Red herrings revisited: spatial autocorrelation and parameter estimation in geographical ecology

There have been numerous claims in the ecological literature that spatial autocorrelation in the residuals of ordinary least squares (OLS) regression models results in shifts in the partial coefficients, which bias the interpretation of factors influencing geographical patterns. We evaluate the validity of these claims using gridded species richness data for the birds of North America, South America, Europe, Africa, the ex‐USSR, and Australia. We used richness in 110×110 km cells and environmental predictor variables to generate OLS and simultaneous autoregressive (SAR) multiple regression models for each region. Spatial correlograms of the residuals from each OLS model were then used to identify the minimum distance between cells necessary to avoid short‐distance residual spatial autocorrelation in each data set. This distance was used to subsample cells to generate spatially independent data. The partial OLS coefficients estimated with the full dataset were then compared to the distributions of coefficients created with the subsamples. We found that OLS coefficients generated from data containing residual spatial autocorrelation were statistically indistinguishable from coefficients generated from the same data sets in which short‐distance spatial autocorrelation was not present in all 22 coefficients tested. Consistent with the statistical literature on this subject, we conclude that coefficients estimated from OLS regression are not seriously affected by the presence of spatial autocorrelation in gridded geographical data. Further, shifts in coefficients that occurred when using SAR tended to be correlated with levels of uncertainty in the OLS coefficients. Thus, shifts in the relative importance of the predictors between OLS and SAR models are expected when small‐scale patterns for these predictors create weaker and more unstable broad‐scale coefficients. Our results indicate both that OLS regression is unbiased and that differences between spatial and nonspatial regression models should be interpreted with an explicit awareness of spatial scale.     

Analysis of determinants of mammalian species richness in South America using spatial autoregressive models

Classically, hypotheses concerning the distribution of species have been explored by evaluating the relationship between species richness and environmental variables using ordinary least squares (OLS) regression. However, environmental and ecological data generally show spatial autocorrelation, thus violating the assumption of independently distributed errors. When spatial autocorrelation exists, an alternative is to use autoregressive models that assume spatially autocorrelated errors. We examined the relationship between mammalian species richness in South America and environmental variables, thereby evaluating the relative importance of four competing hypotheses to explain mammalian species richness. Additionally, we compared the results of ordinary least squares (OLS) regression and spatial autoregressive models using Conditional and Simultaneous Autoregressive (CAR and SAR, respectively) models. Variables associated with productivity were the most important at determining mammalian species richness at the scale analyzed. Whereas OLS residuals between species richness and environmental variables were strongly autocorrelated, those from autoregressive models showed less spatial autocorrelation, particularly the SAR model, indicating its suitability for these data. Autoregressive models also fit the data better than the OLS model (increasing R² by 5–14%), and the relative importance of the explanatory variables shifted under CAR and SAR models. These analyses underscore the importance of controlling for spatial autocorrelation in biogeographical studies.     

Application of a geographically-weighted regression analysis to estimate net primary production of Chinese forest ecosystems

Aim The objective of this paper is to obtain a net primary production (NPP) regression model based on the geographically weighted regression (GWR) method, which includes spatial non‐stationarity in the parameters estimated for forest ecosystems in China. Location We used data across China. Methods We examine the relationships between NPP of Chinese forest ecosystems and environmental variables, specifically altitude, temperature, precipitation and time‐integrated normalized difference vegetation index (TINDVI) based on the ordinary least squares (OLS) regression, the spatial lag model and GWR methods. Results The GWR method made significantly better predictions of NPP in simulations than did OLS, as indicated both by corrected Akaike Information Criterion (AIC_c) and R². GWR provided a value of 4891 for AIC_c and 0.66 for R², compared with 5036 and 0.58, respectively, by OLS. GWR has the potential to reveal local patterns in the spatial distribution of a parameter, which would be ignored by the OLS approach. Furthermore, OLS may provide a false general relationship between spatially non‐stationary variables. Spatial autocorrelation violates a basic assumption of the OLS method. The spatial lag model with the consideration of spatial autocorrelation had improved performance in the NPP simulation as compared with OLS (5001 for AIC_c and 0.60 for R²), but it was still not as good as that via the GWR method. Moreover, statistically significant positive spatial autocorrelation remained in the NPP residuals with the spatial lag model at small spatial scales, while no positive spatial autocorrelation across spatial scales can be found in the GWR residuals. Conclusions We conclude that the regression analysis for Chinese forest NPP with respect to environmental factors and based alternatively on OLS, the spatial lag model, and GWR methods indicated that there was a significant improvement in model performance of GWR over OLS and the spatial lag model.     

Pteridophyte richness, climate and topography in the Iberian Peninsula: comparing spatial and nonspatial models of richness patterns

Aim To describe the spatial variation in pteridophyte species richness; evaluate the importance of macroclimate, topography and within‐grid cell range variables; assess the influence of spatial autocorrelation on the significance of the variables; and to test the prediction of the mid‐domain effect. Location The Iberian Peninsula. Methods We estimated pteridophyte richness on a grid map with c. 2500 km² cell size, using published geocoded data of the individual species. Environmental data were obtained by superimposing the grid system over isoline maps of precipitation, temperature, and altitude. Mean and range values were calculated for each cell. Pteridophyte richness was related to the environmental variables by means of nonspatial and spatial generalized least squares models. We also used ordinary least squares regression, where a variance partitioning was performed to partial out the spatial component, i.e. latitude and longitude. Coastal and central cells were compared to test the mid‐domain effect. Results Both spatial and nonspatial models showed that pteridophyte richness was best explained by a second‐order polynomial of mean annual precipitation and a quadratic elevation‐range term, although the relative importance of these two variables varied when spatial autocorrelation was accounted for. Precipitation range was weakly significant in a nonspatial multiple model (i.e. ordinary regression), and did not remain significant in spatial models. Richness is significantly higher along the coast than in the centre of the peninsula. Main conclusions Spatial autocorrelation affects the statistical significance of explanatory variables, but this did not change the biological interpretation of precipitation and elevation range as the main predictors of pteridophyte richness. Spatial and nonspatial models gave very similar results, which reinforce the idea that water availability and topographic relief control species richness in relatively high‐energy regions. The prediction of the mid‐domain effect is falsified.     

Modelling geographical patterns in species richness using eigenvector-based spatial filters

Aim To test the mechanisms driving bird species richness at broad spatial scales using eigenvector‐based spatial filtering. Location South America. Methods An eigenvector‐based spatial filtering was applied to evaluate spatial patterns in South American bird species richness, taking into account spatial autocorrelation in the data. The method consists of using the geographical coordinates of a region, based on eigenanalyses of geographical distances, to establish a set of spatial filters (eigenvectors) expressing the spatial structure of the region at different spatial scales. These filters can then be used as predictors in multiple and partial regression analyses, taking into account spatial autocorrelation. Autocorrelation in filters and in the regression residuals can be used as stopping rules to define which filters will be used in the analyses. Results Environmental component alone explained 8% of variation in richness, whereas 77% of the variation could be attributed to an interaction between environment and geography expressed by the filters (which include mainly broad‐scale climatic factors). Regression coefficients of environmental component were highest for AET. These results were unbiased by short‐scale spatial autocorrelation. Also, there was a significant interaction between topographic heterogeneity and minimum temperature. Conclusion Eigenvector‐based spatial filtering is a simple and suitable statistical protocol that can be used to analyse patterns in species richness taking into account spatial autocorrelation at different spatial scales. The results for South American birds are consistent with the climatic hypothesis, in general, and energy hypothesis, in particular. Habitat heterogeneity also has a significant effect on variation in species richness in warm tropical regions.     

Model selection and information theory in geographical ecology

Aim   Although parameter estimates are not as affected by spatial autocorrelation as Type I errors, the change from classical null hypothesis significance testing to model selection under an information theoretic approach does not completely avoid problems caused by spatial autocorrelation. Here we briefly review the model selection approach based on the Akaike information criterion (AIC) and present a new routine for Spatial Analysis in Macroecology (SAM) software that helps establishing minimum adequate models in the presence of spatial autocorrelation.
Innovation    We illustrate how a model selection approach based on the AIC can be used in geographical data by modelling patterns of mammal species in South America represented in a grid system ( n  = 383) with 2° of resolution, as a function of five environmental explanatory variables, performing an exhaustive search of minimum adequate models considering three regression methods: non-spatial ordinary least squares (OLS), spatial eigenvector mapping and the autoregressive (lagged-response) model. The models selected by spatial methods included a smaller number of explanatory variables than the one selected by OLS, and minimum adequate models contain different explanatory variables, although model averaging revealed a similar rank of explanatory variables.
Main conclusions    We stress that the AIC is sensitive to the presence of spatial autocorrelation, generating unstable and overfitted minimum adequate models to describe macroecological data based on non-spatial OLS regression. Alternative regression techniques provided different minimum adequate models and have different uncertainty levels. Despite this, the averaged model based on Akaike weights generates consistent and robust results across different methods and may be the best approach for understanding of macroecological patterns.     

Spatial autocorrelation and the selection of simultaneous autoregressive models

Aim Spatial autocorrelation is a frequent phenomenon in ecological data and can affect estimates of model coefficients and inference from statistical models. Here, we test the performance of three different simultaneous autoregressive (SAR) model types (spatial error = SAR_err, lagged = SAR_lag and mixed = SAR_mix) and common ordinary least squares (OLS) regression when accounting for spatial autocorrelation in species distribution data using four artificial data sets with known (but different) spatial autocorrelation structures. Methods We evaluate the performance of SAR models by examining spatial patterns in model residuals (with correlograms and residual maps), by comparing model parameter estimates with true values, and by assessing their type I error control with calibration curves. We calculate a total of 3240 SAR models and illustrate how the best models [in terms of minimum residual spatial autocorrelation (minRSA), maximum model fit (R²), or Akaike information criterion (AIC)] can be identified using model selection procedures. Results Our study shows that the performance of SAR models depends on model specification (i.e. model type, neighbourhood distance, coding styles of spatial weights matrices) and on the kind of spatial autocorrelation present. SAR model parameter estimates might not be more precise than those from OLS regressions in all cases. SAR_err models were the most reliable SAR models and performed well in all cases (independent of the kind of spatial autocorrelation induced and whether models were selected by minRSA, R² or AIC), whereas OLS, SAR_lag and SAR_mix models showed weak type I error control and/or unpredictable biases in parameter estimates. Main conclusions SAR_err models are recommended for use when dealing with spatially autocorrelated species distribution data. SAR_lag and SAR_mix might not always give better estimates of model coefficients than OLS, and can thus generate bias. Other spatial modelling techniques should be assessed comprehensively to test their predictive performance and accuracy for biogeographical and macroecological research.     

Water–energy,land‐cover and heterogeneity drivers of the distribution of plant species richness in a mountain region of the European Alps

Aim To evaluate the relative importance of water–energy, land‐cover, environmental heterogeneity and spatial variables on the regional distribution of Red‐Listed and common vascular plant species richness. Location Trento Province (c. 6200 km²) on the southern border of the European Alps (Italy), subdivided regularly into 228 3′ × 5′ quadrants. Methods Data from a floristic inventory were separated into two subsets, representing Red‐Listed and common (i.e. all except Red‐Listed) plant species richness. Both subsets were separately related to water–energy, land‐cover and environmental heterogeneity variables. We simultaneously applied ordinary least squares regression with variation partitioning and hierarchical partitioning, attempting to identify the most important factors controlling species richness. We combined the analysis of environmental variables with a trend surface analysis and a spatial autocorrelation analysis. Results At the regional scale, plant species richness of both Red‐Listed and common species was primarily related to energy availability and land cover, whereas environmental heterogeneity had a lesser effect. The greatest number of species of both subsets was found in quadrants with the largest energy availability and the greatest degree of urbanization. These findings suggest that the elevation range within our study region imposes an energy‐driven control on the distribution of species richness, which resembles that of the broader latitude gradient. Overall, the two species subsets had similar trends concerning the relative importance of water–energy, land cover and environmental heterogeneity, showing a few differences regarding the selection of some predictors of secondary importance. The incorporation of spatial variables did not improve the explanatory power of the environmental models and the high original spatial autocorrelation in the response variables was reduced drastically by including the selected environmental variables. Main conclusions Water–energy and land cover showed significant pure effects in explaining plant species richness, indicating that climate and land cover should both be included as explanatory variables in modelling species richness in human‐affected landscapes. However, the high degree of shared variation between the two groups made the relative effects difficult to separate. The relatively low range of variation in the environmental heterogeneity variables within our sampling domain might have caused the low importance of this complex factor.     

Autoregressive modelling of species richness in the Brazilian Cerrado.

Spatial autocorrelation is the lack of independence between pairs of observations at given distances within a geographical space, a phenomenon commonly found in ecological data. Taking into account spatial autocorrelation when evaluating problems in geographical ecology, including gradients in species richness, is important to describe both the spatial structure in data and to correct the bias in Type I errors of standard statistical analyses. However, to effectively solve these problems it is necessary to establish the best way to incorporate the spatial structure to be used in the models. In this paper, we applied autoregressive models based on different types of connections and distances between 181 cells covering the Cerrado region of Central Brazil to study the spatial variation in mammal and bird species richness across the biome. Spatial structure was stronger for birds than for mammals, with R(2) values ranging from 0.77 to 0.94 for mammals and from 0.77 to 0.97 for birds, for models based on different definitions of spatial structures. According to the Akaike Information Criterion (AIC), the best autoregressive model was obtained by using the rook connection. In general, these results furnish guidelines for future modelling of species richness patterns in relation to environmental predictors and other variables expressing human occupation in the biome.     

Spatial autocorrelation analysis allows disentangling the balance between neutral and niche processes in metacommunities

One of the most popular approaches for investigating the roles of niche and neutral processes driving metacommunity patterns consists of partitioning variation in species data into environmental and spatial components. The logic is that the distance decay of similarity in communities is expected under neutral models. However, because environmental variation is often spatially structured, the decay could also be attributed to environmental factors that are missing from the analysis. Here, we use a spatial autocorrelation analysis protocol, previously developed to detect isolation‐by‐distance in allele frequencies, to evaluate patterns of species abundances under neutral dynamics. We show that this protocol can be linked with variation partitioning analyses. Moreover, in an attempt to test the neutral model, we derive three predictions to be applied both to original species abundances and to abundances predicted by a pure spatial model species abundances will be uncorrelated; Moran's I correlograms will reveal similar short‐distance autocorrelation patterns; an increasing degree of non‐neutrality will tend to generate patterns of correlation among abundances within groups of species with similar correlograms (i.e. within species with neutral and non‐neutral dynamics). We illustrate our protocol by analyzing spatial patterns in abundance of 28 terrestrially breeding anuran species from Central Amazonia. We recommend that researchers should investigate spatial autocorrelation patterns of abundances predicted by pure spatial models to identify similar patterns of spatial autocorrelation at short distances and lack of correlation between species abundances. Therefore, the hypothesis that spatial patterns in abundances are primarily due to pure neutral dynamics (rather than to missing spatiallystructured environmental factors) can be confirmed after taking environmental variables into account.     

A comparison of simultaneous autoregressive and generalized least squares models for dealing with spatial autocorrelation

Aim  In their recent paper, Kissling & Carl (2008 ) recommended the spatial error simultaneous autoregressive model (SAR_err) over ordinary least squares (OLS) for modelling species distribution. We compared these models with the generalized least squares model (GLS) and a variant of SAR (SAR_vario). GLS and SAR_vario are superior to standard implementations of SAR because the spatial covariance structure is described by a semivariogram model.
Innovation  We used the complete datasets employed by Kissling & Carl (2008 ), with strong spatial autocorrelation, and two datasets in which the spatial structure was degraded by sample reduction and grid coarsening. GLS performed consistently better than OLS, SAR_err and SAR_vario in all datasets, especially in terms of goodness of fit. SAR_vario was marginally better than SAR_err in the degraded datasets.
Main conclusions  GLS was more reliable than SAR-based models, so its use is recommended when dealing with spatially autocorrelated data.     

Effects of woody plant species richness on mammal species richness in southern Africa

Aim To determine the relationship between the species richness of woody plants and that of mammals after accounting for the effect of environmental variables. Location Southern Africa, including Namibia, South Africa, Lesotho, Swaziland, Botswana, Zimbabwe, and part of Mozambique. Methods We used a comprehensive dataset including the species richness of mammals and of woody plants and environmental variables for 118 quadrats (each of 25,000 km²) across southern Africa, and used structural equation models (SEMs) and spatial regressions to examine the relationship between the species richness of woody plants and of mammal trophic guilds (herbivores, insectivores, carni/omnivores) and habitat guilds (aquatic/fossorial, ground‐living, climbers, aerial), after controlling for environment. We compared the results of SEMs with those of single‐predictor regressions (without controlling for environment) and of spatial regressions (controlling for both environment and residual spatial autocorrelation). Results The geographical variation of mammal species richness in southern Africa was strongly and positively related to that of woody plant species richness, and this relationship held for most mammal guilds even when the influence of environment and spatial autocorrelation had been accounted for. However, the effect of woody plant species richness on the richness of aquatic/fossorial species almost disappeared after controlling for environment, suggesting that the congruence in species richness patterns between these two groups results from similar responses to the same environmental variables. For many mammal guilds, the relative role of environmental predictors as measured by standardized partial regression coefficients changed depending on whether non‐spatial single‐predictor regressions, non‐spatial SEMs, or spatial regressions were used. Main conclusions Woody plants are important determinants of the species richness of most mammal guilds in southern Africa, even when controlling for environment and residual spatial autocorrelation. Environmental correlates with animal species richness as measured by simple correlations or single‐predictor regressions might not always reflect direct effects; they might, at least to some degree, result from indirect effects via woody plants. Interpretations of the strength of the effect of environmental variables on mammal species richness in southern Africa depend largely on whether spatial or non‐spatial models are used. We therefore stress the need for caution when interpreting environmental ‘effects’ on broad‐scale patterns of species richness if spatial and non‐spatial methods yield contrasting results.     

Geographical patterns of community‐based tree species richness in Chinese mountain forests: the effects of contemporary climate and regional history

The relationship between climate/productivity and historical/regional contingency and their relative influence on geographical patterns of species richness (GPSR) are still unresolved. Based on field data from 1494 plots from forests on 63 mountains across China, we document the GPSR for forest communities. Regression tree and generalized linear models were used to explore the discreteness and gradient of the distribution of tree species richness (α‐diversity), and to estimate the correlations of climate, historical floristic region, and local habitat with species richness. The collinearity between climatic variables and region were further disentangled; and the spatial autocorrelation in the patterns of α‐diversity and the residuals of alternative predictive models were compared. Overall, 75% of variation in plot‐based α‐diversity of trees was accounted for by all variables included, and about 66.5%, 64.5% and 27.9% by climate, region, and local habitat respectively. Importantly, the explanatory power of these variables differed in particular for coniferous, deciduous broadleaved and evergreen broadleaved species. Ambient temperature was more important for α‐diversity of trees than were the other climatic variables across China. Spatial autocorrelation in the pattern of α‐diversity could be accounted for mainly by spatial variation climate. The concordance between tree α‐diversity, historical flora, contemporary climate, and Quaternary climate change mode suggests the climate/productivity and historical/regional contingency both contribute to the GPSR in a complimentary manner. Taken together, our results provide unique evidence to link of the effects of contemporary climate and historical climate change on species richness across scales.     

Spatial autocorrelation as a tool for identifying the geographical patterns of aphid annual abundance

Abstract 1 A spatial autocorrelation analysis was undertaken to investigate the spatial structure of annual abundance for the pest aphid Myzus persicae collected in suction traps distributed across north‐west Europe. 2 The analysis was applied at two different scales. The Moran index was used to estimate the degree of spatial autocorrelation at all sites within the study area (global level). The contributions of each site to the global index were identified by the use of a local indicator of spatial autocorrelation (LISA). A hierarchical cluster analysis was undertaken to highlight differences between groups of resulting correlograms. 3 Similarity between traps was shown to occur over large geographical distances, suggesting an impact of phenomena such as climatic gradients or land use types. 4 The presence of outliers and zones of similarity (hot‐spots) and of dissimilarity (cold‐spots) were identified indicating a strong impact of local effects. 5 Several groups of traps characterized by similarities in their local spatial structure (correlograms, value of Moran's I_i) also had similar values for land use variables (the area occupied by agricultural zones, forest and sea). 6 It is concluded that trap data can provide information about Myzus persicae that is representative of large geographical areas. Thus, trap data can be used to estimate the aerial abundance of this species, even if the suction traps are not regularly and densely distributed.     

Richness patterns, species distributions and the principle of extreme deconstruction

Aim To analyse the global patterns in species richness of Viperidae snakes through the deconstruction of richness into sets of species according to their distribution models, range size, body size and phylogenetic structure, and to test if environmental drivers explaining the geographical ranges of species are similar to those explaining richness patterns, something we called the extreme deconstruction principle. Location Global. Methods We generated a global dataset of 228 terrestrial viperid snakes, which included geographical ranges (mapped at 1° resolution, for a grid with 7331 cells world‐wide), body sizes and phylogenetic relationships among species. We used logistic regression (generalized linear model; GLM) to model species geographical ranges with five environmental predictors. Sets of species richness were also generated for large and small‐bodied species, for basal and derived species and for four classes of geographical range sizes. Richness patterns were also modelled against the five environmental variables through standard ordinary least squares (OLS) multiple regressions. These subsets are replications to test if environmental factors driving species geographical ranges can be directly associated with those explaining richness patterns. Results Around 48% of the total variance in viperid richness was explained by the environmental model, but richness sets revealed different patterns across the world. The similarity between OLS coefficients and the primacy of variables across species geographical range GLMs was equal to 0.645 when analysing all viperid snakes. Thus, in general, when an environmental predictor it is important to model species geographical ranges, this predictor is also important when modelling richness, so that the extreme deconstruction principle holds. However, replicating this correlation using subsets of species within different categories in body size, range size and phylogenetic structure gave more variable results, with correlations between GLM and OLS coefficients varying from –0.46 up to 0.83. Despite this, there is a relatively high correspondence (r = 0.73) between the similarity of GLM‐OLS coefficients and R² values of richness models, indicating that when richness is well explained by the environment, the relative importance of environmental drivers is similar in the richness OLS and its corresponding set of GLMs. Main conclusions The deconstruction of species richness based on macroecological traits revealed that, at least for range size and phylogenetic level, the causes underlying patterns in viperid richness differ for the various sets of species. On the other hand, our analyses of extreme deconstruction using GLM for species geographical range support the idea that, if environmental drivers determine the geographical distribution of species by establishing niche boundaries, it is expected, at least in theory, that the overlap among ranges (i.e. richness) will reveal similar effects of these environmental drivers. Richness patterns may be indeed viewed as macroecological consequences of population‐level processes acting on species geographical ranges.     

Ambient, productive and wind energy, and ocean extent predict global species richness of procellariiform seabirds

Aims Tests of the energy hypothesis for the large‐scale distribution of species richness have largely been concerned with the influence of two alternative forms of environmental energy, temperature and energy from primary productivity, both of which (at least in terrestrial systems) peak within the tropics. Taxa showing extra‐tropical diversity peaks present a potential challenge to the generality of species–energy theory. One such group are pelagic seabirds of the order Procellariiformes that show not only an extra‐tropical diversity peak but one confined to the Southern Ocean, hence a highly asymmetric one. They are distinct in being exceptionally adapted to take advantage of wind energy, which they may rely on for long‐distance ocean foraging for the patchy resources needed to meet their energetic needs. Wind represents a readily available source of kinetic energy, shows a strong latitudinal gradient, and has been largely omitted from species–energy theory. Moreover, maximal benefits of wind are likely to be afforded in areas of greatest available contiguous ocean extent. We compare the relative importance of wind speed, ocean productivity (chlorophyll concentration), air temperature and available ocean extent (distance) in explaining large‐scale global distribution of procellariiform species richness across the world's oceans. Location Global, oceanic. Methods Hierarchical partitioning, model selection, ordinary least squares (OLS) and spatial generalized least squares (GLS) regression. Results Hierarchical partitioning of non‐spatial regression models indicates that ocean distance is the most important predictor of procellariiform species richness followed by wind speed and then temperature. In contrast, that of spatial regression models indicates the roughly equal importance of ocean distance and temperature, followed by wind speed. Although contributing additional model fit, ocean productivity is consistently the weakest predictor. Best‐fit models include all four predictors and explain 67% of observed variation. The species–productivity relationship is negative overall, while the species–temperature relationship is hump‐shaped. In contrast, ocean distance and wind speed are positively associated with species richness. Conclusions Large‐scale procellariiform species richness distribution may represent a trade‐off in the use of different energy forms, being highest in Southern Ocean areas where productive energy and temperature are relatively low, but where available ocean foraging extent and wind energy required to utilize it are near‐maximal.     

Hot,dry and different: Australian lizard richness is unlike that of mammals,amphibians and birds

Aims (1) To map the species richness of Australian lizards and describe patterns of range size and species turnover that underlie them. (2) To assess the congruence in the species richness of lizards and other vertebrate groups. (3) To search for commonalities in the drivers of species richness in Australian vertebrates. Location Australia. Methods We digitized lizard distribution data to generate gridded maps of species richness and β‐diversity. Using similar maps for amphibians, mammals and birds, we explored the relationship between species richness and temperature, actual evapotranspiration, elevation and local elevation range. We used spatial eigenvector filtering and geographically weighted regression to explore geographical patterns and take spatial autocorrelation into account. We explored congruence between the species richness of vertebrate groups whilst controlling for environmental effects. Results Lizard richness peaks in the central deserts (where β‐diversity is low) and tropical north‐east (where β‐diversity is high). The intervening lowlands have low species richness and β‐diversity. Generally, lizard richness is uncorrelated with that of other vertebrates but this low congruence is strongly spatially structured. Environmental models for all groups also show strong spatial heterogeneity. Lizard richness is predicted by different environmental factors from other vertebrates, being highest in dry and hot regions. Accounting for environmental drivers, lizard richness is weakly positively related to richness of other vertebrates, both at global and local scales. Main conclusions Lizard species richness differs from that of other vertebrates. This difference is probably caused by differential responses to environmental gradients and different centres of diversification; there is little evidence for inter‐taxon competition limiting lizard richness. Local variation in habitat diversity or evolutionary radiations may explain weak associations between taxa, after controlling for environmental variables. We strongly recommend that studies of variation in species richness examine and account for non‐stationarity.