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1) Species distribution models (SDMs) are currently the main tools to derive species niche estimates and spatially explicit predictions for species geographical distribution. However, unobserved environmental conditions and ecological processes may confound the model estimates if they have direct impact on the species and, at the same time, they are correlated with the observed environmental covariates. This, so-called spatial confounding, is a general property of spatial models and it has not been studied in the context of SDMs before. 2) We examine how the estimation accuracy of SDMs depends on the type of spatial confounding. We construct two simulation studies where we alter spatial structures of the observed and unobserved covariates and the level of dependence between them. We fit generalized linear models with and without spatial random effects applying Bayesian inference and recording the bias induced to model estimates by spatial confounding. After this we examine spatial confounding also with real vegetation data from northern Norway. 3) Our results show that model estimates for coarse scale covariates, such as climate covariates, are likely to be biased if a species distribution depends also on an unobserved covariate operating on a finer spatial scale. Pushing higher probability for a relatively weak and smoothly varying spatial random effect compared to the observed covariates improved the model's estimation accuracy. The improvement was independent of the actual spatial structure of the unobserved covariate. 4) Our study addresses the major factors of spatial confounding in SDMs and provides a list of recommendations for pre-inference assessment of spatial confounding and for inference-based methods to decrease the chance of biased model estimates.

This paper uses Hospital Episode Statistics, English administrative data, to investigate the growth in admitted patient health care expenditures and the implications of an ageing population. We use two samples of around 40,000 individuals who (a) used inpatient health care in the financial year 2005/06 and died by the end of 2011/12 and (b) died in 2011/12 and had some hospital utilisation since 2005/06. We use a panel structure to follow individuals over seven years of this administrative data, containing estimates of inpatient health care expenditures (HCE), information regarding individuals' age, time-to-death (TTD), morbidities at the time of an admission, as well as the hospital provider, year and season of admission. We show that HCE is principally determined by proximity to death rather than age, and that proximity to death is itself a proxy for morbidity.

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.

Ongoing statistical sophistication allows a shift from describing species' spatial distributions toward statistically disentangling the possible roles of environmental variables in shaping species distributions. Based on a landscape-scale benthic survey in the Dutch Wadden Sea, we show the merits of spatially explicit generalized estimating equations (GEE). The intertidal macrozoobenthic species, Macoma balthica, Cerastoderma edule, Marenzelleria viridis, Scoloplos armiger, Corophium volutator, and Urothoe poseidonis served as test cases, with median grain-size and inundation time as typical environmental explanatory variables. GEEs outperformed spatially naive generalized linear models (GLMs), and removed much residual spatial structure, indicating the importance of median grain-size and inundation time in shaping landscape-scale species distributions in the intertidal. GEE regression coefficients were smaller than those attained with GLM, and GEE standard errors were larger. The best fitting GEE for each species was used to predict species' density in relation to median grain-size and inundation time. Although no drastic changes were noted compared to previous work that described habitat suitability for benthic fauna in the Wadden Sea, our predictions provided more detailed and unbiased estimates of the determinants of species-environment relationships. We conclude that spatial GEEs offer the necessary methodological advances to further steps toward linking pattern to process.

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.

Issues of residual spatial autocorrelation (RSA) and spatial scale are critical to the study of species-environment relationships, because RSA invalidates many statistical procedures, while the scale of analysis affects the quantification of these relationships. Although these issues independently are widely covered in the literature, only sparse attention is given to their integration. This paper focuses on the interplay between RSA and the spatial scaling of species-environment relationships. Using a hypothetical species in an artificial landscape, we show that a mismatch between the scale of analysis and the scale of a species' response to its environment leads to a decrease in the portion of variation explained by environmental predictors. Moreover, it results in RSA and biased regression coefficients. This bias stems from error-predictor dependencies due to the scale mismatch, the magnitude of which depends on the interaction between the scale of landscape heterogeneity and the scale of a species' response to this heterogeneity. We show that explicitly considering scale effects on RSA can reveal the characteristic scale of a species' response to its environment. This is important, because the estimation of species-environment relationships using spatial regression methods proves to be erroneous in case of a scale mismatch, leading to spurious conclusions when scaling issues are not explicitly considered. The findings presented here highlight the importance of examining the appropriateness of the spatial scales used in analyses, since scale mismatches affect the rigor of statistical analyses and thereby the ability to understand the processes underlying spatial patterning in ecological phenomena.

Aim Anthropogenic fires are a major component of the ecology of rangelands throughout the world. To assess the effects of these fires on the diversity patterns of herbivores, we related gradients in fire occurrence, climate and soil fertility to patterns in alpha and beta diversity of African ungulates. Location West Africa. Methods We used a survey-based approach for ungulates in 37 protected areas in desert, savanna and rain forest habitats throughout West Africa, combined with satellite images of fire occurrence and digital maps of actual evapotranspiration and soil fertility. Alpha diversity was related to the environmental variables using conventional and spatial regression models. We investigated beta diversity using partial Mantel tests and ordination techniques, and by partitioning the variance in assemblage composition into environmental and spatial components. Results The species richness of grazers showed a quadratic relationship with actual evapotranspiration, whereas that of browsers and frugivores showed a linear relationship. However, in the multiple regression models fire occurrence was the only variable that significantly correlated with the species richness of grazers. Soil fertility was weakly related to overall beta diversity and the species richness of browsers, but was non-significant in the multiple regression models. Fire occurrence was the most important variable explaining species composition of the overall species set and of grazers, whereas the assemblage composition of browsers and frugivores was explained mostly by actual evapotranspiration. Main conclusions In contrast to previous studies, our analyses show that moisture and nutrients alone fail to adequately predict the diversity patterns of grazing ungulates. Rather, the species richness and assemblage composition of grazers are largely governed by anthropogenic fires that modify the quality and structure of the grass sward. Diversity patterns of browsers and frugivores are markedly different from grazers and depend mainly on the availability of moisture, which is positively correlated with the availability of foliage and fruits. Our study highlights the importance of incorporating major human-induced disturbances or habitat alterations into analyses of diversity patterns.

1. Comparative analyses of diversity variation among and between regions allow testing of alternative explanatory models and ideas. Here, we explore the relationships between the tree alpha-diversity of small rain forest plots in Africa and in Amazonia and climatic variables, to test the explanatory power of climate and the consistency of relationships between the two continents. 2. Our analysis included 1003 African plots and 512 Amazonian plots. All are located in old-growth primary non-flooded forest under 900 m altitude. Tree alpha-diversity is estimated using Fisher's alpha calculated for trees with diameter at breast height >= 10 cm. Mean diversity values are lower in Africa by a factor of two. 3. Climate-diversity analyses are based on data aggregated for grid cells of 2.5 x 2.5 km. The highest Fisher's alpha values are found in Amazonian forests with no climatic analogue in our African data set. When the analysis is restricted to pixels of directly comparable climate, the mean diversity of African forests is still much lower than that in Amazonia. Only in regions of low mean annual rainfall and temperature is mean diversity in African forests comparable with, or superior to, the diversity in Amazonia. 4. The climatic variables best correlated with the tree alpha-diversity are largely different in the African and Amazonian data, or correlate with African and Amazonian diversity in opposite directions. 5. These differences in the relationship between local/landscape-scale alpha-diversity and climate variables between the two continents point to the possible significance of an array of factors including: macro-scale climate differences between the two regions, overall size of the respective species pools, past climate variation, other forms of long-term and short-term environmental variation, and edaphics. We speculate that the lower alpha-diversity of African lowland rain forests reported here may be in part a function of the smaller regional species pool of tree species adapted to warm, wet conditions. 6. Our results point to the importance of controlling for variation in plot size and for gross differences in regional climates when undertaking comparative analyses between regions of how local diversity of forest varies in relation to other putative controlling factors.