Node‐based analysis of species distributions

Summary

1. The integration of species distributions and evolutionary relationships is one of the most rapidly moving research fields today and has led to considerable advances in our understanding of the processes underlying biogeographical patterns. Here, we develop a set of metrics, the specific overrepresentation score (SOS) and the geographic node divergence (GND) score, which together combine ecological and evolutionary patterns into a single framework and avoids many of the problems that characterize community phylogenetic methods in current use.
2. This approach goes through each node in the phylogeny and compares the distributions of descendant clades to a null model. The method employs a balanced null model, is independent of phylogeny size, and allows an intuitive visualization of the results.
3. We demonstrate how this novel implementation can be used to generate hypotheses for biogeographical patterns with case studies on two groups with well‐described biogeographical histories: a local‐scale community data set of hummingbirds in the North Andes, and a large‐scale data set of the distribution of all species of New World flycatchers. The node‐based analysis of these two groups generates a set of intuitively interpretable patterns that are consistent with current biogeographical knowledge.
4. Importantly, the results are statistically tractable, opening many possibilities for their use in analyses of evolutionary, historical and spatial patterns of species diversity. The method is implemented as an upcoming R package nodiv, which makes it accessible and easy to use.

Introduction

It has long been recognized that evolutionary and ecological processes interact to generate patterns of species diversity (Wallace 1876). The recent explosion of data on species distributions and phylogenetic relationships has made it possible to study these processes quantitatively and has led to the development of new analytical techniques. Studies integrating species distributions and phylogenetic relationships have used two distinct approaches: site‐based approaches, which use phylogenies to answer questions about how the species of communities are related to each other; and clade‐based approaches, which compare the spatial distributions of individual clades. Although using the same data, the two approaches focus on distinct sets of questions and have largely separate literatures.

Site‐based metrics quantify spatial variation in the relatedness of co‐occurring species and include measures of community phylogenetic structure (e.g. the net relatedness index (NRI), Webb et al. 2002), phylogenetic diversity (Faith 1994) and phylogenetic beta‐diversity (Graham & Fine 2008). The basic approach is to calculate a summary metric for all species within each site, describing the phylogenetic relatedness of the species, using for example, the amount of shared branch length or the average phylogenetic distance among species. These metrics have been interpreted in the context of factors such as local competitive exclusion and habitat specialization. Clade‐based approaches focus on comparing specific clades by quantifying spatial overlap between sister clades. These analyses are usually undertaken at larger scales and have been used to answer questions about the importance of allopatry in the process of speciation (Barraclough & Vogler 2000; Fitzpatrick & Turelli 2006).

Both approaches have become widely used in evolutionary ecology. However, concerns have been raised that the apparent simplicity of site‐based metrics such as NRI, which derives from reducing the complexity of relationships across an entire phylogeny to a single, seemingly interpretable value (Webb, Ackerly & Kembel 2008), may in fact obscure the underlying complexity of processes and may thus be misleading. For instance, Parra, McGuire & Graham (2010) demonstrated that some assemblages with neutral NRI values, ostensibly indicating phylogenetically random community assembly, were composed of a mosaic of closely related and distantly related species. This suggests an alternative interpretation, namely that opposing processes of phylogenetic exclusion and filtering take place at different phylogenetic scales. As a solution, they proposed a null model approach using the nodesig algorithm from the software Phylocom, which compares the species richness of each node to that expected from randomly drawing species from the phylogeny (Webb, Ackerly & Kembel 2008). Parra, McGuire & Graham (2010) used nodesig to analyse a phylogeny of hummingbirds from local assemblages in Ecuador and demonstrated a complex spatial pattern of clade overrepresentation. Further analysis showed that sites with overrepresentation of specific clades were spatially and environmentally segregated, indicating that environmental adaptations or isolation of certain clades are responsible for the spatial distribution of species within the group.

Here, we develop a measure of clade overrepresentation that we term the ‘specific overrepresentation score’ (SOS), which combines the clade‐based and site‐based approaches. This measure is related to the metric of Parra, McGuire & Graham (2010), but takes a clade‐based approach by comparing the species richness of sister clades, rather than comparing each clade to the total phylogeny. This means that the SOS is unaffected by how the phylogeny is delimited, that is, a hummingbird clade has the same SOS value in a study of all birds and a study comprising only hummingbirds. The algorithm goes through each node, corresponding to a pair of sister clades in the phylogeny, and compares the species richness of the two clades in each community to the expectation from a null model. The result is a matrix of SOS values for each combination of nodes and communities. These values can be mapped geographically for each node, offering a visual representation of the degree of distributional divergence among sister clades.

All SOS values calculated for a certain node can be summarized across occupied sites to yield the ‘geographic node divergence’ (GND), which quantifies the distributional divergence between the two daughter lineages descending from a given node. The GND score thus identifies which nodes are responsible for observed patterns of phylogenetic structure and species co‐occurrence. Contrasting the nodes identified using GND with those identified by macroevolutionary analyses could provide insight into factors structuring diversity patterns. For instance, comparison of the nodes identified by GND with those where there are changes in diversification rate, or in trait evolution, may facilitate the exploration of the geographic and environmental context of morphological innovations (Parra, McGuire & Graham 2010; Beaulieu et al. 2012). In addition, if a time tree is available, analyses based on GND permit the exploration of relationships between nodes of interest and events in earth and/or climate history. We suggest that the GND metric provides a statistically tractable basis for a unified understanding of the historical mechanisms influencing extant patterns of biological diversity.

To exemplify the approach, we calculate SOS and GND scores for two well‐studied groups of Neotropical birds, each of which has a different scale of spatial resolution. We show how the GND scores highlight nodes that identify evolutionary divergences associated with distributional separation. We also show how mapping SOS values may serve as a basis for further analysis of the biogeography of the group. Finally, we demonstrate how the method can be extended to environmental space, providing a useful tool for exploring the evolution of environmental associations within a clade. Our goal is to use these case studies to demonstrate the method, rather than to provide an extensive account of the biogeographic history of the groups analysed.

Materials and methods

Calculating SOS

The SOS corresponding to a given node in a given site is calculated by comparing the species richness of each daughter clade to random assemblages created by a null model (Fig. 1). Null assemblages are created by extracting all species descending from the focal node and then randomizing their occurrences among all occupied sites. This procedure maintains the richness pattern of the focal node, but randomizes the relative distributions of its two daughter clades.

Figure 1

Calculating the SOS value for one community. The example shows the calculation of specific overrepresentation scores (SOS) for a clade with eight species in the focal community. The two descendant clades have three (shown as white dots) and five species (shown as black dots) in the community. A number of random communities are simulated, creating a distribution of richness values for each descendant clade. From this distribution, two metrics are identified: r, which is the rank of the empirical community in the distribution; and SOS, which is the distance between the empirical richness of a descendant and the simulated mean richness in units of standard deviations.

To avoid biasing null communities by oversampling rare species, the null model must control for differences in species occupancy. The correct way of doing this has been vigorously debated (Gotelli & Graves 1996), but the current consensus is that the best method is random matrix swapping, which swaps occurrences randomly among species in the community matrix while maintaining the species richness of sites, and the range size of species, as constant properties (Gotelli 2000; Gotelli & Entsminger 2003). These swap algorithms remove any systematic pattern of species co‐occurrence, which makes them well suited for evaluating ecological or phylogenetic processes determining species co‐occurrence. However, the procedure is computationally intensive, even using efficient algorithms such as the ‘quasiswap’ algorithm (Miklós & Podani 2004), implemented as a C routine within the R (v 3·0) package ‘vegan’ (Oksanen et al. 2012) (v 2·0‐7).

Repeating the randomization procedure n times creates a distribution of expected richness values for each daughter clade. From this distribution, we can extract two metrics: SR and r (Figs 1 and 2). The SR of a daughter clade is calculated as the standardized residual (or standardized effect size) quantifying the distance between the empirical richness value (e) and the mean of the simulated richness values (s), divided by the standard deviation (σ) of s,

(eqn 1)

Figure 2

Calculating the GND score from multiple communities. (a) The species richness of two hypothetical sister clades, marked in blue and red; the expected species richness of each clade (+− SD) is shown as lines; (b) the value of SOS and r derived from the scenario shown in panel (a); (c) the distribution of P values, derived from the values of r; (d) the distribution of P values after logit transformation: the mean value α (−3·05) is shown, corresponding to a geographic node divergence (GND) value of 0·951 for this clade. The colours of the SOS line in panel (b) are identical to the colour scheme used in Figs 5 and 7.

Standardized residuals are widely used for summarizing null models of phylogenetic distance or trait spacing in community phylogenetics (e.g. NRI is calculated as a standardized residual, Webb et al. 2002), because they quantify the difference between empirical and simulated values in a metric that can be compared among samples with very different properties.

As the focal node is the union of its daughter nodes, the SR value distributions of the two daughter nodes are mirror images, and the distribution of SOS values for the focal node can be calculated as

(eqn 2)

where one SR value is positive and the other negative. These SOS values can be mapped for easy visualization. Positive SOS values in a given assemblage indicate that species from sister clade 1 predominate, whereas negative SOS values indicate predominance of the other sister clade. Values close to zero suggest that species from both descending clades are equally represented.

From the sample distribution, we also extract the metric r, which is the rank of the empirical species richness in the distribution of simulated values divided by the number of simulations. In a one‐sided randomization test, this metric may be interpreted directly as the statistical P‐value (e.g. Manley 1997). In our case, however, the test is two sided, which means that the P‐value should be estimated by a simple transformation:

(eqn 3)

This transformation gives the proportion of the simulated distribution that is more extreme than the empirical value.

Calculating GND

The geographic node divergence (GND) score summarizes the difference between the empirical and simulated co‐occurrence of the sister clades across all occupied sites. It thus highlights nodes where there is strong distributional divergence among the descendant clades. The GND is calculated from the mean of the log odds of P (i.e. logit P) at all sites. The mean of log odds is used because p values are bounded between 0 and 1, and often become highly skewed at values close to the boundaries, which means that a standard mean might not accurately portray the central tendency of the distribution (Fig. 2c,d). This is identical to the approach used for fitting logistic regression models with a logit‐link function. The equation to calculate GND is

(eqn 4)

where

(eqn 5)

and n is the number of simulations. The GND metric is bounded between 0 and 1, where high values indicate a small overlap and thus a high degree of distributional divergence among descendant clades. Because the GND score is calculated from a null model of species distribution, it contrasts the observed distributional divergence among sister clades to the divergence among species within each sister clade. This means that only nodes where the two descendant clades have distinct distributions and whose constituent species have high distributional overlap are highlighted.

SOS/GND scores in environmental space

The approach described here is based on species occurrences in geographic assemblages; however, the analysis can be extended to environmental variables. We do this by gridding the environmental space; that is, we divide the environmental variables into equal‐sized bins and tally the occurrences of species in each bin to form an environment‐by‐species matrix. The node‐based analysis can then be applied to the environment‐by‐species matrix, to calculate SOS and GND in environmental bins. This makes it possible to identify nodes where important changes in the occupancy of environmental conditions arise, as we demonstrate in the hummingbird case study below. By comparing the geographic node‐based analysis to the environmental node‐based analysis, it is also possible to determine whether geographic changes are associated with changes in environmental conditions.

The relationship between climate variables and SOS values can be modelled using regression analysis, which should be especially useful for evaluating the effect of larger numbers of independent climatic factors. Another approach for expanding the environmental analysis is to first fit an environmental niche model to each species and then apply the binning procedure to the modelled niches, as if they were continuous ranges (see e.g. Broennimann et al. 2012). This should create smoother relationships between climate variables and SOS and resolve the issue that bin sizes are arbitrary. Note, though, that the use of environmental niche models is debated and entails a number of important assumptions which complicates the analysis (Araújo & Guisan 2006).

Simulation study

We exemplify the approach and behaviour of the metrics using a pair of simulated sister clades. Each simulated clade consisted of S circular ranges, each with a radius of 15 grid cells (giving a geographic range size of ~479 grid cells). The midpoint of each range was placed randomly around the central point of the associated clade according to an uncorrelated bivariate normal distribution, where the variation of range placement was determined by the standard deviation, that is,

(eqn 6)

where X and Y are the coordinates of the central point of the clade, σ is the standard deviation, I is the identity matrix, and N₂ is the bivariate normal distribution. The standard deviation describes the overlap of ranges of species within the same sister clade. The simulation domain was 100 × 100 grid cells, large enough to ensure that no ranges came into contact with the domain edges.

To assess the sensitivity of the GND metric to clade divergence, we varied the distance between the central points of the two sister clades from 0 to 30, simulating clades at all values in the interval (0, 1, 2, … 30). The maximum distance of 30 grid cells corresponds to a very slight overlap between sister clades, at the given range radius of 15 units. To demonstrate the effect of the range overlap within each sister clade (controlled by the standard deviation, σ) and clade size (S), we reran the simulation at high and low values of these parameters. Within‐clade species overlap was simulated as standard deviation values of 2 and 10 grid cells, corresponding to very high and very low within‐clade overlap. Clade size was simulated using values of 10 and 100 species in each sister clade. Using 200 replicates for each parameter combination, this resulted in 24,800 individual simulation runs.

To achieve this high level of replication, we used the rdtable algorithm in R to create null communities. This algorithm is several orders of magnitude more efficient than the ‘quasiswap’, but can lead to slightly inaccurate results, in that rdtable may yield matrices with elements other than 0 and 1. This will create increased variation in simulated richness values and may lead to underestimation of absolute SOS values (i.e. the bias makes the test for divergence more conservative). To evaluate the size of this potential bias, we also conducted five replicates for 12 different parameter combinations using the quasiswap algorithm and compared the results.

Case study data sets

The interpretation of SOS and GND values depends to some extent on the spatial scale. At larger extents and grain sizes, the analysis mainly detects biogeographical events, such as movement among biomes or continents, whereas local community analysis can be interpreted in the context of metacommunity dynamics and phylogenetic changes of environmental preference, where clades move into and radiate (or persist) in new environments. To illustrate the potential applications of the method, we used two data sets that differ in spatial grain and extent: a large‐scale data set of gridded range maps for New World flycatchers, and a community data set of individual hummingbird assemblages in the Northern Andes.

The large‐scale data set consists of range maps of all species of New World flycatchers (family Tyrannidae in the traditional sense; now subdivided into several families, see Ohlson et al. 2013). The range maps were taken from the Copenhagen data base of bird distributions (originally collated by Rahbek & Graves 2001). This data base provides 1° × 1° resolution range maps of all birds of the world and is continuously updated. We extracted the data on the 26th of June 2012. Phylogenetic information for the 390 species of New World flycatchers was extracted from a supertree of all the world's birds (see Holt et al. 2012 for references), which incorporates a recently revised phylogeny of the Tyrannidae (Ohlson et al. 2013).

The second data set includes 219 hummingbird (Trochilidae) assemblages containing 126 species across Ecuador and Colombia. This data set was used in Graham et al. (2012), and 108 of the species were used in the analysis by Parra, McGuire & Graham (2010). See Graham et al. (2012) for details on the approach taken in compiling the data set. Our molecular phylogeny of hummingbirds included each of the 126 hummingbird species evaluated in this study and is described in Graham et al. (2009).

We also extracted the mean annual temperature and total annual precipitation at each locality in the hummingbird data set from Worldclim (Hijmans et al. 2005). The environmental data were grouped into bins of 2°C for temperature and 400 mm/year for precipitation. For simplicity, we used the raw locality climate data for this comparison, rather than fitting an environmental niche model. The size of the bins was chosen to ensure an even number of bins for temperature and precipitation, a high number of occurrences in each bin (range 0 to 40), and good compliance with the precision of the environmental variables (i.e. no bins should be completely empty along the entire axis of either temperature or precipitation).

R package ‘nodiv’

All codes and functions necessary to calculate GND and SOS scores are available in the R package ‘nodiv’, which should be available on GitHub and CRAN from October 2014. The package integrates with data formats from the existing and widely successful packages ‘ape’ and ‘picante’, and provides functions to calculate the scores, and to perform plots with maps of SOS values and phylogenies with GND scores, similar to the figures presented here.

Results

Simulations

In the simulations, GND values for most clades increased rapidly with increasing distance between the distributional centres of sister clades (Fig. 3). In the case of high standard deviation (8 units) and small species numbers (10 per sister clade), the GND increased only slowly, which is the expected behaviour of the metric: GND scores contrast the overlap of two clades to the overlap of ranges within each clade, and so GND scores are smaller when species within each sister clade have low distributional overlap. Standard deviations of 8–10 units are realistic: the standard deviation among sister clades of New World flycatchers range from 0 to 30 grid cells and vary with the number of species in clades (Fig. S1), notwithstanding that the empirical range sizes are mostly smaller than those in the simulated data set (Fig. S2). GND values greater than 0·65 were consistently associated only with clades that were clearly geographically divergent, and we suggest this value as a rule‐of‐thumb threshold for identifying interesting nodes in the phylogeny. The results based on the more computationally intensive quasiswap algorithm were broadly consistent with the results using rdtable (Fig. 3), indicating that the simulations give an accurate representation of the behaviour of GND.

Figure 3

GND values from simulated clades. The lines show the mean of 200 simulations at each combination of parameter values, and the shaded area indicates the standard deviation. The horizontal dashed line shows the suggested cut‐off of GND = 0·65 for identifying clades with little distributional overlap. The dots show individual sample runs using the more computationally intensive ‘quasiswap’ algorithm.

New World flycatchers

The New World flycatchers comprise a number of small clades and two species‐rich clades, the Rhynchocyclidae (consisting of the Pipromorphines, Todi Tyrants and allies) and Tyrannidae sensu strictu (Ohlson et al. 2013). The GND scores reveal that major distributional divergences are restricted to a relatively small number of nodes (Fig. 4). Here, we focus on six nodes in the phylogeny that exhibit GND scores above 0·65, corresponding to major distributional shifts in flycatcher assemblages (Figs 4 and 5). The nodes with the highest GND scores primarily occur along the lineage leading to the present‐day Fluvicolinae (Fig. 4). The most basal of these nodes (node A) corresponds to the split between the Rhynchocyclidae and the Tyrannidae. The spatial pattern of SOS values (Fig. 5a) illustrates the geography of this divergence, with the Rhynchocyclidae being over‐represented in the lowland rain forest biomes, whereas the Tyrannidae are widely distributed across all of South and North America. The second highlighted node splits the Elaenines, which are over‐represented in the Andean region and the open savanna of eastern South America, from the rest of the group (node B in Figs 4 and 5). The node with the highest GND score (C) separates the tyrant flycatchers (Tyrannidae) from the Fluvicolines. The tyrant flycatchers are primarily distributed in tropical lowland forests but extend to the surrounding savannas and southern North America; whereas the Fluvicolines inhabit colder and drier environments, and extend to the subarctic zones at the poleward tips of South and North America. Within the Fluvicolines, node D (Figs 4 and 5d) separates a small basal group of species, associated with the subtropical and upland savanna biomes characterizing the eastern and northern parts of South America, from the rest of the clade. The remaining Fluvicolines are split (at node E in Figs 4 and 5e) into a group that inhabit Andean cloud forest and woodlands and barren habitats in the southern cone of the continent and a second group of species associated with montane to boreal forest habitats distributed across the Central Andes and into North America. The final node exhibiting strong distributional change (F in Figs 4 and 5) is a relatively young node (below the genus level), which separates kingbirds (Tyrannus) occurring in South America from those in North America.

Figure 4

GND scores of New World flycatchers. The colour scale and symbol sizes are proportional to GND for each node, to highlight nodes with high GND values. Only fully resolved nodes where both descendant clades consist of at least two species are included in the analysis. Nodes labelled A‐F are referenced in the text and correspond to panels (a)–(f) in Fig. 5. Branch lengths are calculated for illustration using Grafen's (1989) method – the analysis itself does not rely on branch lengths. Many genera are unresolved and appear as polytomies on the phylogeny.

Figure 5

Spatial pattern of SOS values for six interesting nodes in the phylogeny of New World flycatchers, in 1° × 1° grid cells. Red colours indicate overrepresentation of one descendant clade; blue colours indicate overrepresentation of the other descendant clade; and pale yellow colours indicate that both descendants are equally represented. Panels (a)–(f) correspond to the nodes labelled a to f in Fig. 4.

Hummingbird assemblages

Three nodes in the regional hummingbird phylogeny exhibit a high degree of node allopatry, indicating distributional segregation among the hummingbird assemblages of the northern Andes (Fig. 6a). These same three nodes feature prominently in the analyses based on environmental bins (Figs 6b and S3). The most basal of the nodes (Fig. 6a node A) represents the phylogenetic split between the hermits and all other hummingbird clades (except topazes, which are basal to the hermits). The geographic distribution of SOS values shows that this node corresponds to a distributional segregation between species assemblages in lowland Amazonia (dominated by hermits) and all other clades, which are broadly distributed across the region (Fig. 7a left).

Figure 6

GND scores for north Andean hummingbird communities, based on the geographical (a) and the environmental (b) analysis. For explanation, see the legend for Fig. 4.

Figure 7

Spatial and environmental patterns of focal nodes for north Andean hummingbirds. SOS values of sister clades in local hummingbirds communities (left column) and environmental bins (right column) of mean annual temperature vs annual precipitation. The colour legend is similar to Fig. 5, that is, red colours indicate overrepresentation of one descendant clade, blue colours overrepresentation of the other clade. Panels (a)–(c) correspond to the labelled nodes in Fig. 6.

For the environmental analysis, values of mean annual temperature were binned. This geographic result is mirrored by the environmental analysis, whereby hermits are confined to wet and warm regions, while all other clades occur across a broad range of environmental conditions (Figs 6b node A and 7a right). The node with highest node allopatry score in both the geographic (Fig. 6a node B) and environmental analyses (Fig. 6b node B) represents the split between the Andean high‐elevation brilliants and coquettes, and the mangoes, bees and emeralds (Fig. 7b left). Brilliants and coquettes have radiated within the Andes (Bleiweiss 1998a, b; McGuire et al. 2007) and occupy environmental conditions of cold temperatures (i.e. high elevation) and intermediate levels of precipitation, while the mangoes, bees and emeralds occur in mid‐ and low‐ elevation sites that are warmer but have varied precipitation conditions (Fig. 7b right). The final highlighted node (C in Fig. 6) represents a split within the coquettes and separates high and mid‐elevation species within the Andes (Fig. 7c left and right).

Discussion

Here, we show that the SOS/GND approach has the potential to be a powerful tool for integrating phylogenetic and spatial information into a statistically tractable framework. The GND identifies key locations within a phylogeny where clades differ in their geographic distribution or environmental associations. GND scores are comparable among nodes in a phylogeny, and between different phylogenies, making it possible to estimate the timing and prevalence of major distributional shifts. Furthermore, maps of SOS depict the geographic context of a given shift and together with the environmental analysis yield insight into the congruence between geographic and environmental divergences in the phylogeny. Because of these characteristics, the approach should afford a more complete understanding of the phylogenetic structure of assemblages than that offered by whole‐tree phylogenetic indices commonly used in community phylogenetics (cf. Parra, McGuire & Graham 2010).

The SOS/GND approach complements several related approaches that attempt to explicitly connect evolutionary patterns within phylogenies with spatial patterns across regions or assemblages (e.g. Leibold, Economo & Peres‐Neto 2010). For instance, ancestral area analysis aims to use present‐day distributions to model the likely distributional history of a clade (Ree et al. 2005). In contrast, the GND score is simply a metric to quantify the degree of distributional divergence among sister clades. As such, GND does not require the geographical distributions of species to be defined a priori as distinct allopatric units. This allows the use of this technique for groups such as the Tyrannidae where clades are partially sympatric. Also, the philosophical underpinnings of the techniques are quite different: ancestral area reconstruction models geographical distribution as a trait that evolves at a certain rate across the phylogeny. This implicitly assumes that range dynamics are slow enough to be modelled as evolutionary traits, and that the ancestral distribution of clades must have been within the current distributional range. This property makes the ancestral area reconstruction method inapplicable for, for example, local community or metacommunity data, and it is, possibly, also unrealistic for analysing continental‐scale range dynamics. The approach presented here is also distinct from traditional clade‐based comparisons, such as the metric for node overlap developed by Barraclough & Vogler (2000), in explicitly linking the pattern to community patterns, and in taking a probabilistic approach. Thus, the SOS/GND method not only computes the distributional overlap between clades, but also controls for the number of co‐occurring species, and for the degree of distributional overlap within clades.

The usefulness of our approach is demonstrated by our two case studies. For the New World flycatchers, the analysis reveals that the current pattern of species distributions is the result of major distributional divergences at a relatively small number of nodes. Most nodes with high GND scores are basal in the phylogeny and correspond to the division between large taxonomic groups of Tyrannidae, which likely diversified in the late Oligocene to mid‐Miocene (Ohlson et al. 2013). Three general patterns characterize the highlighted nodes. The clearest pattern is one of splits between clades over‐represented in wet and warm tropical environments (Amazonia, Central America and the Atlantic forest of Brazil) and clades over‐represented in seasonal environments with open forest structures (Fig. 5a and c). Two other characteristic patterns are splits between clades over‐represented in the lowlands versus the Andes (Fig. 5b–e) and splits between clades over‐represented in North vs. South America (Fig. 5e and f). These results are consistent with the hypothesis that distributional shifts into novel habitats have been followed by local in‐situ radiations, as suggested by Ohlson, Fjeldså & Ericson (2008). Importantly, our analyses provide an objective statistical basis for identifying the nodes where particularly large changes in distribution patterns occurred.

The community‐scale analysis of hummingbirds also identifies relatively few nodes associated with large geographic shifts. There are three nodes associated with clades crossing the transition between high‐elevation and low‐elevation zones, a phenomenon that occurs in many avian lineages (Ribas et al. 2007; Sedano & Burns 2010; Chaves, Weir & Smith 2011). The environmental analysis identifies most of the same nodes, indicating that adaptations to new environments may have led to subsequent radiation in the topographically complex Andean mountains (García‐Moreno, Arctander & Fjeldså 1999; Weir 2006; Fjeldså & Irestedt 2009). This process is demonstrated by the inferred movement of Brilliants and Coquettes into the Andes, a feature of our analysis which is consistent with several lines of evidence that these groups colonized montane environments and diversified in these regions (Bleiweiss 1998a, b). Mangos, whose origin cannot be confidently attributed to either the lowlands or highlands (McGuire et al. 2007), also show a distributional and environmental shift where one clade of mangos seems to have moved into high elevations. Again, these results are in accordance with existing knowledge on biogeographic patterns of hummingbird distribution (Bleiweiss 1998a, b; McGuire et al. 2007; Graham et al. 2009), but advance our understanding by characterizing these phenomena within a transparent statistical framework.

While the patterns found for hummingbirds in this study are consistent with the findings of Parra, McGuire & Graham (2010), there are a number of important differences. Parra, McGuire & Graham (2010) simply identified patterns of over‐representation, whereas we defined specific overrepresentation scores (SOS) that are comparable across analyses and standardized for species richness and geographic occupancy. We also calculated GND scores, allowing us to identify where significant distributional shifts occurred in the evolution of the clade.

Parra, McGuire & Graham (2010) identified 21 significantly over‐represented nodes, many of which were nested in the phylogeny and corresponded to the same geographic sites. The explanation for this pattern is that the algorithm used by Parra, McGuire & Graham (2010) compares the species richness pattern of a node to that of the basal node of the phylogeny used in a given study (Webb, Ackerly & Kembel 2008). With their approach, all nodes that are over‐represented with respect to the basal node will be highlighted, which means that daughter nodes of over‐represented nodes will also tend to be over‐represented. This makes it difficult to identify which nodes are associated with major distributional changes. For instance, a single distributional change, such as a long‐distance dispersal event, may lead to a pattern where all nodes descending from that node will come out as over‐represented; and possibly also some nodes that are ancestral to the one associated with the event. Instead, by contrasting the reference node to its two descendant nodes, the approach presented here can identify the exact node(s) responsible for shifts among geographic regions. The GND scores identify far fewer nodes as over‐represented and can quantify the degree of distributional change at these nodes. One limitation, however, is that nodes that have a single species as one of the descendent nodes cannot be considered.

Whereas Parra, McGuire & Graham (2010) analysed environmental linkages by analyses of environmental conditions for assemblages where nodes were significantly over‐represented, we directly evaluated if nodes were over‐represented in certain environmental conditions. In most cases, our results indicate that geographical shifts were also accompanied by environmental shifts, which might indicate that adaptation to new environments allowed clades to colonize new areas. Generally, comparing geographic and environmental shifts may provide insight into the roles of vicariance events, long‐distance dispersal and adaptive radiation in shaping the biogeographical distribution of clades.

Node‐based methods, in common with most methods in community phylogenetics, rely on appropriate null models (Gotelli & Graves 1996). The choice of null model defines the scientific questions being asked and the processes that are tested by the analysis. The null models employed here are tuned to the question: for each node in the phylogeny, how much stronger is the tendency for species from each of the two descendant clades to co‐occur than expected by chance? Using this null model, we avoid problems associated with tree size, dependence on the basal node and differences in species occupancy that are common to many measures in community phylogenetics.

The interpretation of GND depends, to some extent, on the geographic extent of the study and the grain of the species occurrence data. At the local assemblage scale, high GND scores can be related to changes in environmental preferences, where clades move into and radiate (or persist) in new environments. At larger extents and grain sizes, the analysis mainly detects biogeographical events, such as movement among biomes or continents. However, nodes with low GND may reflect environmental adaptations, even at large scales, as demonstrated here for the divisions between tropical and temperate clades of New World flycatchers. Note that this method does not assume stasis of geographical ranges or environmental conditions over deep time. As the GND is a correlative measure, a high value simply means that the two sister clades are presently more segregated in geographical or environmental space than expected by chance. One interpretation of this segregation is that evolutionary change along one of the branches has altered the environmental associations of the group.

The approach presented here provides a basis for more detailed studies on the geographical and environmental context of macroevolutionary patterns, thereby facilitating the link between macroecological site‐based approaches and macro‐evolutionary clade‐based approaches to the study of patterns of species distribution. Currently, most macroecological and community phylogenetic approaches quantify spatial variation in the relatedness of co‐occurring species (Rahbek & Graves 2001; Webb et al. 2002; Fjeldså and Rahbek 2006; Hawkins and DeVries 2009; Fritz and Rahbek 2012; Jetz and Fine 2012), but generally do not identify which specific lineages are responsible for these spatial patterns. Evolutionary studies use phylogenies to evaluate which lineages evolve to occupy different geographic regions, but rarely relate these evolutionary patterns to geographic patterns of species co‐occurrence (Derryberry et al. 2011; Schnitzler et al. 2012). We hope that the approach developed herein will facilitate future integration across these disciplines.

Acknowledgements

We thank Jonathan Kennedy, Susanne A. Fritz, Robb Brumfield, Cam Webb and Matthew Helmus for insightful comments on an earlier version of the manuscript. MKB is supported by a postdoctoral grant from the Danish Councils for Independent Research. CR and JF acknowledge the Danish National Research Foundation for support of the Center for Macroecology, Evolution and Climate.

Data accessibility

The nodiv package is available from CRAN, for R ≥ 3.1.