Estimation of the spatial autocorrelation function: consequences of sampling dynamic populations in space and time

The estimation of spatial autocorrelation in spatially- and temporally-referenced data is fundamental to understanding an organism's population biology. I used four sets of census field data, and developed an idealized space-time dynamic system, to study the behavior of spatial autocorrelation estimates when a practical method of sampling is employed. Estimates were made using both a classical geostatistical approach and a recently developed non-parametric approach. In field data, the estimate of the local spatial autocorrelation (i.e. autocorrelation as the distance between pairs of sampling points approaches 0), was greatly affected by sample size, while the range of spatial dependence (i.e. the distance at which the autocorrelation becomes negligible) was fairly stable. Similar patterns were seen in the theoretical system, as well as greater variability in local spatial autocorrelation during the invasion stage of colonization. When sampling for the purposes of quantifying spatial patterns, improved estimates of spatial autocorrelation may be obtained by increasing the number of pairs of points that are close in space at the expense of attempting to cover the entire region of interest with equidistant sampling points. Also, results from the theoretical space-time system suggested that greater resolution in sampling may be required in newly establishing populations relative to those already established.     

Biophysical models of ciliary activity: Gaussian frequency distributions

A model of a freely rotating exended scatterer is proposed to describe light scattering from beating cilia. Gaussian rotation frequency distributions, characterized by a mean angular frequency and a standard deviation, are introduced in order to simulate intensity autocorrelation functions and to fit the model to experimental data. Thus the ciliary beats are characterized by a mean beat frequency and a standard deviation of the beat frequency distribution. The standard deviation influences the damping of the intensity autocorrelation function of light scattered from cilia. The calculated intensity autocorrelation function shows a more prominent oscillating behaviour the smaller the standard deviation of the beat frequency. The validity of the model is supported by experimental data in two ways: 1) The model fits very well to experimental data in computer evaluations, 2) Neither the model nor information obtained from measurements are dependent on the measuring angle.The contents were presented in part at the 9th International Biophysics Congress in Jerusalem, Israel, August 23–28, 1987 Offprint requests to: P. Thyberg     

Photon correlation analysis of cytoplasmic streaming

Laser light scattering has been used to investigate particle movements in a plant cell. Intensity autocorrelation functions are obtained by digital photon correlation of laser light scattered from cells of Nitella opaca both during cytoplasmic streaming and during the transitory cessation of streaming induced by electrical stimulation. The average velocity computed from the periodic oscillation in the intensity autocorrelation function during streaming corresponds to the velocity estimated using light microscopy. An estimate of the distribution of streaming velocities has been obtained from the decay in the amplitude of the envelope of the autocorrelation function derived from a streaming cell.     

Prediction of protein helix content from an autocorrelation analysis of sequence hydrophobicities

It is demonstrated that protein α-helix content can be predicted from an autocorrelation analysis of the protein hydrophobicity sequence. The Fourier transform of the autocorrelation function yields the spectral densities or weights of the various frequencies contributing to the autocorrelation function. Using sequence and secondary structure data from more than 160 proteins and domains, a linear relationship was found between spectral density at periodicity 3.7 and protein α-helix content (r = 0.83). This relation permits prediction of the helix content (x) of proteins of known sequence to within ± 15%, i.e., as (x ± 15)%. Predictions based on the autocorrelation procedure are compared with values obtained by other methods.     

Dealing with spatial autocorrelation when learning predictive clustering trees

Spatial autocorrelation is the correlation among data values which is strictly due to the relative spatial proximity of the objects that the data refer to. Inappropriate treatment of data with spatial dependencies, where spatial autocorrelation is ignored, can obfuscate important insights. In this paper, we propose a data mining method that explicitly considers spatial autocorrelation in the values of the response (target) variable when learning predictive clustering models. The method is based on the concept of predictive clustering trees (PCTs), according to which hierarchies of clusters of similar data are identified and a predictive model is associated to each cluster. In particular, our approach is able to learn predictive models for both a continuous response (regression task) and a discrete response (classification task). We evaluate our approach on several real world problems of spatial regression and spatial classification. The consideration of the autocorrelation in the models improves predictions that are consistently clustered in space and that clusters try to preserve the spatial arrangement of the data, at the same time providing a multi-level insight into the spatial autocorrelation phenomenon. The evaluation of SCLUS in several ecological domains (e.g. predicting outcrossing rates within a conventional field due to the surrounding genetically modified fields, as well as predicting pollen dispersal rates from two lines of plants) confirms its capability of building spatial aware models which capture the spatial distribution of the target variable. In general, the maps obtained by using SCLUS do not require further post-smoothing of the results if we want to use them in practice.     

Spatial autocorrelation and sampling design in plant ecology

Using spatial analysis methods such as spatial autocorrelation coefficients (Moran's I and Geary's c) and kriging, we compare the capacity of different sampling designs and sample sizes to detect the spatial structure of a sugar-maple (Acer saccharum L.) tree density data set gathered from a secondary growth forest of southwestern Québec. Three different types of subsampling designs (random, systematic and systematic-cluster) with small sample sizes (50 and 64 points), obtained from this larger data set (200 points), are evaluated. The sensitivity of the spatial methods in the detection and the reconstruction of spatial patterns following the application of the various subsampling designs is discussed. We find that the type of sampling design plays an important role in the capacity of autocorrelation coefficients to detect significant spatial autocorrelation, and in the ability to accurately reconstruct spatial patterns by kriging. Sampling designs that contain varying sampling steps, like random and systematic-cluster designs, seem more capable of detecting spatial structures than a systematic design.Abbreviations UPGMA = Unweighted Pair-Group Method using Arithmetic Averages     

Effects of normalization errors on size distributions obtained from dynamic light scattering data.

This paper presents a study of the influence of normalization errors on size distributions obtained from the analysis of intensity fluctuations by photon correlation spectroscopy. The effects of these errors are demonstrated by means of computer-generated autocorrelation functions simulating light scattered from a monomodal Schulz distribution of small, spherical, unilamellar lipid vesicles. The calculations show that even small errors in the baseline, modifying the data upon normalization systematically, will cause serious errors in the estimated size distribution. As it turns out this is due to the peculiar characteristics of normalization errors in data of the first order autocorrelation function. The errors introduced there are described in parts by functions of the delay time having positive exponents. Such components are not considered in the integral equations commonly used to analyze the measured data. The error's property to be a function of delay time in turn enables us to obtain the relative baseline error from the inversion of the data. The new method for its determination is described in some detail. Here, it has been realized with a modified version of the size distribution algorithm CONTIN.     

Spatially autocorrelated sampling falsely inflates measures of accuracy for presence‐only niche models

Aim Environmental niche models that utilize presence‐only data have been increasingly employed to model species distributions and test ecological and evolutionary predictions. The ideal method for evaluating the accuracy of a niche model is to train a model with one dataset and then test model predictions against an independent dataset. However, a truly independent dataset is often not available, and instead random subsets of the total data are used for ‘training’ and ‘testing’ purposes. The goal of this study was to determine how spatially autocorrelated sampling affects measures of niche model accuracy when using subsets of a larger dataset for accuracy evaluation. Location The distribution of Centaurea maculosa (spotted knapweed; Asteraceae) was modelled in six states in the western United States: California, Oregon, Washington, Idaho, Wyoming and Montana. Methods Two types of niche modelling algorithms – the genetic algorithm for rule‐set prediction (GARP) and maximum entropy modelling (as implemented with Maxent) – were used to model the potential distribution of C. maculosa across the region. The effect of spatially autocorrelated sampling was examined by applying a spatial filter to the presence‐only data (to reduce autocorrelation) and then comparing predictions made using the spatial filter with those using a random subset of the data, equal in sample size to the filtered data. Results The accuracy of predictions from both algorithms was sensitive to the spatial autocorrelation of sampling effort in the occurrence data. Spatial filtering led to lower values of the area under the receiver operating characteristic curve plot but higher similarity statistic (I) values when compared with predictions from models built with random subsets of the total data, meaning that spatial autocorrelation of sampling effort between training and test data led to inflated measures of accuracy. Main conclusions The findings indicate that care should be taken when interpreting the results from presence‐only niche models when training and test data have been randomly partitioned but occurrence data were non‐randomly sampled (in a spatially autocorrelated manner). The higher accuracies obtained without the spatial filter are a result of spatial autocorrelation of sampling effort between training and test data inflating measures of prediction accuracy. If independently surveyed data for testing predictions are unavailable, then it may be necessary to explicitly account for the spatial autocorrelation of sampling effort between randomly partitioned training and test subsets when evaluating niche model predictions.     

The consequences of spatial structure for the design and analysis of ecological field surveys

In ecological field surveys, observations are gathered at different spatial locations. The purpose may be to relate biological response variables (e.g., species abundances) to explanatory environmental variables (e.g., soil characteristics). In the absence of prior knowledge, ecologists have been taught to rely on systematic or random sampling designs. If there is prior knowledge about the spatial patterning of the explanatory variables, obtained from either previous surveys or a pilot study, can we use this information to optimize the sampling design in order to maximize our ability to detect the relationships between the response and explanatory variables?
The specific questions addressed in this paper are: a) What is the effect (type I error) of spatial autocorrelation on the statistical tests commonly used by ecologists to analyse field survey data? b) Can we eliminate, or at least minimize, the effect of spatial autocorrelation by the design of the survey? Are there designs that provide greater power for surveys, at least under certain circumstances? c) Can we eliminate or control for the effect of spatial autocorrelation during the analysis? To answer the last question, we compared regular regression analysis to a modified t‐test developed by Dutilleul for correlation coefficients in the presence of spatial autocorrelation.
Replicated surfaces (typically, 1000 of them) were simulated using different spatial parameters, and these surfaces were subjected to different sampling designs and methods of statistical analysis. The simulated surfaces may represent, for example, vegetation response to underlying environmental variation. This allowed us 1) to measure the frequency of type I error (the failure to reject the null hypothesis when in fact there is no effect of the environment on the response variable) and 2) to estimate the power of the different combinations of sampling designs and methods of statistical analysis (power is measured by the rate of rejection of the null hypothesis when an effect of the environment on the response variable has been created).
Our results indicate that: 1) Spatial autocorrelation in both the response and environmental variables affects the classical tests of significance of correlation or regression coefficients. Spatial autocorrelation in only one of the two variables does not affect the test of significance. 2) A broad‐scale spatial structure present in data has the same effect on the tests as spatial autocorrelation. When such a structure is present in one of the variables and autocorrelation is found in the other, or in both, the tests of significance have inflated rates of type I error. 3) Dutilleul's modified t‐test for the correlation coefficient, corrected for spatial autocorrelation, effectively corrects for spatial autocorrelation in the data. It also effectively corrects for the presence of deterministic structures, with or without spatial autocorrelation.
The presence of a broad‐scale deterministic structure may, in some cases, reduce the power of the modified t‐test.     

Conditionally autoregressive models improve occupancy analyses of autocorrelated data: An example with environmental DNA

Site occupancy‐detection models (SODMs) are statistical models widely used for biodiversity surveys where imperfect detection of species occurs. For instance, SODMs are increasingly used to analyse environmental DNA (eDNA) data, taking into account the occurrence of both false‐positive and false‐negative errors. However, species occurrence data are often characterized by spatial and temporal autocorrelation, which might challenge the use of standard SODMs. Here we reviewed the literature of eDNA biodiversity surveys and found that most of studies do not take into account spatial or temporal autocorrelation. We then demonstrated how the analysis of data with spatial or temporal autocorrelation can be improved by using a conditionally autoregressive SODM, and show its application to environmental DNA data. We tested the autoregressive model on both simulated and real data sets, including chronosequences with different degrees of autocorrelation, and a spatial data set on a virtual landscape. Analyses of simulated data showed that autoregressive SODMs perform better than traditional SODMs in the estimation of key parameters such as true‐/false‐positive rates and show a better discrimination capacity (e.g., higher true skill statistics). The usefulness of autoregressive SODMs was particularly high in data sets with strong autocorrelation. When applied to real eDNA data sets (eDNA from lake sediment cores and freshwater), autoregressive SODM provided more precise estimation of true‐/false‐positive rates, resulting in more reasonable inference of occupancy states. Our results suggest that analyses of occurrence data, such as many applications of eDNA, can be largely improved by applying conditionally autoregressive specifications to SODMs.     

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.     

Incorporating spatial autocorrelation may invert observed patterns

Though still often neglected, spatial autocorrelation can be a serious issue in ecology because the presence of spatial autocorrelation may alter the parameter estimates and error probabilities of linear models. Here I re-analysed data from a previous study on the relationship between plant species richness and environmental correlates in Germany. While there was a positive relationship between native plant species richness and an altitudinal gradient when ignoring the presence of spatial autocorrelation, the use of a spatial simultaneous liner error model revealed a negative relationship. This most dramatic effect where the observed pattern was inverted may be explained by the environmental situation in Germany. There the highest altitudes are in the south and the lowlands in the north that result in some locally or regionally inverted patterns of the large-scale environmental gradients from the equator to the north. This study therefore shows the necessity to consider spatial autocorrelation in spatial analyses.     

Evaluating spatial autocorrelation and depletion in pitfall-trap studies of environmental gradients

Studies of environmental gradients like edge effects commonly employ designs where samples are collected at unequal distances within transects. This approach risks confounding species patterns caused by the environmental gradient with patterns resulting from the spatial arrangement of the sampling scheme. Spatial autocorrelation and depletion (reduced catch) have the potential to influence pitfall-trap collections of invertebrates. Readily available control data from a study of edge and riparian effects on forest litter beetles was used to assess autocorrelation and depletion effects. Data from control transects distant from the treatment transects located at habitat edges and streams were screened to determine whether the study design (pitfall traps at varying distances within transects) was imposing patterns on the data attributable to differential autocorrelation or depletion. Autocorrelation in species composition and assemblage structure was not detected within the 99 m transects. The abundance and species richness of beetles were not lower where traps were in closer proximity, indicating that the transect design was not causing measurable depletion or resulting in differential trap catch. These findings indicate that spatial autocorrelation and depletion are unlikely to impair further analyses of edge and riparian effects on litter beetles.     

中西太平洋鲣鱼围网渔业资源的热点分析和空间异质性

中西太平洋是世界鲣鱼围网主要作业水域。基于我国渔船2005—2009年的中西太平洋鲣鱼围网生产数据,运用空间统计方法对该水域鲣鱼资源的空间自相关性和空间异质性特征进行分析,并结合海洋环境特征分析资源分布的热点区域。(1)通过常规统计学计算获得鲣鱼资源的偏态Sk、峰态数Ku、变异值Cv、s2/m和全局空间自相关Geary c系数,发现中西太平洋鲣鱼资源总体上是以低密度区域为主,高密度区域较少;鱼类资源密度值差异较大,资源表现出强烈集聚分布,总体的空间自相关性中等偏弱。(2)通过局部空间自相关的热点分析方法计算,发现局部空间自相关性较强,存在多个在统计学上通过显著性检验的资源热点和冷点。(3)通过地统计方法研究鲣鱼资源的空间变异性特征和方向变异时,空间自相关类型上最优模型是球形模型,鲣鱼资源密度各向同性,最大相关距离1000km左右。发现空间自相关引起的差异占整个差异的50%左右,为中等强度变异;在方向性变异上,主要体现在南北向上,其该向上结构性误差占67%,而东西向结构性误差占49%。这一结果和海洋环境的南北向上结构性远好于东西向结构性有关;从各方向的分维数看,数值介于1.876—1.9之间,数值较大,空间自相关较弱。(4)以资源热点区域作为区域性渔场,结合海洋温度和叶绿素场海洋环境特征,将中西太平洋鲣鱼资源分为3个不同的局部渔场,即2个暖池渔场,1个冷舌渔场。冷舌渔场由中东太平洋赤道上升流引起,在锋面地带提供了较为丰富的初级生产力,便于鱼类获得丰富的食物;暖池渔场靠近岛屿和陆地区域,近岸上升流系统提供了丰富的初级生产力。(5)将热点分析和渔场重心方法及栖息地指数的优缺点做了对比,建议以后采用空间残差模型深入研究空间自相关问题。     

Revealing biogeographical patterns by nonlinear ordinations and derived anisotropic spatial filters

Aim Spatial floristic and faunistic data bases promote the investigation of biogeographical gradients in relation to environmental determinants on regional to continental scales. Our aim was to extract major gradients in the distribution of vascular plant species from a grid‐based inventory (the German FLORKART data base) and relate them to long‐term precipitation and temperature records as well as soil conditions. We present an ordination technique capable of coping with this complex data array. The goal was also to sort out the influence of spatial autocorrelation, assuming floristic autocorrelation is anisotropic. Location Germany, at a spatial resolution of 6′ × 10′. Methods Isometric feature mapping (Isomap) was applied as a nonlinear ordination method. Isomap was coupled to ‘eigenvector‐based filters’ for generating spatial reference models representing spatial autocorrelation. What is novel here is that the derived filters are not based on the assumption of equidirectional autocorrelation. Instead, the so‐called ‘principal coordinates of anisotropic neighbour matrices’ build filters to test the influence of geographical vicinity in directions of high similarity among observations. Results The Isomap ordination of floristic data explained more than 95% of the data variance in six dimensions. The leading two dimensions (representing about 80% of the FLORKART data variance) revealed clear spatial gradients that could be related to independent effects of temperature, precipitation and soil observations. By contrast, the third and higher FLORKART dimensions were dominated by an antagonism of anisotropic spatial autocorrelation and soil conditions. A subsequent cluster analysis of the floristic Isomap coordinates educed the spatial organization of the floristic survey, indicating a considerable sampling bias. Conclusions We showed that Isomap provides a consistent methodical framework for both ordination and derived spatial filters. The technique is useful for tracing the often nonlinear features of species occurrence data to environmental drivers, taking into account anisotropic spatial autocorrelation. We also showed that sampling biases are a conspicuous source of variance in a frequently used floristic data base.     

Nonlinear Mixed-Effects (NLME) Diameter Growth Models for Individual China-Fir (Cunninghamia lanceolata) Trees in Southeast China

An individual-tree diameter growth model was developed for Cunninghamia lanceolata in Fujian province, southeast China. Data were obtained from 72 plantation-grown China-fir trees in 24 single-species plots. Ordinary non-linear least squares regression was used to choose the best base model from among 5 theoretical growth equations; selection criteria were the smallest absolute mean residual and root mean square error and the largest adjusted coefficient of determination. To account for autocorrelation in the repeated-measures data, we developed one-level and nested two-level nonlinear mixed-effects (NLME) models, constructed on the selected base model; the NLME models incorporated random effects of the tree and plot. The best random-effects combinations for the NLME models were identified by Akaike''s information criterion, Bayesian information criterion and −2 logarithm likelihood. Heteroscedasticity was reduced with two residual variance functions, a power function and an exponential function. The autocorrelation was addressed with three residual autocorrelation structures: a first-order autoregressive structure [AR(1)], a combination of first-order autoregressive and moving average structures [ARMA(1,1)] and a compound symmetry structure (CS). The one-level (tree) NLME model performed best. Independent validation data were used to test the performance of the models and to demonstrate the advantage of calibrating the NLME models.     

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.     

Incorporating the temporal autocorrelation of demographic rates into structured population models

Population dynamics are typically temporally autocorrelated: population sizes are positively or negatively correlated with past population sizes. Previous studies have found that positive temporal autocorrelation increases the risk of extinction due to ‘inertia’ that prolongs downward fluctuations in population size. However, temporal autocorrelation has not yet been analyzed at the level of life cycle transitions. We developed an R package, colorednoise, which creates stochastic matrix population projections with distinct temporal autocorrelation values for each matrix element. We used it to analyze long-term demographic data on 25 populations from the COMADRE and COMPADRE databases and simulate their stochastic dynamics. We found a broad range of temporal autocorrelation across species, populations and life cycle stages. The number of stage-classes in the matrix strongly affected the temporal autocorrelation of the growth rate. In the plant populations, reproduction transitions had more negative temporal autocorrelation than survival transitions, and matrices dominated by positive temporal autocorrelation had higher extinction risk, while in animal populations transition type was not associated with noise color. Our results indicate that temporal autocorrelation varies across life cycle transitions, even among populations of the same species. We present the colorednoise package for researchers to analyze the temporal autocorrelation of structured demographic rates.     

Evaluating,partitioning, and mapping the spatial autocorrelation component in ecological niche modeling: a new approach based on environmentally equidistant records

Most species data display spatial autocorrelation that can affect ecological niche models (ENMs) accuracy‐statistics, affecting its ability to infer geographic distributions. Here we evaluate whether the spatial autocorrelation underlying species data affects accuracy‐statistics and map the uncertainties due to spatial autocorrelation effects on species range predictions under past and future climate models. As an example, ENMs were fitted to Qualea grandiflora (Vochysiaceae), a widely distributed plant from Brazilian Cerrado. We corrected for spatial autocorrelation in ENMs by selecting sampling sites equidistant in geographical (GEO) and environmental (ENV) spaces. Distributions were modelled using 13 ENMs evaluated by two accuracy‐statistics (TSS and AUC), which were compared with uncorrected ENMs. Null models and the similarity statistics I were used to evaluate the effects of spatial autocorrelation. Moreover, we applied a hierarchical ANOVA to partition and map the uncertainties from the time (across last glacial maximum, pre‐insustrial, and 2080 time periods) and methodological components (ENMs and autocorrelation corrections). The GEO and ENV models had the highest accuracy‐statistics values, although only the ENV model had values higher than expected by chance alone for most of the 13 ENMs. Uncertainties from time component were higher in the core region of the Brazilian Cerrado where Q. grandiflora occurs, whereas methodological components presented higher uncertainties in the extreme northern and southern regions of South America (i.e. outside of Brazilian Cerrado). Our findings show that accounting for autocorrelation in environmental space is more efficient than doing so in geographical space. Methodological uncertainties were concentrated in outside the core region of Q. grandiflora's habitat. Conversely, uncertainty due to time component in the Brazilian Cerrado reveals that ENMs were able to capture climate change effects on Q. grandiflora distributions.