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.     

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 genetic effects of major genes and polygenes on quantitative traits I. Genetic model for diploid plants and animals

A genetic model was proposed to simultaneously investigate genetic effects of both polygenes and several single genes for quantitative traits of diploid plants and animals. Mixed linear model approaches were employed for statistical analysis. Based on two mating designs, a full diallel cross and a modified diallel cross including F₂, Monte Carlo simulations were conducted to evaluate the unbiasedness and efficiency of the estimation of generalized least squares (GLS) and ordinary least squares (OLS) for fixed effects and of minimum norm quadratic unbiased estimation (MINQUE) and Henderson III for variance components. Estimates of MINQUE (1) were unbiased and efficient in both reduced and full genetic models. Henderson III could have a large bias when used to analyze the full genetic model. Simulation results also showed that GLS and OLS were good methods to estimate fixed effects in the genetic models. Data on Drosophila melanogaster from Gilbert were used as a worked example to demonstrate the parameter estimation. Received: 11 November 2000 / Accepted: 2 May 2001     

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.     

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.     

Trees Grow on Money: Urban Tree Canopy Cover and Environmental Justice

This study examines the distributional equity of urban tree canopy (UTC) cover for Baltimore, MD, Los Angeles, CA, New York, NY, Philadelphia, PA, Raleigh, NC, Sacramento, CA, and Washington, D.C. using high spatial resolution land cover data and census data. Data are analyzed at the Census Block Group levels using Spearman’s correlation, ordinary least squares regression (OLS), and a spatial autoregressive model (SAR). Across all cities there is a strong positive correlation between UTC cover and median household income. Negative correlations between race and UTC cover exist in bivariate models for some cities, but they are generally not observed using multivariate regressions that include additional variables on income, education, and housing age. SAR models result in higher r-square values compared to the OLS models across all cities, suggesting that spatial autocorrelation is an important feature of our data. Similarities among cities can be found based on shared characteristics of climate, race/ethnicity, and size. Our findings suggest that a suite of variables, including income, contribute to the distribution of UTC cover. These findings can help target simultaneous strategies for UTC goals and environmental justice concerns.     

Analysis of genetic effects of major genes and polygenes on quantitative traits. II. Genetic models for seed traits of crops

Genetic models for quantitative seed traits with effects of several major genes and polygenes, as well as their GE interaction, were proposed. Mixed linear model approaches were suggested for analyzing the genetic models. Monte Carlo simulations were conducted to evaluate unbiasedness and efficiency for estimating fixed effects and variance components of the embryo and the endosperm models, including effects of a major gene from an unbalanced modified diallel mating design with nine parents, respectively. Simulation results showed that estimates of generalized least squares (GLS) were unbiased and efficient, while those of ordinary least squares (OLS) were almost as good as GLS. Minimum norm quadratic unbiased estimation (MINQUE) could obtain unbiased estimates of the variance components. It was also suggested that precision of MINQUE estimation would be improved with augmentation of experimental size. Data from a modified diallel design in upland cotton ( Gossypium hirsutum L.) were used as a worked example to illustrate the parameter estimation.     

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。     

The Applicability of Ordinary Least Squares to Consistently Short Distances between Taxa in Phylogenetic Tree Construction and the Normal Distribution Test Consequences

Short phylogenetic distances between taxa occur, for example, in studies on ribosomal RNA-genes with slow substitution rates. For consistently short distances, it is proved that in the completely singular limit of the covariance matrix ordinary least squares (OLS) estimates are minimum variance or best linear unbiased (BLU) estimates of phylogenetic tree branch lengths. Although OLS estimates are in this situation equal to generalized least squares (GLS) estimates, the GLS chi-square likelihood ratio test will be inapplicable as it is associated with zero degrees of freedom. Consequently, an OLS normal distribution test or an analogous bootstrap approach will provide optimal branch length tests of significance for consistently short phylogenetic distances. As the asymptotic covariances between branch lengths will be equal to zero, it follows that the product rule can be used in tree evaluation to calculate an approximate simultaneous confidence probability that all interior branches are positive.     

Rapid Evaluation of Least-Squares and Minimum-Evolution Criteria on Phylogenetic Trees

We present fast new algorithms for evaluating trees with respectto least squares and minimum evolution (ME), the most commonlyused criteria for inferring phylogenetic trees from distancedata. The new algorithms include an optimal O(N2) time algorithmfor calculating the edge (branch or internode) lengths on atree according to ordinary or unweighted least squares (OLS);an O(N3) time algorithm for edge lengths under weighted leastsquares (WLS) including the Fitch-Margoliash method; and anoptimal O(N4) time algorithm for generalized least-squares (GLS)edge lengths (where N is the number of taxa in the tree). TheME criterion is based on the sum of edge lengths. Consequently,the edge lengths algorithms presented here lead directly toO(N2), O(N3), and O(N4) time algorithms for ME under OLS, WLS,and GLS, respectively. All of these algorithms are as fast asor faster than any of those previously published, and the algorithmsfor OLS and GLS are the fastest possible (with respect to orderof computational complexity). A major advantage of our new methodsis that they are as well adapted to multifurcating trees asthey are to binary trees. An optimal algorithm for determiningpath lengths from a tree with given edge lengths is also developed.This leads to an optimal O(N2) algorithm for OLS sums of squaresevaluation and corresponding O(N3) and O(N4) time algorithmsfor WLS and GLS sums of squares, respectively. The GLS algorithmis time-optimal if the covariance matrix is already inverted.The speed of each algorithm is assessed analytically—thespeed increases we calculate are confirmed by the dramatic speedincreases resulting from their implementation in PAUP* 4.0.The new algorithms enable far more extensive tree searches andstatistical evaluations (e.g., bootstrap, parametric bootstrap,or jackknife) in the same amount of time. Hopefully, the fastalgorithms for WLS and GLS will encourage the use of these criteriafor evaluating trees and their edge lengths (e.g., for approximatedivergence time estimates), since they should be more statisticallyefficient than OLS.     

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.     

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.     

Thermophilic degradation of cellulose by a triculture of Clostridium thermocellum, Methanobacterium sp. and Methanosarcina MP

Abstract The fermentation of cellulose at 55°C by different associations of the 3 bacteria Clostridium thermocellum, Methanobacterium sp. and Methanosarcina MP, was studied. C. thermocellum alone produced acetate, lactate, ethanol, H₂ and CO₂. The co-culture C. thermocellum-Methanobacterium sp. produced more acetate and less ethanol than the monoculture of Clostridium .
Methanosarcina MP used acetate only in the triculture including Methanobacterium sp. When methanol was added (5 mM) to the triculture, Methanosarcina MP had a shorter lag phase on acetate and degraded much more acetate. maximum methane production was 8.5 mmol CH₄/g cellulose degraded.     

ESTIMATION OF THE KINETIC PARAMETERS OF UNIDIRECTIONAL TRANSPORT ACROSS THE BLOOD-BRAIN BARRIER

Abstract— The unidirectional transport of metabolic substrates from blood to brain may be defined in terms of Michaelis-Menten saturable ( K m, V _max) and non-saturable ( K _d) components of influx. Various computation procedures have been previously reported to estimate the kinetic parameters when an intracarotid injection technique is used. Transformations of the influx data which allow linear plots to obtain estimates were compared with estimates obtained directly from a best fit on a least means squares criterion for both experimental and simulated data. Large discrepancies were apparent between the various estimates of the kinetic parameters when an equal weight was given to transformed data. For pyruvate (21-day-old rats), K _m, values varied between 1.02 and 6.25 mM and V _max varied between 0.68 and 2.30 μmol g⁻¹ min⁻¹. The estimates were almost equivalent when pyruvate data was re-analysed using a weighting scheme based on the finding that the absolute value of the S.D. of influx increased in proportion to influx. It is recommended that estimates of kinetic parameters be obtained by an iterative, non-linear least squares method to fit appropriately weighted data directly.     

Roles of endothermy in niche differentiation for ball-rolling dung beetles (Coleoptera: Scarabaeidae) along an altitudinal gradient

Abstract.  1. An analysis of whether niche differentiation in ball-rolling dung beetles can be explained by the way in which they regulate their body temperature was conducted.
2.  A priori assumptions were: (i) if thermoregulation affects niche partitioning, sympatric species must have different endothermic strategies that minimise encounters; or, alternatively (ii) if two co-occurring species show the same thermoregulation pattern and their flight periods overlap, they might be avoiding competition by exhibiting different resource preferences or different food relocation behaviour.
3. The ball-rolling dung beetles studied showed a hierarchical structure based on the species' endothermic capacity, measured as temperature excess [ T _ex= difference between body temperature ( T _b) and ambient temperature ( T _a)]. Those with a high T _ex (10–15 °C) were located exclusively at altitudes >1000 m a.s.l. On the coastal plains, species with a high T _ex were restricted to flying at night when the T _a was lower. Species with a lower T _ex (less than 10 °C higher than T _a) were found in the coastal plains zone.
4. Where there was sympatry with similar trophic habits, the species involved showed very different thermal niches, and where there was significant overlap of thermal niches between sympatric species, trophic habits of species were very different.
5. The results suggest that it is possible to use the concept of the thermal niche as a tool to explain interspecific interactions and the spatial distribution of species.     

不同模型对拟合大兴安岭林火发生与气象因素关系的适用性

选用符合林火发生数据结构的Poisson和零膨胀Poisson(ZIP)模型对大兴安岭林区1980—2005年间林火发生与气象因素关系进行建模分析,并与普通最小二乘回归(ordinary least squares,OLS)方法的结果进行了对比分析.结果表明:OLS模型对研究区域林火发生与气象因素关系的拟合结果较差(R2=0.215);Poisson和ZIP模型的拟合效果较好,具有较好的火灾次数预测能力,且ZIP模型的预测能力高于Poisson模型.运用AIC和Vuong检验方法对Poisson和ZIP模型的拟合水平进行进一步检验,表明ZIP模型的数据拟合度优于Poisson模型.     

Estimating effects of a single gene and polygenes on quantitative traits from a diallel design

A genetic model is developed with additive and dominance effects of a single gene and polygenes as well as general and specific reciprocal effects for the progeny from a diallel mating design. The methods of ANOVA, minimum norm quadratic unbiased estimation (MINQUE), restricted maximum likelihood estimation (REML), and maximum likelihood estimation (ML) are suggested for estimating variance components, and the methods of generalized least squares (GLS) and ordinary least squares (OLS) for fixed effects, while best linear unbiased prediction, linear unbiased prediction (LUP), and adjusted unbiased prediction are suggested for analyzing random effects. Monte Carlo simulations were conducted to evaluate the unbiasedness and efficiency of statistical methods involving two diallel designs with commonly used sample sizes, 6 and 8 parents, with no and missing crosses, respectively. Simulation results show that GLS and OLS are almost equally efficient for estimation of fixed effects, while MINQUE (1) and REML are better estimators of the variance components and LUP is most practical method for prediction of random effects. Data from a Drosophila melanogaster experiment (Gilbert 1985a, Theor appl Genet 69:625–629) were used as a working example to demonstrate the statistical analysis. The new methodology is also applicable to screening candidate gene(s) and to other mating designs with multiple parents, such as nested (NC Design I) and factorial (NC Design II) designs. Moreover, this methodology can serve as a guide to develop new methods for detecting indiscernible major genes and mapping quantitative trait loci based on mixture distribution theory. The computer program for the methods suggested in this article is freely available from the authors.     

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。     

An ecosystem model-based estimate of changes in water availability differs from water proxies that are commonly used in species distribution models

Aim  To assess whether the water availability measures commonly used in species distribution models might be misleading because they do not account for the hydrological effects of changes in vegetation structure and functioning.
Location  Europe.
Methods  We compared different methods for estimating water availability in species distribution models with the soil water content predicted by a process-based ecosystem model. The latter also accounted for the hydrological effects of dynamic changes in vegetation structure and functioning, including potential physiological effects of increasing CO₂.
Results  All proxies showed similar patterns of water availability across Europe for current climate, but when projected into the future, the changes in the simpler water availability measures showed no correlation with those projected by the more complex ecosystem model, even if CO₂ effects were switched off.
Main conclusions  Results from species distribution modelling studies concerning future changes in species ranges and biodiversity should be interpreted with caution, and more process-based representations of the water balance of terrestrial ecosystems should be considered within these models.