## Introduction

A fundamental goal of evolutionary biology and related disciplines is to understand why some clades have more species than others1. In general, differences in current species richness between clades will be explained by either their age (e.g., older clades with more species) or by differences in how quickly they have accumulated species (i.e., net diversification rate). The net diversification rate of a clade is the outcome of speciation and extinction over time2,3,4. Differences in species richness among clades of the same rank (e.g., families, phyla) seem to be explained largely by differences in these net diversification rates5. Therefore, to understand richness patterns among clades, it is essential to uncover the ecological and evolutionary processes that determine differences in diversification rates among clades.

Climatic niches may be one of the key factors that drive variation in diversification rates and species richness among clades. Every terrestrial species has a realized climatic niche, which is the set of large-scale temperature and precipitation conditions where that species occurs6,7,8. The realized climatic niche can reflect physiological tolerances to these climatic conditions, but can also be influenced by other abiotic and biotic factors. The climatic niche of a species may strongly influence where it can occur over space and time7, and thus may be critically important for both speciation (e.g., ecological speciation through climatic niche divergence9,10), and extinction (e.g., due to climate change). We can thus expect a relationship between patterns of variation in climatic niches across clades and their net diversification rates. In support of this idea, some studies have shown that the climatic regime where a clade occurs can influence its diversification rate (e.g., faster diversification in tropical clades11). Similarly, other studies have shown that the rate of change in climatic niches among species within a clade can be positively related to species diversification12,13,14,15,16.

Gómez-Rodríguez et al.17 tested these hypotheses using climatic, distributional, and phylogenetic data from amphibian species and families. They found that diversification rates of families were strongly and positively related to family-level niche widths, but weakly related to mean species niche widths of families. Additionally, the variable that explained the most variance in diversification rates of amphibian families (53%) was an indirect measure of niche divergence (i.e. families with narrow species-level niche widths but wide family-level niche widths). Taken together, the results were consistent with the hypothesis that diversification rates were strongly influenced by speciation linked to climatic niche divergence (H2).

In that study, niche divergence was quantified in absolute terms (i.e. present day differences in climatic niches between species in clades), ignoring the evolutionary rate of change. However, if niche divergence is linked to speciation and hence to diversification rate, then the rate of niche divergence over time should be associated with diversification rate even more strongly than with absolute niche divergence. Previous studies have tested the relationship between rates of climatic niche evolution and diversification in several groups, including the Cape flora13, plethodontid salamanders12, frogs16, all amphibians25, and birds14,15,26. A positive relationship was generally supported (but not across amphibians25). Likewise, absolute niche divergence was the strongest correlate of variation in diversification rate among amphibian families17. However, to our knowledge, no study has assessed the relative importance of absolute niche divergence and rates of niche evolution in explaining variation in diversification rates among clades.

Here we perform such an analysis across mammals. Our results shed light on the ecological factors linked to patterns of macroevolution and species richness in a major clade of vertebrates. They also address whether clade diversification is more strongly related to the absolute differences in the environmental conditions occupied by the species in a clade or to the velocity with which they occupy different environmental conditions, and how these latter two variables are related.

We analyse diversification rates in mammal families (dependent variable), and their relationship to climatic niche width, niche divergence, and rate of niche evolution (independent variables). Previous studies have addressed some related issues in mammals, but not the specific questions we address here. For example, Cooper et al.27 examined patterns of climatic niche evolution in mammals, and found that tropical, small-ranged, and specialized mammals tended to have slower rates of thermal-niche evolution than temperate, large-ranged, and generalist mammals (see also Cadena et al.28). However, they did not relate climatic niche evolution to patterns of diversification. Past studies showed that diversification rates in mammals are related to geographic or life-history factors (e.g., in Australian mammals21), trophic strategy29, and climatic niche width30, but did not address how much variation in diversification rates across mammals is explained by these variables. Latitudinal patterns in diversification rates among mammalian species and clades were also assessed in previous analyses, with the goal of explaining higher tropical species richness. These studies found higher diversification rates in tropical lineages at broad phylogenetic scales11, but not among genera31 or species32. However, they did not test if tropical distribution helps explain patterns of diversification and richness among mammalian families. Other studies have addressed patterns of diversification over time across all mammals33,34,35 or at lower taxonomic levels36,37,38,39, but did not focus on the correlates of diversification rates or richness among clades.

Here we test the relationships between niche evolution and diversification using climatic, distributional, and phylogenetic data for 3335 terrestrial mammal species in 92 families. We explore the relationships between diversification rates and: (i) average species niche widths within clades (families), (ii) clade-level niche widths (range of climatic conditions across all species within a family), (iii) absolute niche divergence among species within clades, (iv) rates of niche evolution within clades, (v) the mean position of the clade’s niche (e.g., tropical vs. temperate), and (vi) the geographic range area of the clade. Note that we treat diversification rate as the dependent variable, and therefore describe how much variation in diversification rate is explained by other variables (following standard statistical terminology). Nevertheless, we are initially neutral about the direction of causality underlying the relationship between niche divergence and diversification. However, by testing these alternate hypotheses we can gain insights on the causality and mechanisms involved (see Discussion).

## Materials and Methods

### Climatic niche width

All range maps for terrestrial mammal species available from the IUCN database40 were downloaded (n = 5285). This GIS database basically covers all described mammal species (5488 known species, including marine species). By “terrestrial” we mean non-marine, and thus marine species and families were excluded (given that we lack climatic data for these species). Species climatic niches were estimated from their distributions, as the climatic conditions in which each species lives (a Grinnellian niche operationally estimated following Peterson et al.41). Specifically, climatic data at 2.5 arc-minutes (or approximately 4.5 km) resolution were downloaded from the WorldClim database42, and niches were estimated by extracting the climatic values in the geographic range of a species or clade using the package raster43 in R44. Details on the functions used are given in Appendix S1 in the Supplementary Material. Six variables were selected to represent the climatic niche of mammal species, following standard practice in similar studies17,24: annual mean temperature (BIO1), maximum temperature of the warmest month (BIO5), minimum temperature of the coldest month (BIO6), annual precipitation (BIO12), precipitation of the wettest quarter (BIO16), and precipitation of the driest quarter (BIO17). These variables represent annual means and extreme values of temperature and precipitation, so it is assumed that they can give a robust description of species’ climatic niches. Other climatic variables in the WorldClim dataset generally represent minor variations on these six.

For each species, the climatic niche width was calculated following Gómez-Rodríguez et al.17. The niche width for each variable and species was defined as the difference between the minimum and maximum values across the species’ geographic range (extracted for each grid cell). The overall climatic niche width for each species was then the product of the species’ climatic ranges (niche widths) multiplied across the six variables. The climatic niche could not be estimated for three species having very small geographic ranges in areas with no climatic data available. To allow the inclusion of variables in different units (temperature and precipitation) in niche-width estimation, niche widths for each species for each climatic niche variable were standardized considering the maximum and minimum values for that variable across all species. Thus, for each species i in a set of j species, the standardized climatic range (niche width) is:

$${{\rm{StRg}}}_{{\rm{i}}}={[\mathrm{Rg}}_{{\rm{i}}}-{\min (\mathrm{Rg}}_{{\rm{1}}}{:\mathrm{Rg}}_{j)}]/[\,\max ({{\rm{Rg}}}_{1}\,{:\mathrm{Rg}}_{{\rm{j}}})-\,{\rm{\min }}({{\rm{Rg}}}_{1}{:\mathrm{Rg}}_{{\rm{j}}})],$$

with Rgi being the range of species i and max(Rg1:Rgj) and min(Rg1:Rgj) being the maximum and minimum values of the ranges in the set of j species, respectively. Additionally, for each species and each climatic variable, the average of all observed values across all the grid cells of the species geographic range was calculated. These mean values were used to define the species’ niche position. The niche width and niche position of each family were computed following the same protocol as above, considering the distribution area occupied by all the species in the family as the family’s distribution range.

We also explored an alternative approach, computing family niche width after summarising the six climatic variables through a principal components analysis (PCA). This yielded equivalent results. Specifically, the first two PCA axes accounted for 97% of the variance among the climatic variables, and family niche widths based on these two PCA axes were highly correlated (Pearson’s r = 0.937) with niche widths computed as described above (Appendix S12).

The mean species niche width for a family was computed as the average value of all the species’ climatic niche widths in that family. Finally, the geographic extent (in km2) of each family was also computed, again considering the union of the ranges of all the species in the family as the range. All GIS analyses were conducted in R using the packages rgdal45, geosphere46, maptools47, and raster43. Details on R functions are provided in the Supplementary Material (Appendix S1).

We acknowledge that outliers or erroneous localities could cause errors in our estimates of climatic niche width. However, this should be a source of random error, and not bias. Further, our use of range maps (rather than point localities) to estimate climate niche values should tend to ameliorate rather than exacerbate such effects.

### Diversification rates

The net diversification rate for each family was estimated given the species richness and age of each family. The species richness of each family was based on the number of species in each family for which climatic niche data were obtained. These data include all species included in the IUCN40 database (with exception of three species for which the niche could not be computed) and guarantees that both family species richness and niche width are computed for exactly the same set of species. Ages of families were estimated from a time-calibrated phylogeny of mammals34. The phylogeny is based on a concatenated analysis of 26 genes, and the divergence dates were estimated incorporating autocorrelated evolutionary rates and hard-bounded age constraints. Although other mammal phylogenies are available, this phylogeny is based on extensive molecular data and is well-resolved at the family level. This phylogeny includes 164 mammal species, representing 147 terrestrial and marine families. Four terrestrial families (i.e. Aotidae, Lepilemuridae, Pitheciidae, and Platacanthomyidae) were not included in this phylogeny and were therefore excluded here. However, these four families collectively include only 80 species, and so their exclusion should have limited impact on the results. Diversification rates could be computed for all the terrestrial families included in the tree.

Family diversification rates were estimated following the method-of-moments estimator for stem groups described in Magallón & Sanderson48 (their equation 6). This method typically incorporates an assumed value of the relative extinction rate (ε = extinction rate/speciation rate) for calculating diversification rates:

$${\hat{r}}_{\varepsilon }=\frac{1}{t}\,\mathrm{ln}[n(1-\varepsilon )+\varepsilon ]$$

$${\hat{r}}_{\varepsilon }$$ represents diversification rate under a certain relative extinction fraction (ε), which accounts for the fact that only clades that survive to the present day are included (and thus might lead to bias in estimating rates). t is the family stem group age (i.e. the time of divergence between a family and its sister clade, so that the stem group age of two sister families is the same). n is the number of extant species in the family. Following standard practice, three different values for the relative extinction fraction were assumed (ε = 0, no extinction; ε = 0.45, intermediate rate; and ε = 0.9, high rate). Results were similar using all three values. Therefore, for brevity, only the results for ε = 0.45 are presented in the main text (see Appendix S3 in Supplementary Material for analyses using ε = 0 and ε = 0.9). We used the stem-group estimator because it is more accurate in simulations than the crown-group estimator and (unlike the crown-group estimator) is not affected by incomplete taxon sampling within clades49.

We note that many possible approaches are available to analysing diversification. The approach that we use here focuses on estimating net rates for individual clades, which is our main focus. Therefore, the estimator that we used here should be the most appropriate for our research question. This is also the same estimator used in previous studies on this topic12,15,16,17, which allows our results to be directly compared to earlier studies.

### Rates of niche evolution

Rates of niche evolution were calculated separately for each family and for both temperature and precipitation. Rates were calculated based on the phylogeny of species within each family, using species values for annual mean temperature (BIO1) and annual mean precipitation (BIO12), using average values across the range of each species. We focused on these two variables because they should reflect the most important aspects of the species climatic distribution (e.g., BIO1: tropical vs. temperate; BIO12: arid vs. mesic), and more so than short-term, extreme values (BIO5, BIO6, BIO16, BIO17). For the phylogeny within each family, we used the species-level tree of mammals from Rolland et al.11 (their maximum clade credibility consensus tree). These authors generated this tree by redating the species-level tree of Bininda-Emonds et al.33 (as modified by Fritz et al.54) using dates from Meredith et al.34. They also randomly resolved polytomies in this tree using the method of Kuhn et al.55 to generate 100 trees, and then obtained a consensus tree from those 100 trees. We conducted analyses on this consensus tree. Only one terrestrial family (Diatomyidae) was not represented in this phylogeny. This tree includes 5020 terrestrial and marine mammal species.

The rate of niche evolution was estimated as the sigma parameter of a Brownian-motion model of evolution (for details see O’Meara et al.56). The lambda model of evolution57 actually showed a better fit both for BIO1 and BIO12 than the Brownian-motion model (or than the Ornstein-Uhlenbeck [OU] model, see Table S6.1 in Supplementary Material), but the sigma parameter of a lambda or a OU model could only be computed for families with three or more species in the tree (76 families), which would further reduce the dataset. However, sigma values calculated using the lambda and Brownian-motion models have a strong, positive correlation (Pearson’s r = 0.90 for BIO1 and r = 0.80 for BIO12, see Fig. S6.1 in Supplementary Material), as expected given the close relationship between these models when lambda is high (i.e. fitted lambda = 0.89 for both BIO1 and BIO12, and lambda = 1 is the Brownian-motion model). Therefore, the sigma values for the Brownian-motion model were used, as they could be computed for more families. Furthermore, using the same set of families in all phylogenetic regressions is necessary in order to partition the variance among competing models. The sigma parameter was computed for all monophyletic families with two or more species in the tree with the command fitContinuous in the R package geiger58. All families that were monospecific (n = 20) or paraphyletic (n = 17) in the tree of Rolland et al.11 were excluded, since estimation of ages, richness, and rates of niche evolution and diversification would be problematic for these families. We also excluded two families that each had two species in the IUCN database but with only one of those species in the tree (Mystacinidae and Myzopodidae). Therefore, in all subsequent analyses, the dataset was composed of 92 families (spanning 3335 species).

We also performed alternative analyses to address whether our estimates of rates of niche evolution were affected by the algorithms used to resolve polytomies59. We tested the correlation between our niche-evolution rates (from the tree of Rolland et al.11) and an alternative set of rates for 18 mammal families computed from alternative trees. These trees were from Arnold et al.60, and included version 3 of the primates dataset (based on sequences from 17 genes) and version 1 of the Perissodactyla (15 genes), Cetartiodactyla (20 genes), and Carnivora (29 genes) datasets (see Appendix S7 in Supplementary Material). The niche evolution rates computed for these families from these two sources were strongly correlated (Pearson’s r = 0.91, P < 0.001 for temperature niche rate, and r = 0.70, P = 0.001 for precipitation niche rate). Therefore, we considered the estimates of niche evolution rate derived from the tree of Rolland et al.11 to be robust and used them in subsequent analyses. We also note that the strong phylogenetic signal in the temperature and precipitation variables (see above) suggests that random resolution of polytomies within families has not strongly influenced our inferences of evolutionary patterns in these variables (i.e. if random resolutions had a strong effect, there should be limited phylogenetic signal instead of lambda values close to 1). Furthermore, random resolution of polytomies should have no impact on our estimates of diversification rates.

### Phylogenetic regression

Regression analyses were conducted using phylogenetic methods to control for the effect of shared phylogenetic history on diversification rates and niche attributes among families61. We conducted phylogenetic generalized least-squares regressions62 (PGLS) using the R package caper63. We used lambda values estimated by maximum likelihood to transform branch lengths and with kappa and delta values both set to 1.

The relationship between family niche width and mean species niche width can indicate levels of niche divergence among species within a family17. A PGLS between family niche width and mean species niche width was fitted and the residuals of this relationship were used as a proxy for niche divergence. With perfect niche conservatism among the species in a family, mean species niche width and family niche width would be the same, with the residuals of the relationship close to zero. Therefore, residuals reflect non-overlap of species niches within families (i.e. niche divergence17). However, we acknowledge that this index may not be as informative as using direct estimates of rates of niche evolution, and comparing these indices is one of our goals here. For example, niche divergence ignores the phylogeny within clades, whereas rates of niche change incorporate this information.

Five linear regression analyses were conducted to evaluate the hypotheses presented in Gómez-Rodríguez et al.17 Specifically, we assessed the relationships between diversification rate and (i) family niche width, (ii) mean species niche width, (iii) family niche divergence, (iv) family niche position for each individual climatic variable (i.e. defined as the mean climatic conditions across the geographic range of the family), and (v) family geographic extent. Given that niche position was defined by six variables, a forward stepwise procedure was used to select the most parsimonious model (based on F-statistic) explaining diversification rate. We note that our index of family niche position is not weighted towards the climatic conditions where most species in a family occur. However, using an index that does include such a weighting (i.e. taking the mean of species means across species in each family) yields values of niche position that are strongly correlated with the index that we used (Pearson’s r between indices among families: BIO1 = 0.896, BIO5 = 0.875, BIO6 = 0.881, BIO12 = 0.830, BIO16 = 0.899, BIO17 = 0.785).

We also compared the explanatory power of niche divergence (the aforementioned residuals of family vs. mean species niche width) relative to the rate of niche evolution. First, a bivariate linear regression was conducted to assess the relationships between niche divergence and niche evolution rate for BIO1 (hereafter “rate of temperature niche evolution”) and niche evolution rate for BIO12 (hereafter “rate of precipitation niche evolution”). Second, two linear regressions were conducted to test the relationships between diversification rate and rate of temperature niche evolution and rate of precipitation niche evolution. Third, we performed a multiple regression analysis including both temperate and precipitation niche rates as independent variables (this should be more comparable to niche divergence, which combines both temperature and precipitation). Finally, to partition the unique contribution of those models explaining an important portion of the variance in diversification rate (i.e. ~20% or more), four models (i.e. family niche width, geographic extent, niche divergence, and niche evolution rate) were combined in a full model and variance partitioning was used to compute their unique and joint contributions to the explained variance.

We performed null models in order to assess if the observed relationships between niche width and diversification rate appear because families with more species span more divergent climatic conditions due to sampling alone (H0). We tested the relationship between (a) family niche width vs. mean species niche width, (b) diversification rate vs. family niche width, (c) diversification rate vs. mean species niche width, and (d) diversification rate vs. niche divergence (residuals of regression “a”) using PGLS in the null families. We sampled with replacement 92 null families with the same species richness as the original ones. Three different null models were considered: (1) species sampled from the pool of all mammal species (unconstrained model), (2) species sampled from the pool of species within the latitudinal and longitudinal range of the original family (spatially constrained model), and (3) species sampled from the pool of species within the original family climatic niche (climatically constrained model). We took 1000 samples of 92 null families and compared the distribution of the r2 of the aforementioned PGLS among these 1000 replicates with the observed r2 in the original families.

An additional robustness test was performed to ensure that results were not influenced by the different ages of clades. We defined major clades of similar age in the species-level tree of Bininda-Emonds et al.33 with dates from Meredith et al.34, regardless of whether they corresponded to a named higher taxon or not. Specifically, we went through the tree and identified the clades with stem ages that were closest to the average stem age of all families (41.65 Ma), but with the restriction that the clades selected were older than that mean age. We then computed climatic niches and niche evolution rates for these clades, excluding those that were monospecific (86 clades were used in these analyses). We conducted the same regression analyses and variance partitioning described before, with the richness of these clades as the dependent variable.

All variables (unless otherwise noted in the Results) were logarithmically transformed (natural logarithm) to improve the normality of model residuals. All analyses were conducted in R. Raw data (e.g., diversification rates, niche widths, niche evolution rates) used for statistical analyses are provided in the Supplementary Material (Appendix S2).

### Data Availability

Range maps of mammals are available at http://www.iucnredlist.org/technical-documents/spatial-data. Two published mammal phylogenies were used (species-level phylogeny in Rolland et al.11 and family-level phylogeny in Meredith et al.34). Climatic data were obtained from http://worldclim.org/current (Hijmans et al.42).

## Results

A positive and strong relationship was observed between family niche width and mean species niche width (r2 = 0.73, F1,90 = 243.8, P < 0.001, n = 92 families, Fig. 1A). The relationship between diversification rate and family niche width was positive and significant (r2 = 0.20, F1,90 = 22.92, P < 0.001, Table 1, Fig. 2A). In contrast, there was not a significant relationship between diversification rate and mean species niche width (r2 < 0.001, F1,90 < 0.001, P = 0.99; Table 1, Fig. 2B). A strong positive relationship (r2 = 0.59, F1,90 = 130, P < 0.001; Table 1, Fig. 2C) was observed between diversification rate and absolute niche divergence (i.e. the residuals of the family niche width vs. mean species niche width relationship). A significant, positive relationship was also observed between diversification rate and geographic extent (r2 = 0.19, F1,90 = 21.65, P < 0.001; Table 1, Fig. 2E) and a weak negative one with niche position (r2 = 0.07, F1,90 = 6.341, P = 0.014; Table 1, Fig. 2D). Niche position was defined by the minimum temperature of the coldest month (BIO6) after a forward stepwise procedure to select the most parsimonious model (see Appendix S8 in Supplementary Material). However, both geographic range area and niche position explained little variation in diversification rates relative to climatic niche divergence. There was a strong positive relationship between diversification rate and species richness of families (r2 = 0.79; F1,90 = 342.7, P < 0.001).

Niche divergence showed a positive relationship with rates of temperature and precipitation niche evolution in a bivariate model (r2 = 0.50, F2, 89 = 44.87, P < 0.001). This shows that greater niche divergence among species within a family is generally related to a higher rate of niche evolution in that family. A strong positive relationship was also found between diversification rate and rate of temperature-niche evolution (r2 = 0.38, F1,90 = 55.04, P < 0.001; Table 1, Fig. 2F) and rate of precipitation-niche evolution (r2 = 0.44, F1,90 = 69.31, P < 0.001; Table 1, Fig. 2G). A multiple regression model including rates of both temperature and precipitation niche evolution explained more than half of the variation in diversification rates (r2 = 0.51, F1,89 = 46.73, P < 0.001), similar to the level explained by niche divergence.

A model assessing the relationship between diversification rate and all independent variables explaining an important portion of its variance was also tested. These independent variables included family niche width, geographic extent, rate of niche evolution (with temperature and precipitation rates as independent variables), and niche divergence from the residuals of the regression of family niche width vs. mean species niche width. This model explained a large proportion of the variation in diversification rates (r2 = 0.65, F5,86 = 31.55, P < 0.001). Variance partitioning (Fig. 3) showed that most of the variance explained by this model (64.7% explained variance) was shared among the variables (46.3%). The variance explained exclusively by family niche width (0.5%) and geographic extent (0.5%) was negligible, and relatively low for rates of niche evolution (5.1%). Niche divergence was the variable with the largest unique contribution (12.4%). Most of the variance was shared between niche divergence and niche evolution rate (26.4%) and between all variables (14.5%).

To assess the robustness of our results regarding the estimates of diversification rates, the full model was conducted with species richness instead of diversification rate as the dependent variable, and results were similar. Family richness was strongly and positively related to niche divergence (r2 = 0.70, F1,90 = 207.9, P < 0.001), rate of temperature niche evolution (r2 = 0.34, F1,90 = 45.47, P < 0.001) and precipitation niche evolution rate (r2 = 0.38, F1,90 = 55.43, P < 0.001). In a variance partitioning of a full model, niche divergence was again the variable with the largest unique contribution (21.9%). Most of the variance was shared between niche divergence and rates of niche evolution (25.4%; see Appendix S4 in Supplementary Material).

In the null models (unconstrained, geographically constrained, and climatically constrained) in which we sampled 1000 replicates of 92 null families, the relationship between diversification rate and mean species niche width and between diversification rate and family niche width was generally stronger than the observed relationship (see Appendix S11). However, the relationship between diversification rate and niche divergence was comparable to the observed relationship only in the case of the unconstrained model (P = 0.056), and was weaker in the spatially and climatically constrained models (P <= 0.002 in both cases). The r2 in the relationship between family niche width and mean species niche width was higher in the null models (P <= 0.011 in the spatially and climatically constrained models), except in the unconstrained null model (P = 0.428). These results suggest that the observed relationship between diversification rate and niche divergence between species within families is comparable to sampling these species from the pool of all mammals, from any biome or world region.

We then used major clades stemming from the nodes closest to (but older than) the average family age (41.65 Ma) instead of families as units of analysis. Using these clades (mean stem age = 54.7 Ma, standard deviation = 20.2, n = 86), strong positive relationships were again found between clade richness and niche divergence (r2 = 0.58, F1,84 = 114.9, P < 0.001), rate of temperature-niche evolution (r2 = 0.46, F1,84 = 70.47, P < 0.001) and rate of precipitation-niche evolution (r2 = 0.46, F1,84 = 72.79, P < 0.001). Partitioning of variance in species richness among all predictors also yielded results similar to those reported above (Appendix S9 in Supplementary Material).

## Discussion

Overall, our results show that two measures of niche change among species within clades (absolute climatic niche divergence and rates of climatic niche evolution) are each strongly related to diversification rates among mammal clades. In regression models, absolute climatic niche divergence and rates of climatic niche evolution each explain over half of the variation in diversification rates among mammal families. Diversification rates in turn explain most (79%) of the variation in species richness. These results parallel those for amphibians16,17 and birds15, and together they suggest that changes in climatic niches are broadly important in understanding large-scale patterns of diversification and richness. We also show here that our measures of absolute niche divergence and climatic niche rates are strongly related, and explain similar amounts of variation in diversification rates.