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.     

Towards an integrated computational tool for spatial analysis in macroecology and biogeography

Because most macroecological and biodiversity data are spatially autocorrelated, special tools for describing spatial structures and dealing with hypothesis testing are usually required. Unfortunately, most of these methods have not been available in a single statistical package. Consequently, using these tools is still a challenge for most ecologists and biogeographers. In this paper, we present sam (Spatial Analysis in Macroecology), a new, easy-to-use, freeware package for spatial analysis in macroecology and biogeography. Through an intuitive, fully graphical interface, this package allows the user to describe spatial patterns in variables and provides an explicit spatial framework for standard techniques of regression and correlation. Moran's I autocorrelation coefficient can be calculated based on a range of matrices describing spatial relationships, for original variables as well as for residuals of regression models, which can also include filtering components (obtained by standard trend surface analysis or by principal coordinates of neighbour matrices). sam also offers tools for correcting the number of degrees of freedom when calculating the significance of correlation coefficients. Explicit spatial modelling using several forms of autoregression and generalized least-squares models are also available. We believe this new tool will provide researchers with the basic statistical tools to resolve autocorrelation problems and, simultaneously, to explore spatial components in macroecological and biogeographical data. Although the program was designed primarily for the applications in macroecology and biogeography, most of sam 's statistical tools will be useful for all kinds of surface pattern spatial analysis. The program is freely available at http://www.ecoevol.ufg.br/sam (permanent URL at http://purl.oclc.org/sam/ ).     

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.     

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.     

空间分析方法在微生物生态学研究中的应用

微生物生态正在受到越来越多的关注,对其研究也渐趋深入。然而由于微生物个体微小的特点及研究手段的限制,多数研究还停留在探索阶段,研究方法也在不断完善当中。近年来,较多的研究开始探讨空间因素在微生物多样性和分布中的影响,对空间分布的探讨有助于更好地认识生态过程,是一种有力的研究手段。微生物空间分析方法已经成为微生物生态学领域中重要的研究方向之一,我国空间方法在微生物生态研究中的应用还没有得到普遍的重视。从不同研究角度出发,结合空间统计的作用,对空间统计方法在微生物生态研究中的应用的必要性及现状做了评述。介绍了空间自相关性的检验,方差图,Mantel检验,Kriging插值等方法在微生物生态研究中的应用,并论述了微生物研究中的尺度问题。这一梳理,对丰富微生物生态学研究中的新方法、新手段具有一定价值。     

Inferring population history from fine-scale spatial genetic analysis in Oryza rufipogon (Poaceae)

Determining the genetic structure of an in situ conserved population can provide insight into the dynamics of population genetic processes associated with successful plant conservation. We used 21 microsatellite loci to analyse the genetic relationships among individuals (n = 813) collected from a small Oryza rufipogon population conserved since 1993 in Hunan Province of China. The analysis revealed four distinct genetic subpopulations (F(ST) = 0.145) without geographic isolation. One subpopulation was composed of possible introgressed individuals, two subpopulations were composed of seed recruits and their descendants, and the fourth subpopulation consisted of reintroduced individuals, seed recruits and their descendants. Positive spatial genetic structures were detected by spatial autocorrelation statistics at the population (c. 63 m) and subpopulation levels (11-30 m), but the degree of autocorrelation was stronger at the population level. These results showed that prejudging the cryptic structure is important before autocorrelation analysis for the entire population. Our study suggests that population history can be a significant determinant on population structure for plant restoration projects.     

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.     

基于空间自相关的东海带鱼聚集特征年代际变化

海洋鱼类通常以集群的形式分布在特定空间内,具有高度的空间异质性特征.基于1971—2011年中国机轮拖网渔业捕捞统计及底拖网科学调查获取的东海带鱼数据,并结合夏季研究水域内海表温度及黑潮区PN断面表层盐度数据,利用空间统计方法对东海带鱼资源的聚集特征进行年代际分析.全局自相关性分析显示,1971—2011年Moran I指数先减小再增大且均为正值,表明东海带鱼聚集性呈先减弱再增强的趋势;PN断面表层盐度均值变化趋势与之相反.局部自相关性分析显示,除1971年带鱼热点分布受作业水域范围限制而集中在中部外,1981—2011年带鱼分布热点区域呈现先向南部外海移动,随后逐步向北部外海移动的格局,且相应的热点分布范围亦呈现先集中后扩散的趋势.带鱼热点分布区域随海表温度第一模态变化做适应性移动,且均靠近黑潮北分支左侧水域.     

Isolation by distance,based on microsatellite data,tested with spatial autocorrelation (spaida) and assignment test (spassign)

spassign and spaida are two small programs useful to detect isolate by distance of microsatellite loci. The programs are written in C and are available for Linux and Windows system at http://www.hi.is/~snaebj/programs.html . spaida calculates two estimates of spatial autocorrelation, Moran's I and Geary's c, first by assuming the infinite allele model, and second by assuming a stepwise mutational model. spassign calculates the assignment probabilities of an individuals genotype to the location where it was sampled and compares probabilities of assignment to other locations. Genetic distances among regions based on the overall differences in likelihoods are calculated.     

A simulation study of microevolutionary inferences by spatial autocorrelation analysis

To explore the extent to which microevolutionary inference can be made using spatial autocorrelation analysis of gene frequency surfaces, we simulated sets of surfaces for nine evolutionary scenarios, and subjected spatially-based summary statistics of these to linear discriminant analysis. Scenarios varied the amounts of dispersion, selection, migration, and deme sizes, and included: panmixia, drift, intrusion, and stepping-stone models with 0–2 migrations, 0–2 selection gradients, and migration plus selection. To discover how weak evolutionary forces could be and still allow discrimination, each scenario had both a strong and a weak configuration. Discriminant rules were calculated using one collection of data (the training set) consisting of 250 sets of 15 surfaces for each of the nine scenarios. Misclassification rates were verified against a second, entirely new set of data (the test set) equal in size. Test set misclassification rates for the 20 best discriminating variables ranged from 39.3% (weak) to 3.6% (strong), far lower than the expected rate of 88.9% absent any discriminating ability. Misclassification was highest when discriminating the number of migrational events or the presence or number of selection events. Discrimination of drift and panmixia from the other scenarios was perfect. A subsequent subjective analysis of a subset of the data by one of us yielded comparable, although somewhat higher, misclassification rates. Judging by these results, spatial autocorrelation variables describing sets of gene frequency surfaces permit some microevolutionary inferences.     

基于TM影像的景观空间自相关分析——以北京昌平区为例

格局与尺度之间的关系是景观生态学的核心研究内容。景观格局发生在不同的尺度 ,而尺度又影响格局的研究 ,因而 ,在景观生态学研究中应用多种量化研究方法于一系列尺度来确定和特征化空间格局研究 ,并探求空间格局与生态学功能和生态学过程之间的关系是非常必要的。以北京昌平区为例 ,从 TM影像中选取 5个具有突出自然和社会经济背景差异的景观 ,即林地景观、农田景观、都市边缘景观、卫星城景观和灌丛景观为研究对象 ,基于归一化植被指数 (N DVI) ,采用常用空间自相关指数 ,即 Moran的 I系数和 Geary的 c系数进行一系列的空间自相关分析 ,旨在阐明 :变化的空间粒度如何影响空间分析 ?以及空间分析如何响应划区效应 ?此外 ,基于 N DVI和数字高程模型 (DEM)也探讨了对于不同的数据类型 ,格局的尺度依赖性如何变化。研究结果表明 :空间粒度的变化对于景观分析有着显著的影响 ,随着空间粒度的增加 ,空间自相关均呈下降趋势 ;不同景观类型对于空间粒度的变化有着不同的响应 ,人为干扰较多的景观具有较低的空间自相关 ,但对空间粒度的变化表现出较强的敏感性 ;对于不同的数据类型 ,格局分析对空间粒度变化的响应是不同的     

Distribution patterns in butterflies and birds of the Czech Republic: separating effects of habitat and geographical position

Aim To evaluate the relative role of environmental factors and geographical position (latitude and longitude) in determining species distribution and composition of local assemblages of butterflies and birds. Location Czech Republic, central Europe. Methods Canonical correspondence analysis that ordinates species and samples (grid cells in distribution atlases) such that interspecific and intersample differences attributable to environmental factors are maximized. The technique allowed us to test the significance of individual factors, including the geographical ones, by controlling the other factors and accounting for spatial autocorrelation. Results Altitude and climate (temperature and precipitation) accounted for most variance in the interspecific differences in distribution of both butterflies and birds. The distribution of birds was also strongly affected by the area of water bodies, and less strongly, but still significantly, by the area of meadows and mountain open habitats. Habitat types important for the differences in butterfly distribution were deciduous forests, meadows, swamps and mountain open habitats. Some less common habitat types were important only because of the presence of rare species. Latitude and longitude invariably accounted for a large proportion of total variance, and their effect was highly significant even after controlling for the effect of all other environmental factors. Main conclusions Although environmental factors, especially those related to elevation and climate, represent the main determinants of species distribution and composition of local assemblages, the geographical position is very important on this scale of resolution. Understanding distribution patterns, thus, must include not only an understanding of species ecological requirements, but also an understanding of geographical context, which affects structure and dynamics of species’ geographical ranges.     

三江平原湿地鸟类丰富度的空间格局及热点地区保护

全球气候变化和人类的开垦开发活动使湿地生物多样性遭到严重的干扰和破坏,导致生物多样性空间分布格局及热点地区的保护成为研究的热点。在对三江平原湿地鸟类预测的基础上,利用空间自相关方法分析三江平原湿地鸟类丰富度的空间分布格局,并找出湿地鸟类多样性的热点地区及优先保护顺序。研究结果表明,三江平原湿地鸟类丰富度高高集聚区主要分布在保护区及周边地区、河流和湖泊沿岸,是新建和扩建自然保护区的最佳区域。湿地鸟类丰富度高低集聚区主要分布在农田景观中,将它们设立成微型保护地块对于区域景观生态安全具有重要意义;利用湿地鸟类物种丰富度、国家级保护湿地鸟类、生境类型和结构、距最近保护区距离、破碎度、干扰度等指标,在研究区内共找到13个热点地区,总面积为1018.7km²,占研究区总面积的8%;利用系统聚类分析,将13个热点地区划分成3种优先保护顺序。构建的小区域范围内寻找生物多样性热点地区的方法,为相关政府部门更有效地进行湿地生物多样性的保护和管理提供科学依据。     

Gradients in stream fish assemblages across a Mediterranean landscape: contributions of environmental factors and spatial structure

1. Despite wide recognition that fish assemblages are influenced by factors operating over a range of spatial scales, little effort has been devoted to quantifying large‐scale variation and the multiscale dependencies of assemblage patterns and processes. This is particularly true for Mediterranean streams, where seasonally predictable drying‐up may lead to a strong association between assemblage attributes and large‐scale factors affecting the distribution of population sources and extinction likelihood. 2. The contribution of large‐scale factors to stream fish assemblage variation was quantified across a Mediterranean landscape, in south‐west Portugal. Fish abundance and species composition were estimated at 166 sites across third‐ to sixth‐order streams, in March–July 1998. Variance partitioning by redundancy analyses was used to analyse assemblage variation against three sets of predictor variables: environmental (catchment position, and geomorphic and hydrological factors), large‐scale spatial trends and neighbourhood effects. 3. Environmental variables and spatial trends accounted for 34.6% of the assemblage variation across the entire region, and for 36.6 and 57.8% within the two largest catchments (Mira and Seixe). Neighbourhood effects were analysed at the catchment scale, increasing the explained variation to 56.1% (Mira) and 70.7% (Seixe). 4. A prevailing environmental gradient was reflected in an increase in the abundance of all species and size‐classes in relation to catchment position, with more fish present in larger streams and in downstream reaches. Variables describing geomorphic and hydrological settings were less important in explaining assemblage variation. 5. Spatial trends always accounted for the smallest fraction of assemblage variation, and they were probably associated with historical barriers to fish dispersal. The strong neighbourhood effects may be related to spatially autocorrelated habitat conditions, but they are also a likely consequence of fish emigration/extinction and colonisation processes. 6. These results emphasise that a substantial proportion of fish assemblage variation in Mediterranean streams may be explained by large‐scale factors, irrespective of microhabitats and local biotic interactions. It is suggested that this pattern results to a large extent from the seasonal drying‐up, with the summer shortage of surface water limiting fish occurrence in headwaters, and consequently the key core areas for fish concentrating in larger streams and tributaries adjacent to large streams because of neighbourhood effects.     

Character analysis and taxonomic revision of the Microtoena insuavis complex (Lamiaceae)

The taxonomy of the Microtoena insuavis complex (Lamiaceae) is controversial. No agreement on the taxonomic treatments of M. esquirolii, M. insuavis, M. mollis and M. patchoulii has been reached. In addition, some species and varieties described on the basis of a single specimen or a limited number of specimens are doubtful. Based on the examination of a large number of herbarium specimens, extensive field observations, population sampling, scanning electron microscopy observation and statistical analysis of some characters, M. esquirolii is separated from the M. insuavis complex, and M. subspicata and M. subspicata var. intermedia are treated as synonyms of M. esquirolii, M. pauciflora is treated as a synonym of M. patchouli, and M. siamica is treated as a synonym of M. insuavis. Only three species (M. insuavis, M. mollis and M. patchouli) are recognized in this complex. © 2011 The Linnean Society of London, Botanical Journal of the Linnean Society, 2011, 165 , 315–327.     

Small mammal (rodents and lagomorphs) European biogeography from the Late Oligocene to the mid Pliocene

Aim To analyse the fossil species assemblages of rodents and lagomorphs from the European Neogene in order to assess what factors control small mammal biogeography at a deep‐time evolutionary time‐scale. Location Western Europe: 626 fossil‐bearing localities located within 31 regions and distributed among 18 successive biochronological units ranging from c. 27 Ma (million years ago; Late Oligocene) to c. 3 Ma (mid Pliocene). Methods Taxonomically homogenized pooled regional assemblages are compared using the Raup and Crick index of faunal similarity; then, the inferred similarity matrices are visualized as neighbour‐joining trees and by projecting the statistically significant interregional similarities and dissimilarities onto palaeogeographical maps. The inferred biogeographical patterns are analysed and discussed in the light of known palaeogeographical and palaeoclimatic events. Results Successive time intervals with distinct biogeographical contexts are identified. Prior to c. 18 Ma (Late Oligocene and Early Miocene), a relative faunal homogeneity (high interregional connectivity) is observed all over Europe, a time when major geographical barriers and a weak climatic gradient are known. Then, from the beginning of the Middle Miocene onwards, the biogeography is marked by a significant decrease in interregional faunal affinities which matches a drastic global climatic degradation and leads, in the Late Miocene (c. 11 Ma), to a marked latitudinal pattern of small mammal distribution. In spite of a short rehomogenization around the Miocene/Pliocene boundary (6–4 Ma), the biogeography of small mammals in the mid Pliocene (c. 3 Ma) finally closely reflects the extant situation. Main conclusions The resulting biogeographical evolutionary scheme indicates that the extant endemic situation has deep historical roots corresponding to global tectonic and climatic events acting as primary drivers of long‐term changes. The correlation of biogeographical events with climatic changes emphasizes the prevalent role of the climate over geography in generating heterogeneous biogeographical patterns at the continental scale.     

Inferring recruitment history from spatial genetic structure within populations of the colonizing tree Albizia julibrissin (Fabaceae)

Comparative analyses of spatial genetic structure (SGS) among species, populations, or cohorts give insight into the genetic consequences of seed dispersal in plants. We analysed SGS of a weedy tree in populations with known and unknown recruitment histories to first establish patterns in populations with single vs. multiple founders, and then to infer possible recruitment scenarios in populations with unknown histories. We analysed SGS in six populations of the colonizing tree Albizia julibrissin Durazz. (Fabaceae) in Athens, Georgia. Study sites included two large populations with multiple, known founders, two small populations with a single, known founder, and two large populations with unknown recruitment histories. Eleven allozyme loci were used to genotype 1385 individuals. Insights about the effects of colonization history from the SGS analyses were obtained from correlograms and Sp statistics. Distinct differences in patterns of SGS were identified between populations with multiple founders vs. a single founder. We observed significant, positive SGS, which decayed with increasing distance in the populations with multiple colonists, but little to no SGS in populations founded by one colonist. Because relatedness among individuals is estimated relative to a local reference population, which usually consists of those individuals sampled in the study population, SGS in populations with high background relatedness, such as those with a single founder, may be obscured. We performed additional analyses using a regional reference population and, in populations with a single founder, detected significant, positive SGS at all distances, indicating that these populations consist of highly related descendants and receive little seed immigration. Subsequent analyses of SGS in size cohorts in the four large study populations showed significant SGS in both juveniles and adults, probably because of a relative lack of intraspecific demographic thinning. SGS in populations of this colonizing tree is pronounced and persistent and is determined by the number and relatedness of founding individuals and adjacent seed sources. Patterns of SGS in populations with known histories may be used to indirectly infer possible colonization scenarios for populations where it is unknown.