Less than eight (and a half) misconceptions of spatial analysis

Spatial analyses are indispensable analytical tools in biogeography and macroecology. In a recent Guest Editorial, Hawkins (Journal of Biogeography, 2012, 39 , 1–9) raised several issues related to spatial analyses. While we concur with some points, we here clarify those confounding (1) spatial trends and spatial autocorrelation, and (2) spatial autocorrelation in the response variable and in the residuals. We argue that recognizing spatial autocorrelation in statistical modelling is not only a crucial step in model diagnostics, but that disregarding it is essentially wrong.     

Effects of incorporating spatial autocorrelation into the analysis of species distribution data

Aim  Spatial autocorrelation (SAC) in data, i.e. the higher similarity of closer samples, is a common phenomenon in ecology. SAC is starting to be considered in the analysis of species distribution data, and over the last 10 years several studies have incorporated SAC into statistical models (here termed 'spatial models'). Here, I address the question of whether incorporating SAC affects estimates of model coefficients and inference from statistical models.
Methods  I review ecological studies that compare spatial and non-spatial models.
Results  In all cases coefficient estimates for environmental correlates of species distributions were affected by SAC, leading to a mis-estimation of on average c . 25%. Model fit was also improved by incorporating SAC.
Main conclusions  These biased estimates and incorrect model specifications have implications for predicting species occurrences under changing environmental conditions. Spatial models are therefore required to estimate correctly the effects of environmental drivers on species present distributions, for a statistically unbiased identification of the drivers of distribution, and hence for more accurate forecasts of future distributions.     

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.     

EcoGenetics: An R package for the management and exploratory analysis of spatial data in landscape genetics

The integration of ecology and genetics has become established in recent decades, in hand with the development of new technologies, whose implementation is allowing an improvement of the tools used for data analysis. In a landscape genetics context, integrative management of population information from different sources can make spatial studies involving phenotypic, genotypic and environmental data simpler, more accessible and faster. Tools for exploratory analysis of autocorrelation can help to uncover the spatial genetic structure of populations and generate appropriate hypotheses in searching for possible causes and consequences of their spatial processes. This study presents EcoGenetics, an R package with tools for multisource management and exploratory analysis in landscape genetics.     

Eight (and a half) deadly sins of spatial analysis

Biogeography is spatial by nature. Over the past 20 years, the literature related to the analysis of spatially structured data has exploded, much of it focused on a perceived problem of spatial autocorrelation and ways to deal with it. However, there are a number of other issues that permeate the biogeographical and macroecological literature that have become entangled in the spatial autocorrelation web. In this piece I discuss some of the assumptions that are often made in the analysis of spatially structured data that can lead to misunderstandings about the nature of spatial data, the methods used to analyse them, and how results can be interpreted.     

Combining spatial and phylogenetic eigenvector filtering in trait analysis

Aim To analyse the effects of simultaneously using spatial and phylogenetic information in removing spatial autocorrelation of residuals within a multiple regression framework of trait analysis. Location Switzerland, Europe. Methods We used an eigenvector filtering approach to analyse the relationship between spatial distribution of a trait (flowering phenology) and environmental covariates in a multiple regression framework. Eigenvector filters were calculated from ordinations of distance matrices. Distance matrices were either based on pure spatial information, pure phylogenetic information or spatially structured phylogenetic information. In the multiple regression, those filters were selected which best reduced Moran's I coefficient of residual autocorrelation. These were added as covariates to a regression model of environmental variables explaining trait distribution. Results The simultaneous provision of spatial and phylogenetic information was effectively able to remove residual autocorrelation in the analysis. Adding phylogenetic information was superior to adding purely spatial information. Applying filters showed altered results, i.e. different environmental predictors were seen to be significant. Nevertheless, mean annual temperature and calcareous substrate remained the most important predictors to explain the onset of flowering in Switzerland; namely, the warmer the temperature and the more calcareous the substrate, the earlier the onset of flowering. A sequential approach, i.e. first removing the phylogenetic signal from traits and then applying a spatial analysis, did not provide more information or yield less autocorrelation than simple or purely spatial models. Main conclusions The combination of spatial and spatio‐phylogenetic information is recommended in the analysis of trait distribution data in a multiple regression framework. This approach is an efficient means for reducing residual autocorrelation and for testing the robustness of results, including the indication of incomplete parameterizations, and can facilitate ecological interpretation.     

Climate change and opposing spatial conservation priorities for anuran protection in the Brazilian hotspots

In conservation biogeography, the process of spatial conservation prioritization (SCP) aims to select areas that meet biodiversity targets at a minimum set coverage. Here, we propose a SCP scheme for the highly endemic and diverse anuran fauna of the Atlantic Forest (AF) and Cerrado (CER) South American hotspots under different climate change scenarios. Specifically, we make use of predicted anuran occurrences, built for baseline and future (2050 and 2070) time slices, and address biological and conservation metrics to identify potential priority regions for anuran conservation over time using the software MARXAN. Considering each time slice separately, the percentage area needed for total anuran representation varies at magnitudes of 9.8–10.66% for the AF and 6.4–8.8% for the CER. Pooling all time slices together in the selected conservation network, the identified spatial priorities account for 15.56% and 13.25% of the total AF and CER areas respectively. However, we identified opposing strategies for the anuran spatial conservation prioritization in the AF and CER over the different time periods; the increasing of priority cells across time considering the potential species redistribution under climate change in the AF, and the selection of fewer priority cells in the future than the identified for the baseline climate in the CER. The southeastern AF coast was identified as a priority area for amphibian conservation in this hotspot, as well as some other smaller areas in the northern and southern regions. Priority areas identified in the CER, although patchy distributed across the hotspot, are found in specific central-northern, western, and southeastern regions. The different conservation strategies identified in the present SCP emphasize the need for establishing different conservation efforts according to a sequential scheduling of priority areas that optimizes the long-term conservation goals.     

Improving generalized regression analysis for the spatial prediction of forest communities

Aim This study used data from temperate forest communities to assess: (1) five different stepwise selection methods with generalized additive models, (2) the effect of weighting absences to ensure a prevalence of 0.5, (3) the effect of limiting absences beyond the environmental envelope defined by presences, (4) four different methods for incorporating spatial autocorrelation, and (5) the effect of integrating an interaction factor defined by a regression tree on the residuals of an initial environmental model. Location State of Vaud, western Switzerland. Methods Generalized additive models (GAMs) were fitted using the grasp package (generalized regression analysis and spatial predictions, http://www.cscf.ch/grasp ). Results Model selection based on cross‐validation appeared to be the best compromise between model stability and performance (parsimony) among the five methods tested. Weighting absences returned models that perform better than models fitted with the original sample prevalence. This appeared to be mainly due to the impact of very low prevalence values on evaluation statistics. Removing zeroes beyond the range of presences on main environmental gradients changed the set of selected predictors, and potentially their response curve shape. Moreover, removing zeroes slightly improved model performance and stability when compared with the baseline model on the same data set. Incorporating a spatial trend predictor improved model performance and stability significantly. Even better models were obtained when including local spatial autocorrelation. A novel approach to include interactions proved to be an efficient way to account for interactions between all predictors at once. Main conclusions Models and spatial predictions of 18 forest communities were significantly improved by using either: (1) cross‐validation as a model selection method, (2) weighted absences, (3) limited absences, (4) predictors accounting for spatial autocorrelation, or (5) a factor variable accounting for interactions between all predictors. The final choice of model strategy should depend on the nature of the available data and the specific study aims. Statistical evaluation is useful in searching for the best modelling practice. However, one should not neglect to consider the shapes and interpretability of response curves, as well as the resulting spatial predictions in the final assessment.     

genalex 6: genetic analysis in Excel. Population genetic software for teaching and research

genalex is a user‐friendly cross‐platform package that runs within Microsoft Excel, enabling population genetic analyses of codominant, haploid and binary data. Allele frequency‐based analyses include heterozygosity, F statistics, Nei's genetic distance, population assignment, probabilities of identity and pairwise relatedness. Distance‐based calculations include amova , principal coordinates analysis (PCA), Mantel tests, multivariate and 2D spatial autocorrelation and twogener . More than 20 different graphs summarize data and aid exploration. Sequence and genotype data can be imported from automated sequencers, and exported to other software. Initially designed as tool for teaching, genalex 6 now offers features for researchers as well. Documentation and the program are available at http://www.anu.edu.au/BoZo/GenAlEx/     

Estimating and controlling for spatial structure in the study of ecological communities

Aim Variation partitioning based on canonical analysis is the most commonly used analysis to investigate community patterns according to environmental and spatial predictors. Ecologists use this method in order to understand the pure contribution of the environment independent of space, and vice versa, as well as to control for inflated type I error in assessing the environmental component under spatial autocorrelation. Our goal is to use numerical simulations to compare how different spatial predictors and model selection procedures perform in assessing the importance of the spatial component and in controlling for type I error while testing environmental predictors. Innovation We determine for the first time how the ability of commonly used (polynomial regressors) and novel methods based on eigenvector maps compare in the realm of spatial variation partitioning. We introduce a novel forward selection procedure to select spatial regressors for community analysis. Finally, we point out a number of issues that have not been previously considered about the joint explained variation between environment and space, which should be taken into account when reporting and testing the unique contributions of environment and space in patterning ecological communities. Main conclusions In tests of species‐environment relationships, spatial autocorrelation is known to inflate the level of type I error and make the tests of significance invalid. First, one must determine if the spatial component is significant using all spatial predictors (Moran's eigenvector maps). If it is, consider a model selection for the set of spatial predictors (an individual‐species forward selection procedure is to be preferred) and use the environmental and selected spatial predictors in a partial regression or partial canonical analysis scheme. This is an effective way of controlling for type I error in such tests. Polynomial regressors do not provide tests with a correct level of type I error.     

Differences in the occurrence and abundance of batoids across an oceanic archipelago using complementary data sources: Implications for conservation

Batoids, distributed from shallow to abyssal depths, are considerably vulnerable to anthropogenic threats. Data deficiencies on the distribution patterns of batoids, however, challenge their effective management and conservation. In this study, we took advantage of the particular geological and geomorphological configuration of the Canary Islands, across an east‐to‐west gradient in the eastern Atlantic Ocean, to assess whether patterns in the occurrence and abundance of batoids varied between groups of islands (western, central, and eastern). Data were collected from shallow (<40 m, via underwater visual counts and by a local community science program) and deep waters (60–700 m, via ROV deployments). Eleven species of batoids, assessed by the IUCN Red List of Threatened Species, were registered, including three “Critically Endangered” (Aetomylaeus bovinus, Dipturus batis, and Myliobatis aquila), three “Endangered” (Gymnura altavela, Mobula mobular, and Rostroraja alba), two “Vulnerable” (Dasyatis pastinaca and Raja maderenseis), and two “Data Deficient” (Taeniurops grabata and Torpedo marmorata). Also, a “Least Concern” species (Bathytoshia lata) was observed. Overall, batoids were ~1 to 2 orders of magnitude more abundant in the central and eastern islands, relative to the western islands. This pattern was consistent among the three sources of data and for both shallow and deep waters. This study, therefore, shows differences in the abundance of batoids across an oceanic archipelago, likely related to varying insular shelf area, availability of habitats, and proximity to the nearby continental (African) mass. Large variation in population abundances among islands suggests that “whole” archipelago management strategies are unlikely to provide adequate conservation. Instead, management plans should be adjusted individually per island and complemented with focused research to fill data gaps on the spatial use and movements of these iconic species.     

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.     

基于ArcGIS的下辽河平原地下水脆弱性评价及空间结构分析

以下辽河平原为研究区,通过选取1991、2000和2010年3个代表年的相关参数,在DRASTIC模型基础上构建评价指标体系进行地下水脆弱性评价,并以地下水中氮元素浓度为响应指标通过显著性检验,在此基础上借助GS+、Arc GIS和Geoda095i等软件的制图功能和空间统计分析功能,对下辽河平原地下水脆弱性的空间分布特征、变异规律以及空间关联格局进行研究分析,结果表明:11991—2010年下辽河平原地下水脆弱性总体上呈先增后减趋势,空间分布上以沈阳市为中心的地下水高脆弱区向南部沿海方向扩散;21991—2010年研究区地下水脆弱性Moran's I表现为较强正相关现象,且关联程度呈略微下降趋势;31991—2010年研究区地下水脆弱性局部空间自相关和显著性水平均发生了明显的变化;4研究区内地下水脆弱性受结构性因素和随机性因素共同作用,且随机性因素在3个时期内有逐步上升趋势。研究成果反映了研究区地下水脆弱性空间结构的变异规律及驱动机制,为决策者在未来地下水污染防治方面提供相关参考依据。     

三江平原湿地生态风险评价及空间阈值分析

湿地生态风险评价对区域自然资源保护及规划管理具有重要意义。以三江平原湿地为研究区域,基于2000年、2005年、2010年、2015年4期土地利用数据,以城市扩张导致的土地利用变化、道路建设等人类活动为风险源,景观生态格局、生态系统服务价值为风险受体构建了三江平原湿地生态风险综合评价体系,分析三江平原湿地生态风险时空变化特征。进而,利用距离阈值确定空间距离权重,采用双变量空间自相关模型揭示了不同时间尺度下生态风险的空间集聚分布特征。结果显示：从风险源角度,人类活动风险源强度呈增加趋势,松花江、穆棱河、倭肯河地区一直处于中高风险水平;从风险受体角度,景观生态风险的中高风险地区重点集中在湿地与水体分布区,生态系统服务低价值区主要分布在中部水田、旱田、建设用地以及东北部与东南小范围的湿地区域。综合生态风险结果显示,三江平原生态风险在时间上呈增加趋势,空间上由松花江河滩型湿地区与穆棱河地区逐渐向四周蔓延。此外,生态风险的强弱受到空间距离的影响显著,选取5km为自相关分析的距离阈值,土地利用与综合生态风险的空间格局存在显著的空间正相关关系,高-高地区集中分布在研究区内的松花江流域及周围滩地地区,随着土地利用变化及转移,空间关联逐渐增强且区域分布不断扩大。研究结果可从人类活动控制、景观格局优化、生态服务价值提升等方面为三江平原生态风险防控分区管理提供理论依据。     

A review of techniques for spatial modeling in geographical, conservation and landscape genetics

Most evolutionary processes occur in a spatial context and several spatial analysis techniques have been employed in an exploratory context. However, the existence of autocorrelation can also perturb significance tests when data is analyzed using standard correlation and regression techniques on modeling genetic data as a function of explanatory variables. In this case, more complex models incorporating the effects of autocorrelation must be used. Here we review those models and compared their relative performances in a simple simulation, in which spatial patterns in allele frequencies were generated by a balance between random variation within populations and spatially-structured gene flow. Notwithstanding the somewhat idiosyncratic behavior of the techniques evaluated, it is clear that spatial autocorrelation affects Type I errors and that standard linear regression does not provide minimum variance estimators. Due to its flexibility, we stress that principal coordinate of neighbor matrices (PCNM) and related eigenvector mapping techniques seem to be the best approaches to spatial regression. In general, we hope that our review of commonly used spatial regression techniques in biology and ecology may aid population geneticists towards providing better explanations for population structures dealing with more complex regression problems throughout geographic space.