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.     

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.     

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。     

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.     

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.     

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.     

基于不同空间模型的马尾松林生态系统碳密度研究

以江西省马尾松林生态系统为研究对象,基于样地调查及样品碳含量测定结果计算其碳密度,并选取立地、植被及气象等方面的15个因子,采用多元线性逐步回归方法筛选出对生态系统碳密度影响显著的因子,然后分别利用最小二乘模型(OLS)、空间误差模型(SEM)、空间滞后模型(SLM)和地理加权回归模型(GWR)构建生态系统碳密度与其影响因子之间的关系模型,筛选出最优的拟合模型。结果表明:对马尾松林生态系统碳密度影响显著的因子分别为海拔、坡度、土层厚度、胸径、年均温度和年均降水量。4种模型拟合结果均显示碳密度与坡度呈负相关,与海拔、土层厚度、胸径呈正相关。模型的决定系数(R~2)由大到小分别为GWR(0.8043)SEM(0.6371)SLM(0.6364)OLS(0.6321),模型均方误差(MSE)与赤池信息准则(AIC)最大的均为OLS模型,最小的均为GWR模型;残差检验表明GWR模型能有效降低模型残差的空间自相关性。综合分析得出GWR模型的拟合效果最优,更适用于江西省马尾松林生态系统碳密度的估测。     

Can niche‐based distribution models outperform spatial interpolation?

Aim Distribution modelling relates sparse data on species occurrence or abundance to environmental information to predict the population of a species at any point in space. Recently, the importance of spatial autocorrelation in distributions has been recognized. Spatial autocorrelation can be categorized as exogenous (stemming from autocorrelation in the underlying variables) or endogenous (stemming from activities of the organism itself, such as dispersal). Typically, one asks whether spatial models explain additional variability (endogenous) in comparison to a fully specified habitat model. We turned this question around and asked: can habitat models explain additional variation when spatial structure is accounted for in a fully specified spatially explicit model? The aim was to find out to what degree habitat models may be inadvertently capturing spatial structure rather than true explanatory mechanisms. Location We used data from 190 species of the North American Breeding Bird Survey covering the conterminous United States and southern Canada. Methods We built 13 different models on 190 bird species using regression trees. Our habitat‐based models used climate and landcover variables as independent variables. We also used random variables and simulated ranges to validate our results. The two spatially explicit models included only geographical coordinates or a contagion term as independent variables. As another angle on the question of mechanism vs. spatial structure we pitted a model using related bird species as predictors against a model using randomly selected bird species. Results The spatially explicit models outperformed the traditional habitat models and the random predictor species outperformed the related predictor species. In addition, environmental variables produced a substantial R² in predicting artificial ranges. Main conclusions We conclude that many explanatory variables with suitable spatial structure can work well in species distribution models. The predictive power of environmental variables is not necessarily mechanistic, and spatial interpolation can outperform environmental explanatory variables.     

Patterns of island occupancy in bats: influences of area and isolation on insular incidence of volant mammals

Aim  The influence of landscape structure on the distribution patterns of bats remains poorly understood for many species. This study investigates the relationship between area and isolation of islands and the probability of occurrence of six bat species to determine whether persistence and immigration abilities vary among bat species and foraging guilds.
Location  Thirty-two islands in the Gulf of California near the Baja California peninsula in north-west Mexico.
Methods  Using logistic regression and Akaike information criterion (AIC) model selection, we compared five a priori models for each of six bat species to explain patterns of island occupancy, including random patterns, minimum area effects, maximum isolation effects, additive area and isolation effects and compensatory area and isolation effects.
Results  Five species of insectivorous bats ( Pipistrellus hesperus , Myotis californicus , Macrotus californicus , Antrozous pallidus and Mormoops megalophylla ) displayed minimum area thresholds on incidence. The probability of occurrence tended to decrease at moderate distances of isolation ( c . 10–15 km) for these species (excepting A. pallidus ). The distributions of two non-insectivorous species ( Leptonycteris curasoae and Myotis vivesi ) were not influenced by island size and isolation.
Main conclusions  Minimum area thresholds on incidence suggest that island occupancy by insectivorous bats may be limited by resource requirements. Islands smaller than 100 ha typically did not support occupancy or use by insectivorous bats, except at minimal isolation distances. Insectivorous bat species may also be more sensitive to moderate levels of habitat isolation in some landscape contexts than previously expected. Our results suggest that differences in foraging habits may have important implications for understanding the distribution patterns of bats.     

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.     

Modelling the occurrence of threatened plant species in taiga landscapes: methodological and ecological perspectives

Aim Understanding the spatial patterns of species distribution and predicting the occurrence of high biological diversity and rare species are central themes in biogeography and environmental conservation. The aim of this study was to model and scrutinize the relative contributions of climate, topography, geology and land‐cover factors to the distributions of threatened vascular plant species in taiga landscapes in northern Finland. Location North‐east Finland, northern Europe. Methods The study was performed using a data set of 28 plant species and environmental variables at a 25‐ha resolution. Four different stepwise selection algorithms [Akaike information criterion (AIC), Bayesian information criterion (BIC), adaptive backfitting, cross selection] with generalized additive models (GAMs) were fitted to identify the main environmental correlates for species occurrences. The accuracies of the distribution models were evaluated using fourfold cross‐validation based on the area under the curve (AUC) derived from receiver operating characteristic plots. The GAMs were tentatively extrapolated to the whole study area and species occurrence probability maps were produced using GIS techniques. The effect of spatial autocorrelation on the modelling results was also tested by including autocovariate terms in the GAMs. Results According to the AUC values, the model performance varied from fair to excellent. The AIC algorithm provided the highest mean performance (mean AUC = 0.889), whereas the lowest mean AUC (0.851) was obtained from BIC. Most of the variation in the distribution of threatened plant species was related to growing degree days, temperature of the coldest month, water balance, cover of mire and mean elevation. In general, climate was the most powerful explanatory variable group, followed by land cover, topography and geology. Inclusion of the autocovariate only slightly improved the performance of the models and had a minor effect on the importance of the environmental variables. Main conclusions The results confirm that the landscape‐scale distribution patterns of plant species can be modelled well on the basis of environmental parameters. A spatial grid system with several environmental variables derived from remote sensing and GIS data was found to produce useful data sets, which can be employed when predicting species distribution patterns over extensive areas. Landscape‐scale maps showing the predicted occurrences of individual or multiple threatened plant species may provide a useful basis for focusing field surveys and allocating conservation efforts.     

Mapping species density of trees,shrubs and vines in a tropical forest,using field measurements,satellite multiespectral imagery and spatial interpolation

We estimated the number of species in a tropical forest landscape in Quintana Roo, Mexico, based on the relationship between reflectance values of satellite imagery and field measurements of plant species density (mean number of species per plot). Total species density as well as that of tree, shrub and vine species were identified from 141 sampling quadrats (16543 individuals sampled). Spatial prediction of plant diversity was performed using universal kriging. This approach considered the linear relationship between plant species density and reflectance values of Thematic Mapper™, as well as the spatial dependence of the observations. We explored the linear relationships between spectral properties of TM bands and the species density of trees, shrubs and vines, using regression analysis. We employed Akaike Information Criterion (AIC) to select a set of candidate models. Based on Akaike weights, we calculated model-averaged parameters. Linear regression between number of species and reflectance values of TM bands yielded regression residuals. We used variogram analysis to analyze the spatial structure of these residuals. Results show that accounting for spatial autocorrelation in the residual variation improved model R² from 0.57 to 0.66 for number of all species, from 0.58 to 0.65 for number of tree species, from 0.26 to 0.41 for number of shrub species and from 0.13 to 0.17 for species density of vines. The empirical models we developed can be used to predict landscape-level species density in the Yucatan Peninsula, helping to guide and evaluate management and conservation strategies.     

Assessing species density and abundance of tropical trees from remotely sensed data and geostatistics

Question: What relationships exist between remotely sensed measurements and field observations of species density and abundance of tree species? Can these relationships and spatial interpolation approaches be used to improve the accuracy of prediction of species density and abundance of tree species? Location: Quintana Roo, Yucatan peninsula, Mexico. Methods: Spatial prediction of species density and abundance of species for three functional groups was performed using regression kriging, which considers the linear relationship between dependent and explanatory variables, as well as the spatial dependence of the observations. These relationships were explored using regression analysis with species density and abundance of species of three functional groups as dependent variables, and reflectance values of spectral bands, computed NDVI (normalized difference vegetation index), standard deviation of NDVI and texture measurements of Landsat 7 Thematic Mapper (TM) imagery as explanatory variables. Akaike information criterion was employed to select a set of candidate models and calculate model‐averaged parameters. Variogram analysis was used to analyze the spatial structure of the residuals of the linear regressions. Results: Species density of trees was related to reflectance values of TM4, NDVI and spatial heterogeneity of land cover types, while the abundance of species in functional groups showed different patterns of association with remotely sensed data. Models that accounted for spatial autocorrelation improved the accuracy of estimates in all cases. Conclusions: Our approach can substantially increase the accuracy of the spatial estimates of species richness and abundance of tropical tree species and can help guide and evaluate tropical forest management and conservation.     

Comparison of approaches to combine species distribution models based on different sets of predictors

Distribution models should take into account the different limiting factors that simultaneously influence species ranges. Species distribution models built with different explanatory variables can be combined into more comprehensive ones, but the resulting models should maximize complementarity and avoid redundancy. Our aim was to compare the different methods available for combining species distribution models. We modelled 19 threatened vertebrate species in mainland Spain, producing models according to three individual explanatory factors: spatial constraints, topography and climate, and human influence. We used five approaches for model combination: Bayesian inference, Akaike weight averaging, stepwise variable selection, updating, and fuzzy logic. We compared the performance of these approaches by assessing different aspects of their classification and discrimination capacity. We demonstrated that different approaches to model combination give rise to disparities in the model outputs. Bayesian integration was systematically affected by an error in the equations that are habitually used in distribution modelling. Akaike weights produced models that were driven by the best single factor and therefore failed at combining the models effectively. The updating and the stepwise approaches shared recalibration as the basic concept for model combination, were very similar in their performance, and showed the highest sensitivity and discrimination capacity. The fuzzy‐logic approach yielded models with the highest classification capacity according to Cohen's kappa. In conclusion: 1) Bayesian integration, employing the currently used equation, and the Akaike weight procedure should be avoided; 2) the updating and stepwise approaches can be considered minor variants of the same recalibrating approach; and 3) there is a trade‐off between this recalibrating approach, which has the highest sensitivity, and fuzzy logic, which has the highest overall classification capacity. Recalibration is better if unfavourable conditions in one environmental factor may be counterbalanced with favourable conditions in a different factor, otherwise fuzzy logic is better.     

Predicting the future of species diversity: macroecological theory, climate change, and direct tests of alternative forecasting methods

Accurate predictions of future shifts in species diversity in response to global change are critical if useful conservation strategies are to be developed. The most widely used prediction method is to model individual species niches from point observations and project these models forward using future climate scenarios. The resulting changes in individual ranges are then summed to predict diversity changes; multiple models can be combined to produce ensemble forecasts. Predictions based on environment-richness regressions are rarer. However, richness regression models, based on macroecological diversity theory, have a long track record of making reliable spatial predictions of diversity patterns. If these empirical theories capture true functional relationships between environment and diversity, then they should make consistent predictions through time as well as space and could complement individual species-based predictions. Here, we use climate change throughout the 20th century to directly test the ability of these different approaches to predict shifts of Canadian butterfly diversity. We found that all approaches performed reasonably well, but the most accurate predictions were made using the single best richness-environment regression model, after accounting for the effects of spatial autocorrelation. Spatially trained regression models based on macroecological theory accurately predict diversity shifts for large species assemblages. Global changes provide pseudo-experimental tests of those macroecological theories that can then generate robust predictions of future conditions.     

基于地理加权回归拓展模型的天然次生林碳储量空间分布

为精准获取区域尺度天然次生林的碳储量及其空间分布格局,以吉林省汪清林业局浪溪林场的天然次生林为研究对象,基于165块局级固定样地,以林分因子、地形因子和土壤因子为影响因子,将普通地理加权回归模型(GWR)作为基础,从空间维度、参数异质性特征和残差空间自相关性3个方面进行改进,构建7类拓展模型,即地理海拔加权回归模型(G...     

Empirical modelling of lake water-temperature relationships: a comparison of approaches

1.  As a result of the role that temperature plays in many aquatic processes, good predictive models of annual maximum near-surface lake water temperature across large spatial scales are needed, particularly given concerns regarding climate change. Comparisons of suitable modelling approaches are required to determine their relative merit and suitability for providing good predictions of current conditions. We developed models predicting annual maximum near-surface lake water temperatures for lakes across Canada using four statistical approaches: multiple regression, regression tree, artificial neural networks and Bayesian multiple regression.
2.  Annual maximum near-surface (from 0 to 2 m) lake water-temperature data were obtained for more than 13 000 lakes and were matched to geographic, climatic, lake morphology, physical habitat and water chemistry data. We modelled 2348 lakes and three subsets thereof encompassing different spatial scales and predictor variables to identify the relative importance of these variables at predicting lake temperature.
3.  Although artificial neural networks were marginally better for three of the four data sets, multiple regression was considered to provide the best solution based on the combination of model performance and computational complexity. Climatic variables and date of sampling were the most important variables for predicting water temperature in our models.
4.  Lake morphology did not play a substantial role in predicting lake temperature across any of the spatial scales. Maximum near-surface temperatures for Canadian lakes appeared to be dominated by large-scale climatic and geographic patterns, rather than lake-specific variables, such as lake morphology and water chemistry.     

Macroecology and extinction risk correlates of frogs

Aim  Our aim was to test whether extinction risk of frog species could be predicted from their body size, fecundity or geographical range size. Because small geographical range size is a correlate of extinction risk in many taxa, we also tested hypotheses about correlates of range size in frogs.
Location  Global.
Methods  Using a large comparative data set ( n  = 527 species) compiled from the literature, we performed bivariate and multiple regressions through the origin of independent contrasts to test proposed macroecological patterns and correlates of extinction risk in frogs. We also created minimum adequate models to predict snout–vent length, clutch size, geographical range size and IUCN Red List status in frogs. Parallel non-phylogenetic analyses were also conducted. We verified the results of the phylogenetic analyses using gridded data accounting for spatial autocorrelation.
Results  The most threatened frog species tend to have small geographical ranges, although the relationship between range and extinction risk is not linear. In addition, tropical frogs with small clutches have the smallest ranges. Clutch size was strongly positively correlated with geographical range size ( r ² = 0.22) and body size ( r ² = 0.28).
Main conclusions  Our results suggest that body size and fecundity only affect extinction risk indirectly through their effect on geographical range size. Thus, although large frogs with small clutches tend to be endangered, there is no comparative evidence that this relationship is direct. If correct, this inference has consequences for conservation strategy: it would be inefficient to allocate conservation resources on the basis of low fecundity or large body size; instead it would be better to protect areas that contain many frog species with small geographical ranges.     

基于地理加权回归模型探究环境异质性对秦岭大熊猫空间利用的影响

环境异质性对野生动物分布的影响具有明显的空间不均匀性。传统分析中多采用经典线性回归模型来量化野生动物分布与环境变量之间的关系,难以准确反映物种-环境关系的空间异质特征。地理加权回归(GWR)是近年来提出的一种新的空间分析方法,通过将空间结构嵌入线性回归模型中,以此来探测空间关系的非均匀性。以秦岭大熊猫为例,应用GWR模型分析大熊猫空间分布与环境异质性特征之间的潜在关系,并同经典的全局最小二乘回归法(OLS)进行比较。结果表明,GWR模型的AIC、R~2和校正R~2均显著优于OLS模型,GWR模型的局部回归系数估计能够更加深刻地揭示大熊猫空间分布与环境变量间的复杂空间关系,且GWR模型能够为物种的科学保护提供更加有效的理论支撑。因此,GWR模型可为探究物种-环境关系的空间异质特征提供一种新的方法,在物种栖息地选择与利用研究中具有一定的应用前景。