Spatial autocorrelation and red herrings in geographical ecology

Aim Spatial autocorrelation in ecological data can inflate Type I errors in statistical analyses. There has also been a recent claim that spatial autocorrelation generates ‘red herrings’, such that virtually all past analyses are flawed. We consider the origins of this phenomenon, the implications of spatial autocorrelation for macro‐scale patterns of species diversity and set out a clarification of the statistical problems generated by its presence. Location To illustrate the issues involved, we analyse the species richness of the birds of western/central Europe, north Africa and the Middle East. Methods Spatial correlograms for richness and five environmental variables were generated using Moran's I coefficients. Multiple regression, using both ordinary least‐squares (OLS) and generalized least squares (GLS) assuming a spatial structure in the residuals, were used to identify the strongest predictors of richness. Autocorrelation analyses of the residuals obtained after stepwise OLS regression were undertaken, and the ranks of variables in the full OLS and GLS models were compared. Results Bird richness is characterized by a quadratic north–south gradient. Spatial correlograms usually had positive autocorrelation up to c. 1600 km. Including the environmental variables successively in the OLS model reduced spatial autocorrelation in the residuals to non‐detectable levels, indicating that the variables explained all spatial structure in the data. In principle, if residuals are not autocorrelated then OLS is a special case of GLS. However, our comparison between OLS and GLS models including all environmental variables revealed that GLS de‐emphasized predictors with strong autocorrelation and long‐distance clinal structures, giving more importance to variables acting at smaller geographical scales. Conclusion Although spatial autocorrelation should always be investigated, it does not necessarily generate bias. Rather, it can be a useful tool to investigate mechanisms operating on richness at different spatial scales. Claims that analyses that do not take into account spatial autocorrelation are flawed are without foundation.     

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.     

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.     

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.     

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.     

Evidence of history in explaining diversity patterns in tropical riverine fish

Aim Documentation of the ongoing effect of rain forest refuges at the last glacial maximum (LGM) on patterns of tropical freshwater fish diversity. Location Tropical South and Central America, and West Africa. Methods LGM rain forest regions and species richness by drainage were compiled from published data. GIS mapping was applied to compile drainage area and contemporary primary productivity. We used multiple regression analyses, applied separately for Tropical South America, Central America and West Africa, to assess differences in species richness between drainages that were connected and disconnected to rain forest refuge zones during the LGM. Spatial autocorrelation of the residuals was tested using Moran's I statistic. We added an intercontinental comparison to our analyses to see if a historical signal would persist even when a regional historical effect (climate at the LGM) had already been accounted for. Results Both area and history (contact with LGM rain forest refuge) explained the greatest proportions of variance in the geographical pattern of riverine species richness. In the three examined regions, we found highest richness in drainages that were connected to the rain forest refuges. No significant residual spatial autocorrelation was detected after considering area, primary productivity and LGM rain forest refuges. These results show that past climatic events still affect West African and Latin American regional and continental freshwater fish richness. At the continental scale, we found South American rivers more species‐rich than expected on the basis of their area, productivity and connectedness to rain forest refuge. Conversely, Central American rivers were less species‐diverse than expected by the grouped model. African rivers were intermediate. Therefore, a historical signal persists even when a regional historical effect (climate at the LGM) had already been accounted for. Main conclusions It has been hypothesized that past climatic events have limited impact on species richness because species have tracked environmental changes through range shifts. However, when considering organisms with physically constrained dispersal (such as freshwater fish), past events leave a perceptible imprint on present species diversity. Furthermore, we considered regions that have comparable contemporary climatic and environmental characteristics, explaining the absence of a productivity effect. From the LGM to the present day (a time scale of 18,000 years), extinction processes should have played a predominant role in shaping the current diversity pattern. By contrast, the continental effects could reflect historical contingencies explained by differences in speciation and extinction rates between continents at higher time scales (millions of years).     

Type and spatial structure of distribution data and the perceived determinants of geographical gradients in ecology: the species richness of African birds

Aim Studies exploring the determinants of geographical gradients in the occurrence of species or their traits obtain data by: (1) overlaying species range maps; (2) mapping survey‐based species counts; or (3) superimposing models of individual species’ distributions. These data types have different spatial characteristics. We investigated whether these differences influence conclusions regarding postulated determinants of species richness patterns. Location Our study examined terrestrial bird diversity patterns in 13 nations of southern and eastern Africa, spanning temperate to tropical climates. Methods Four species richness maps were compiled based on range maps, field‐derived bird atlas data, logistic and autologistic distribution models. Ordinary and spatial regression models served to examine how well each of five hypotheses predicted patterns in each map. These hypotheses propose productivity, temperature, the heat–water balance, habitat heterogeneity and climatic stability as the predominant determinants of species richness. Results The four richness maps portrayed broadly similar geographical patterns but, due to the nature of underlying data types, exhibited marked differences in spatial autocorrelation structure. These differences in spatial structure emerged as important in determining which hypothesis appeared most capable of explaining each map's patterns. This was true even when regressions accounted for spurious effects of spatial autocorrelation. Each richness map, therefore, identified a different hypothesis as the most likely cause of broad‐scale gradients in species diversity. Main conclusions Because the ‘true’ spatial structure of species richness patterns remains elusive, firm conclusions regarding their underlying environmental drivers remain difficult. More broadly, our findings suggest that care should be taken to interpret putative determinants of large‐scale ecological gradients in light of the type and spatial characteristics of the underlying data. Indeed, closer scrutiny of these underlying data — here the distributions of individual species — and their environmental associations may offer important insights into the ultimate causes of observed broad‐scale patterns.     

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.     

Incorporating spatial autocorrelation into species distribution models alters forecasts of climate‐mediated range shifts

Species distribution models (SDMs) are widely used to forecast changes in the spatial distributions of species and communities in response to climate change. However, spatial autocorrelation (SA) is rarely accounted for in these models, despite its ubiquity in broad‐scale ecological data. While spatial autocorrelation in model residuals is known to result in biased parameter estimates and the inflation of type I errors, the influence of unmodeled SA on species' range forecasts is poorly understood. Here we quantify how accounting for SA in SDMs influences the magnitude of range shift forecasts produced by SDMs for multiple climate change scenarios. SDMs were fitted to simulated data with a known autocorrelation structure, and to field observations of three mangrove communities from northern Australia displaying strong spatial autocorrelation. Three modeling approaches were implemented: environment‐only models (most frequently applied in species' range forecasts), and two approaches that incorporate SA; autologistic models and residuals autocovariate (RAC) models. Differences in forecasts among modeling approaches and climate scenarios were quantified. While all model predictions at the current time closely matched that of the actual current distribution of the mangrove communities, under the climate change scenarios environment‐only models forecast substantially greater range shifts than models incorporating SA. Furthermore, the magnitude of these differences intensified with increasing increments of climate change across the scenarios. When models do not account for SA, forecasts of species' range shifts indicate more extreme impacts of climate change, compared to models that explicitly account for SA. Therefore, where biological or population processes induce substantial autocorrelation in the distribution of organisms, and this is not modeled, model predictions will be inaccurate. These results have global importance for conservation efforts as inaccurate forecasts lead to ineffective prioritization of conservation activities and potentially to avoidable species extinctions.     

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.     

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.     

宏生态尺度上景观破碎化对物种丰富度的影响

生物多样性的地理格局及其形成机制是宏生态学与生物地理学的研究热点。大量研究表明,景观尺度上的生境破碎化对物种多样性的分布格局具有重要作用,但目前尚不清楚这种作用是否足以在宏生态尺度上对生物多样性地理格局产生显著影响。利用中国大陆鸟类和哺乳动物的物种分布数据,在100 km×100 km网格的基础上生成了这两个类群生物的物种丰富度地理格局,进一步利用普通最小二乘法模型和空间自回归模型研究了物种丰富度与气候、生境异质性、景观破碎化的相关关系。结果表明,景观破碎化因子与鸟类和哺乳动物的物种丰富度都具有显著的关联关系,其方差贡献率可达约30%—50%(非空间模型)和60%—80%(空间模型),略低于或接近于气候和生境异质性因子。方差分解结果显示,景观破碎化因子与气候和生境异质性因子的方差贡献率的重叠部分达20%—40%。相对鸟类而言,景观破碎化对哺乳动物物种丰富度的地理格局具有更高的解释率。     

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.     

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.     

Comparison of native and exotic distribution and richness models across scales reveals essential conservation lessons

Comparing native and exotic plant species distribution and richness models can help to reveal the causes of invasive exotic species proliferation and provide recommendations for preserving native‐dominated ecosystems. However, models may have limited applicability if potentially divergent patterns across scales, spatial autocorrelation and correspondence with community‐wide patterns such as species richness are not considered. I modeled the distributions of 20 dominant native and 20 dominant exotic species among and within patches in a heavily‐invaded and threatened ecosystem in western North America, examining the roles of scale and species origin on variable selection, spatial autocorrelation and model accuracy to determine conditions that favour native over exotic dominants, and derive recommendations for effective management. I also compared distribution models with native and exotic species richness models, to determine the extent to which dominant native and exotic species were representative of synoptic community patterns. Predictability was lower for exotic dominants, possibly because they are environmental generalists, and was lower within than among patches. Predictors were generally shared between distribution and richness models; however, species‐specific differences were common within both native and exotic species groups. Predictors for individual species across scales were frequently different and sometimes opposing. Distribution and richness models suggest that management assuming environmental affiliation at one scale may be ineffective at another; that site prioritization to maximize native versus exotic richness may not preserve the habitat of some common native species; and that intensive management to reduce exotics may be difficult due to low predictability and shared affiliations with natives. Comparing native and exotic distribution and richness models at two scales enabled scale‐specific conservation recommendations and elucidated trade‐offs between management for richness and representation that distribution models at an individual scale would not have allowed.     

Non-stationarity and local approaches to modelling the distributions of wildlife

Despite a growing interest in species distribution modelling, relatively little attention has been paid to spatial autocorrelation and non-stationarity. Both spatial autocorrelation (the tendency for adjacent locations to be more similar than distant ones) and non-stationarity (the variation in modelled relationships over space) are likely to be common properties of ecological systems. This paper focuses on non-stationarity and uses two local techniques, geographically weighted regression (GWR) and varying coefficient modelling (VCM), to assess its impact on model predictions. We extend two published studies, one on the presence–absence of calandra larks in Spain and the other on bird species richness in Britain, to compare GWR and VCM with the more usual global generalized linear modelling (GLM) and generalized additive modelling (GAM). For the calandra lark data, GWR and VCM produced better-fitting models than GLM or GAM. VCM in particular gave significantly reduced spatial autocorrelation in the model residuals. GWR showed that individual predictors became stationary at different spatial scales, indicating that distributions are influenced by ecological processes operating over multiple scales. VCM was able to predict occurrence accurately on independent data from the same geographical area as the training data but not beyond, whereas the GAM produced good results on all areas. Individual predictions from the local methods often differed substantially from the global models. For the species richness data, VCM and GWR produced far better predictions than ordinary regression. Our analyses suggest that modellers interpolating data to produce maps for practical actions (e.g. conservation) should consider local methods, whereas they should not be used for extrapolation to new areas. We argue that local methods are complementary to global methods, revealing details of habitat associations and data properties which global methods average out and miss.     

Predicting alpha diversity of African rain forests: models based on climate and satellite‐derived data do not perform better than a purely spatial model

Aim Our aim was to evaluate the extent to which we can predict and map tree alpha diversity across broad spatial scales either by using climate and remote sensing data or by exploiting spatial autocorrelation patterns. Location Tropical rain forest, West Africa and Atlantic Central Africa. Methods Alpha diversity estimates were compiled for trees with diameter at breast height ≥ 10 cm in 573 inventory plots. Linear regression (ordinary least squares, OLS) and random forest (RF) statistical techniques were used to project alpha diversity estimates at unsampled locations using climate data and remote sensing data [Moderate Resolution Imaging Spectroradiometer (MODIS), normalized difference vegetation index (NDVI), Quick Scatterometer (QSCAT), tree cover, elevation]. The prediction reliabilities of OLS and RF models were evaluated using a novel approach and compared to that of a kriging model based on geographic location alone. Results The predictive power of the kriging model was comparable to that of OLS and RF models based on climatic and remote sensing data. The three models provided congruent predictions of alpha diversity in well‐sampled areas but not in poorly inventoried locations. The reliability of the predictions of all three models declined markedly with distance from points with inventory data, becoming very low at distances > 50 km. According to inventory data, Atlantic Central African forests display a higher mean alpha diversity than do West African forests. Main conclusions The lower tree alpha diversity in West Africa than in Atlantic Central Africa may reflect a richer regional species pool in the latter. Our results emphasize and illustrate the need to test model predictions in a spatially explicit manner. Good OLS or RF model predictions from inventory data at short distance largely result from the strong spatial autocorrelation displayed by both the alpha diversity and the predictive variables rather than necessarily from causal relationships. Our results suggest that alpha diversity is driven by history rather than by the contemporary environment. Given the low predictive power of models, we call for a major effort to broaden the geographical extent and intensity of forest assessments to expand our knowledge of African rain forest diversity.     

Spatial autocorrelation patterns of stream invertebrates: exogenous and endogenous factors

Aim To investigate spatial autocorrelation of taxonomic stream invertebrate groups (richness and composition) at a large geographical scale and to analyse the importance of exogenous and endogenous factors. Location The Mediterranean Basin. Methods For exogenous factors, we used large‐scale factors related to climate, geology and river zonation; for endogenous factors, we used the dispersal mode of each taxonomic group. After describing and analysing spatial patterns of genus richness and genus composition of stream invertebrate groups in the Mediterranean Basin, we computed Moran’s I before and after accounting for the exogenous factors and related it to the endogenous factors. Results In relation to genus richness, most of the taxonomic groups did not show significant spatial autocorrelation, suggesting that no main large‐scale exogenous or endogenous factors were important and that local‐scale factors were probably controlling taxonomic richness. In contrast, for genus composition, all taxonomic groups except Odonata had significant spatial autocorrelation before accounting for the environment. After accounting for the environment, most taxonomic groups still had a significant spatial autocorrelation, but it decreased with their increasing dispersal ability (from Crustacea to Coleoptera). Thus, spatial taxonomic composition of groups with the strongest dispersal potential is mainly related to exogenous factors, whereas that of groups with weaker dispersal potential is related to a combination of exogenous and endogenous factors. Main conclusions Our results illustrate the importance of dispersal as an endogenous factor causing spatial autocorrelation and suggest that ignoring endogenous factors can lead to misunderstandings when explaining large‐scale community patterns.