Main

It is not clear why greater species richness is observed in warmer and more humid regions. Since the first description of large-scale patterns of species diversity by Alexander von Humboldt in 1807 (ref. 9), differences in climatic conditions between tropical and extratropical regions have been considered a plausible explanation for global diversity gradients. It is now well established that species richness is often strongly correlated with climatic conditions, namely temperature, water availability and resulting ecosystem productivity1,2,3,4,5,6. Although several causal pathways link climatic variables to species diversity including both current ecology and deep-time evolutionary processes5,10, we lack an understanding of how the geography of climate is associated with diversity patterns. Specifically, it is unknown whether greater diversity in warmer and more humid regions results from the effect of the climate itself, or from the geographic area occupied by these climatic conditions (that is, climate area) and the spatial isolation between similar climatic conditions (that is, climate isolation), both of which could lead to higher diversity.

In an influential piece7, John Terborgh argued that “unusual environmental situations will carry impoverished flora in relation to nearby sites incorporating more usual conditions”. Conversely, more usual or common climatic conditions (that is, those that cover a greater geographic area) will have high species richness7. The relationship between climate area and species richness led to the area hypothesis to explain global patterns of species diversity, originally arguing that climatic conditions occurring in the tropics are more common than those conditions occurring in extratropical regions. The area hypothesis was further popularized and amplified by Michael Rosenzweig8, but the emphasis on climate area was lost. At present, the area hypothesis is considered in a very broad geographic context building on the idea that tropical regions have more land than extratropical regions, thereby offering a reasonable explanation for why greater species richness is observed in the tropics. More recently, the commonness of climatic conditions (that is, the total global extent of a given climatic condition) has been used to explain empirical patterns of species richness11, leading to the formalization of species–area relationship within climate12. In addition to area, the isolation of fragments of a given climatic condition on the surface of the Earth can also be expected to affect species diversity. Speciation rates are expected to increase as a result of reduced gene flow and increased environmental heterogeneity13,14,15. The same expectation applies when biodiversity is analysed within different climates. Climatic conditions with isolated and larger extent across the surface of the globe should reduce extinction rates, facilitate allopatric speciation and shelter biotas that evolved independently, and therefore strongly affect climatic gradients of diversity at the global scale. However, the combined effects of the geography of climate (that is, climate area and isolation) and climatic conditions per se on global patterns of diversity remain unknown.

A substantial challenge in assessing the impact of the geography of climate, specifically climate area and isolation, arises from the necessity to reorient traditional biodiversity studies—typically focused on geographic landscapes—towards the realm of climate space. This pivot demands a fresh perspective on examining the relationships between diversity and climate. Using multidimensional space, defined by climatic conditions, to study biodiversity patterns is not a new concept. It has been previously proposed in the literature16,17,18. Primarily, this approach has been used for the classification of life zones and biomes19,20, as well as in species distribution modelling and its various applications21,22. By contrast, this perspective has been generally overlooked in studies investigating the emergence and maintenance of large-scale diversity patterns11,12. Here we investigate tetrapod diversity patterns thoroughly in climate space, disentangling the effects of the geography of climate and climate conditions per se, on diversity–climate relationships. We anticipate finding a higher number of species in climatic conditions that both cover large geographic areas and exhibit characteristics of isolation or fragmentation. We believe that these findings will hold true regardless of the inherent differences in thermal physiologies, such as endothermy and ectothermy, among tetrapod groups. These expectations are aligned with empirical evidence showing the effect of geographic area and isolation on geographic patterns of species richness independent of species’ thermal and metabolic physiologies8,13,15,23. The shift towards understanding diversity as a pattern in climate space, driven by a process in climate space, can reveal insights into how climate is structured globally and help face the challenges imposed by climate change.

We used the first two axes of a principal component analysis of 12 global-scale climate variables to define a two-dimensional orthogonal climate space (Fig. 1a–c) that represents thermal and water availability limits to species distribution. Each axis of the climate space was then divided into climate cells of equal climate intervals (Fig. 1c; results robust to interval size, Supplementary Information). Thus, each climate cell represents several geographic locations that fall within a specific climate interval. Likewise, several geographic locations belong to a unique climate cell (Fig. 1d). This connection between climate and geographic space, referred to as Hutchinson’s duality18, allows geographic information to be mapped in climate space and vice versa. Using this approach, we computed the geographic extent of a climatic condition that we refer to as climate area (Fig. 1f). As a climate condition is scattered on the surface of the planet, we identified the individual fragments of a climate condition (that is, regions within a climate cell that are geographically isolated from other regions within the same climate cell) and measured the average geodesic distance among climate fragments, which we refer to as climate isolation (Fig. 1e). Climate area and climate isolation represent the geography of global climate. We also computed the within-climate-cell average of the first two principal components for each climate cell to evaluate the effect of the climate itself. Finally, for each climate cell we counted the number of species that fall within that climatic condition (Fig. 2) using range distribution data for terrestrial amphibians, reptiles, mammals and birds, and investigated the effect of the climate, and its area and isolation on richness patterns and species composition of each tetrapod group.

Fig. 1: From geographic to climate space.
figure 1

a,b, Scores of the first and second principal components (PC1 and PC2) mapped across the world. c, Climatic information represented in a two-dimensional coordinate plane in which the x axis and y axis are represented by PC1 and PC2 and each point represents the climatic information of each geographic location (n = 13,312 geographic cells). d, Using the gridded climatic space created with PC1 and PC2 (c), the duality between climate and geographic spaces is shown by matching colours between climate and geographic grids, in which similarity in colour tone indicates similarity in climatic condition. The duality between geographic and climate space refers to the relationship between geographic and climate space: a given climatic condition (climate cell in climate space) is observed in several geographic locations, and several geographic locations belong to a unique climate condition. e, Climate area representing the sum of land surface area of a given climatic condition (that is, climate cell). f, Climate isolation representing the average geodesic distance among climate fragments (that is, geographic cells connected to each other that occur within a single climate).

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Fig. 2: Terrestrial tetrapod richness in climate space.
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a–d, Number of species that fall within a climatic condition counted for birds (n = 180 climate cells; a), mammals (n = 178 climate cells; b), amphibians (n = 174 climate cells; c) and reptiles (n = 165 climate cells; d). PC1 and PC2 represent the first and second axes of a principal component analysis of 12 global-scale climate variables (Supplementary Information).

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For each tetrapod group, we fitted a Poisson-distributed generalized additive mode to account for nonlinearity in model residuals with species richness in climate space as the response variable, and the geography of climate (that is, climate area and isolation) and climate itself (that is, first and second principal components) as predictors (Extended Data Table 1). Our model explained nearly 90% of the variation in richness for birds (proportion of null deviance = 0.90, adjusted R2 = 0.92), mammals (proportion of null deviance = 0.90, adjusted R2 = 0.91), amphibians (proportion of null deviance = 0.88, adjusted R2 = 0.90) and reptiles (proportion of null deviance = 0.88, adjusted R2 = 0.91)–results hold consistent when nonlinearity is addressed through polynomial regressions (Supplementary Information). These results indicate that for all tetrapod groups, the geography of climate and climate itself can explain most of the variability of tetrapod richness in climate space. For all groups (Extended Data Figs. 1–3), partial residual richness (that is, richness not explained by other predictors) increases with area (Fig. 3a) and with isolation (Fig. 3b), even though climates occurring on opposite poles are isolated, their extreme conditions are suitable to only a few species. Thus, the geographic distribution of polar climates does not effectively isolate a substantial number of species. Partial residual richness is positively related to the first principal component (Fig. 3c) that is composed mostly by temperature variables and has a hump-shaped relationship with the second principal component that is defined by a balance of energy and water availability (Fig. 3d). The explanatory power of the geography of climate and climate itself is very similar for all groups (Fig. 4). In terms of proportion of null deviance, climate area contributes about 10%, whereas climate isolation accounts for roughly 5%. Comparatively, the first and second principal components contribute around 13% and 2%, respectively. Shared explanatory power within the geography of climate totals about 12%, whereas within climate itself it is around 2%. Thus, when considering both isolated and shared contributions, the impact of the geography of climate is nearly double that of climate itself (Fig. 4). The remaining 45% of shared explanatory power comes from overlapping contributions of geography of climate and climate itself. Using different resolutions and combinations of variables to define climate space did not qualitatively change the results (Supplementary Information).

Fig. 3: Relationships between partial residual richness of birds (that is, richness not explained by other predictors of the multivariate model) and each model predictor.
figure 3

a,b, Partial residual richness versus climate area and isolation. c,d, Partial residual richness versus climate itself here represented by the first two principal components. The grey shading around each regression line represents the 95% confidence interval. Identical patterns are observed for other tetrapod groups (Extended Data Figs. 2 and 3).

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Fig. 4: Relative contribution of climate and the geography of climate.
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For each tetrapod group, we separated how much of the variability in species richness on the climate space is explained exclusively by climate area and climate isolation (geography of climate) and principal components one and two (climate itself). We also computed the joint contribution within the geography of climate and climate itself and between the geography of climate and climate itself.

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Our results reinforce previous findings that the geographic extent of climatic conditions is positively associated with species diversity7,11,12, but further highlight that only 10% of the variation in richness comes exclusively from climate area alone. The mechanisms underlying the species–area relationship in climate space are different from those proposed for geographic space because similar climatic conditions are not continuously distributed across geography. In geographicl space, a continuous large area often leads to higher environmental heterogeneity and consequently different species exploring different ecological opportunities24. However, scattered climatic conditions in climate space, that sum up to define climate area, represent several geographic locations within the same type of environment. As a result, within a given climate, there is little environmental heterogeneity (assuming climate variation influences environmental heterogeneity) that could lead to specialization for different environmental conditions. Therefore, the finding of more species occurring with homogeneous climatic conditions that occupy larger geographic extents is probably attributable to capacity rules25. Climatic conditions that cover more extensive land areas are believed to support more individuals, leading to larger populations. Larger populations, in turn, are associated with increased rates of speciation and reduced rates of extinction5,25,26.

Another aspect of the geography of climatic conditions is that a larger climate area does not necessarily translate to larger continuous habitat. In fact, climate area is strongly correlated with the number of climate fragments (that is, geographic cells connected to each other that occur within a single climate; Pearson’s r = 0.95; Fig. 5a and Extended Data Fig. 4). However, the correlation between the number of climate fragments or climate area and climate isolation (measured as the average distance between climate fragments) is weak, with Pearson’s correlation coefficients of 0.23 and 0.11, respectively. These observations highlight the importance of characterizing climate isolation in addition to the area of climatic conditions when macroecological patterns are analysed in climate space.

Fig. 5: The geography of climate across the globe and its relationship with bird community composition.
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a, The relationship between climate area and the number of climate fragments (n = 164 climate cells; Extended Data Fig. 4). b, The relationship between average absolute latitudes of each climate cell in climate space and climate isolation (n = 1,028 climate cells) at a resolution of 60 equal intervals (Extended Data Fig. 5). In b, τ expresses the quantiles in which quantile regressions are fitted and OLS represents the ordinary least squares regression (dashed line). c,e, The relationship between the geography of climate and the turnover component of taxonomical β-diversity (n = 164 climate cells; Extended Data Figs. 6–8). d,f, The relationship between the geography of climate and the nestedness component of β-diversity (n = 164 climate cells; Extended Data Figs. 6–8). The grey shading around regression lines represents the 95% confidence interval.

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The mechanism underlying the association between species richness and climate isolation is probably linked to climate isolation influencing gene flow among diverging populations. Over deep time, at the global scale, climate change, continental drift and mountain uplift can affect the spatial connection among similar climatic conditions. Populations of a species dispersing to follow their optimum climatic conditions expand, contract and fragment their geographic distribution within climatic conditions27. The isolation of populations within spatially disconnected climatic conditions increases the chances of allopatric speciation events and founder speciation events caused by long-distance dispersal27,28. Therefore, at the global scale we expect that locations where climatic conditions are more isolated will also have more species, which is consistent with our findings. In addition, isolated climatic conditions shelter biotas that independently evolved within that climatic condition making it likely that different species pools will be sampled. This is in fact evidenced by the increase in the turnover of species composition with the increase of climate isolation (Fig. 5c).

Notably, the most conspicuous and discussed pattern of climate isolation at the global scale is that of two broad climatic zones in high latitudes, with northern and southern polar and temperate zones being disjunct and separated by a large contiguous tropical zone8,29. However, our results show that tropical climates, spread across several continents, are more isolated than polar and temperate climates. There is an envelope relationship between the distance of similar climates (distance among climate fragments) and latitude (Fig. 5b and Extended Data Fig. 5), with a tendency of shorter distances among similar climates at higher latitudes (Fig. 5b, ordinary least squares model) and greater variability in geographic isolation of similar climates in tropical zones. The general tendency of greater isolation in lower latitudes increases the probability of independent pools of species evolving within warmer and more humid climates spread in a mosaic of similar but isolated climatic conditions. We find that climates occupying large and isolated areas have increased community differentiation with both area and isolation of climate (Fig. 5c,d and Extended Data Figs. 6–8), indicating that ecological communities occurring within larger and isolated climates have high replacement of species among communities. The likely mechanism behind this pattern is that independent pools of species evolve as a consequence of dispersal limitation and historical changes in the geography of climate30. In addition, climates occupying small and connected areas have a nested community structure with fewer species that are a subset of richer communities within climates (Fig. 5e,f and Extended Data Figs. 6–8). This pattern probably emerges because of lower dispersal limitation within smaller and connected climatic conditions. These results demonstrate how the area and isolation of climate strongly capture changes in community composition even within homogeneous climatic conditions. Thus, climate area and isolation capture patterns of community differentiation across the globe.

The area hypothesis to explain latitudinal diversity gradients emerged through observations that climatic conditions that occur in tropical environments are more common than climatic conditions that occur in extratropical regions7,8. However, with the observed reduction in climate isolation at higher latitudes, it becomes evident that not only the commonness of climatic conditions, but also the geographic distribution and isolation of similar climatic conditions, need to be taken into account. Here we propose that the area hypothesis to explain global-scale patterns of species diversity should be modified into an area–isolation hypothesis because not only do lower-latitude climates have larger geographic extent, but climate isolation decreases towards the poles. Thus, tropical climates, characterized by large areas that are both fragmented and isolated, tend to have more observed species. Such climatic structures could promote greater speciation rates through capacity rules and reduced gene flow. Our results show: (1) increase of species richness and turnover with climate area and isolation; (2) larger isolation of tropical climates; and (3) the degree of fragmentation of larger climates call for a revision of the area hypothesis. Although climates occurring in the tropics are more common, these climates are also more fragmented and isolated.

Even though our model, considering all geographic features of climate, explains a large fraction of the variation in tetrapod diversity, the remaining 10% of unexplained variation showed interesting patterns when projected to climate and geographic space (Fig. 6). Along with the model’s goodness of fit, residual patterns are consistent among tetrapod groups (Fig. 6). These residual patterns highlight an important aspect of analysing species diversity directly in climate space. Historical contingencies of different regions with the same climatic conditions are disregarded by combining the presence and absence of all species in those regions, regardless of whether the regions are clustered or scattered around the globe. However, geographic patterns of model residuals can give insights into why more or fewer species are observed under certain climatic conditions after controlling for the effects of the geography of climate and climate itself.

Fig. 6: Species richness that is not explained by climate itself and the geography of climate (that is, model residuals).
figure 6

a–d, The residual richness is mapped in climate and geographic space for birds (a), mammals (b), amphibians (c) and reptiles (d). Blue areas express locations where fewer species are predicted than expected by model predictors and red areas express locations where more species are predicted than expected by model predictors.

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With few exceptions, parts of mountainous climates across all continents have more species than expected by the climate and climate geography. However, the spatial resolution in our global-scale study may not be enough to precisely characterize mountainous climates. These climates usually occupy a small geographic extent (25% of terrestrial landmass31) when compared to lowlands and yet, especially in tropical environments, are home to approximately 90% of tetrapod species31. Tropical mountains usually have more species than expected by climate itself (that is, positive residuals31,32) and the same occurs when the geography of climate is also considered (Fig. 6). Using the present climate to define the effect of climate on mountainous regions misses one important aspect, namely the great importance of mountains for biodiversity refugia under climatic oscillations31. Therefore, both the area and isolation of climate and climate per se are not enough to explain the building of mountain diversity, especially in tropical mountains such as the Andes.

Lower species richness than expected by climate itself and the geography of climate (that is, negative residuals) are observed in many arid regions across the world with few exceptions. In South America, the eastern dry diagonal connecting Caatinga, Cerrado and Chaco and the western dry diagonal connecting Patagonia, Monte, Prepruna dry Pruna and the Atacama Desert, and in Africa, part of the Sahara Desert and the Somalian Desert, among other dry regions (Fig. 6), show a very clear pattern of fewer species than expected by the geography of climate and climate itself. Contrary to mountainous regions, dry regions occupy a large geographic extent, which given the expected species–area relationship, should support a greater number of species. However, their extreme climates act as a barrier for lineages that are not capable of surviving in such arid environments33. The difficulty of adapting to extreme conditions33, even if these conditions are common on the surface of the planet, could explain why fewer species are observed in these regions than expected by climate itself and the geography of climate.

Here we demonstrated that the present geography of climate and climate itself can explain a large fraction of the tetrapod diversity and that the isolated effect of the geography of climate almost doubles the effect of climate itself. However, species richness might not be associated only with the present climate, but also with past climate and past geographic structures of climate. It should be expected that over deep time some climatic conditions were more common than others, that connections and disconnections of climatic conditions occurred and that some conditions appear and disappear across millions of years. Therefore, exploring the dynamics of the geography of climate over deep time is a natural next step for studying diversity–climate relationships in climate space. The same rationale for past climatic dynamics can also be used for future climate change. Ongoing climate changes may alter the commonness of climatic conditions as well as their connection and isolation. For example, climate velocity, representing the direction and speed that species move to maintain their current climatic condition under climate change34,35, is largely affected by climate connectivity36 and can benefit from better understanding of the effect of the geography of climate on biodiversity patterns. If many species have their optimum climate within a climatic condition that contracts its geographic extent with climate change, then competition might increase, potentially influencing species coexistence. In addition, the contraction of the geographic extent of a climatic condition imposes evolutionary pressure for individuals to shift their optimum to other similar climatic conditions that are either less saturated with species or have expanded their geographic extent on the surface of the planet. Finally, connections and disconnections of climate affect the ability of species to disperse between similar climatic conditions affecting the isolation among populations and consequently influencing their gene flow. Therefore, understanding how the geography of climate is associated with biodiversity is key to better understand and mitigate the impacts of climate change on biodiversity.

Building on these insights, we underline the urgent necessity to incorporate the geography of climate into studies examining the impact of climate change on biodiversity patterns. This crucial element has been largely disregarded. Recognizing the demonstrated connection between these geographic factors and species richness, it is critical that we unravel their temporal dynamics for effective biodiversity conservation. We must look beyond mere changes in climate and also consider their commonness and isolation across the planet. Neglecting these factors may result in unexpected climate change impacts on biodiversity, stemming from our failure to track changes in the geography of climate.

Key considerations that emerge include whether our current conservation efforts are inadvertently biased towards protecting common climates, thereby neglecting rarer climates that may harbour unique species. Furthermore, we must understand how ongoing climate change might influence the prevalence and isolation of various climatic conditions. Climate change could fragment previously continuous climates, intensifying the challenges for species to disperse and maintain their preferred climatic conditions. Likewise, if a previously extensive climate shrinks owing to climate change, this could influence species coexistence.

In essence, to mitigate the impacts of climate change on biodiversity, it is paramount that we deepen our understanding of the geography of climate and its shifts over time. This approach  could represent a substantial contribution to conservation biology, providing more comprehensive and effective strategies for biodiversity preservation.

Conclusions

Here we show that the observation of greater species richness in warmer and more humid regions relies not only on climate itself but also on how climate is distributed on the surface of the planet. We demonstrate that the geography of climate plays a key role in the diversity–climate relationship of tetrapods. Its effect can be separated from the effect of climate itself, and the amount of explanation attributed to the geography of climate is almost double the effect of climate itself. Unexplained variation can be clearly linked to historical processes among different regions that are removed when diversity is analysed directly in climatic dimensions. Moreover, shifting the focus of macroecological studies from geographic to climate space allowed us to describe basic properties of the geography of climate. We showed that climate area can precisely capture the number of climate fragments across the globe but is not a good representative of climate isolation. Finally, we showed that climate isolation decreases towards the poles, but has a high variability in the tropics.

Our model, considering both climate and climate geography, explains nearly all of the variability in species richness for each tetrapod group. Even though ectotherms do not occupy all available climates on the planet, ectotherms and endotherms are consistent in their response to climate and the geography of climate with similar patterns even when unexplained richness is mapped. Given the positive effects of climate area and isolation on species richness and how these geographic properties of the climate are structured on the surface of the Earth, we propose that the area hypothesis to explain large-scale patterns of species diversity should be merged into an area and isolation hypothesis. Such a shift in studies exploring diversity patterns directly in climate dimensions could bring a much-needed focus to how ongoing climate change can alter both the geographic extent and isolation of climatic conditions. Describing patterns at large taxonomic, spatial and temporal scales directly in climate space promises substantial new insights into macroecology and biogeography by revealing previously hidden effects of climate on global biodiversity patterns.

Methods

Biological data in geographic space

We obtained vector range maps of all amphibians and mammals available from the International Union for Conservation of Nature (https://iucn.org). We obtained bird and updated squamate range maps, respectively, from BirdLife (version 2020.1; http://datazone.birdlife.org) and ref. 37 (Global Assessment of Reptile Distributions internal version 1.5). Resident and native current distribution ranges of the species were gridded at about 110-km resolution with Behrmann equal area projection (approximately 1° resolution). This resolution has been suggested as the most appropriate grain for this type of data38,39, being less prone to incur false presence of species at the global scale, our geographic scale of exploration in this study.

From geographic to climate space

Species distributions and their habitats can inform us about the n-dimensional hypervolume of biotic and abiotic conditions in which each species can maintain viable populations17,18. As the climatic information underlying a species’ distribution (that is, Grinellian niche) is easier to access than biotic conditions (that is, Eltonian niche), an n-dimensional environmental space, built with climatic variables (that is, climate space), can be constructed and used to measure biodiversity within climate space. Here we defined a two-dimensional climate space that considers the limits imposed by temperature and water availability for terrestrial species. A two-dimensional climate space allows us to use the same methodologies to study diversity patterns as traditionally used in two-dimensional (that is, longitude and latitude) geographic space. To establish each axis, we first averaged several current climatic variables within each spatial grid cell of approximately 110-km resolution. These variables describe variations in temperature and water availability, and include mean annual air temperature, mean diurnal air temperature, isothermality, temperature seasonality, mean daily maximum air temperature of the warmest month, mean daily minimum air temperature of the coldest month, annual range of air temperature, annual precipitation amount, precipitation amount of the wettest month, precipitation amount of the driest month, precipitation seasonality and potential evapotranspiration. Subsequently, we computed the principal components on the correlation matrix of these averaged variables (Supplementary Information). We obtained the bioclimatic variables from the Climatologies at High Resolution for the Earth’s Land Surface Areas (CHELSA; https://chelsa-climate.org/bioclim/) dataset40 and potential evapotranspiration from the CGIAR (Consultative Group on International Agricultural Research) Consortium for Spatial Information (https://cgiarcsi.community)41. The two axes of the principal component analysis captured about 80% of the global variation in climate. Using different combinations of variables, such as replacing potential evapotranspiration by net primary production, also obtained from CHELSA40 (Supplementary Tables 3–6), log transforming skewed variables or defining a two-dimensional climate space with mean annual temperature and mean annual precipitation (Supplementary Tables 7–10) did not qualitatively change the results (Supplementary Information). Defining a space with independent axes can be complex when dealing with correlated variables, such as mean annual temperature and precipitation. Their interrelation can challenge the concept of a genuine two-dimensional space, similar to geographic mapping with longitude and latitude. To overcome this challenge, we used principal components from a principal component analysis to define our climate space in the primary results. This method not only incorporates several variables reflecting energy and water availability constraints but also ensures the creation of truly orthogonal climate axes. Future studies of different organism groups should define an environmental space in line with the specifics of the group under investigation, as different organisms (for instance, aquatic versus terrestrial) might face different limiting variables.

We extracted the scores of each principal component for the gridded map at about 110 km (Fig. 1a,b) that were used to define species presence and absence for tetrapod groups. Choosing a procedure similar to that of defining a gridded geographic map through intervals of latitudinal and longitudinal degrees (or kilometres), we defined a gridded climate domain by assuming intervals of equal size within the climatic axes. Based on adjustable equal intervals across the climatic axes, a gridded climate domain can be defined at any desired resolution. Resolutions below 20 intervals in each climate variable produce a small number of climate cells that are too few to fit the nonlinear models used in our study. Resolutions above 60 intervals in climate variables do not substantially increase the amount of climate cells. Therefore, we tested the sensitivity of our model to different resolutions of climate space by defining climate spaces with 20, 30, 40, 50 and 60 equal intervals attributed to each climatic variable (Supplementary Information). We showed the results for 20 equal intervals in the main text, which is the resolution that maximizes model fit for all groups. Results are consistent for all resolutions and tetrapod groups (Supplementary Information). On the one hand, each climate cell of the climate domain represents several geographic locations that fall within the climatic intervals defined by the two climatic variables (Fig. 1). On the other hand, each geographic location belongs to a unique climate cell (Fig. 1). These properties represent the duality between geographic and climate space18, allowing geographic information to be mapped in climate space and vice versa.

The presence and absence information of species within climate cells is thus dependent on the geographic locations that occur within a given climatic interval. With this information, species richness is computed for all tetrapod groups by summing the presence of species within climate cells. The presence and absence information of species on the geographic cells that occur within a given climatic interval is also used to compute the multi-site β-diversity within a climate cell. The turnover component of β-diversity is computed through the Simpson index of dissimilarity, and the nestedness component of β-diversity is computed through the difference between Simpson and Sorensen dissimilarities42. The area of each climate cell (that is, climate area) is computed by summing the land surface area of all the geographic cells that occur within each climate cell (that is, all geographic cells with that respective climatic condition). To better represent climate isolation, we used three alternative metrics, but because some of them are strongly correlated with climate area and also correlated to each other we chose one of the three for the final analysis. We measured climate isolation as (1) the mean geodesic distance among all geographic cells that occur within a climate cell. Alternatively, we considered that some geographic cells that occur within a climate cell form fragments of climates (geographic cells connected to each other that occur within a single climate). Therefore, the size of climate fragments could affect the isolation measures. To control for this effect, we measured (2) the average distance between climate fragments that occur within a climate cell and (3) the number of climate fragments within a climate cell. The total count of fragments within a climate cell has a strong link with the overall climate area (with a Pearson’s correlation of 0.94). Similarly, the average distance between all geographic cells within a climate cell is also strongly related to the average distance between climate fragments (Pearson’s correlation of 0.88). In a process in which we calculate the average distance between all geographic cells within a climate cell, larger climate fragments may have a greater impact on the average because they provide more points of comparison. Therefore, in our final models, we chose to use the average distance between climate fragments within a climate cell. Finally, to represent the effect of the climate itself we computed the average principal components (PC1 and PC2) for each climate cell.

Statistical analysis

The main questions we investigated in our study are whether gradients of species richness (response variable) are associated with climate (PC1 and PC2) and the geography of climate (climate area and isolation). Model predictors were also inspected for multicollinearity with the variance inflation factor but showed very low collinearity (VIF < 1.5).

As our response variable is richness, a count data value represented by an integer variable equal to or greater than 1, a Poisson link is a natural choice. We fitted a Poisson generalized linear model with richness as response variable and geography of climate (that is, area and isolation) and climate itself (PC1 and PC2) as predictors. The generalized linear model explains approximately 75% of richness as measured by the proportion of null deviance and R2 (MacFadden’s R2; Supplementary Table 19); however, the linear model violates the assumptions of linearity, deeming estimated parameters uninterpretable (Supplementary Fig 15). Nonlinear models implemented either by polynomial generalized linear models and general additive models are equivalent (Supplementary Information). In the main text, we opted to use general additive models because these are extensions of generalized linear models, being a safer and simpler option over polynomial regressions, which were originally designed for linear regression with normally distributed errors (Supplementary Information). Thus, we replace the β-coefficients from linear regression with flexible functions that allow nonlinear association between the variables in our dataset. For this matter, we used Poisson generalized additive models with penalized smooth functions conducted through generalized cross-validation43,44. Generalized cross-validation trades-off curve complexity against goodness of fit to avoid complex overfitted estimates. Basis dimension choices for smooth terms were set to four (k = 4) as patterns in our residuals are not better explained by higher dimensions of k. In our general additive models assuming Poisson distribution, the response variable for each tetrapod group consisted of the richness observed in climate space and the predictors consisted of climate area, climate isolation and the average principal components of the first two axis of our climatic principal component analysis (PC1 and PC2). We assess the goodness of fit for our model with three metrics: proportion (or percentage) of null deviance, adjusted R2 and predicted R2. The percentage of null deviance, suitable for nonlinear models with non-normally distributed errors, measures the divergence between the observed data and the model’s predictions. It compares the null deviance (the fit for a baseline model with only an intercept and, if applicable, an offset) to the residual deviance (the deviance of the fitted model). Lower deviance values indicate a better model fit. The adjusted R2 is a modified version of a standard R2 value that accounts for the number of predictors in the model, providing a more precise measure of the model’s explanatory power. The predicted R2 measures the association between the predicted values produced by the model and the observed data, thus reflecting the model’s predictive capacity. Values across the three metrics were similar (Supplementary Information). We retain the percentage of null deviance in the main text as it is more suitable for nonlinear models with non-normally distributed errors.

On the basis of the complete model incorporating all predictors, we wanted to know how much of the proportion of null deviance can be attributed to each predictor alone, the joint effect of the geography of climate (climate area and isolation), the joint effect of climate itself (principal components one and two) and the joint effect between the geography of climate and climate itself. To do so, we fitted alternative models without each predictor and pairs of predictors and computed a reduction in deviance. In this case, the reduced models used the same smoothing parameters as the complete model.

Model residuals were inspected for climate autocorrelation using Moran’s I correlogram45 as the existence of climate autocorrelation can upward bias the significance of predictor variables and their coefficients. Spatial autocorrelation was removed by adding axes of principal components of neighbour matrices45 that were created from a distance matrix among climate cells. As principal components of neighbour matrices are used only to check whether predictors remain significant in the absence of spatial autocorrelation in the model’s residuals, the model’s R2 values are reported without the addition of axes of principal components of neighbour matrices because these spatially structured variables are added to our models to solve a statistic problem of upward bias in the significance (Extended Data Table 1). Finally, we used quantile regression to analyse the envelope pattern46 emerging from the relationship between average absolute latitudes and climate isolation with lower and upper boundaries of the relationship modelled with 0.05 and 0.95 quantiles.

Reporting summary

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