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.     

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

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

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。     

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.     

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.     

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

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

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.     

Importance of spatial autocorrelation in modeling bird distributions at a continental scale

Spatial autocorrelation in species' distributions has been recognized as inflating the probability of a type I error in hypotheses tests, causing biases in variable selection, and violating the assumption of independence of error terms in models such as correlation or regression. However, it remains unclear whether these problems occur at all spatial resolutions and extents, and under which conditions spatially explicit modeling techniques are superior. Our goal was to determine whether spatial models were superior at large extents and across many different species. In addition, we investigated the importance of purely spatial effects in distribution patterns relative to the variation that could be explained through environmental conditions. We studied distribution patterns of 108 bird species in the conterminous United States using ten years of data from the Breeding Bird Survey. We compared the performance of spatially explicit regression models with non-spatial regression models using Akaike's information criterion. In addition, we partitioned the variance in species distributions into an environmental, a pure spatial and a shared component. The spatially-explicit conditional autoregressive regression models strongly outperformed the ordinary least squares regression models. In addition, partialling out the spatial component underlying the species' distributions showed that an average of 17% of the explained variation could be attributed to purely spatial effects independent of the spatial autocorrelation induced by the underlying environmental variables. We concluded that location in the range and neighborhood play an important role in the distribution of species. Spatially explicit models are expected to yield better predictions especially for mobile species such as birds, even in coarse-grained models with a large extent.     

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

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

Phylogeny, regression, and the allometry of physiological traits

Physiological and ecological allometries often pose linear regression problems characterized by (1) noncausal, phylogenetically autocorrelated independent (x) and dependent (y) variables (characters); (2) random variation in both variables; and (3) a focus on regression slopes (allometric exponents). Remedies for the phylogenetic autocorrelation of species values (phylogenetically independent contrasts) and variance structure of the data (reduced major axis [RMA] regression) have been developed, but most functional allometries are reported as ordinary least squares (OLS) regression without use of phylogenetically independent contrasts. We simulated Brownian diffusive evolution of functionally related characters and examined the importance of regression methodologies and phylogenetic contrasts in estimating regression slopes for phylogenetically constrained data. Simulations showed that both OLS and RMA regressions exhibit serious bias in estimated regression slopes under different circumstances but that a modified orthogonal (least squares variance-oriented residual [LSVOR]) regression was less biased than either OLS or RMA regressions. For strongly phylogenetically structured data, failure to use phylogenetic contrasts as regression data resulted in overestimation of the strength of the regression relationship and a significant increase in the variance of the slope estimate. Censoring of data sets by simulated extinction of taxa did not affect the importance of appropriate regression models or the use of phylogenetic contrasts.     

Can patterns of spatial autocorrelation reveal population processes? An analysis with the fire salamander

Spatial autocorrelation (SAC) is often observed in species distribution data, and can be caused by exogenous, autocorrelated factors determining species distribution, or by endogenous population processes determining clustering such as dispersal. However, it remains debated whether SAC patterns can actually reveal endogenous processes. We reviewed studies measuring dispersal of the salamander Salamandra salamandra, to formulate a priori hypotheses on the scale at which dispersal is expected to determine population distribution. We then tested the hypotheses by analysing SAC in distribution data, and evaluating whether controlling for the effect of environmental variables can reveal endogenous processes. We surveyed 565 streams to obtain species distribution data; we also recorded landscape and microhabitat features known to affect the species. We used multiple approaches to tease apart endogenous and exogenous SAC: the analysis of residuals of logistic regression models considering different environmental variables; the analysis of eigenvectors extracted by several implementations of spatial eigenvector mapping. In capture–mark–recapture studies, 98% of individuals moved 500 m or less. Both species distribution and environmental features were strongly autocorrelated. The residuals of logistic regression relating species to environmental variables were autocorrelated at distances up to 500 m; analyses considering different sets of environmental variables, or assuming non‐linear species habitat relationships, yielded identical results. The results of spatial eigenvector mapping strongly depended on the matrix of distances used. Nevertheless, the eigenvectors of models with best fit were autocorrelated at distances up to 200–500 m. The concordance between multiple approaches suggests that 500 m is the scale at which dispersal connects breeding localities, increasing probability of occurrence. If exogenous variables are correctly identified, the analysis of SAC can provide important insights on endogenous population processes, such as the flow of individuals. SAC analysis can also provide important information for conservation, as the existence of metapopulations or population networks is essential for long term persistence of amphibians.     

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.     

Spatial autocorrelation and the analysis of invasion processes from distribution data: a study with the crayfish <Emphasis Type="Italic">Procambarus clarkii</Emphasis>

Complex spatial dynamics are frequent in invasive species; analyzing distribution patterns can help to understand the mechanisms driving invasions. We used different spatial regression techniques to evaluate processes determining the invasion of the red swamp crayfish Procambarus clarkii. We evaluated four a priori hypotheses on processes that may determine crayfish invasion: landscape alteration, connectivity, wetland suitability for abiotic and biotic features. We assessed the distribution of P. clarkii in 119 waterbodies in a recently invaded area. We used spatially explicit statistical techniques (spatial eigenvector mapping, generalized additive models, Bayesian intrinsic conditional autoregressive models) within an information-theoretic framework to assess the support of hypotheses; we also analyzed the pattern of spatial autocorrelation of data, model residuals, and eigenvectors. We found strong agreement between the results of spatial eigenvector mapping and Bayesian autoregressive models. Procambarus clarkii was significantly associated with the largest, permanent wetlands. Additive models suggested also association with human-dominated landscapes, but tended to overfit data. The results indicate that abiotic wetlands features and landscape alteration are major drivers of the species’ distribution. Species distribution data, residuals of ordinary least squares regression, and spatial eigenvectors all showed positive and significant spatial autocorrelation at distances up to 2,500 m; this may be caused by the dispersal ability of the species. Our analyses help to understand the processes determining the invasion and to identify the areas most at risk where screening and early management efforts can be focused. The comparison of multiple spatial techniques allows a robust assessment of factors determining complex distribution patterns.     

The biogeography of invasive alien plants in California: an application of GIS and spatial regression analysis

The spatial distribution of invasive alien plants has been poorly documented in California. However, with the increased availability of GIS software and spatially explicit data, the distribution of invasive alien plants can be explored. Using bioregions as defined in Hickman (1993 ), I compared the distribution of invasive alien plants (n = 78) and noninvasive alien plants (n = 1097). The distribution of both categories of alien plants was similar with the exception of a higher concentration of invasive alien plants in the North Coast bioregion. Spatial autocorrelation analysis using Moran's I indicated significant spatial dependence for both invasive and noninvasive alien plant species. I used both ordinary least squares (OLS) and spatial autoregressive (SAR) models to assess the relationship between alien plant species distribution and native plant species richness, road density, population density, elevation, area of sample unit, and precipitation. The OLS model for invasive alien plants included two significant effects; native plant species richness and elevation. The SAR model for invasive alien plants included three significant effects; elevation, road density, and native plant species richness. The SAR model for noninvasive alien plants resulted in the same significant effects as invasive alien plants. Both invasive and noninvasive alien plants are found in regions with low elevation, high road density, and high native‐plant species richness. This is in congruity with previous spatial pattern studies of alien plant species. However, the similarity in effects for both categories of alien plants alludes to the importance of autecological attributes, such as pollination system, dispersal system and differing responses to disturbance in the distribution of invasive plant species. In addition, this study emphasizes the critical importance of testing for spatial autocorrelation in spatial pattern studies and using SAR models when appropriate.     

Trapped in the web of water: Groundwater‐fed springs are island‐like ecosystems for the meiofauna

We investigated whether the equilibrium theory of island biogeography (ETIB) can be applied to the meiofauna of groundwater‐fed springs. We tested whether copepod species richness was related with spring area, discharge, and elevation. Additionally, five hypotheses are tested based on species distribution patterns, dispersal ability, and life‐history characteristics of several guilds (stygobiotic, nonstygobiotic, cold stenotherm, and noncold stenotherm species). Thirty springs in the central Apennines (Italy) were considered. A multimodel selection procedure was applied to select best‐fit models using both ordinary least‐squares regressions and autoregressive models. Mantel tests were used to investigate the impact of spatial autocorrelation in determining interspring similarity (ßsor), pure turnover (ßsim), intersite nestedness (ßnest = ßsor ? ßsim), and matrix nestedness (measured using NODF and other metrics). Explicit consideration of spatial correlations reduced the importance of predictors of overall species richness, noncold stenotherm species (both negatively affected by elevation), cold stenotherm species, and nonstygobiotic species, but increased the importance of area for the stygobiotic species. We detected nested patterns in all cases, except for the stygobites. Interspring distances were positively correlated with ßsor and ßnest (but not with ßsim) for the entire data set and for nonstygobiotic, cold stenotherm, and noncold stenotherm species. In the case of stygobites, interspring geographical distances were marginally correlated with ßsor and no correlation was found for ßsim and ßnest. We found support for ETIB predictions about species richness, which was positively influenced by area and negatively by elevation (which expresses the size of source of immigrants). Low turnover and high nestedness are consistent with an equilibrium scenario mainly regulated by immigration and extinction. Stygobites, which include many distributional and evolutionary relicts, have a low capability to disperse through the aquifers and tend to be mainly confined to the springs where they drifted out and were trapped by springbed sediments.     

Environmental determinants of geographic butterfly richness pattern in eastern China

A long-standing task for ecologists and biogeographers is to reveal the underlying mechanisms accounting for the geographic pattern of species diversity. The number of hypotheses to explain geographic variation in species diversity has increased dramatically during the past half century. The oldest and the most popular one is environmental determination. However, seasonality, the intra-annual variability in climate variables has been rarely related to species richness. In this study, we assessed the relative importance of three environmental hypotheses: energy, seasonality and heterogeneity in explaining species richness pattern of butterflies in Eastern China. In addition, we also examined how environmental variables affect the relationship between species richness of butterflies and seed plants at geographic scale. All the environmental factors significantly affected butterfly richness, except sampling area and coefficient of variation of mean monthly precipitation. Energy and seasonality hypotheses explained comparable variation in butterfly richness (42.3 vs. 39.3 %), higher than that of heterogeneity hypothesis (25.9 %). Variation partitioning indicated that the independent effect of seasonality was much lower (0.0 %) than that of energy (5.5 %) and heterogeneity (6.3 %). However, seasonality performed better in explaining butterfly richness in topographically complex areas, reducing spatial autocorrelation in butterfly richness, and more strongly affect the association between butterflies and seed plants. The positive relationship between seed plant richness and butterfly richness was most likely the result of environmental variables (especially seasonality) influencing them in parallel. Insufficient sampling may partly explain the low explanatory power of environmental model (52.1 %) for geographic butterfly richness pattern. Our results have important implications for predicting the response of butterfly diversity to climate change.     

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.     

Bird species richness is associated with phylogenetic relatedness,plant species richness,and altitudinal range in Inner Mongolia

Bird species richness is mediated by local, regional, and historical factors, for example, competition, environmental heterogeneity, contemporary, and historical climate. Here, we related bird species richness with phylogenetic relatedness of bird assemblages, plant species richness, topography, contemporary climate, and glacial‐interglacial climate change to investigate the relative importance of these factors. This study was conducted in Inner Mongolia, an arid and semiarid region with diverse vegetation types and strong species richness gradients. The following associated variables were included as follows: phylogenetic relatedness of bird assemblages (Net Relatedness Index, NRI), plant species richness, altitudinal range, contemporary climate (mean annual temperature and precipitation, MAT and MAP), and contemporary‐Last Glacial Maximum (LGM) change in climate (change in MAT and change in MAP). Ordinary least squares linear, simultaneous autoregressive linear, and Random Forest models were used to assess the associations between these variables and bird species richness across this region. We found that bird species richness was correlated negatively with NRI and positively with plant species richness and altitudinal range, with no significant correlations with contemporary climate and glacial–interglacial climate change. The six best combinations of variables ranked by Random Forest models consistently included NRI, plant species richness, and contemporary‐LGM change in MAT. Our results suggest important roles of local ecological factors in shaping the distribution of bird species richness across this semiarid region. Our findings highlight the potential importance of these local ecological factors, for example, environmental heterogeneity, habitat filtering, and biotic interactions, in biodiversity maintenance.