Phylogenetic Eigenvector Regression Research Articles

Autumn phenology of tree species in China is associated more with climate than with spring phenology and phylogeny.

Both biotic and abiotic factors restrict changes in autumn phenology, yet their effects remain ambiguous, which hinders the accurate prediction of phenology under future climate change. In this study, based on the phenological records of 135 tree species at ten sites in China during 1979-2018, we first investigated the effects of climatic factors (temperature, precipitation, insolation and wind speed) and spring phenology on interannual changes in leaf coloring date (LCD) with the partial correlation analysis, and assessed the relative importance of phylogeny and native climate to LCD differences among species by using multivariate regression and phylogenetic eigenvector regression approach. The results showed that the effects of climate factors on interannual changes in LCD were more significant than spring phenology. In general, temperature played a more important role in cold regions (e.g. the northeast region), while the control of insolation on LCD was stronger in the warmer and wetter regions (e.g. the north, east and southwest regions). In addition, the effects of precipitation and wind speed were more evident in arid regions (e.g. the northwest region). We also found considerable effects of both native climate and phylogeny on the LCD differences among species, despite the contribution of native climate being almost 2~5 times greater than that of the phylogeny. Our findings confirmed and quantified the combined effects of climate, spring phenology and phylogeny on the autumn phenology of plants, which could help better understand the driving factors and influencing mechanism of plant phenology and provide a reference for the calibration and optimization of phenological models.

Association of spring phenological traits with phylogeny and adaptation to native climate in temperate plant species in Northeast China

• Spring phenological traits of plant species in Northeast China are analyzed. • Spring phenological traits of plants are phylogenetically conserved. • Reproductive phenology is more phylogenetically conserved than vegetative phenology. • Native climate has a stronger effect than phylogeny on spring phenological traits. The effects of climate change on plant phenology have been widely recognized around the world. However, the effect of plant internal factors (such as phylogeny) on the variations in phenology among plant species remains unclear. In this study, we investigated the phylogenetic conservatism in spring phenological traits using phylogenetic signal and evolutionary models, including Brownian motion (BM) model, Ornstein–Uhlenbeck (OU) model and white noise (WN) model, based on the phenological data of 48 temperate plant species in Northeast China. We also explored the relative contributions of phylogeny and adaptation to native climate (i.e., the climate in native range of species) to the variations in the phenological traits among species using phylogenetic eigenvector regression and variance partitioning analysis. The results showed thatspring phenological traits conformed to the OU model, indicating thatspring traits were phylogenetically conserved. The effect of phylogeny on flowering traits was stronger than that on leaf-out traits. Additionally, the adaptation to native climate contributed more to the variations in spring phenological traits among species than phylogeny, and adaptation to native climate explained more variations in leaf-out traits than in flowering traits. Our results suggested that the spring phenological traits were constrained by both phylogeny and adaptation to native climate. However, the adaptation to native climate had a stronger effect on the variations in phenological traits than phylogeny. Therefore, the degree of similarity in spring phenological traits across closely related species depends on the degree of similarity in the environmental conditions where these close relatives are distributed.

Reflections of Grinnellian and Eltonian niches on the distribution of phyllostomid bats in the Atlantic Forest

AbstractAimEcological niches are complex and result from interactions with biotic and abiotic environments across the entire geographic range of species. One recent distinction is between Grinnellian niche characteristics that reflect influences at large spatial scales such as climate and Eltonian niche characteristics that reflect influences at the local level such as distribution of resources and their allocation among species. Aims of this research were to estimate Grinnellian and Eltonian niche characteristics of phyllostomid bats distributed throughout the Atlantic Forest, examine degree of phylogenetic non‐independence of distribution and niche characteristics, and estimate the relative contribution of niche characteristics to distribution across this large Neotropical region.LocationThe Atlantic Forest.TaxonPhyllostomid bats.MethodsCanonical correlation analysis was used to characterize the association between Grinnellian and Eltonian niche characteristics. Phylogenetic non‐independence of distribution and niche characteristics was estimated with phylogenetic eigenvector regression. Variation partitioning was used to distinguish relative contributions of Grinnellian and Eltonian niche characteristics to the distribution of bats.ResultsGrinnellian and Eltonian niche characteristics were strongly and significantly associated. Phylogenetic signal was weak for Grinnellian and strong for Eltonian niche characteristics. Both suites accounted for significant unique variation in the distribution of phyllostomid bats in the Atlantic Forest. Grinnellian niche characteristics accounted for more than five times the variation in distribution than Eltonian characteristics.Main ConclusionsDistinct Grinnellian and Eltonian perspectives on the niche provide valuable insights into the distribution of species. The degree to which these two different sets of characteristics account for distribution is likely scale dependent with Grinnellian characteristics more important at geographic spatial scales and Eltonian characteristics more important at local spatial scales. Grinnellian and Eltonian niches are important corollaries of α‐ and β‐ niches and their associated traits and similarities and differences in the two distinct concepts should be better explored across different taxa and geographic domains.

Karyological traits related to phylogenetic signal and environmental conditions within the Hymenaea clade (Leguminosae, Detarioideae)

The Hymenaea clade is a lineage of the subfamily Detarioideae of Leguminosae. The clade is currently composed of three genera: Guibourtia, Hymenaea, and Peltogyne. The genera Guibourtia and Hymenaea present an Amphi-Atlantic distribution, whereas Peltogyne is exclusively found in the Neotropics. Previous studies have focused on the phylogeny of the group but there are no studies that demonstrate mechanisms that could be involved in the evolution of this Amphi-Atlantic clade. The present work is the largest cytogenetic analysis for the group published so far. We aimed to provide a study of karyotypic characteristics of the Hymenaea clade, interpreted using the plastidial trnK phylogenetic reconstruction as background. We analyzed karyological characteristics such as chromosome number, chromosome size, centromeric position, CMA/DAPI patterns, and banding for 5S and 45S rDNA. With the present data available, multivariate analyses (PCA) and Phylogenetic Eigenvector Regression (PVR) demonstrated that centromeric asymmetry and number of 5S rDNA sites may present a strong phylogenetic signal, whereas number of CMA+ sites is associated with geography/climate characteristics. The association of CMA bands and geography has been reported for other legumes of the Caesalpinia group. This study demonstrates that the use of statistical tools for analyzing karyotypic characteristics can result in more precise interpretation of evolutionary processes related to structural changes in chromosomes and how these changes can also be related to environmental conditions.

Plant evolutionary history mainly explains the variance in biomass responses to climate warming at a global scale.

Evolutionary history shapes the interspecific relatedness and intraspecific variation, which has a profound influence on plant functional traits and productivity. However, it is far from clear how the phylogenetic relatedness among species and intraspecific variation could contribute to the observed variance in plant biomass responses to climate warming. We compiled a dataset with 284 species from warming experiments to explore the relative importance of phylogenetic, intraspecific, experimental and ecological factors to warming effects on plant biomass, using phylogenetic eigenvector regression and variance decomposition. Our results showed that phylogenetic relatedness could account for about half the total variance in biomass responses to warming, which were correlated with leaf economic traits at the family level but not at species level. The intraspecific variation contributed to approximately one-third of the variance, whereas the experimental design and ecological characteristics only explained 7-17%. These results suggest that intrinsic factors (evolutionary history) play more important roles than extrinsic factors (experimental treatment and environment) in determining the responses of plant biomass to warming at the global scale. This highlights the urgent need for land surface models to include evolutionary aspects in predicting ecosystem functions under climate change.

PHYLOGENETIC EIGENVECTOR REGRESSION IN PALEOBIOLOGY

ABSTRACT – Phylogenetic Eigenvector Regression (PVR) is a fl exible comparative method that allows testing several hypotheses on phylogenetic signal and correlated evolution among traits. Selected phylogenetic eigenvectors extracted from a phylogenetic distance matrix among taxa allow representing their phylogenetic relatedness in a raw-data form (i.e. instead of a distance matrix) and can then be used as explanatory variables in statistical models aiming to estimate phylogenetic signal or phylogenetically corrected correlations. Because of the growing use of PVR by paleobiologists in recent times, here the main theoretical/statistical basis of the method and the developments made in the 15 years after its original proposition are reviewed, highlighting further potential applications in paleobiology. For the fi rst time, a multivariate extension of the phylogenetic signal-representation curve for estimating phylogenetic signal is presented. Another innovation is to show how PVR can be used to assess morphological disparity in a phylogenetic context. A dataset of cranial morphology and function of 35 theropod dinosaur genera is used to illustrate the applications of PVR and how it can be used to answer four questions: (i) what are the phylogenetic patterns in theropod skull shape? (ii) is possible to tease apart the evolutionary models underlying variation in traits? (iii) how are evolutionary history, function, and diet related to variation in theropod skulls? (iv) what are the evolutionary components of morphological disparity in theropod skulls? Answering these questions provide a roadmap for using PVR to address a range of issues relevant to contemporary paleobiology research programs.

Phylogenetic conservatism and climate factors shape flowering phenology in alpine meadows.

The study of phylogenetic conservatism in alpine plant phenology is critical for predicting climate change impacts; currently we have a poor understanding of how phylogeny and climate factors interactively influence plant phenology. Therefore, we explored the influence of phylogeny and climate factors on flowering phenology in alpine meadows. For two different types of alpine plant communities, we recorded phenological data, including flowering peak, first flower budding, first flowering, first fruiting and the flowering end for 62 species over the course of 5years (2008-2012). From sequences in two plastid regions, we constructed phylogenetic trees. We used Blomberg's K and Pagel's lambda to assess the phylogenetic signal in phenological traits and species' phenological responses to climate factors. We found a significant phylogenetic signal in the date of all reproductive phenological events and in species' phenological responses to weekly day length and temperature. The number of species in flower was strongly associated with the weekly day lengths and followed by the weekly temperature prior to phenological activity. Based on phylogenetic eigenvector regression (PVR) analysis, we found a highly shared influence of phylogeny and climate factors on alpine species flowering phenology. Our results suggest the phylogenetic conservatism in both flowering and fruiting phenology may depend on the similarity of responses to external environmental cues among close relatives.

Testing the climate variability hypothesis in thermal tolerance limits of tropical and temperate tadpoles

AbstractAimThe climate variability hypothesis (CVH) states that a positive relationship may exist between the breadth of thermal tolerance range and the level of climatic variability experienced by taxa with increasing latitude, especially in terrestrial ectotherms. UnderCVH, we expected to find a correspondence between both thermal tolerance limits (CTmax andCTmin), ambient extreme temperature and the range sizes of species. We examined the validity of these predictions in a lowland tropical and a temperate tadpole assemblage.LocationLowland Neotropics (Bahia, Brazil) and Palaearctic (Iberian Peninsula and North Africa).MethodWe employed phylogenetic eigenvector regression (PVR) and Pagel's lambda to analyse phylogenetic signals inCTmax andCTmin. We used phylogenetic regression analyses (PGLS) to test the relationships between thermal limits, range size and temperature predictors (measured at the macroscale and microhabitat levels) and phy‐ANOVAto compare both the physiological traits and thermal regimen in both tropical and temperate assemblages.ResultsWe documented moderate‐to‐strong phylogenetic signal in both heat and cold tolerance. Temperate‐zone tadpoles had broader thermal tolerances than tropical ones. Thermal tolerance range was correlated with range sizes and was explained by seasonal thermal range predictors at the global scale. Both macro‐ and microclimate temperature variables provided the best predictive multivariate models of thermal limits at the global scale. Microclimatic predictors, however, were the main determinants ofCTmax andCTmin variation at the local level of tropical and temperate communities respectively.Main conclusionsThermal tolerance range increases with latitude in tadpoles due to the higher increase in cold tolerance in temperate tadpoles. At the global scale, both macro‐ and microenvironment thermal information were reliable predictors of critical thermal limits and thermal tolerance range, asCVHpredicts. However, thermal limits were best predicted by temperatures of the micro‐habitat at the regional level, thus suggesting that physiological thermal boundaries may be governed by thermal selection.

Morphometric traits capture the climatically driven species turnover of 10 spruce taxa across China.

This study explored the relative roles of climate and phylogenetic background in driving morphometric trait variation in 10 spruce taxa in China. The study further addressed the hypothesis that these variations are consistent with species turnover on climatic gradients. Nine morphometric traits of leaves, seed cones, and seeds for the 10 studied spruce taxa were measured at 504 sites. These data were analyzed in combination with species DNA sequences from NCBI GenBank. We detected the effects of phylogeny and climate through trait-variation-based K statistics and phylogenetic eigenvector regression (PVR) analyses. Multivariate analyses were performed to detect trait variation along climatic gradients with species replacement. The estimated K-values for the nine studied morphometric traits ranged from 0.19 to 0.68, and the studied environmental variables explained 39-83% of the total trait variation. Trait variation tended to be determined largely by a temperature gradient varying from wet-cool climates to dry-warm summers and, additionally, by a moisture gradient. As the climate became wetter and cooler, spruce species tended to be replaced by other spruces with smaller needle leaves and seeds but larger cones and seed scales. A regression analysis showed that spruce species tended to be successively replaced by other species, along the gradient, although the trends observed within species were not necessarily consistent with the overall trend. The climatically driven replacement of the spruces in question could be well indicated by the between-species variation in morphometric traits that carry lower phylogenetic signal. Between-species variation in these traits is driven primarily by climatic factors. These species demonstrate a narrower ecological amplitude in temperature but wider ranges on the moisture gradient.

The best of both worlds: Phylogenetic eigenvector regression and mapping.

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.

Phylogenetic eigenvectors and nonstationarity in the evolution of theropod dinosaur skulls.

Despite the long-standing interest in nonstationarity 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 nonstationarity. The PSR curve 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 nonstationarity in trait evolution. As an applied example, we show that the main evolutionary pattern of variation in the theropod dinosaur skull was nonstationary, with a significant shift in evolutionary rates in derived oviraptorosaurs, an aberrant group of mostly toothless, crested, birdlike 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.

Phylogenetic eigenvector regression in paleobiology

ABSTRACT – Phylogenetic Eigenvector Regression (PVR) is a fl exible comparative method that allows testing several hypotheses on phylogenetic signal and correlated evolution among traits. Selected phylogenetic eigenvectors extracted from a phylogenetic distance matrix among taxa allow representing their phylogenetic relatedness in a raw-data form (i.e. instead of a distance matrix) and can then be used as explanatory variables in statistical models aiming to estimate phylogenetic signal or phylogenetically corrected correlations. Because of the growing use of PVR by paleobiologists in recent times, here the main theoretical/statistical basis of the method and the developments made in the 15 years after its original proposition are reviewed, highlighting further potential applications in paleobiology. For the fi rst time, a multivariate extension of the phylogenetic signal-representation curve for estimating phylogenetic signal is presented. Another innovation is to show how PVR can be used to assess morphological disparity in a phylogenetic context. A dataset of cranial morphology and function of 35 theropod dinosaur genera is used to illustrate the applications of PVR and how it can be used to answer four questions: (i) what are the phylogenetic patterns in theropod skull shape? (ii) is possible to tease apart the evolutionary models underlying variation in traits? (iii) how are evolutionary history, function, and diet related to variation in theropod skulls? (iv) what are the evolutionary components of morphological disparity in theropod skulls? Answering these questions provide a roadmap for using PVR to address a range of issues relevant to contemporary paleobiology research programs.

Explorando patrones en rasgos macroecológicos utilizando regresión secuencial de autovectores filogenéticos.

Bini, L.M., Villalobos, F., Diniz-Filho, J.A.F. 2014. Exploring patterns in macroecological traits using sequential phylogenetic eigenvector regression. Ecosistemas 23(1):21-26. Doi.: 10.7818/ECOS.2014.23-1.04 A number of methods have been proposed to estimate the level of phylogenetic signal (autocorrelation) in macroecological traits. These methods are useful to devise alternative ways to circumvent the problem of lack of independence among species and, recently, they have also proved valuable to infer how fast a trait has evolved in comparison with alternative evolutionary models, such as a Brownian motion or Ornstein-Uhlenbeck process. Recently, we developed a method called phylogenetic signal-representation (PSR) curve, an expansion of the phylogenetic eigenvector regression (PVR) proposed in 1998, which consists in estimating different coefficients of determination by regressing a trait of interest on the eigenvectors extracted from a phylogenetic distance matrix. The first model uses only the first of these eigenvectors as an explanatory variable; the second model uses both the first and the second and so on. After, the resultant coefficients of determination are plotted against the cumulative eigenvalues, and the shape of this curve is related to evolutionary models driving trait variation (i.e., a linear pattern is expected under Brownian evolution). Here, we used the PSR curve to study patterns of interspecific variation in Carnivora body size and geographical range size, and compared them with simulated curves under distinct evolutionary processes. Our results unequivocally support our expectations based on previous studies that body size has a strong phylogenetic signal, approximated by an OU pattern with low restraining force, whereas geographic range size is more labile and better fits the null expectations (i.e., absence of phylogenetic signal)

Phylogenetic signal in bone histology of amniotes revisited

Legendre, L, Le Roy, N, Martinez‐Maza, C, Montes, L, Laurin, M & Cubo, J. (2012). Phylogenetic signal in bone histology of amniotes revisited. —Zoologica Scripta,42, 44–53.There is currently a debate about the presence of a phylogenetic signal in bone histological data, but very few rigorous tests have fuelled the discussions on this topic. Here, we performed new analyses using a larger set of seven histological traits and including 25 taxa (nine extinct and 16 extant taxa), using three methods: the phylogenetic eigenvector regression, the tree length distribution and the regressions on distance matrices. Our results clearly show that the phylogenetic signal in our sample of bone histological characters is strong, even after correcting for multiple testing. Most characters exhibit a significant phylogenetic signal according to at least one of our three tests, with the phylogeny often explaining 20–60% of the variation in the histological characters. Thus, we conclude that the phylogenetic comparative method should be systematically used in interspecific analyses of bone histodiversity to avoid problems of non‐independence among observations.

The Strength of Nocomis Nest Association Contributes to Patterns of Rarity and Commonness among New River, Virginia Cyprinids

Many North American minnows (Cyprinidae) exhibit nest association, a spawning mode in which one species (associate) uses nests constructed by another species (host). Although this relationship may be obligate for some species, many nest associates can use alternative reproductive modes, indicating that the strength of the relationship between associate and host may vary. Quantifying the strength of the nest association relationship represents a necessary first step for understanding the importance of this interaction to stream fish communities. To address this question, we conducted a literature review of ecological and ethological reproductive traits for 11 nest associates of Nocomis occurring in the New River basin, Virginia. We used phylogenetic eigenvector regression (PVR) to remove the effects of phylogenetic relatedness among species and used nonmetric multidimensional scaling (NMS) to ordinate a phylogenetically independent trait similarity matrix of the 11 species. Based on the ordination results, we delineated a group of strong and weak nest associates. Strong nest associates showed significant geographic range overlap with Nocomis, while weak ones did not. No difference in spawning temperature range overlap occurred between the two groups. We then tested for effects of nest association strength on species' rarity and found that most (6 of 7) strong nest associates held rare classifications based on one or more of geographic extent, habitat breadth, or local abundance. Conversely, all weak nest associates reflected common classifications. These results indicate that nest association strength is related to rarity; this potentially crucial aspect of conservation has been previously overlooked. Clearly, conservation of rare and imperiled nest associates should be pursued through protection of their host and, consequently, the mutualism they have evolved to exploit.

Deep phylogeny, net primary productivity, and global body size gradient in birds

Body size is evolutionarily constrained, but the influence of phylogenetic relationships on global body size (i.e. body mass) gradients is unexplored. We quantify and map the family-level phylogenetic and non-phylogenetic structure of the global gradient of birds, evaluating the extent to which it is influenced by phylogenetic inertia in contrast to heat conservation, resource availability, starvation resistance, niche conservatism, or interspecific competition. Phylogenetic eigenvector regression (PVR) partitioned the global bird body size gradient into phylogenetically autocorrelated (PA) and phylogenetically independent (PI) components. Simple, piecewise, and partial regressions were used to investigate associations between the PA and PI components of body size and environmental correlates, and to quantify independent and overlapping contributions of environment, phylogenetic autocorrelation, and species richness to the body size gradient. Two-thirds of the geographic variation in bird body size can be explained by phylogenetic relationships at the family level. The global variation in body size, independent of phylogenetic relationships, is most strongly associated with net primary productivity, which is consistent with ‘starvation resistance’. However, the New and Old worlds have very different patterns. We found no independent association of species richness with body size. Despite major unresolved regional differences, deep phylogenetic relationships, heat conservation, and starvation resistance probably operate in concert in shaping the global bird body size gradient in different parts of the world. © 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, , –.

On the selection of phylogenetic eigenvectors for ecological analyses

Among the statistical methods available to control for phylogenetic autocorrelation in ecological data, those based on eigenfunction analysis of the phylogenetic distance matrix among the species are becoming increasingly important tools. Here, we evaluate a range of criteria to select eigenvectors extracted from a phylogenetic distance matrix (using phylogenetic eigenvector regression, PVR) that can be used to measure the level of phylogenetic signal in ecological data and to study correlated evolution. We used a principal coordinate analysis to represent the phylogenetic relationships among 209 species of Carnivora by a series of eigenvectors, which were then used to model log‐transformed body size. We first conducted a series of PVRs in which we increased the number of eigenvectors from 1 to 70, following the sequence of their associated eigenvalues. Second, we also investigated three non‐sequential approaches based on the selection of 1) eigenvectors significantly correlated with body size, 2) eigenvectors selected by a standard stepwise algorithm, and 3) the combination of eigenvectors that minimizes the residual phylogenetic autocorrelation. We mapped the mean specific component of body size to evaluate how these selection criteria affect the interpretation of non‐phylogenetic signal in Bergmann's rule. For comparison, the same patterns were analyzed using autoregressive model (ARM) and phylogenetic generalized least‐squares (PGLS). Despite the robustness of PVR to the specific approaches used to select eigenvectors, using a relatively small number of eigenvectors may be insufficient to control phylogenetic autocorrelation, leading to flawed conclusions about patterns and processes. The method that minimizes residual autocorrelation seems to be the best choice according to different criteria. Thus, our analyses show that, when the best criterion is used to control phylogenetic structure, PVR can be a valuable tool for testing hypotheses related to heritability at the species level, phylogenetic niche conservatism and correlated evolution between ecological traits.

A comparison of metrics for estimating phylogenetic signal under alternative evolutionary models

Several metrics have been developed for estimating phylogenetic signal in comparative data. These may be important both in guiding future studies on correlated evolution and for inferring broad-scale evolutionary and ecological processes (e.g., phylogenetic niche conservatism). Notwithstanding, the validity of some of these metrics is under debate, especially after the development of more sophisticated model-based approaches that estimate departure from particular evolutionary models (i.e., Brownian motion). Here, two of these model-based metrics (Blomberg’s K-statistics and Pagel’s λ) are compared with three statistical approaches [Moran’s I autocorrelation coefficient, coefficients of determination from the autoregressive method (ARM), and phylogenetic eigenvector regression (PVR)]. Based on simulations of a trait evolving under Brownian motion for a phylogeny with 209 species, we showed that all metrics are strongly, although non-linearly, correlated to each other. Our analyses revealed that statistical approaches provide valid results and may be still particularly useful when detailed phylogenies are unavailable or when trait variation among species is difficult to describe by more standard Brownian or O-U evolutionary models.

EXPLORING PATTERNS OF INTERSPECIFIC VARIATION IN QUANTITATIVE TRAITS USING SEQUENTIAL PHYLOGENETIC EIGENVECTOR REGRESSIONS

A number of metrics have been developed for estimating phylogenetic signal in data and to evaluate correlated evolution, inferring broad-scale evolutionary and ecological processes. Here, we proposed an approach called phylogenetic signal-representation (PSR) curve, built upon phylogenetic eigenvector regression (PVR). In PVR, selected eigenvectors extracted from a phylogenetic distance matrix are used to model interspecific variation. In the PSR curve, sequential PVR models are fitted after successively increasing the number of eigenvectors and plotting their R(2) against the accumulated eigenvalues. We used simulations to show that a linear PSR curve is expected under Brownian motion and that its shape changes under alternative evolutionary models. The PSR area, expressing deviations from Brownian motion, is strongly correlated (r= 0.873; P < 0.01) with Blomberg's K-statistics, so nonlinear PSR curves reveal if traits are evolving at a slower or higher rate than expected by Brownian motion. The PSR area is also correlated with phylogenetic half-life under an Ornstein-Uhlenbeck process, suggesting how both methods describe the shape of the relationship between interspecific variation and time since divergence among species. The PSR curve provides an elegant exploratory method to understand deviations from Brownian motion, in terms of acceleration or deceleration of evolutionary rates occurring at large or small phylogenetic distances.

Comparative Methods as a Statistical Fix: The Dangers of Ignoring an Evolutionary Model

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.