/jzo.12274 · 1.95 Impact Factor
    • "Abbreviations: CL, Cowichan Lake; GL, Graham Lake; KR, Keogh River; MCL, McCreight Lake; NKL, Nimpkish Lake; NL, North Lake; NR, Nass River; P, Prospect Lake; PAQ, Paq Lake; PI, Poirier Lake; PR, Parsnip River; RL, Ruby Lake; SL, Skidegate Lake; WC, Williams Creek. Journal of Biogeography ª 2015 John Wiley & Sons Ltd a size-corrected analysis (Berner, 2011 "
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    ABSTRACT: AimGlacial cycles during the Pleistocene may have frequently contributed to parallel evolution of phenotypes across independently evolving genetic lineages associated with separate glacial refugia. Previous studies based on morphology suggested that the prickly sculpin (Cottus asper) survived the Last Glacial Maximum (LGM) in southern coastal and inland refugia, favouring allopatric divergence between coastal and inland prickling phenotypes, which vary in the degree to which spine-like scales cover the body of the fish. Herein, we aimed to test whether parallel evolution across multiple genetic lineages rather than a single-lineage origin of highly prickled inland sculpins could serve as an explanation for the biogeographical distribution of prickling phenotypes.LocationNorth-western North America, Southeast Alaska and Canada (British Columbia).Methods We used data from mitochondrial haplotypes and 19 microsatellite loci to identify distinct genetic lineages as a basis to interpret patterns of phenotypic evolution.ResultsThe occurrence of multiple mtDNA groups suggests that highly prickled inland phenotypes comprise more than one genetic lineage. Both mtDNA and microsatellite data are consistent with post-glacial dispersal along the coast and repeated coastal to inland colonization events, as opposed to inland dispersal of a single lineage from a southern refugium to northern regions.Main conclusionsOur results suggest that highly prickled inland phenotypes evolved repeatedly following multiple inland colonization events, probably via coastal rivers. The prickly sculpin therefore provides an example of recent (post-glacial) parallel evolution, potentially facilitated by standing genetic variation already present in the ancestral coastal populations.
    Journal of Biogeography 04/2015; 42(9). DOI:10.1111/jbi.12527 · 4.59 Impact Factor
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    • "In addition to body size, population (western, central, or eastern BC) was included as a factor in the GLM following established protocols (Mila et al. 2008; Berner 2011). The rationale for including the population adjustment was to differentiate the association between population and body size within populations from the effect among populations. "
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    ABSTRACT: Migratory divides, the boundary between adjacent bird populations that migrate in different directions, are of considerable interest to evolutionary biologists because of their alleged role in speciation of migratory birds. However, the small size of many passerines has traditionally limited the tools available to track populations and as a result, restricted our ability to study how reproductive isolation might occur across a divide. Here, we integrate multiple approaches by using genetic, geolocator, and morphological data to investigate a migratory divide in hermit thrushes (Catharus guttatus). First, high genetic divergence between migratory groups indicates the divide is a region of secondary contact between historically isolated populations. Second, despite low sample sizes, geolocators reveal dramatic differences in overwintering locations and migratory distance of individuals from either side of the divide. Third, a diagnostic genetic marker that proved useful for tracking a key population suggests a likely intermediate nonbreeding location of birds from the hybrid zone. This finding, combined with lower return rates from this region, is consistent with comparatively lower fitness of hybrids, which is possibly due to this intermediate migration pattern. We discuss our results in the context of reproductive isolating mechanisms associated with migration patterns that have long been hypothesized to promote divergence across migratory divides.
    Ecology and Evolution 09/2014; 4(17). DOI:10.1002/ece3.1205 · 2.32 Impact Factor
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