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Keywords:

  • Carnivora;
  • Hellinger distances;
  • Mantel test;
  • MAXENT;
  • niche conservatism;
  • phylogenetic non-stationarity

ABSTRACT

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. INNOVATION
  5. RESULTS
  6. DISCUSSION
  7. ACKNOWLEDGEMENTS
  8. REFERENCES
  9. BIOSKETCH

Aim  Despite the importance of the niche concept in ecological and evolutionary theory, there are still many discussions about its definition and operational evaluation, especially when dealing with niche divergence and conservatism in an explicit phylogenetic context. Here we evaluate patterns of niche evolution in 67 New World Carnivora species, measured using Hellinger distances based on MAXENT models of species distribution. We show how inferences on niche conservatism or divergence depend on the way phylogenetic patterns are analysed using matrix comparison techniques.

Innovation  Initially we used the simplest approach of Mantel tests to compare Hellinger distances (N) derived from MAXENT and phylogenetic distances (P) among species. Then we extended the Mantel test to generate a multivariate correlogram, in which phylogenetic patterns are analysed at multiple levels in the phylogeny and can reveal nonlinearity in the relationship between divergence and time. Finally, we proposed a new approach to generate ‘local’ (or ‘specific’) leverages of components for Mantel correlation, evaluating the non-stationarity in the relationship between N and P for each species. This new approach was used to show if some lineages are more prone to niche shift or conservatism than others.

Main conclusions  Standard Mantel tests indicated a poor correspondence between N and P matrices, discarding the idea of niche conservatism for Carnivora, but the correlogram supports that closely related species tend to be more similar than expected by chance. Moreover, the variance among Hellinger distances between pairs of closely phylogenetically related species is much larger than for the entire clade. Phylogenetic non-stationarity analysis shows that in some Carnivora families the niche tends to divergence (Mustelidae and Canidae), whereas in others it tends to conservatism (Procyonidae and Mustelidae) at short phylogenetic distances. Our analyses clearly show that misleading results may appear if niche divergence is analysed only by simple matrix correlations not taking into account complex patterns of phylogenetic nonlinearity and non-stationarity.


INTRODUCTION

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. INNOVATION
  5. RESULTS
  6. DISCUSSION
  7. ACKNOWLEDGEMENTS
  8. REFERENCES
  9. BIOSKETCH

The ecological niche is one of the central concepts in ecological and evolutionary theory, even though there are still discussions about its definition and operational evaluation (Araújo & Guisan, 2006; Soberón, 2007; Warren et al., 2008; Colwell & Rangel, 2009; Ricklefs, 2010). Although its role in structuring ecological communities and explaining patterns of species co-occurrences has been recognized for a long time in classical ecological theory (see Chase & Leibold, 2003), only recently have broad-scale patterns of niche dynamics in space and time become a major topic in macroecological analyses. One of the main underlying issues is to what extent macroecological patterns can be explained by species niche dynamics throughout evolutionary time (see Wiens & Graham, 2005; Losos, 2008a; Pearman et al., 2008 for recent reviews).

Niche conservatism is the idea that a species' niche remains constant, or changes very little, during evolution and after speciation processes (or even causes the speciation, as suggested by Wiens, 2004). The evaluation of niche conservatism is important because it is now an important component of models developed to understand many ecological phenomena at different space–time scales, including trait evolution allowing or constraining the coexistence of species in local assemblages (Webb et al., 2002; Ackerly, 2003; Ackerly et al., 2006; Kraft et al., 2007; Swenson & Enquist, 2009), current patterns of species distribution and range dynamics after the Pleistocene (Peterson et al., 1999; Martínez-Meyer et al., 2004; Martínez-Meyer & Peterson, 2006; Nogués-Bravo, 2009), patterns of biological invasion (Peterson, 2003; Peterson & Nakazawa, 2008; Rödder & Lötters, 2009; but see Broennimann et al., 2007), species responses to global climatic change, both in geographic distribution and adaptive traits (Peterson et al., 2002; Araújo & Guisan, 2006; Diniz-Filho & Bini, 2008), geographical modes of speciation (Graham et al., 2004; Wiens, 2004; see also Rangel et al., 2007) and broad-scale gradients in species richness (see Wiens & Donoghue, 2004; Wiens et al., 2006; Diniz-Filho et al., 2007; Hawkins et al., 2007; Rangel et al., 2007; Laanisto et al., 2008; Pyron & Burbrink, 2009).

In a recent review Losos (2008a) pointed out that niche conservatism must be properly measured and not assumed a priori when trying to understand the patterns and processes described above (see also Wiens, 2008; Losos, 2008b). Niche conservatism and divergence among species can be evaluated using a variety of approaches, by comparing distributional patterns or by evaluating phylogenetic patterns in species traits that may be directly linked with niches (i.e. surrogate traits for niche divergence), such as physiological traits or morphological structures related to resource acquisition (Ackerly, 2004; Kraft et al., 2007; see also Freckleton et al., 2002). In any case, it is important to recognize that because niche conservatism and niche divergence are frequently based on comparing different species or taxa, all these analyses must be performed within an explicit phylogenetic framework (see Verbruggen et al., 2009).

Adding an explicit phylogenetic component to niche differentiation analyses leads to a series of conceptual and methodological problems that have long been known in comparative analyses (see Freckleton, 2009, for a recent review). For instance, as pointed out by Losos (2008a), significant phylogenetic patterns in niche surrogates among species do not necessarily provide evidence for niche conservatism. It has been recognized that, under pure stochastic (neutral) processes of species divergence, phenotypic traits or species niches would diverge, forming a linear relationship with phylogenetic distances and resulting in a very strong phylogenetic signal (Hansen & Martins, 1996; Diniz-Filho, 2001; Blomberg & Garland, 2002; Revell et al., 2008). Thus, conservatism of ecological niches throughout evolutionary time should be better established if species diverge less in niche space than what is expected by a purely stochastic process, usually modelled under a Brownian motion process (Felsenstein, 1988; Hansen & Martins, 1996; Revell et al., 2008; Verbruggen et al., 2009). There are several ways to evaluate whether a quantitative trait variation among species fits to a Brownian motion pattern (see Freckleton et al., 2002; Ackerly et al., 2006; Revell et al., 2008). Therefore, establishing the existence of niche conservatism, in this context, would be straightforward.

On the other hand, it is also important to note that the absence of phylogenetic patterns (implying a lack of phylogenetic niche conservatism according to Losos, 2008a) cannot be interpreted in a simple way. When using a comparative approach, the phylogenetic structure is usually expressed by pairwise distances or by a general phylogeny (used to calculate pairwise contrasts, for example), so that it may be difficult to obtain information on the timing and distribution of niche changes in a clade (Pearman et al., 2008). Some techniques, including phylogenetic correlograms, nested analysis of variance (ANOVA) designs and more specific metrics, such as the recent divergence order test (DOT) index from Ackerly et al. (2006), have been proposed to deal with this problem and thus can reveal at which hierarchical level a trait variation (expressing niche divergence, for instance) occurs. However, these approaches do not allow for the detection of groups of species within a larger clade that suffered niche stasis or that shifted more than others and with which ecological or life-history traits are potentially related to these processes, because all comparative methods implicitly assume phylogenetic stationarity (i.e. that parameters driving evolutionary changes are constant throughout the phylogeny). Mixing these groups into a single analysis can hide patterns that are expected from niche shift or conservatism in particular subclades and can lead to incorrect conclusions about the evolutionary dynamics of traits and the ecological niche. To our knowledge, no methods have been proposed to analytically deal with this problem, although testing for heterogeneity of variance in comparative methods such as the nested ANOVA could be useful in detecting the problem (see Harvey & Pagel, 1991).

Several comparative analysis tools can be used when patterns in niche shift and conservatism are evaluated using surrogate traits. However, when niche differences among species are expressed in a pairwise matrix containing distances in multivariate trait space or in some measure of overlap of species distribution in ecological or geographical space, fewer options are available. In this case, the most common approach has been to compare species divergence and phylogenetic distances using the Mantel test and related randomization approaches (e.g. Losos et al., 2003; Harmon et al., 2005; Böhning-Gaese et al., 2003, 2006; Knouft et al., 2006; Warren et al., 2008). In this case, the phylogenetic structure is usually expressed by a single matrix, and thus a single correlation coefficient is calculated, so that it may be difficult to get information on the timing and distribution of niche changes in a clade (Pearman et al., 2008). Moreover, a single correlation coefficient does not allow for the detection of groups of species within a larger clade that suffered niche stasis or that shifted more than the others and with which ecological or life-history traits are potentially related to these processes.

Here, we evaluate patterns of niche evolution and conservatism in New World terrestrial Carnivora (Mammalia) species and show how to apply the general Mantel test of matrix correspondence to overcome the two problems pointed out by Pearman et al. (2008; see also Losos, 2008a) and already solved (in part) by other comparative methods based on surrogate traits. First, we compared the niche similarity in geographical space (measured by similarity of MAXENT geographical projections of broad-scale environmental components, thus being the Eltonian component of ecological niche; see Soberón, 2007) and phylogenetic distances using a standard Mantel test, to test whether there is a correlation among these metrics. We then extended this approach by using a Mantel correlogram to evaluate how niche similarity changes at multiple phylogenetic levels (time steps), accounting for potential nonlinearity in the relationship. Furthermore, we present a new approach to partition the Mantel correlation into ‘local’ (specific) components, so that we can measure how each individual species contributes to the global Mantel statistics. Using this new approach allows us to evaluate whether there are different groups of species within Carnivora that are more prone to niche shift or conservatism (phylogenetic non-stationarity) and how this disturbs a general phylogenetic analysis of niche differentiation among species. These expansions to the Mantel tests were proposed to deal with non-stationarity problems when niche differences are expressed as a pairwise similarity between species, as usually happens in the context of species distribution modelling. Nonetheless, the overall reasoning for dealing with the phylogenetic non-stationarity discussed herein, based on ‘local’ autocorrelation statistics, can be extended to any form of comparative analysis.

INNOVATION

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. INNOVATION
  5. RESULTS
  6. DISCUSSION
  7. ACKNOWLEDGEMENTS
  8. REFERENCES
  9. BIOSKETCH

Data and species distribution modelling

The first step of our analysis involved modelling the ecological niches of 67 New World carnivore species (Carnivora, Mammalia), employing the maximum entropy method (MAXENT; Phillips et al., 2006). Occurrence data were obtained from online databases – SpeciesLink (http://splink.cria.org.br/), Animal Diversity Web (http://animaldiversity.ummz.umich.edu/site/index.html), Museum of Vertebrate Zoology (http://mvz.berkeley.edu/), Global Biodiversity Information Facility Data Portal (GBIF, http://www.gbif.org/) and the Mammal Networked Information System (http://manisnet.org/) – and from Redford & Eisenberg (1992, 1999) and Wilson & Reeder (2005). A total of 14,618 sampling points were obtained for all species, ranging from 5 to 1109 records per species, with a median value of 107 occurrences per species.

For the ecological niche modelling, we used six climatic variables: annual mean temperature, temperature seasonality (coefficient of variation), mean temperature of driest quarter, annual precipitation, precipitation seasonality (coefficient of variation) and precipitation of warmest quarter. These variables were derived from the WorldClim interpolated map database. Three topographic variables (altitude, aspect and slope) were also used, derived from the US Geological Survey's Hydro-1K data set.

The suitability vectors (one for each species) generated by MAXENT were rasterized for a grid with 4187 cells of 1° latitude and longitude covering the New World. The MAXENT iterative algorithm was run for 1000 rounds or until the change in the objective function on a single round fell below 10−5. For the regularization parameter (β), we used a value of 1.0 (see Phillips et al., 2006). MAXENT is now one of the most popular techniques for species distribution modelling and niche modelling, showing very good statistical performance (Elith et al., 2006). Although there are discussions about the ecological meaning of this high fit and even about which metrics should be used (see Lobo et al., 2008), the potential overfitting problem of MAXENT is not totally undesired in our analyses because it minimizes the differences between niche divergence among species in ecological (E-) space and the geographic (G-) space projection (recently referred to by Colwell & Rangel, 2009, as Hutchinson's duality; see the Discussion).

We measured niche similarity by calculating pairwise Hellinger distances between species, which are Euclidean distances between square-root transformations of suitabilities (probabilities of occurrence) across cells (see Warren et al., 2008). These Hellinger distances vary between 0 (complete niche similarity) and 2.0 (maximum divergence).

Multivariate phylogenetic autocorrelation analysis

Phylogenetic autocorrelation analysis is usually performed using correlograms based on Moran's I (Gittleman & Kot, 1990; Diniz-Filho, 2001; Lockwood et al., 2002; Pavoine et al., 2008), which tests whether closely related species tend to be similar or dissimilar for a given trait and how this changes with increasing phylogenetic distances. However, in our analysis, the niche is not expressed as a species level ‘surrogate trait’ but rather as pairwise Hellinger distances measuring the similarity of species niche models (suitabilities from MAXENT) projected into geographical space. Thus, the simplest approach to deal with this is by means of Mantel tests of matrix correspondence, as done in many papers dealing with niche conservatism and evolution based on multidimensional ecological data (e.g. Losos et al., 2003; Böhning-Gaese et al., 2003, 2006; Knouft et al., 2006).

In this context, the Mantel Z-statistics is given by the Hadamard product between phylogenetic (P) and niche (N) pairwise distances among species, so that

  • image

and the statistical significance of Z can be established by randomization of one of the matrices (Manly, 1998; see below). When standardized, this Z-value becomes a Pearson correlation between matrices, and thus the Mantel test can be viewed as a way to test the statistical significance of matrix correlation, avoiding problems involving the lack of independence created by the interdependence of elements from the similarity matrix in hyperspace.

For the analysis with the 67 New World Carnivora species, we defined the P matrix based on the supertrees of Bininda-Emonds et al. (1999; see also Bininda-Emonds et al., 2007) (see Fig. 1) and defined divergence among species in millions of years since the most recent common ancestor. Other phylogenies for some particular groups of Carnivora were derived after publication of the supertree (e.g. Johnson et al., 2006) from Bininda-Emonds et al. (1999), but we still used the original supertree because it provides a complete phylogeny for all species analysed herein. Incorporating these new phylogenies would actually require rebuilding the supertree, which is clearly beyond the scope of this paper. In addition, although New World Carnivora is not a monophyletic group, pairwise phylogenetic distances (rather than number of nodes) can be safely used to measure the overall patterns in niche distances among species (at least as geographically expressed in the New World). Even if phylogenetically structured patterns of relationship between E-space and G-space exist, the lack of other species is not expected to bias our analyses because the pairwise evolutionary distances are calculated independently of these gaps.

image

Figure 1. Phylogenetic tree of 67 New World Carnivora species derived from Bininda-Emonds et al. (1999). The pie charts represent the proportion of species in each family for which the divergence of niches is greater or less than the average global phylogenetic divergence measured as Hellinger distances. These proportions were built based on the division of the full vector of local Mantel's Z-values in three classes, so that low and high values roughly represent niche conservatism (light grey) and divergence (black), respectively.

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Beyond calculating a single Mantel Z-value, it is possible to generalize this to a multivariate correlogram (Oden & Sokal, 1986) by comparing the N matrix with several connectivity matrices P1, P2, P3. . . Pk, obtained by partitioning the pairwise phylogenetic distances into classes (i.e. evolutionary time steps) and assigning a value of 1.0 if the pair i,j of species in Pk is within the class and zero elsewhere. In this case, the plot of Mantel statistics against phylogenetic distance class defines a correlogram, which under a stochastic process of neutral divergence such as Brownian motion tends to generate a linear relationship between Z-values and phylogenetic distances (see Diniz-Filho, 2001). For the correlogram, we broke the P-matrix into several Pk matrices based on the supertree from Bininda-Emonds et al. (1999), using 11 time slices separated by 5 million years.

Notice that, in a phylogenetic Mantel correlogram, each Z-value is actually the sum of niche distances within a phylogenetic distance class because P becomes a discrete 0 or 1 matrix. Dividing this Z-value by the number of comparisons in a phylogenetic distance class gives the mean Hellinger distance between species within the same class. Therefore, the test of this Z-value by permutation is actually checking whether the pairwise niche distances within a phylogenetic distance class are more similar than expected by chance alone, with respect to all pairs of niche distances among non-connected species at that phylogenetic distance class. Using this same information, we can calculate the mean and variances of these distances, a plot of which will show explicitly how niche distances are related to phylogeny in different time steps.

Phylogenetic non-stationarity

When calculating the Mantel Z-values, one can actually evaluate if they are smaller than a random sample of niche distances (see below). However, this Mantel value is calculated by comparing all species that diverged recently across the entire phylogeny, which can be characterized as a ‘global’ metric of divergence at a given distance in time. Suppose that in one of the clades that comprise this phylogeny, niches are quite conserved (such that distances are very similar among closely related species), while in another clade they are very different because those species are colonizing a new region and are quickly adapting to new environments (with strong niche shifts). In this case, the ‘global’Z-value will actually express the mean of the divergence within these two clades, which will tend to cancel each other and provide a mean that is similar to randomized distances. In reality, this constancy of processes among clades (i.e. the phylogenetic stationarity) is a hidden assumption in all comparative methods, but its validity is rarely questioned or discussed. Thus, especially when no significant phylogenetic patterns are observed in a ‘global analysis’, it is actually necessary to evaluate how each species contributes to this global metric. This can be used to disentangle different processes that are happening in different ‘parts’ (i.e. clades) of the phylogeny.

Sokal et al. (1998) proposed, in a spatial context, that non-stationarity should be measured using a ‘local’ version of autocorrelation coefficients, such as Moran's I and Geary's c. (Anselin, 1995). For example, recall that Moran's I is given by

  • image

where yi and yj are the values of a given variable in different sampling locations or species (i and j), n is the sample size and W is the total number of connected pairs within the distance class. All autocorrelation indices have their ‘local’ counterparts, and thus the local Moran's I is given by

  • image

where Ii is the Moran's I for each spatial unity or species, given by the sum of lines of the cross-product matrix used to calculate Moran's I. Consequently, the sum of local Moran's I-values across units gives the overall Moran's I (this is one of the required properties of local statistics; see Anselin, 1995).

If a researcher is dealing with non-stationarity in niche divergence using a surrogate trait, the local Moran's I defined above can be applied as it stands. However, to deal with niche divergence based on pairwise distances, it is possible to extend the reasoning of the local Moran's I and to define a local Mantel's Z. This would be given by the average niche distance from each species (the ‘focal’ species) to all other species in the phylogeny to which this focal species is connected at a given phylogenetic distance class. Because the main discussion on niche conservatism appears among closely related species (see Results below), it would be necessary to calculate the local Mantel's Z for the first distance class, i.e. as an unweighted mean of the Hellinger distances between focal species and all other species linked to the focal species (whose mean common ancestor is at a phylogenetic distance smaller than 5 million years). However, in this case, because there are many species whose most recent common ancestor (MRCA) occurs beyond this first distance, the local Mantel's Z could only be calculated for 39 out of the 67 species analysed (with information losses for some important clades, such as some South American canid radiations). Thus, we have established the local Mantel's Z as a weighted mean of each focal species to all other species, where weights are given by the inverse of the phylogenetic distances between focal species and all other species. Thus, this local Z-value would be a phylogenetic analogue to a spatial correlation for each observation performed by geographically weighted regression (GWR) (see Fotheringham et al., 2002).

When the vector of the local Mantel's Z is obtained, it is possible to establish comparatively which focal species tend to diverge more (niche divergence) or less (niche conservatism) from the other species with respect to the phylogenetic distance. The statistical significance test for these local Z-values (assuming that this average distance to focal species is close to a random average of distances) can once again be established by randomization, as discussed above. However, because the expected Hellinger distance under neutral stochastic divergence is not theoretically established, it is difficult to decide if a given species' niche diverged more or less than expected and explicitly test Losos' (2008a) proposition. Even so, it is possible to test for phylogenetic non-stationarity by verifying if the local Z-values differ for different clades within Carnivora. We roughly divided the full vector of Z-values into three classes (in which classes with low and high values roughly represent niche conservatism and divergence, respectively) and established the frequency of species per family that falls within each class. We also calculated the mean local Mantel's Z among families using an ANOVA to evaluate if species in different families tend towards niche conservatism or niche divergence.

RESULTS

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. INNOVATION
  5. RESULTS
  6. DISCUSSION
  7. ACKNOWLEDGEMENTS
  8. REFERENCES
  9. BIOSKETCH

The niche divergence among the 67 New World Carnivora species, measured as pairwise Hellinger distances from MAXENT models (matrix N), varies between 0.186 and 1.414, with an average equal to 1.048 ± 0.297. The matrix N is poorly correlated with pairwise phylogenetic distances (r= 0.039; P= 0.166 with 1000 random permutations for Mantel's Z), suggesting that no phylogenetic patterns exist. The standardized Mantel's test (squared matrix correlation) shows that only 0.15% of the variance in Hellinger distances in N is explained by phylogeny in P and no clear patterns can be observed in the scatterplot (Fig. 2a).

image

Figure 2. Lack of correlation (standardized Mantel's Z= 0.039; P= 0.166) between the pairwise matrices of Hellinger distances (matrix N) and phylogenetic distances (matrix P in millions of years) for the 67 New World Carnivora species (a), and the pattern of variance of the average Hellinger distances ± SE (unstandardized Mantel's Z) at each evolutionary class (i.e. at each interval of 5 million years) (b).

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However, partitioning the phylogenetic distances into 11 classes and generating the Mantel's correlogram (in which Z-values are actually average pairwise distances within a phylogenetic distance class) makes it easier to demonstrate that pairwise average Hellinger distances are not constant across the phylogeny (Fig. 2b), although they do not evolve linearly with time. Among species that diverged before 5 Ma, the average niche distance was equal to 0.584 ± 0.497, which is much smaller than the global average among the analysed species. The average Hellinger distances tend to stabilize after 10 Ma for a value around 1.0, close to the global average. For the first distance class, the observed pairwise distances are smaller than those that would arise by chance (P= 0.001 based on 1000 bootstrapped samples), revealing a phylogenetic signal among species that evolved recently.

Even more importantly, the variance of distances among closely related species is higher than those for the other phylogenetic distance classes (Fig. 2b), indicating that niches among some pairs of closely related species may diverge but may also be conserved among others. Thus, deviations from the average expectation within a class should also be evaluated for the local Mantel's Z coefficients, which can indicate sets of species whose niches are conserved or not with respect to their ancestors. Local Mantel's Z-values show that the species in the five analysed Carnivora families (Mustelidae, Procyonidae, Ursidae, Canidae and Mustelidae) have significantly different patterns for niche divergence or conservatism (F= 5.07; P < 0.01; Fig. 3). When we analysed the patterns within families, we saw that, for Mustelidae and Canidae, about 50% of the focal species tend to diverge more than the other species in the group (niche divergence), whereas in Procyonidae and Felidae the opposite pattern appears (Fig. 1).

image

Figure 3. Pattern of variance of the weighted averaged Hellinger distances ± SE (local Mantel's Z) in each Carnivora family. ANOVA supports that families differ in the average local Mantel's Z (F= 5.07; P < 0.01).

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DISCUSSION

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. INNOVATION
  5. RESULTS
  6. DISCUSSION
  7. ACKNOWLEDGEMENTS
  8. REFERENCES
  9. BIOSKETCH

Our analyses do not show a direct relationship between niche divergence, measured as Hellinger distances based on MAXENT probabilities, and phylogeny. Thus, according to Losos (2008a), this lack of phylogenetic signal would be enough to rule out any process (or pattern) related to niche conservatism. However, further analyses of the relationship between N and multiple P matrices in a correlogram (and other extensions) reveal a more complex pattern.

When dividing the phylogenetic distances into intervals of 5 million years, we can observe that, in the first distance class, average Hellinger distances among connected species are significantly smaller than expected by chance (i.e. which approximates to the global average distances). Increasing phylogenetic distances will increase Hellinger distances up to approximately 1.0, stabilizing at this value after the second distance class, i.e. 10 million years, which is close to the global pairwise distance. Thus, this nonlinear profile of the Mantel's correlogram suggests three important additional pieces of information: (1) although a global Mantel test did not reveal a general phylogenetic pattern, species that are very close in the phylogeny tend to have more similar niches; (2) this pattern disappears when using the global Mantel test because it is restricted to very short distance classes and is counteracted by random differentiation at larger phylogenetic distances and, more importantly, because even at smaller classes some pairs of species are more dissimilar than others (the variances are significantly larger at these phylogenetic distances); and (3) the stabilization profile of the correlogram suggests that more complex non-Brownian processes are operating, because a more linear increase in Hellinger distances would be expected for a neutral differentiation of niches throughout the entire phylogeny (see Diniz-Filho, 2001).

Thus, a first improvement of our analyses with respect to the standard Mantel test that is commonly used in the analysis of niche conservatism is that correlograms show that patterns are not constant throughout the phylogeny. Therefore, niche conservatism and niche divergence are not expected to be entirely predictable when comparing all different pairs, or sets, of species. Our analyses indeed show that closely related species tend to have more similar niches and that the divergence tends to stabilize at large distances. This stabilization pattern could be associated with a more complex Ornstein–Uhlenbeck diffusion process (see Diniz-Filho, 2001), in which closely related species tend to diverge at random (following a Brownian expectation). However, after a given time, some form of constraint acts to generate boundaries for the divergence.

Based on this reasoning, we can establish that closely related species, although more similar than expected by chance, would be already diverging under a neutral expectation, and that processes operating at very large time-scales (i.e. constraints in life history or ecological patterns of the species) would tend to generate a conservatism of niches for the entire (Carnivora) clade. In this case, as pointed out by Losos (2008a), it would be necessary to test whether closely related species are diverging more or less than expected by neutral dynamics in niche space. Although it is not difficult to evaluate the fit of a quantitative trait to a Brownian motion model (see Verbruggen et al., 2009), at this time it is not straightforward to directly establish the neutral expectation for Hellinger distances.

Even so, the most important issue is to realize that although distances among closely related species are smaller than the overall distances and larger than neutral expectation, indicating a phylogenetic pattern in niche similarities (when compared to all species), the variance among pairs of species in the first distance class is also much higher. This indicates that different patterns of niche shift or conservatism may be occurring within different groups of closely related species, which can be comparatively established using local Mantel's Z.

Indeed, when analysing the Hellinger distances of each ‘focal’ species in relation to the other species in the clades, a phylogenetically structured pattern of niche divergence (i.e. phylogenetic non-stationarity) appears for groups of species. Based on our observations, the pattern of niche shift is more common in Mustelidae and Canidae, whereas Procyonidae and Felidae show the opposite pattern (see Fig. 1). Although it is not quantitatively possible to establish whether these Hellinger distances are really larger or smaller than neutral expectations, these differences in local Mantel coefficients are coherent with patterns of historical divergence and colonization patterns from North to South America during the great American interchange. Some canids adapted to the Neotropics and diversified after the colonization of South America, giving opportunity for niche shifts. However, after this a quick diversification occurred and some of the new species were restricted to and occupied, for example, savanna areas (such as Chrysocyon brachiurus). Some of the new species are always restricted to their past original environments, so it is clear that niches tend to be more conserved than for the overall Carnivora clade. A similar process has happened to the felids, although in this case the species tend to have much higher geographic ranges and then broader niches, so that it would be much more difficult to detect patterns even in Hellinger distances.

Methodologically, it is important to realize that we defined niche similarities here based on Hellinger distances, which leads to two important discussions. First, there would be other possibilities for establishing a pairwise similarity among species, including the direct measurement of distances among species centroids in environmental space (avoiding the need for using MAXENT or any other SDM). The problem with this approach is that, for large-ranged species, the centroid would converge with the centroid of the entire environmental space, and thus would create an intrinsic correlation between range size and centroid value [a ‘mid-domain’ effect in the environmental space (Colwell & Lees, 2000), that would be taken into account]. Moreover, metrics based on centroid distances do not take into account the variation in niche overlap (it is actually assumed that niche sizes would be equal and then distances would capture different ‘positions’ of species in environmental or niche space). Suppose, for example, that one species is completely nested within another but possesses a much narrower niche: in this case, their centroid distance will tend to zero despite clear differences in niche. Hellinger distances based on a continuous niche space, on the other hand, would explicitly account for parts of the E-space (which would be also reflected in G-space) that are not occupied by both species, and thus would not achieve a minimum value even if niches are completely nested within others (i.e. they would reveal that the niches are different).

The problems above could be resolved by adopting well-known metrics for niche overlap (see Krebs, 1998) or, when dealing with niche differences inferred by SDMs, it would be possible to establish a similarity among species by model overlap, in area or number of reciprocally estimated occurrences (see Martínez-Meyer & Peterson, 2006). However, in this case the similarity matrix would be non-symmetrical, and this would lead to problems performing the Mantel test (although this could be taken into account without further problems for non-stationarity analyses, which are based on lines of the similarity matrix, and not on the full matrix, see below).

Second, our Hellinger distances were defined based on MAXENT suitabilities mapped in G-space (see Warren et al., 2008). Thus, they are based on modelled patterns and not on the bioclimatic envelope ‘per se’. Thus, we followed some of the studies on niche divergence that were based on model overlaps or cross-predictions (see Rice et al., 2003; Martínez-Meyer & Peterson, 2006). The main problem is that instead of working directly in niche or E-space, the metrics are calculated based on a transcription of E-space into G-space (see also Colwell & Rangel, 2009). This should not be a serious problem if the modelling technique creates a very high fit between them, which is the case with MAXENT (Elith et al., 2006; see also Peterson et al., 2008). Although it would be possible to perform this directly in E-space by dividing each dimension into bits and assigning each species to a series of environmental bits, this would be more difficult computationally and would not take into account the covariance among the environmental variables.

Therefore, comparing MAXENT suitability maps is an easy alternative solution, as suggested by Warren et al. (2008). Notice also that we are not truncating the probabilities to generate distribution maps, so that none of the problems that are related to evaluation statistics such as AUC and kappa appear (see Lobo et al., 2008; Peterson et al., 2008). We are also not using the significance tests proposed by Warren et al. (2008), given that we are only using Hellinger distances as a descriptive metric for niche similarity. Finally, although further analyses may be useful to reveal the best way to measure niche overlap in a macroecological context, our approach will be useful to deal with any estimator of niche divergence expressed as a pairwise matrix among species.

In conclusion, our analyses show that patterns in niche divergence among species cannot be analysed only by correlations between divergence and phylogenetic distances. More complex patterns can appear and, even when a Mantel test is not significant, phylogenetic patterns may exist at very small and restricted time-scales. Only by partitioning the phylogenetic distances into classes can one detect these patterns. Worst of all, even if it is possible to establish Brownian expectations and compare the observed niche divergence with these neutral expectations (which should indicate a global and unique pattern of niche shift or conservatism), it is still important to test the assumption of phylogenetic stationarity. Our analyses with New World Carnivora suggest that this assumption may not always be true, especially when dealing with large and old diversifying clades that possess different evolutionary, ecological and life-history patterns. This complexity can generate different responses in each of the subclades and thus can promote niche divergence, neutral evolution or conservatism for different species or groups of species.

ACKNOWLEDGEMENTS

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. INNOVATION
  5. RESULTS
  6. DISCUSSION
  7. ACKNOWLEDGEMENTS
  8. REFERENCES
  9. BIOSKETCH

We thanks to Townsend Peterson, Miguel Araújo, John Wiens, Paulo De Marco, Luis Mauricio Bini and two anonymous referees for useful discussions on niche models and niche similarity measures. Work by J.A.F.D.-F. is supported by a CNPQ researcher fellowship. L.C.G.V. developed this work when receiving financial support from the PNPD (National Program for Post-Doctoral) program from CNPq.

REFERENCES

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. INNOVATION
  5. RESULTS
  6. DISCUSSION
  7. ACKNOWLEDGEMENTS
  8. REFERENCES
  9. BIOSKETCH

BIOSKETCH

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. INNOVATION
  5. RESULTS
  6. DISCUSSION
  7. ACKNOWLEDGEMENTS
  8. REFERENCES
  9. BIOSKETCH

José Alexandre Felizola Diniz-Filho is Professor and Head of the Ecology Department of the Universidade Federal de Goias, Brazil, and is a 1A Productivity Researcher of the Brazilian Council for Scientific Development and Technology (CNPq). His main research interests are the evolutionary aspects of macroecological theory and the application of spatial statistical methods in macroecology, evolutionary biology, population biology and conservation. He is currently one of the editors of Global Ecology and Biogeography.

Editor: Brian McGill