Testing the spatial phylogenetic structure of local

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1 Journal of Ecology 2008, 96, doi: /j x Testing the spatial phylogenetic structure of local Blackwell ublishing Ltd communities: statistical performances of different null models and test statistics on a locally neutral community Olivier J. Hardy* Behavioural and Evolutionary Ecology Unit, C 160/12, Faculté des Sciences, Université Libre de Bruxelles, 50 Av. F. Roosevelt, B-1050 Brussels, Belgium Summary 1. Analyzing the phylogenetic structure of natural communities may illuminate the processes governing the assembly and coexistence of species. For instance, an association between species cooccurrence in local communities and their phylogenetic proximity may reveal the action of habitat filtering, niche conservatism and/or competitive exclusion. 2. Different methods were recently proposed to test such community-wide phylogenetic patterns, based on the phylogenetic clustering or overdispersion of the species in a local community. This provides a much needed framework for addressing long standing questions in community ecology as well as the recent debate on community neutrality. The testing procedures are based on (i) a metric measuring the association between phylogenetic distance and species co-occurrence, and (ii) a data set ization algorithm providing the distribution of the metric under a given null model. However, the statistical properties of these approaches are not well-established and their reliability must be tested against simulated data sets. 3. This paper reviews metrics and null models used in previous studies. A locally neutral subdivided community model is simulated to produce data sets devoid of phylogenetic structure in the spatial distribution of species. Using these data sets, the consistency of Type I error rates of tests based on 10 metrics combined with nine null models is examined. 4. This study shows that most tests can become liberal (i.e. tests rejecting too often the null hypothesis that only neutral processes structured spatially the local community) when the ization algorithm breaks down a structure in the original data set unrelated to the null hypothesis to test. Hence, when overall species abundances are distributed non-ly across the phylogeny or when local abundances are spatially autocorrelated, better statistical performances were achieved by ization algorithms preserving these structural features. The most reliable ization algorithm consists of permuting species with similar abundances among the tips of the phylogenetic tree. One metric, R D-DO, also proved to be robust under most simulated conditions using a variety of null models. 5. Synthesis. Given the suboptimal performances of several tests, attention must be paid to the testing procedures used in future studies. Guidelines are provided to help choosing an adequate test. Key-words: community ecology, neutral model, null model, phylogenetic structure, ization test, simulation, Type I error rate Introduction Useful knowledge about ecological processes governing species assemblages can be inferred from community biodiversity patterns, and integrating phylogenetic information can add further insights because a phylogeny conveys indirect information on the shared origin, the shared adaptations, and *Correspondence author. ohardy@ulb.ac.be the potential for competition between species (Webb et al. 2002). For example, if related species tend to be adapted to similar habitats because they share similar traits (a pattern called niche conservatism ; Lord et al. 1995), local communities distributed along an ecological gradient may show an excess of related species co-occurring locally, that is, a pattern of spatial community phylogenetic clustering. Conversely, a pattern of spatial community phylogenetic overdispersion (i.e. sister-species co-occur within sites less often than 2008 The Author. Journal compilation 2008 British Ecological Society

2 Testing spatial community phylogenetic structure 915 expected by chance) can result from (i) competitive exclusion between related species that share similar ecological requirements, (ii) mortality dependence on the density of related species (e.g. Gilbert & Webb 2007), or (iii) ecological speciation causing habitat differentiation between sister-species (Cavender- Bares et al. 2004, 2006). Hints about these processes can thus be gathered from the correlation between co-occurrence and phylogenetic distance of species pairs in natural communities. Note that such spatial phylogenetic structure may also have a biogeographic origin when the speciation rate exceeds the dispersal rate across biogeographic barriers (Webb et al. 2002; Hardy & Senterre 2007). The phylogenetic structure of communities is particularly informative to the current debate on neutrality because, in a neutral community no ecological process regarding species species or species environment interactions can generate a phylogenetic structure in the spatial distribution of species. However, purely neutral processes can create complex structures in the spatial distribution of species (Ulrich 2004), so that testing for a spatial phylogenetic structure by izing a data set, for example, permuting species abundances among locations (and there are many ways to do so see Gotelli 2000) may not be adequate. A relaxed and more realistic version of community neutrality is the concept of locally neutral communities, where neutrality (i.e. species equivalence) holds within a focal community but not necessarily outside this community (Dolman & Blackburn 2004; Ulrich & Zalewski 2007). If the locally neutral community receives migrants from a regional species pool at locations, the spatial distribution of species will depend only on neutral processes (dispersal, ecological drift) and should be devoid of any phylogenetic structure, though a phylogenetic structure could occur in the species abundance distribution because the latter can be influenced by non-neutral processes occurring outside the focal community. Hence, it is important to be able to test separately the occurrence of a spatial phylogenetic structure (Are species found in a given site more, or less, related on average than species found in distinct sites?) from the occurrence of an abundance phylogenetic structure (Is the distribution of overall species abundances non- in the phylogeny?) (Helmus et al. 2007a). Recently, different testing procedures have been applied to detect non- community phylogenetic structure (e.g. Webb 2000; Webb et al. 2002; Cavender-Bares et al. 2004, 2006; Kembel & Hubbell 2006; Horner-Devine & Bohannan 2006; Slingsby & Verboom 2006; Hardy & Senterre 2007; Helmus et al. 2007a,b), and computer programs were developed to test community phylogenetic structure (e.g. software hylocom, Webb et al. 2007; software Ecohyl version 2.0, Cavender-Bares & Lehman 2007; Matlab code, Helmus et al. 2007a,b). Tests are based on (i) a metric measuring the association between phylogenetic distance and species cooccurrence, and (ii) a ization algorithm to assess the distribution of the metric under a given null model. When testing for a spatial phylogenetic structure, the ization procedure should break down any association between species phylogeny and co-occurrence. It can be applied on the species by site matrix or on the phylogenetic tree (e.g. Cavender-Bares et al. 2004). The null model approach has been widely used in community ecology, in particular to test whether patterns of species co-occurrence is, a context in which its interpretation has been much debated (e.g. Diamond 1975; Connor & Simberloff 1979; Gotelli & Graves 1996; Gotelli 2000; Gotelli & McCabe 2002; Ulrich 2004; Ulrich & Gotelli 2007a,b). Defining a null model algorithm adequate for the specific null hypothesis to be tested is not straightforward because different ization schemes can be conceived and they are not necessarily congruent (Gotelli 2000). Actually, a null model, defined by a specific ization algorithm, always tests correctly an implicitly defined null hypothesis (i.e. it tests whether the observed pattern conforms to the possible set of patterns generated by the ization scheme). However, the latter can differ from the explicitly defined null hypothesis one wishes to test (e.g. Does the observed pattern conform to a neutral community?). The problem may arise when the ization algorithm breaks down a structure in the original data set unrelated to the null hypothesis to test. Although testing procedures to detect non- community phylogenetic structure are becoming routinely used, their statistical behaviour and their reliability to detect the imprint of non-neutral ecological processes has rarely been discussed (Kembel & Hubbell 2006; Kraft et al. 2007; Helmus et al. 2007a). For tests originally designed by Webb (2000), Kraft et al. (2007) reported consistent Type I error rates when applying them on a single simulated community created under various assembly models. Many empirical studies, however, are based on multiple communities, so that the problem of the statistical independence of community samples, a feature than can greatly affect the validity of tests, must be evaluated. To investigate how tests perform on multiple community samples, I simulate a locally neutral community that is spatially subdivided and devoid of spatial phylogenetic structure. I then assess the validity of different testing procedures, each corresponding to a particular combination of a metric and a ization algorithm ( null model ), based on the rate of rejection of the null hypothesis that the community is locally neutral. The Type I error rate (i.e. proportion of false positives) is explored when the community is subject to restricted dispersal, variable sub-community sizes, and/or a non- phylogenetic distribution of global species abundances, thus under conditions that affect structural features of the community that ization algorithms do not necessarily preserve. In the following, I first present the different metrics and null models that will be investigated, then the simulation algorithm and data analyses. Metrics of spatial community phylogenetic structure Different metrics using presence/absence or abundance data have been developed to describe the extent of community

3 916 O. J. Hardy Table 1. Metrics to characterize the spatial phylogenetic structure of communities Metric Verbal definition (details given in Appendix S1) Data* References Metrics based on the mean phylogenetic distance (D) within site and/or between sites mmntd Mean D to the nearest relative for all species occurring together within a site, averaged over sites (value for a single site: MNTD) mmd Mean phylogenetic distance between species occurring within a site, averaged over sites (value for a single site: MD) D W Mean phylogenetic distance between individuals occurring within a site, averaged over sites Π ST Relative increase of the mean phylogenetic distance between species sampled among sites versus within sites B ST Relative increase of the mean phylogenetic distance between individuals from different species sampled among sites versus within sites O Webb (2000); Webb et al. (2002) O Webb (2000); Webb et al. (2002); SV and SR in Helmus et al. (2007a) A Hardy & Senterre (2007); SE in Helmus et al. (2007a) O Hardy & Senterre (2007) A Hardy & Jost (2008); ( ST I ST ) in Hardy & Senterre (2007) Metrics based on the earson s correlation coefficient between D and co-occurrence when: R D-CA Co-occurrence = Schoener s proportional similarity of local abundances A Cavender-Bares et al. (2004, 2006) R D-CO Co-occurrence = Schoener s proportional similarity of local occurrences O Cavender-Bares et al. (2004, 2006) R D-RA Co-occurrence = earson s correlation between local abundances A Helmus et al. (2007b) R D-RO Co-occurrence = earson s correlation between local occurrences O Helmus et al. (2007b) R D-DO Co-occurrence = deviation from expected rate of co-occurrence O Slingsby & Verboom (2006) *O, occurrence data; A, abundance data. Symbol ~ indicates that the metric is proportional to the one specified in the given reference. phylogenetic structuring (Table 1; a more detailed description is available on line in the Appendix S1 in the Supplementary Material). Two categories can be distinguished: (i) metrics expressing the relatedness between species or individuals co-occurring within a site, in absolute terms (MD, MNTD, D W, SV, SR, SE) or relative to the relatedness between species or individuals from distinct sites (B ST, Π ST, or the difference ST I ST ), and (ii) metrics expressing the correlation between the matrix of phylogenetic distances between species and a matrix of pairwise co-occurrence indices between species (R D-CA, R D-CO, R D-RA, R D-RO, R D-DO, which differ by the way co-occurrence is estimated). The metrics described above and in Table 1 usually seek to characterize a spatial phylogenetic structure : Are co-occurring species more related than expected? There could also be an abundance phylogenetic structure : Are abundant species ly distributed across the phylogeny? The latter pattern can be quantified by the Abundance hylogenetic Deviation index, which I define as AD = (Δ D B )/Δ, where Δ n n = i j idij / n( n 1) is the mean phylogenetic distance between distinct species in the whole community (D ij is the phylogenetic distance between species i and j), and B n n n n D = i j ifi fjdij / i j ifi fj is the mean phylogenetic distance between individuals of distinct species (n being the number of species and f i the relative abundance of species i in whole community). Thus, D B is a species abundance weighted version of Δ. If abundant species tend to belong mostly to one or several related clades, D B < Δ, so that AD > 0, a situation I will name species abundance phylogenetic clustering. On the contrary, if abundant species tend to be spread among distant clades, D B > Δ, so that AD < 0, a situation I will name species abundance phylogenetic overdispersion. Note that AD can also be defined using the number of sites in which a species is found to compute relative species abundances. Null models for testing community phylogenetic structure Randomization can be applied on the inter-species phylogenetic distance matrix, that is on the phylogenetic tree (Fig. 1), or on the species by site matrix, that is on the species spatial distribution (Fig. 2). Here I detail nine variants (i.e. distinct null models) and emphasize their impact on the structure of the ized data set (Table 2). The simplest phylogeny ization consists of reshuffling species positions among the tips of the phylogenetic tree (null models 1, Fig. 1), thereby keeping the tree topology and branch lengths unchanged. If a reference species pool is defined and contains non-sampled species, there are two variants of this null model depending on whether the phylogenetic tree contains only the species sampled in the set of sites studied (null model 1s; Fig. 1), or all the species of a reference species pool (null model 1p; Fig. 1). A third variant considers the overall abundance (or the occurrence frequency among sites) of each species, restricting permutation among species with similar abundances. To this end, species are grouped into distinct abundance classes characterized by a fixed ratio K = maximal abundance / minimal abundance (e.g. for K = 4, the limits between abundance classes could be 1, 4, 16,... ) and species are ly permuted within each class (null model 1a; Fig. 1). This ization algorithm maintains most of the abundance phylogenetic structure originally present in a data set (Table 2). Note that class limits follow a geometric progression but it is preferable to change them from one ization to the next (e.g. for K = 4, class limits could also be 0.5, 2, 8, 32,..., then 0.3, 1.2, 4.8,... ) to avoid that species with similar abundance could not be permuted because they would always belong to distinct abundance classes. The species by site matrix can be ized in different ways by permuting the elements of the matrix within each site

4 Testing spatial community phylogenetic structure 917 Fig. 1. Schematic representation of different ization schemes of a phylogenetic tree. Numbers represent global species abundances (or number of occurrences) observed in the studied community. Shaded areas indicate groups within which species represented by their abundance are ly permuted. Null model 1p izes all species in the phylogenetic tree containing a reference species pool. Null model 1s izes all species sampled in the studied community, that is, with abundance > 0. Null model 1a izes species in a constrained way so that only species with similar abundances are permuted among themselves (here, the maximal/minimal species abundance ratio within each permutation group K = 4). Fig. 2. Schematic representation of different ization schemes of a species by site abundance (or presence/absence) matrix where elements are permuted within sites (null models 2) or within species (null models 3). Shaded areas indicate elements of the matrix ly permutated among themselves (null models 2p, 2s and 3i where izations occurs independently within each shaded area). The set of species considered in null model 2s is limited to the sampled species (i.e. species with at least one occurrence), whereas a larger reference species pool is considered in null model 2p. Double pairs of arrows in null models 2x and 3x show the inversion of two pairs of elements chosen ly as done by the swap algorithm (many such swapping are carried out). This algorithm preserves the species richness per site as well as the number of sites in which each species occurs. With presence/absence data (matrix of 0 and 1 values), null models 2x and 3x are strictly equivalent. With abundance data, null models 2x and 3x also swap double pairs of elements when the latter are all different from zero. The arrows in null model 3t show the translation of all the elements within a species, as would occur if the sites are spatially arranged along a transect in the same order as in the matrix (independent translations of different amplitudes and/or directions are performed for each species), so that the spatial autocorrelation of local species abundances is conserved.

5 918 O. J. Hardy Table 2. Constraints of the different null models on the structural features of data. Equivalences with previous works are given as footnotes Constraints (structural features of data left unchanged after ization) Null model (equivalence) Local species diversity per site Among sites abundance distribution per species Spatial autocorrelation of local abundances for each species hylogenetic distribution of global species abundances 1s 1 X X X 1p 2 X X X 1a X X X (X) 9 2s 3 X 2p 4 X 2x 6 X (X) 8 (X) 10 3i 5 X X 3x 6 (X) 7 X X 3t X X X 1 Equivalent to null model 1 in Cavender-Bares et al. (2004). 2 Equivalent to model 0 of function comstruct in hylocom 3.41 (Webb et al. 2007). 3 Equivalent to model 1 of function comstruct in hylocom 3.41 (Webb et al. 2007), to the unconstrained null model in Kembel & Hubbell (2006), and to null 1 in Helmus et al. (2007a). 4 Equivalent to model 2 of function comstruct in hylocom 3.41 (Webb et al. 2007). 5 Equivalent to null model 2 in Cavender-Bares et al. (2004), null model 1 in Cavender-Bares et al. (2006), and to null 1 in Helmus et al. (2007a). 6 With presence/absence data, equivalent to model 3 of function comstruct in hylocom 3.41 (Webb et al. 2007), to the constrained null model in Kembel & Hubbell (2006), to null model 3 in Cavender-Bares et al. (2004), to null model 2 in Cavender-Bares et al. (2006), and to null 3 in Helmus et al. (2007a). 7 Only local species richness is left unchanged (the distribution of species abundances per site is affected). 8 Only the number of sites where each species occurs is left unchanged (for each species, the distribution of abundances among sites is affected). 9 Approximately true according to the criterion defining when species have similar enough abundances to be permuted. 10 True only for presence/absence data. (null models 2), or within each species (null models 3), independently or not (Fig. 2). Each ization algorithm may constrain different features of the data set (Table 2) and six null models are described below. A first simple algorithm consists of permuting, independently for each site, the local species abundances among species (null models 2s and 2p; Fig. 1). As for null model 1, if a reference species pool is defined and contains non-sampled species, there exist two variants depending on whether the species by site matrix includes only the sampled species (null model 2s) or all species from the reference species pool (null model 2p). The local species diversity is maintained within each site but not the original inter-site abundance distribution of each species. With presence/absence data, this null model is equivalent to ly sampling species from the pool of species (without replacement) until the original species richness in each site is achieved. It has often been used to test community phylogenetic structuring (e.g. Webb et al. 2002; Horner- Devine & Bohannan 2006; Kembel & Hubbell 2006). Helmus et al. (2007a) noted that these null models break down both the spatial and the abundance phylogenetic structures so that the two types of patterns can be confounded. A second simple algorithm consists of permuting, independently for each species, the local abundances among sites (null model 3i; Fig. 2). Here, the inter-site abundance distributions are maintained for each species but not the original local species diversities per site (Table 2). This approach has been applied by Cavender-Bares et al. (2004, 2006) and is advocated by Helmus et al. (2007a) for testing if there is a significant spatial phylogenetic structure (independently of an abundance phylogenetic structure). The species by site matrix can also be ized in a more constrained way by maintaining both local richness and total species occurrences (null models 2x and 3x). This is achieved by the Gotelli swap algorithm (Gotelli & Graves 1996; Gotelli 2000; Gotelli & Entsminger 2001). The latter seeks out ly in the matrix for submatrices of four elements (where rows and columns do not need to be adjacent) showing a (1, 0)(0, 1) or a (0, 1)(1, 0) presence/absence configuration, then it swaps the values to get a (0, 1)(1, 0) or a (1, 0)(0, 1) configuration, respectively. Hence, the rows and columns total of the original matrix are preserved. The matrix ization is achieved by repeating this swapping procedure many times. Although the Gotelli swap algorithm was designed for presence/absence data, I extend it for abundance data where submatrices are in (x, 0)(0, y) configuration. The latter can thus be swapped into (0, x)(y, 0) or into (0, y)(x, 0) configurations, defining two variants: one maintains local diversities (null model 2x; Fig. 2), the other maintains inter-site species abundances distributions (null model 3x; Fig. 2). For these models, submatrices in (r, s)(t, u) configuration, where r, s, t, u are all 0, are also swapped into (s, r)(u, t) in null model 2x and into (t, u)(r, s) in null model 3x. All the preceding species by site matrix ization schemes breaks down any spatial autocorrelation of local species abundances (although constraints induced by the swap

6 Testing spatial community phylogenetic structure 919 algorithm may maintain some spatial autocorrelation). To avoid this, when sites are arranged regularly on a rectangular lattice (or along a transect), the whole spatial pattern of each species local abundances can be translated by a number of lattice units in each direction, independently for each species (null model 3t; Fig. 2). Such ization displaces some sites beyond the lattice boundary, in which case the sites are wrapped around on to the opposite boundary, as in torus-translation tests (Harms et al. 2001). Except for disruptions at the boundaries, this procedure holds the within-species spatial structure intact while rendering the spatial structures of different species independent, though it does not preserve local species diversity. Simulation model of a subdivided community To verify the statistical properties of tests of community phylogenetic structuring, I developed an individual-based model of a locally neutral community subdivided into n sites. Each site contains a fixed number of individuals and replacement follows a lottery model where individuals of all species have the same competitive ability (Chesson & Warner 1981). This community is connected to a constant large regional species pool defined by a set of species with predefined relative abundances. Contrary to Hubbell s neutral model (but as the 3L-SINM model of Munoz et al. 2008) relative species abundances in the regional species pool is not assumed to result from an ecological drift-speciation equilibrium but is assumption-free and can take any form, or result from any kind of processes (neutral or not). The only assumption is that it is stable on the time-scale investigated. Hence, species equivalence is assumed only within the focal subdivided community (hence the expression locally neutral community ). The initial community is composed of a sample from the regional species pool, that is, individuals are sampled from the source community (with replacement) with probability equal to the pre-defined species relative abundances. At each time step, or generation, all individuals die and are replaced by the progeny of individuals from the previous generation. rogeny can come from (i) the same site (no migration), (ii) the regional species pool (at rate Mp), or (iii) another site. In the latter case, there are three possible patterns of migration between sites: (i) all sites are interconnected and migration occurs ly between sites (rate Mr); (ii) sites are arranged in a spatially explicit way and migration is limited by spatial distance, occurring only between adjacent sites (rate Md); or (iii) sites are organized into distinct groups and migration is limited by group membership, occurring only between sites from a same group (rate Mg). High Mp would result in sub-communities essentially identical to the regional species pool whereas if the rate of local recruitment is close to one (very low migration rates), monodominance would result as a consequence of ecological drift. To obtain a balanced level of local diversity and correlated species composition among sites, one needs 0 < Mp < Mr or Md or Mg << 1. Md causes a spatial correlation between nearby sites whereas Mr tends to homogenize composition among sites and Mg results in a homogenization of sites within groups and a differentiation among groups. Hence, all pairs of sub-communities are expected to show equal level of differentiation under Mr whereas differentiation will vary according to spatial distance under Md and according to group membership under Mg. The relationships between species are defined by a dated phylogenetic tree providing a phylogenetic distance for each pair of species in terms of divergence time (see below). This model was simulated using a C-coded program. Simulations were run for T generations before analyzing the phylogenetic structure, and 1000 replicates were run for each parameter set (see below). It is assumed that T is sufficiently short that speciation and drift in the regional species pool can both be neglected (driftmigration equilibrium is not necessarily reached). In the simulations presented here, the regional species pool (source community) is composed of = 227 species, the number of angiosperm trees with DBH > 10 cm in the 50- hectare Forest Dynamics lot on Barro Colorado Island, anama (BCI data set; Condit 1998). The species phylogeny for the 227 BCI species was constructed from a dated phylogenetic tree of all angiosperm families (Davies et al. 2004) using the hylomatic software (Webb & Donoghue 2005). Within families, genera and species are positioned as polytomies with node ages equal to, respectively, 2/3 and 1/3 the age of the family (Hardy & Senterre 2007). Relative species abundances in the source community follow one of three possible modes: (1) the actual abundances observed on BCI (available on line in the Table S1), (2) the abundance distribution observed on BCI but ized among species, (3) the 34 highest species abundances observed on BCI (which constitutes 72% of the community) are re-attributed ly to the 34 species belonging to the (AG) Fabaceae family (AGII 2003), the other abundances being re-attributed ly to non-fabaceae species. Thus, the frequency distribution of species abundances is the one observed on BCI but the phylogenetic distribution of species abundances is realistic (case 1), (case 2), or highly clustered (case 3). Simulations consider n = 100 sites on a grid arranged in a toroidal fashion (i.e. opposite sides of the grid are connected, so that there are no borders). The number of individuals per site (i.e. per sub-community) is constant (Ns = 100) or variable (Ns alternates spatially between 40 and 160), but the overall number of individuals is fixed (10 000). Immigration from the source community occurs at a rate Ms = Species migration among sites is (Mr = 0.1 and Md = Mg = 0), limited by distance (Md = 0.1 and Mr = Mg = 0), or limited by group membership within each of four groups of 5 5 sites (Mg = 0.1 and Mr = Md = 0). There are thus three variable parameters (three states for the phylogenetic distribution of species abundances, three states for the migration pattern and two states for sub-community sizes) that are combined in a factorial way, leading to 18 parameter sets. For each set, after T = 100 generations, the global and average local species richness is computed, as well as the abundance phylogenetic deviation index, AD. Then, each metric quantifying community phylogenetic structuring

7 920 O. J. Hardy Table 3. Mean global and local species richness, mean abundance phylogenetic deviation index (AD), and mean values of the metrics characterizing the spatial phylogenetic structure of a simulated locally neutral community for different sets of simulation parameters Species abundances* BCI clustered clustered Species migration Random Random Limited distance Limited group Random Random Limited group Sub-community size Constant Variable Constant Constant Constant Constant Variable Global/local richness 85/24 78/21 85/21 85/19 85/24 85/25 79/15 AD mmntd mmd D W Π ST B ST R D-CA R D-CO R D-RA R D-RO R D-DO *Species abundances in the source community:, realistic using BCI data, or phylogenetically clustered. Species migration among sites: spatially, limited by distance, or limited by group membership. Sub-community size: Constant (Ns = 100 individuals) or Variable (Ns alternates spatially between 40 and 160). Other simulation parameters are fixed (see text). arameters different from the first parameters set are highlighted (bold). (Table 1, including the MD and MNTD metrics for a single site) are computed and tested by each of the nine null models (Table 2). For null models 1p and 2p, the reference species pool is constituted by the 227 species of the regional species pool, whereas null models 1s and 2s considered only species sampled in the focal community (84 species on average). For null model 1a, the threshold ratio was set to K = 3, using species abundances or species occurrence frequencies in accordance with the type of data treated by each metric. For null models 2x and 3x, the number of submatrix swapping (Fig. 2) used to ize the species by site matrix is equal to five times the matrix size (i.e = ) for the first ized data set, which starts from the original data set, and equal to the matrix size for the next ized data sets, where each starts from the previously produced ized data set. For each metric by null model combination, the number of significant tests over 1000 replicates was recorded at α = 0.05, distinguishing phylogenetic clustering and overdispersion (i.e. there are two one-sided tests at α = 0.025). For exact tests, there should be by chance an average of 25 replicates where phylogenetic clustering is detected and 25 replicates where phylogenetic overdispersion is detected (false positives). Deviations from these expectations are significant when the number of significant tests exceeds 37 or is less than 13 (χ 2 test at < 0.01, 1ddl). To get an overall assessment of Type I error rate conformity of a given test across a range of parameter sets, the mean square error is computed: MSE = 2 ( Nobs Nexp) where Nobs and Nexp are, respectively, the observed and expected numbers of replicates for which the test suggests significant clustering, or overdispersion (here, Nexp = 25). Results For brevity, results (Tables 3 and 4) are presented for seven of the 18 parameter sets, 5 of the 10 metrics, and five of the nine null models. Complete results are available in the online supplementary material (Tables S2 and S3). In the simulated community, the mean species richness is about 85 overall and about 24 within a given site, these values being lower when the sub-community size was variable and local richness was reduced furthermore when migration between sites was limited by group membership (Table 3). As expected, AD = 0 when species abundances are phylogenetically in the source community, whereas it is positive (AD = 0.27 ± 0.04 SD) under phylogenetically clustered species abundances (simulations with Fabaceae species very abundant). Interestingly, the actual species abundances found on BCI lead to slightly negative values (AD = 0.02 ± 0.02 SD), indicating that species abundances are phylogenetically overdispersed on BCI (note that although c. 81% of replicates gave negative AD, application of null model 1s failed to detect significance in the majority of cases). Within sites, the mean phylogenetic distance between species (mmd) ranges from 79 to 115 million years, being highest when BCI species frequencies are used in the source community, and lowest when species frequencies are phylogenetically clustered. The within site mean nearest taxon distance between species (mmntd) and mean phylogenetic distance between individuals ( D W ) follow the same trends (Table 3). Π ST and B ST are very close to zero, as expected in the absence of spatial phylogenetic structure. R D-CA and R D-CO are much affected by the phylogenetic distribution of species abundances in the source community, being close to zero

8 Testing spatial community phylogenetic structure 921 Table 4. Results of different tests of phylogenetic structuring applied on a simulated locally neutral community under various simulation parameters (see text and Table 3 for details). Each test is a particular combination of a metric and a null model. Values (X/Y) indicate the number of replicates over 1000 for which each test detects significant phylogenetic clustering (X) or overdispersion (Y) at 0.05 (25/25 is expected for exact tests). In bold: cases where Type I error rate (α) is consistent for both clustering and overdispersion (values inside the range, 0.01). In italic: cases where the test is extremely liberal, being significant at a frequency at least four times the fixed α (values 100 for clustering or for overdispersion) Species abundance BCI Clustered Clustered Inter-site migration Random Random Limited distance Limited group Random Random Limited group Sub-community size Constant Variable Constant Constant Constant Constant Variable Null model 1s mmd 21/18 22/27 28/30 19/25 2/70 996/0 997/0 Π ST 22/28 27/31 27/24 33/15 23/21 131/27 34/264 B ST 19/28 22/29 27/27 23/28 30/25 45/42 79/116 R D-CO 29/21 21/23 25/28 17/22 3/ /0 943/0 R D-DO 31/23 25/30 26/36 25/24 16/27 13/4 9/41 Null model 1a (K = 3) mmd 0/0 0/0 0/0 0/0 0/0 130/0 133/0 Π ST 17/24 7/10 30/30 27/19 25/17 33/19 31/20 B ST 20/24 25/23 20/32 22/26 17/27 31/11 36/15 R D-CO 0/0 0/0 1/0 7/1 0/0 56/0 88/0 R D-DO 27/22 24/29 22/24 26/24 25/26 26/19 30/16 Null model 2s mmd 362/ / / /327 49/ /0 1000/0 Π ST 3/6 65/69 34/21 145/157 9/3 71/11 128/510 B ST 3/4 7/9 32/24 101/110 3/3 17/13 197/224 R D-CO 113/126 84/97 90/120 50/71 5/ /0 979/0 R D-DO 38/33 6/2 35/46 49/24 34/49 23/15 6/16 Null model 2x mmd 25/23 38/37 61/64 184/232 29/25 20/44 330/119 Π ST 25/23 38/37 61/64 184/232 29/25 20/44 330/119 B ST 9/9 48/58 34/37 119/138 13/7 0/ /31 R D-CO 18/17 34/29 64/64 227/216 19/22 25/33 1/955 R D-DO 23/22 34/30 26/33 34/22 21/28 20/25 58/32 Null model 3i mmd 16/21 212/245 62/52 171/208 22/14 47/3 137/557 Π ST 16/21 213/245 62/52 171/208 22/14 47/3 137/557 B ST 3/5 30/26 25/27 110/111 12/8 1/0 122/115 R D-CO 19/24 110/137 51/51 213/207 22/17 28/16 0/989 R D-DO 28/22 39/58 23/33 30/26 25/31 30/15 28/157 Null model 3t mmd 21/21 195/228 17/14 71/66 22/13 38/6 77/423 Π ST 21/21 195/228 17/14 71/66 22/13 38/6 77/425 B ST 6/6 15/17 7/7 48/46 9/7 1/0 50/44 R D-CO 17/17 109/123 23/25 87/102 14/16 25/10 4/868 R D-DO 20/21 35/47 25/36 28/20 24/27 17/24 34/163 under a phylogenetically distribution, very negative under a phylogenetically clustered distribution, and somewhat positive with the phylogenetically overdispersed BCI distribution (Table 3). By contrast, R D-RA, R D-RO and R D-DO metrics are much less affected by the phylogenetic distribution of species abundances and remain always close to zero (Table 3). When the phylogenetic tree is ized without constraint on species abundances (null models 1s and 1p), the tests respect the Type I error rates for all the metrics as long as the distribution of species abundances is phylogenetically (Table 4, Table S3). Under abundance phylogenetic structuring, most metrics lead to (sometimes extreme) liberal tests. However, some metrics such as B ST and R D-DO provide (near) exact tests with the phylogenetically overdispersed BCI abundance distribution and they are the most reliable metrics using null models 1s and 1p (Table 5). Results obtained using null models 1s and 1p are similar, though deviations from expected Type I error rates are somewhat higher for null model 1p. When permutations are allowed only among species having similar abundances (null model 1a), conformance of Type I error rates improve substantially for most metrics, even under extreme abundance phylogenetic clustering, and tests become satisfactory using Π ST, B ST, R D-RA, R D-RO and R D-DO (Tables 4 and 5). Hence, in the absence of a phylogenetic structure in the species abundance distribution one can

9 922 O. J. Hardy Table 5. Summary of Type I error rate conformance of the different tests (combination of a metric with a null model) applied on the simulated data sets conforming to the null hypothesis to be tested (local neutrality). Values are the quadratic averages of the absolute difference between observed and expected number of significant tests over 1000 replicates, averaged over the 18 parameter sets (MSE 1/2 ). Low values (in bold) indicate the best tests (Type I error rates nearly conforming to nominal values in all simulation conditions) whereas high values (in italic) indicate potentially highly liberal tests (high risk of false positive in some simulation conditions). The statistical properties of mmd and D W are representative of the properties of, respectively, the SV (and SR) metric and the SE metric defined by Helmus et al. (2007a), when applied on multiple samples Metric Null model 1s 1p 1a 2s 2p 2x 3x 3i 3t MNTD (one site) MD (one site) mmntd mmd D W Π ST B ST R D-CA R D-CO R D-RA R D-RO R D-DO advise to use null model 1s, otherwise izations should be constrained to preserve the pre-existing abundance phylogenetic structure (null model 1a). I now consider the tests based on species by site matrix ization. Essentially all the tests based on null models 2p and 2s are highly liberal (Tables 4 and 5). Resampling species from the reference species pool (null model 2p) worsens the statistical properties (Table S3). Hence, these ization procedures are clearly inadequate to test whether non-neutral processes generate a spatial phylogenetic structure. The tests based on null model 3i are generally valid as long as subcommunity sizes remain constant and migration is, otherwise they are too liberal, especially when migration is limited by group membership (Table 4, Table S3). The tests based on the swap algorithm (null models 2x and 3x) are valid in the same conditions as the preceding one (null model 3i) but perform better when sub-community size varies among sites, at least for the metrics based on presence/absence data (Table 4). Nevertheless, they remain too liberal when migration is not, or when abundance phylogenetic clustering is combined with varying sub-community sizes, though the R D-DO metric keeps good statistical properties (Table 4, Table S3). Finally, null model 3t, which is similar to null model 3i but maintains the spatial autocorrelation of local abundances for each species, recovers good statistical performance on most metrics when migration is limited by distance, provided that sub-community size is constant, although it is too conservative with B ST and it is not very effective when migration is limited by group membership (Table 4). This null model seems thus adequate to test patterns generated under limited dispersal but it requires constant sample sizes and sampling sites located on a regular rectangular grid or on a transect. Overall, very few tests gave consistent Type I error rates in all conditions (c. 15 over 108 tests; Table 5), liberal tests being usually observed when some structural feature of the data set was lost by the ization algorithm. However, R D-DO proved very robust with all ization algorithms (except null model 2p; Table 5). Among the metrics based on abundance data, R D-RA and B ST used with null model 1a provided the most satisfactory tests (Table 5). MNTD and MD assessed for a single site, which are the main test metrics used by the software hylocom, show better conformance with Type I error rates than their multiple sample counterparts (mmntd and mmd, Table 5). They were often used with null model 2s, in which case they perform satisfactorily provided that there is no strong phylogenetic structure in the species abundance distribution (whereas mmntd and mmd give highly liberal tests in all conditions, Table S3). However, they are expected to suffer low testing power because they do not provide a global test for multiple samples. Discussion The neutral model is a mechanistic model of community assuming species equivalence (identical per capita rates of birth, death, migration and speciation; Hubbell 2001). The more realistic variant of the neutral model considered here, the locally neutral model, assumes that neutrality holds at some defined scale (a set of sub-communities) but not necessarily at a higher level (regional species pool). Gotelli & McGill (2006) insisted on the difference between neutral and null models. The latter are pattern-generating models based on data ization whereby certain structural features are held constant while others are allowed to vary stochastically in order to create new somehow patterns. Null models are particularly suited to design tests by generating the distribution of a particular metric. A well chosen null model (i.e. a particular ization algorithm) is expected to allow testing the absence of a particular ecological mechanism that affects a feature of species assembly pattern. Hence, null models can be of interest to test the neutral assumption. A locally neutral community is expected to show no spatial phylogenetic structure, as long as biogeographic effects can be neglected (speciation rate << large scale migration rate), though it may show an abundance phylogenetic structure, in particular when non-neutral processes affect abundances in the regional species pool. The goal of this study was to assess the conformance of Type I error rates of different null models used to test the locally neutral assumption considering different metrics describing the spatial phylogenetic structure. A potential problem with null models is that data ization may simultaneously affect not only the association between phylogenetic distance and the co-occurrence patterns of species, but also species abundances across samples, the spatial autocorrelation of local species abundances, and/ or the phylogenetic distribution of species abundances.

10 Testing spatial community phylogenetic structure 923 Simulations of locally neutral communities have shown that most of the tests do not respect Type I error rates in all simulated conditions, though they usually perform satisfactorily under specific and often predictable conditions (Table 4). This is not unexpected because most of the null models cannot constrain all the features of the data set listed in Table 2, except null model 1a which performs satisfactorily with most metrics (Table 5). Hence, the simulation results suggest that null models should ideally preserve all structural features of the data unrelated to the spatial phylogenetic structure, otherwise ization tests can become too liberal. Similar problems were reported in related ization tests, for instance to assess whether patterns of species co-occurrence is (Gotelli 2000; Ulrich & Gotelli 2007a,b), or with partial Mantel tests (Raufaste & Rousset 2001). The conditions leading to valid tests are largely predictable from the features of the ized data set that are preserved. For instance, phylogenetic tree ization (null models 1s and 1p) keeps all features listed in Table 2 except the species abundance phylogenetic structure, which is ized. Consequently, it leads to exact tests when global species abundances show no phylogenetic structure (Table 4). For similar reasons, null models based on species by site matrix izations that do not preserve the spatial autocorrelation of local species abundances (null models 2s, 2p, 2x, 3i, 3x) generally provided liberal tests under limited dispersal (migration limited by distance or by group membership, Table 4). Null models 3i and 3t are similar (Fig. 1) except that only the latter preserves the spatial autocorrelation of local species abundances. When applied on a data set where such spatial autocorrelation occurs because migration is limited by spatial distance, the frequency distributions of all metrics are more dispersed under null model 3t (not shown). Hence, null models not preserving spatial autocorrelation tend to be liberal under limited dispersal because they underestimate the stochastic variance of the metric. More generally, it seems that when there is a complex pattern of differentiation between sub-communities (dependency on spatial distance or group membership), ization of species-site matrix must preserve this complex pattern otherwise liberal tests may result. Therefore, for the simulated data where dispersal was limited by group membership, we can expect that a null model applying the swap algorithm within each subgroup would probably show good statistical properties because group membership would have been preserved. By analogy with the present results, it is likely that dispersal limitation also affect Type I error rates of null model based tests of nestedness and co-occurrence patterns. Hence, the swap algorithm, which is usually considered as the most reliable to test these patterns (Gotelli 2000; Ulrich & Gotelli 2007a,b), should be evaluated further under dispersal limitation. Interestingly, some metrics provide more robust tests than others. This is particularly the case of the R D-DO metric (Table 5). The robustness of some metrics is probably due to their way of quantifying the phylogenetic structure in a more standardized or relative fashion. For example, mmd is an absolute inter-species divergence time within sites whereas Π ST is a ratio involving inter-species divergence time within sites ( Δ w ) and among sites ( Δ a ): mmd = Δ w and Π ST = ( Δa Δw )/ Δa. Therefore, if global species abundances are phylogenetically clustered (AD > 0), the ization of the phylogenetic tree following null model 1s or 1p will increase Δa and Δw, affecting mmd but not necessarily Π ST. In other words, mmd confounds abundance and spatial phylogenetic structures, whereas Π ST reveals only the spatial phylogenetic structure. This explains why, using null model 1s or 1p, Π ST provide more robust tests than mmd under species abundance phylogenetic structuring (Table 4). Similarly, R D-CO and R D-CA are based on a co-occurrence index (proportional similarity, C ij, Schoener 1970; see Appendix S1) sensitive to the global abundance of the species being compared because C ij tends to be high for common species and low for rare species, whereas R D-DO, R D-RO and R D-RA are based on measures of species co-occurrences more standardized, which are close to zero for species showing independent spatial distributions whatever their global abundances. Consequently, the latter metrics, and particularly R D-DO, appear much more robust than the former (Table 5). For example, in R D-DO, co-occurrence is computed as DO ij = ( ij i j )/( i j ), where i, j and ij are the proportions of sites where species i occurs, species j occurs, and both species occur, respectively, so that DO ij 0 under independent distributions of species i and j because the product i j is the expectation of ij. Recently, Kraft et al. (2007) simulated the species assembly of a single local community connected to a source community under various scenarios of species trait evolution and community assembly processes, to assess the statistical properties of the single sample MD and MNTD metrics combined with null model 2p. Contrary to the present study, they found consistent Type I error rates under scenarios that do not generate community phylogenetic structure. However, as they acknowledged, their species (rather than individual) based model did not consider species abundance variation so that each species had the same probability of migrating into the local community. In addition, because a single local community was considered, dispersal spatial limitation and community size variation were not relevant. Hence, there is no contradiction with the present results which also predict consistent Type I error rates under the model simulated by Kraft et al. (2007). An important conclusion of the present study is that the statistical properties of the tests can change substantially when applied on multiple samples, and null models 2s and 2p then become highly unreliable to test for the absence of a spatial phylogenetic structure because they underestimate the variance and/or shift the frequency distribution of the metrics (Fig. 3). This is clearly revealed by the statistical behaviour of the single-site MD and MNTD metrics (used in the software hylocom, Webb et al. 2007) which lead to correct tests when combined with null model 2p, which consists in resampling species at from a reference species pool, whenever there is no species abundance phylogenetic structuring, whereas the all-site average mmd and mmntd metrics always perform very badly with this null model (Table S3).