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.     

Disentangling drivers of spatial autocorrelation in species distribution models

Species distribution models (SDMs) are frequently used to understand the influence of site properties on species occurrence. For robust model inference, SDMs need to account for the spatial autocorrelation of virtually all species occurrence data. Current methods do not routinely distinguish between extrinsic and intrinsic drivers of spatial autocorrelation, although these may have different implications for conservation. Here, we present and test a method that disentangles extrinsic and intrinsic drivers of spatial autocorrelation using repeated observations of a species. We focus on unknown habitat characteristics and conspecific interactions as extrinsic and intrinsic drivers, respectively. We model the former with spatially correlated random effects and the latter with an autocovariate, such that the spatially correlated random effects are constant across the repeated observations whereas the autocovariate may change. We tested the performance of our model on virtual species data and applied it to observations of the corncrake Crex crex in the Netherlands. Applying our model to virtual species data revealed that it was well able to distinguish between the two different drivers of spatial autocorrelation, outperforming models with no or a single component for spatial autocorrelation. This finding was independent of the direction of the conspecific interactions (i.e. conspecific attraction versus competitive exclusion). The simulations confirmed that the ability of our model to disentangle both drivers of autocorrelation depends on repeated observations. In the case study, we discovered that the corncrake has a stronger response to habitat characteristics compared to a model that did not include spatially correlated random effects, whereas conspecific interactions appeared to be less important. This implies that future conservation efforts should primarily focus on maximizing habitat availability. Our study shows how to systematically disentangle extrinsic and intrinsic drivers of spatial autocorrelation. The method we propose can help to correctly identify the main drivers of species distributions.     

Analysis of determinants of mammalian species richness in South America using spatial autoregressive models

Classically, hypotheses concerning the distribution of species have been explored by evaluating the relationship between species richness and environmental variables using ordinary least squares (OLS) regression. However, environmental and ecological data generally show spatial autocorrelation, thus violating the assumption of independently distributed errors. When spatial autocorrelation exists, an alternative is to use autoregressive models that assume spatially autocorrelated errors. We examined the relationship between mammalian species richness in South America and environmental variables, thereby evaluating the relative importance of four competing hypotheses to explain mammalian species richness. Additionally, we compared the results of ordinary least squares (OLS) regression and spatial autoregressive models using Conditional and Simultaneous Autoregressive (CAR and SAR, respectively) models. Variables associated with productivity were the most important at determining mammalian species richness at the scale analyzed. Whereas OLS residuals between species richness and environmental variables were strongly autocorrelated, those from autoregressive models showed less spatial autocorrelation, particularly the SAR model, indicating its suitability for these data. Autoregressive models also fit the data better than the OLS model (increasing R² by 5–14%), and the relative importance of the explanatory variables shifted under CAR and SAR models. These analyses underscore the importance of controlling for spatial autocorrelation in biogeographical studies.     

Predicting forest grouse distribution taking account of spatial autocorrelation

Spatially explicit, multi-scale models for predictions of species potential distribution can be useful tools for integrating biodiversity considerations in planning and strategic environmental assessment. In such models, the occurrences of focal species are related to habitat and landscape variables, which in urbanising areas should also include effects of urban disturbances. Moreover, the accuracy of the spatial predictive models may be affected by spatial autocorrelation, which means that a part of the variance is explained by neighbouring values. The aim of this study was to explore the effects of habitat and disturbance patterns on the distribution of two forest grouse species, Tetrao urogallus and Bonasa bonasia, and to detect and model the effects of spatial autocorrelation. The distribution of the two species could be explained in terms of reduction of a main predator, habitat quality, quantity and connectivity, including urban disturbances. The residuals of the initial regressions showed positive spatial autocorrelation that could be quantified by using a spatial probit model. The application of the spatial probit model revealed strongly significant spatial dependencies for both species. Furthermore, the model fit could be increased for T. urogallus by applying this model. The results implied that both species distributions might be affected by both reactions to the underlying land-use pattern, but also by interaction with neighbours. The use of the spatial probit model is a way to incorporate spatial interactions that otherwise cannot be captured by the independent variables.     

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.     

Do biogeographic parameters matter? Plant species richness and distribution of macrophytes in relation to area and isolation of ponds in NW Polish agricultural landscape

Effects of pond size and isolation on total vascular plant species richness and number of obligate wetland species were compared. Subsequently, the potential for the presence of spatial patterns in wetland species distribution among ponds in an agricultural landscape was explored. Relationships between species richness and two main biogeographic parameters were analysed using simple and multiple linearised regression models. Spatial patterns were looked for by means of analyses carried out with the R CRAN software (join-count statistics). Simple regression analyses performed on the regional scale (n = 50) revealed the significance of the effect of pond size only (r = 0.46 for total plant species richness and r = 0.28 for wetland species richness vs. pond area). Further analyses conducted on the local scale identified the best multiple regression models in the largest pond cluster (n = 20); the models showed statistical significance of relationships between the species richness and both independent variables (r = 0.80 for total plant species richness and r = 0.70 for wetland species richness vs. pond area and isolation, including mean distance to the nearest ten ponds). Spatial analyses were performed for 26 obligate wetland species selected from 149 species recorded in all the 50 ponds. Exploratory spatial data analysis revealed the presence of significant positive spatial autocorrelation in the distribution of 8 species. In such cases, it is possible to reject the random distribution hypothesis, which justifies exploration of spatial regimes. In practice, correct spatial model specifications may have implications for predicting species occurrences under changing environmental conditions, e.g. changes in the number of ponds.     

Accounting for multi‐scale spatial autocorrelation improves performance of invasive species distribution modelling (iSDM)

Aim Analyses of species distributions are complicated by various origins of spatial autocorrelation (SAC) in biogeographical data. SAC may be particularly important for invasive species distribution models (iSDMs) because biological invasions are strongly influenced by dispersal and colonization processes that typically create highly structured distribution patterns. We examined the efficacy of using a multi‐scale framework to account for different origins of SAC, and compared non‐spatial models with models that accounted for SAC at multiple levels. Location We modelled the spatial distribution of an invasive forest pathogen, Phytophthora ramorum, in western USA. Methods We applied one conventional statistical method (generalized linear model, GLM) and one nonparametric technique (maximum entropy, Maxent) to a large dataset on P. ramorum occurrence (n = 3787) to develop four types of model that included environmental variables and that either ignored spatial context or incorporated it at a broad scale using trend surface analysis, a local scale using autocovariates, or multiple scales using spatial eigenvector mapping. We evaluated model accuracies and amounts of explained spatial structure, and examined the changes in predictive power of the environmental and spatial variables. Results Accounting for different scales of SAC significantly enhanced the predictive capability of iSDMs. Dramatic improvements were observed when fine‐scale SAC was included, suggesting that local range‐confining processes are important in P. ramorum spread. The importance of environmental variables was relatively consistent across all models, but the explanatory power decreased in spatial models for factors with strong spatial structure. While accounting for SAC reduced the amount of residual autocorrelation for GLM but not for Maxent, it still improved the performance of both approaches, supporting our hypothesis that dispersal and colonization processes are important factors to consider in distribution models of biological invasions. Main conclusions Spatial autocorrelation has become a paradigm in biogeography and ecological modelling. In addition to avoiding the violation of statistical assumptions, accounting for spatial patterns at multiple scales can enhance our understanding of dynamic processes that explain ecological mechanisms of invasion and improve the predictive performance of static iSDMs.     

水菜花种群潜在生境选择与空间格局预测

国家二级保护野生植物水菜花(Ottelia cordata)，喜生于清洁的水环境中，对环境变化极为敏感，是检验湿地环境及气候变化的关键指示物种之一，在我国仅零星分布于海南北部的火山熔岩湿地区，生存状况不容乐观。研究水菜花种群潜在生境选择及其空间格局演变，有利于加强濒危物种保护保育及湿地生态系统修复、管理。该研究基于GIS平台和MaxEnt模型，结合气候、地形和土壤因子，探究水菜花种群环境限制因子及其在气候变化背景下潜在适宜生境的演变格局。结果表明，水菜花种群对温差与降水量变化敏感，等温性、最冷季度降水量、土壤类型和年均降水量对水菜花种群分布影响显著；全新世中期-当前-2070年气候变化背景下，水菜花适宜生境面积先减小后增大，分布重心呈西南-东北-西南转移格局；未来气候情景下，水菜花种群高度和中度适宜生境缩减，低适宜生境增加，南部地区将出现新增适宜生境，东北、西北及西南部适宜生境将发生消减。该研究从气候环境角度论证了水菜花种群的潜在生境选择及空间变化特征，可为濒危物种保护保育、湿地管理及其生物多样性维护工作提供参考和指导。     

Prediction of humpback whale group densities along the Brazilian coast using spatial autoregressive models

At the breeding grounds of most baleen whales the patchiness and gaps in spatial distribution results from interactions between behavior patterns and environmental conditions. We evaluated the influence of environmental factors (bathymetry and distance from shore with quadratic terms, and wind speed), effort, and spatial autocorrelation effects to predict humpback whale group density in the Southwest Atlantic Ocean. Count data of groups by grid cells were fitted with conditional autoregressive models (CAR). Bayesian inference was performed via integrated nested Laplace approximation. The best‐fit model contained distance from shore and its quadratic term, bathymetry, and the autoregressive component. Occupancy probability was high for the Abrolhos Bank, some cells from the northeast continental shelf and southeast margin, but gaps in occurrence were identified. High densities were estimated in the east continental margin, with the highest density in the Abrolhos Bank, in some cells of the northeast continental margin and in the southernmost area. We report that intermediate distances from the coast, and shallow waters were preferred for breeding and calving activities. We suggest that CAR models may incorporate aggregation mechanisms into habitat modeling and may provide advances in marine mammal analyses by accounting for residual autocorrelation.     

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.     

Can niche‐based distribution models outperform spatial interpolation?

Aim Distribution modelling relates sparse data on species occurrence or abundance to environmental information to predict the population of a species at any point in space. Recently, the importance of spatial autocorrelation in distributions has been recognized. Spatial autocorrelation can be categorized as exogenous (stemming from autocorrelation in the underlying variables) or endogenous (stemming from activities of the organism itself, such as dispersal). Typically, one asks whether spatial models explain additional variability (endogenous) in comparison to a fully specified habitat model. We turned this question around and asked: can habitat models explain additional variation when spatial structure is accounted for in a fully specified spatially explicit model? The aim was to find out to what degree habitat models may be inadvertently capturing spatial structure rather than true explanatory mechanisms. Location We used data from 190 species of the North American Breeding Bird Survey covering the conterminous United States and southern Canada. Methods We built 13 different models on 190 bird species using regression trees. Our habitat‐based models used climate and landcover variables as independent variables. We also used random variables and simulated ranges to validate our results. The two spatially explicit models included only geographical coordinates or a contagion term as independent variables. As another angle on the question of mechanism vs. spatial structure we pitted a model using related bird species as predictors against a model using randomly selected bird species. Results The spatially explicit models outperformed the traditional habitat models and the random predictor species outperformed the related predictor species. In addition, environmental variables produced a substantial R² in predicting artificial ranges. Main conclusions We conclude that many explanatory variables with suitable spatial structure can work well in species distribution models. The predictive power of environmental variables is not necessarily mechanistic, and spatial interpolation can outperform environmental explanatory variables.     

Spatial genetic structure within two populations of a self-incompatible perennial,Chionographis japonica var.japonica (Liliaceae)

Intrapopulational spatial genetic structure was examined in two populations ofChionographis japonica var.japonica, a self-incompatible perennial, by spatial autocorrelation analysis of enzyme polymorphism. Although most spatial autocorrelation indices (Moran'sI) in the shortes distance class were significantly positive, most in the other distance classes did not significantly deviate from the values expected from random distributions of genotypes in both populations. This contrasts with a spatial genetic pattern previously reported for a population of the predominantly selfing congener,C. japonica var.kurohimensis, indicating that pollen-mediated gene flow highly impedes genetic substructuring within populations of outcrossingC. japonica var.japonica. Genetic similarity in very proximate distance found in outcrossingC. japonica var.japonica is probably due to restricted dispersal of seeds.     

Geostatistical distribution modelling of two invasive crayfish across dendritic stream networks

Species distribution models combining environmental and spatial components are increasingly used to understand and forecast species invasions. However, modelling distributions of invasive species inhabiting stream networks requires due consideration of their dendritic spatial structure, which may strongly constrain dispersal and colonization pathways. Here we evaluate the application of novel geostatistical tools to species distribution modelling in dendritic networks, using as case study two invasive crayfish (Procambarus clarkii and Pacifastacus leniusculus) in a Mediterranean watershed. Specifically, we used logistic mixed models to relate the probability of occurrence of each crayfish to environmental variables, while specifying three spatial autocorrelation components in random errors. These components described spatial dependencies between sites as a function of (1) straight-line distances (Euclidean model) between sites, (2) hydrologic (along the waterlines) distances between flow-connected sites (tail-up model), and (3) hydrologic distances irrespective of flow connection (tail-down model). We found a positive effect of stream order on P. clarkii, indicating an association with the lower and mid reaches of larger streams, while P. leniusculus was affected by an interaction between stream order and elevation, indicating an association with larger streams at higher altitude. For both species, models including environmental and spatial components far outperformed the pure environmental models, with the tail-up and the Euclidean components being the most important for P. clarkii and P. leniusculus, respectively. Overall, our study highlighted the value of geostatistical tools to model the distribution of riverine and aquatic invasive species, and stress the need to specify spatial dependencies representing the dendritic network structure of stream ecosystems.     

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.     

Effects of advance and retreat of agricultural landscapes on Rana japonica and R. ornativentris

Paddy fields are essential habitats for frogs. We evaluated the impacts of both farmland consolidation including agricultural road improvement and farmland abandonment on the two Rana species using a model incorporating spatial autocorrelation. A sampling unit consists of several paddy fields that share a ditch and are isolated from other blocks by roads or other land covers. We surveyed 619 blocks in an area of about 1000 km² from the plain to the mountains of Toyota City in central Japan. Among them, 124 blocks included at least a flooded paddy field where frogs could lay eggs. R. ornativentris and R. japonica bred in 50 and 25 blocks, respectively. We constructed models to explain the presence/absence of two species by GLM (non-spatial model) and hierarchical Bayesian model with INLA (spatial model) that includes spatial autocorrelation as a random effect. Explanatory variables of the local scale were the altitude, location of the paddy field (yatsuda (valley bottom paddy fields) or non-yatsuda), farmland consolidated or not consolidated, and under cultivation or abandoned. Those of the landscape scale were areas of forest and paddy fields, and road density in 14 circles with different radius from 50 to 2000 m. Both species’ distribution had significant spatial autocorrelation. The spatial model had a higher discriminative ability than the non-spatial model. Farmland consolidation and the forest area in the 400 m radius had a positive effect on R. ornativentris. Altitude and road density in the 50 m radius had negative effects, cultivation had a positive effect, and farmland consolidation and yatsuda had no or negative effects on R. japonica. R. ornativentris was threatened by farmland abandonment, but the urbanization and/or farmland consolidation threatened R. japonica.

     

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.     

Limited transferability of stream‐fish distribution models among river catchments: reasons and implications

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Complementary strengths of spatially-explicit and multi-species distribution models

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吉林蛟河针阔混交林树木生长的空间关联格局

以吉林蛟河21.12hm2(660m×320m)针阔混交林样地为对象,利用2009年和2014年森林生长观测数据,研究树木生长的空间自相关格局及其生境影响机制。在样地生境型划分结果的基础上,采用Ripley's L(r)函数分析不同生境型中树木种群空间分布特征;利用标记相关函数分析不同生境型中树木生长特征的空间关联格局。研究结果表明:(1)红松(生境型3:1—5m)、蒙古栎(生境型3:1—3m)、胡桃楸(生境型2:1—2m;生境型3:1—7m)、黄檗(生境型2:1—3m;生境型4:1—5m)、水曲柳(生境型3:1—2m;生境型4:1—2m)、瘤枝卫矛(生境型2:1—15m)在特定生境和空间尺度上呈随机分布,但空间格局仍以聚集性分布为主;其余10个物种则在全部0—30m尺度上呈聚集分布。(2)标记相关函数分析显示春榆、毛榛、色木槭、瘤枝卫矛和千金榆的径向生长至少在一个生境中表现出正相关格局;暴马丁香、胡桃楸、裂叶榆、瘤枝卫矛、水曲柳、紫椴、糠椴、毛榛、色木槭和白牛槭的径向生长至少在一个生境中表现出负相关格局;红松、黄檗、蒙古栎和簇毛槭的径向生长在全部尺度上均未检测到显著的空间关联格局。因此,不同树种径向生长的空间自相关特征不同,树种生长特征的空间关联格局具有明显的生境依赖性。