Comparative Methods as a Statistical Fix: The Dangers of Ignoring an Evolutionary Model
Department of Animal and Plant Sciences, University of Sheffield, Sheffield S10 2TN, United Kingdom. The American Naturalist
(Impact Factor: 3.83).
07/2011; 178(1):E10-7. DOI: 10.1086/660272
Abstract Comparative methods are widely used in ecology and evolution. The most frequently used comparative methods are based on an explicit evolutionary model. However, recent approaches have been popularized that are without an evolutionary basis or an underlying null model. Here we highlight the limitations of such techniques in comparative analyses by using simulations to compare two commonly used comparative methods with and without evolutionary basis, respectively: generalized least squares (GLS) and phylogenetic eigenvector regression (PVR). We find that GLS methods are more efficient at estimating model parameters and produce lower variance in parameter estimates, lower phylogenetic signal in residuals, and lower Type I error rates than PVR methods. These results can very likely be generalized to eigenvector methods that control for space and both space and phylogeny. We highlight that GLS methods can be adapted in numerous ways and that the variance structure used in these models can be flexibly optimized to each data set.
Available from: Fabricio Villalobos
- "ediction abil - ity , especially when there is strong phylogenetic signal ( low a values - see Table 1 ) . Also , it is more general than the original PVR because it allows incorporating explicit evolutionary models . Thus , it may solve , perhaps with fur - ther improvements in the process of eigenvector selection , some of the problems raised by Freckleton et al . ( 2011 ) in respect to poorer ( in comparison with PGLS ) statistical per - formance of PVR . Our results show that PEM , however , does not provide entirely accurate Type I errors under Brownian motion and so does not perform better than PGLS ( according to the previous analyses from the litera - ture ; e . g . , Freckelton et al . [ 2011 ] )"
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ABSTRACT: Eigenfunction analyses have been widely used to model patterns of autocorrelation in time, space and phylogeny. In a phylogenetic context, Diniz-Filho et al. (1998) proposed what they called Phylogenetic Eigenvector Regression (PVR), in which pairwise phylogenetic distances among species are submitted to a Principal Coordinate Analysis, and eigenvectors are then used as explanatory variables in regression, correlation or ANOVAs. More recently, a new approach called Phylogenetic Eigenvector Mapping (PEM) was proposed, with the main advantage of explicitly incorporating a model-based warping in phylogenetic distance in which an Ornstein-Uhlenbeck (O-U) process is fitted to data before eigenvector extraction. Here we compared PVR and PEM in respect to estimated phylogenetic signal, correlated evolution under alternative evolutionary models and phylogenetic imputation, using simulated data. Despite similarity between the two approaches, PEM has a slightly higher prediction ability and is more general than the original PVR. Even so, in a conceptual sense, PEM may provide a technique in the best of both worlds, combining the flexibility of data-driven and empirical eigenfunction analyses and the sounding insights provided by evolutionary models well known in comparative analyses.
- "For instance, if a small number of eigenvectors are selected, one can underestimate the phylogenetic signal. This is so because different eigenvectors represent different parts of the phylogenetic relationships among the species, making the comparison with other model-based results difficult and introducing some subjectivity in the modelling process (which is usually criticized – see Freckleton et al., 2011). However, when thinking in nonstationarity, this seems to be an advantage. "
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ABSTRACT: Despite the longstanding interest in non-stationarity of both phenotypic evolution and diversification rates, only recently have methods been developed to study this property. Here, we propose a methodological expansion of the Phylogenetic Signal Representation (PSR) curve based on phylogenetic eigenvectors to test for non-stationarity. The PSR is built by plotting the coefficients of determination R(2) from Phylogenetic Eigenvector Regression (PVR) models increasing the number of phylogenetic eigenvectors against the accumulated eigenvalues. The PSR curve is linear under a stationary model of trait evolution (i.e., the Brownian motion model). Here we describe the distribution of shifts in the models R(2) and used a randomization procedure to compare observed and simulated shifts along the PSR curve, which allowed detecting non-stationarity in trait evolution. As an applied example, we show that the main evolutionary pattern of variation in the theropod dinosaur skull was non-stationary, with a significant shift in evolutionary rates in derived oviraptorosaurs, an aberrant group of mostly toothless, crested, bird-like theropods. This result is also supported by a recently proposed Bayesian-based method (AUTEUR). A significant deviation between Ceratosaurus and Limusaurus terminal branches was also detected. We purport that our new approach is a valuable tool for evolutionary biologists, owing to its simplicity, flexibility and comprehensiveness. This article is protected by copyright. All rights reserved.
This article is protected by copyright. All rights reserved.
Available from: Alex Slavenko
- "A method for incorporating phylogeny into assemblage-level grid-cell analyses, phylogenetic eigenvector regression, exists (Diniz-Filho et al., 1998). However , this method has severe statistical limitations and probably does not adequately account for the effects of phylogeny (Adams & Church, 2011; Freckleton et al., 2011). "
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ABSTRACT: Aim: Climate is thought to exert a strong influence on animal body sizes. We examined the relationship between amphibian body size and several climatic variables to discern which climatic variables, if any, affect amphibian size evolution.
Location: Europe and North America.
Methods: We assembled a dataset of mean sizes of 356 (out of 360) amphibian species in Europe, the USA and Canada, and tested how they are related to temperature, precipitation, primary productivity and seasonality. First, we examined the body size distributions of all the species inhabiting equal-area grid cells (of 96.3 km 9 96.3 km) using randomizations to account for the effects of species richness. Second, we examined the relationship between mean species body size and the environmental predictors across their ranges accounting for phylogenetic effects.
Results: The observed amphibian body size distributions were mostly statistically indistinguishable from distributions generated by random assignment of species to cells. Median sizes in grid cells were negatively correlated with temperature in anurans and positively in urodeles. The phylogenetic analysis revealed opposite trends in relation to temperature. In both clades most climatic variables were not associated with size and the few significant relationships were very weak.
Main conclusions: Spatial patterns in amphibian body size probably reflect diversity gradients, and relationships with climate could result from spurious effects of richness patterns. The large explanatory power of richness in the grid-cell analysis, and the small explanatory power of climate in the interspe-cific analysis, signify that climate per se has little effect on amphibian body sizes.
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