Space versus phylogeny: disentangling phylogenetic and spatial signals in comparative data Robert P. Freckleton1,* and Walter Jetz2 1Department of Animal and Plant Sciences, University of Sheffield, Sheffield S10 2TN, UK 2 Division of Biological Sciences, University of California, San Diego, La Jolla, CA 92093-0116, USA Variation in traits across species or populations is the outcome of both environmental and historical factors. Trait variation is therefore a function of both the phylogenetic and spatial context of species. Here we introduce a method that, within a single framework, estimates the relative roles of spatial and phylogenetic variations in comparative data. The approach requires traits measured across phylogenetic units, e.g. species, the spatial occurrences of those units and a phylogeny connecting them. The method modifies the expected variance of phylogenetically independent contrasts to include both spatial and phylogenetic effects. We illustrate this approach by analysing cross-species variation in body mass, geographical range size and species-typical environmental temperature in three orders of mammals (carnivores, artiodactyls and primates). These species attributes contain highly disparate levels of phylogenetic and spatial signals, with the strongest phylogenetic autocorrelation in body size and spatial dependence in environmental temperatures and geographical range size showing mixed effects. The proposed method successfully captures these differences and in its simplest form estimates a single parameter that quantifies the relative effects of space and phylogeny. We discuss how the method may be extended to explore a range of models of evolution and spatial dependence. Keywords: comparative method spatial analysis mammals 1. INTRODUCTION Organisms are the dual products of the environment in which they currently live and their evolutionary history. Thus, species that live in similar environments, or have similar ecologies, would be expected to have common adaptations, and their similarity should be correlated with spatial proximity (Cliff & Ord 1981 Ripley 1981 Borcard et al. 1992 Legendre 1993 Legendre et al. 1997 Lennon 2000) similarly, closely related species would be expected to show more similarity than those that are distantly related because they share more common evolutionary history (Ridley 1986 Harvey & Pagel 1991 Harvey & Purvis 1991 Price 1997 Harvey & Rambaut 2000 Freckleton & Harvey 2006). In other words, species��� traits may be conserved across both space and phylogeny as a consequence of selection for ecological adaptation and the constraints of past evolutionary history. Potential ecologi- cal or environmental determinants of trait variation may similarly contain both phylogenetic (Grafen 1989 Westoby et al. 1995 Diniz-Filho et al. 1998 Desdevises et al. 2003 Wiens & Graham 2005) and spatial (Sokal 1983 Borcard et al. 1992 Legendre 1993 Peres-Neto 2006) signals and both need to be identified. The comparative approach seeks to disentangle the roles of such processes. In analyses looking at cross-species variation in traits, similarity resulting from shared evolution is regarded as a potentially confounding factor by incorporating phylogenetic information into compara- tive analyses, it is possible to address these statistically while analysing correlations between traits and the environment in order to reveal environmentally driven evolutionary patterns (Felsenstein 1985 Grafen 1989 Harvey & Pagel 1991 Lynch 1991). The phylogenetic component of trait variation is typically marginalized, so that such approaches do not explicitly measure what proportion of the variation in trait values in a clade is driven by the environment relative to the proportion that is explained by history. Consequently, it is not generally well understood which of history or environment is more important in determining trait variation across species. Yet, the distinction between phylogenetically structured and more plastic and environmentally driven trait variations has gained new and particular importance in the context of potential range shifts under climate change (Ackerly 2003 Diniz-Filho & Bini 2008). In analyses with a geographical focus, the importance of spatial non-independence of data has become appreci- ated, and various techniques have been developed to address it (e.g. reviews by Clifford et al. 1989 Haining 1990 Legendre et al. 2002 Dormann et al. 2007). To date, these approaches have found extensive use for modelling the spatial abundance or richness of species (Borcard et al. 1992 Lennon 2000 Jetz & Rahbek 2002 Lichstein et al. 2002 Diniz et al. 2003 McPherson & Jetz 2007), and also the spatial analysis of genetic variation and diversity (Sokal & Oden 1978 Sokal et al. 1989 Escudero et al. 2003). Common to both phylogenetic and spatial analyses is the problem of non-independence, and any process that yields non-independence can result in unwelcome Proc. R. Soc. B (2009) 276, 21���30 doi:10.1098/rspb.2008.0905 Published online 16 September 2008 * Author for correspondence (r.freckleton@sheffield.ac.uk). Received 2 July 2008 Accepted 6 August 2008 21 This journal is q 2008 The Royal Society

correlation structures in data when confronted with statistical methods that assume independence. In the analyses of spatial and time-series data, it has been recogn- ized thatdiagnosingandmeasuringsuchnon-independence is an important step in analysing and understanding data (e.g. for overviews see Haining 1990 Chatfield 1996). In those cases, model choice for the spatial pattern is often not easy. By contrast, in comparative analysis, we have the advantage that it is frequently possible to specify models of trait evolution on the phylogeny (e.g. Hansen 1997 Pagel 1997, 1999 Felsenstein 2008) and hence tackle the source of non-independence head-on. As yet, there have been few attempts to synthesize methods for measuring spatial and phylogenetic signals in comparative datasets. Of course, many studies have looked at how the effects of environmental drivers (e.g. latitude, temperature, altitude) influence species��� traits (Ashton et al. 2000 Freckleton et al. 2003 Blackburn & Hawkins 2004 McKechnie et al. 2006). However, spatial non- independence can be pervasive: the influence of unmeasured and hidden variables can dramatically affect the analyses (Lennon 2000). Comparative biologists have developed a suite of statistical techniques for analysing trait data containing phylogenetic signal. Although the issue has been recognized and possible methods discussed (e.g. Legendre et al. 2004), so far none have considered how spatial effects may be also included within a single statistical framework. In this paper, we provide an illustration of the joint effects of phylogenetic and spatial dependence on trait variation across species, the 891 species of carnivores, even-toed ungulatesand primatesoftheworld.Weintroduceamethod allowing the effects of phylogenetic and spatial processes to be measured simultaneously, and show how it may be used to reveal how spatial and phylogenetic factors simul- taneously shape the evolution and distribution of traits. 2. MATERIAL AND METHODS (a) Phylogenetic distribution of traits The model of trait distribution we use is the Brownian model, which forms the basis for many commonly employed phylogenetic methods (Felsenstein 1985 Harvey & Pagel 1991 Martins & Hansen 1997 Pagel 1997, 1999). The Brownian model is essentially a neutral model of trait evolution in which changes in trait values occur continuously and in which increases and decreases in traits are equally as likely and independent of the current state. This is a simple model however, a range of more complex models can be reduced to a Brownian form or accommodated in the same framework (Hansen 1997 Pagel 1997). We consider a single trait evolving among a set of n species. The state of the trait is denoted by a vector x. Under the Brownian model, if t is the time over which the trait is evolving, then Dx, the change in x, is a multivariate normal (MVN) random deviate, Dx Z MVN��0 s2St�� ��2:1�� where S is a (n!n) matrix proportional to the expected variances and covariances for trait changes among species, which are given by the shared path lengths on the phylogeny (e.g. Martins & Hansen 1997 Pagel 1997), and s2 is the rate at which variance accumulates per unit time. After T units of time, x(T ) is a multivariate normally distributed with mean x(0) and variance���covariance matrix s2ST. (b) Phylogenetic contrasts In order to develop the method for simultaneously incorpor- ating spatial and phylogenetic effects, we estimated phyloge- netic contrasts. This is a computationally efficient method for fitting a Brownian model to comparative data and for estima- ting the parameters of the Brownian process. The unstandardi- zedcontrasts (u) and their variances (v) are calculated following the detailed algorithm given in Felsenstein (1985). (c) Incorporating spatial effects In order to model the spatial effect, we assume an analogous linear variance model of spatial similarity and modify the method of contrasts to account for additional processes (see Garland et al. (1992) for an earlier discussion of the idea of modifying contrasts). If dij is the spatial distance between species i and j, and the phylogenetic distance is pij, then the net variance for the distance between their traits is vij Z ��1Kf��pij Cfdij : ��2:2�� In this model, f measures the relative contribution of phylogenetic and spatial effects. A value of f equal to 0 is a model in which there are only phylogenetic effects and a value of 1 is the one in which there are only spatial effects. According to this model, traits evolve as a function of both phylogenetic and spatial distances. This model therefore allows for closely related species to be geographically close together, as would be expected in many datasets. Alternative models are possible and we outline in table 1 a series of simple functions varying in complexity, in terms of nonlinearity and number of parameters that could be used in applications of this approach. Exploratory analysis however Table 1. Possible alternative models of spatial versus phylogenetic effects. These could be used to replace equation (2.2) in the text. equation description vij Z ��1Kf��pij Cfdij variance is a linear function of spatial and phylogenetic distances f measures the relative contribution of each. vij Z ��1Kf��pij Cf exp��adij �� variance is a linear function of phylogenetic distance and an exponential function of spatial distance. f measures the relative contribution of each a models the change in autocorrelation in space. vij Z ��1Kf��pij Cfd a ij variance is a linear function of phylogenetic distance and a power function of spatial distance. f measures the relative contribution of each a models the change in autocorrelation in space. vij Za����1Kf��pijCfdij ��C ��1Ka��vm variance is a linear function of spatial and phylogenetic distances, plus a term measuring the contribution of other effects (vm) f measures the relative contribution of spatial and phylogenetic effects a measures the relative contribution of the spatialCphylogenetic versus other effects. 22 R. P. Freckleton & W. Jetz Space versus phylogeny Proc. R. Soc. B (2009)