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.     

Host plant associations and geography interact to shape diversification in a specialist insect herbivore

Disentangling the processes underlying geographic and environmental patterns of biodiversity challenges biologists as such patterns emerge from eco‐evolutionary processes confounded by spatial autocorrelation among sample units. The herbivorous insect, Belonocnema treatae (Hymenoptera: Cynipidae), exhibits regional specialization on three plant species whose geographic distributions range from sympatry through allopatry across the southern United States. Using range‐wide sampling spanning the geographic ranges of the three host plants and genotyping‐by‐sequencing of 1,217 individuals, we tested whether this insect herbivore exhibited host plant‐associated genomic differentiation while controlling for spatial autocorrelation among the 58 sample sites. Population genomic structure based on 40,699 SNPs was evaluated using the hierarchical Bayesian model entropy to assign individuals to genetic clusters and estimate admixture proportions. To control for spatial autocorrelation, distance‐based Moran's eigenvector mapping was used to construct regression variables summarizing spatial structure inherent among sample sites. Distance‐based redundancy analysis (dbRDA) incorporating the spatial variables was then applied to partition host plant‐associated differentiation (HAD) from spatial autocorrelation. By combining entropy and dbRDA to analyse SNP data, we unveiled a complex mosaic of highly structured differentiation within and among gall‐former populations finding evidence that geography, HAD and spatial autocorrelation all play significant roles in explaining patterns of genomic differentiation in B. treatae. While dbRDA confirmed host association as a significant predictor of patterns of genomic variation, spatial autocorrelation among sites explained the largest proportion of variation. Our results demonstrate the value of combining dbRDA with hierarchical structural analyses to partition spatial/environmental patterns of genomic variation.     

Microhabitat analyses support relationships between niche breadth and range size when spatial autocorrelation is strong

Multiple evidence of positive relationships between nice breadth and range size (NB–RS) suggested that this can be a general ecological pattern. However, correlations between niche breadth and range size can emerge as a by-product of strong spatial structure of environmental variables. This can be problematic because niche breadth is often assessed using broad-scale macroclimatic variables, which suffer heavy spatial autocorrelation. Microhabitat measurements provide accurate information on species tolerance, and show limited autocorrelation. The aim of this study was to combine macroclimate and microhabitat data to assess NB–RS relationships in European plethodontid salamanders (Hydromantes), and to test whether microhabitat variables with weak autocorrelation can provide less biased NB–RS estimates across species. To measure macroclimatic niche, we gathered comprehensive information on the distribution of all Hydromantes species, and combined them with broad-scale climatic layers. To measure microhabitat, we recorded salamander occurrence across > 350 caves and measured microhabitat features influencing their distribution: humidity, temperature and light. We assessed NB–RS relationships through phylogenetic regression; spatial null-models were used to test whether the observed relationships are a by-product of autocorrelation. We observed positive relationships between niche breadth and range size at both the macro- and microhabitat scale. At the macroclimatic scale, strong autocorrelation heavily inflated the possibility to observe positive NB–RS. Spatial autocorrelation was weaker for microhabitat variables. At the microhabitat level, the observed NB–RS was not a by-product of spatial structure of variables. Our study shows that heavy autocorrelation of variables artificially increases the possibility to detect positive relationships between bioclimatic niche and range size, while fine-scale data of microhabitat provide more direct measure of conditions selected by ectotherms, and enable less biased measures of niche breadth. Combining analyses performed at multiple scales and datasets with different spatial structure provides more complete niche information and effectively tests the generality of niche breadth–range size relationships.     

Dispersal, philopatry, and infidelity: dissecting local genetic structure in superb fairy-wrens (Malurus cyaneus)

Dispersal influences evolution, demography, and social characteristics but is generally difficult to study. Here we combine long-term demographic data from an intensively studied population of superb fairy-wrens (Malurus cyaneus) and multivariate spatial autocorrelation analyses of microsatellite genotypes to describe dispersal behavior in this species. The demographic data revealed: (1) sex-biased dispersal: almost all individuals that dispersed into the study area over an eight-year period were female (93%; n = 153); (2) high rates of extragroup infidelity (66% of offspring), which also facilitated local gene dispersal; and (3) skewed lifetime reproductive success in both males and females. These data led to three expectations concerning the patterns of fine-scale genetic structure: (1) little or no spatial genetic autocorrelation among females, (2) positive spatial genetic autocorrelation among males, and (3) a heterogeneous genetic landscape. Global autocorrelation analysis of the genotypes present in the study population confirmed the first two expectations. A novel two-dimensional local autocorrelation analysis confirmed the third and provided new insight into the patterns of genetic structure across the two-dimensional landscape. We highlight the potential of autocorrelation analysis to infer evolutionary processes but also emphasize that genetic patterns in space cannot be fully understood without an appropriate and intensive sampling regime and detailed knowledge of the individuals genotyped.     

Spatial characterization of arbuscular mycorrhizal fungal molecular diversity at the submetre scale in a temperate grassland

Although arbuscular mycorrhizal fungi (AMF) form spatially complex communities in terrestrial ecosystems, the scales at which this diversity manifests itself is poorly understood. This information is critical to the understanding of the role of AMF in plant community composition. We examined small-scale (submetre) variability of AMF community composition (terminal restriction fragment length polymorphism fingerprinting) and abundance (extraradical hyphal lengths) in two 1 m(2) plots situated in a native grassland ecosystem of western Montana. Extraradical AMF hyphal lengths varied greatly between samples (14-89 m g soil(-1)) and exhibited spatial structure at scales <30 cm. The composition of AMF communities was also found to exhibit significant spatial autocorrelation, with correlogram analyses suggesting patchiness at scales <50 cm. Supportive of overall AMF community composition analyses, individual AMF ribotypes corresponding to specific phylogenetic groups exhibited distinct spatial autocorrelation. Our results demonstrate that AMF diversity and abundance can be spatially structured at scales of <1 m. Such small-scale heterogeneity in the soil suggests that establishing seedlings may be exposed to very different, location dependent AMF communities. Our results also have direct implications for representative sampling of AMF communities in the field.     

Spatial genetic structure in populations of the terrestrial orchid Orchis cyclochila (Orchidaceae)

Orchid seeds are minute, dust-like, wind-borne and, thus, would seem to have the potential for long-distance dispersal. Based on this perception, one may predict near-random spatial genetic structure within orchid populations. In reality we do not know much about seed dispersal in orchids and the few empirical studies of fine-scale genetic structure have revealed significant genetic structure at short distances (< 5m), suggesting that most seeds of orchids fall close to the maternal plant. To obtain more empirical data on dispersal, Ripley’s L(d)-statistics, spatial autocorrelation analyses (coancestry, f_ij analyses) and Wright’s F statistics were used to examine the distribution of individuals and the genetic structure within two populations of the terrestrial orchid Orchis cyclochila in southern Korea. High levels of genetic diversity (H_e = 0.210) and low between-population variation were found (F_ST = 0.030). Ripley’s L(d)-statistics indicated significant aggregation of individuals, and patterns varied depending on populations. Spatial autocorrelation analysis revealed significant positive genetic correlations among individuals located <1 m, with mean f_ij values expected for half sibs. This genetic structure suggests that many seeds fall in the immediate vicinity of the maternal plant. The finding of significant fine-scale genetic structure, however, does not have to preclude the potential for the long distance dispersal of seeds. Both the existence of fine-scale genetic structure and low F_ST are consistent with a leptokurtic distribution of seed dispersal distances with a very flat tail.     

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.     

Spatial autocorrelation analysis offers new insights into gene flow in the Australian bush rat,Rattus fuscipes

Dispersal is a fundamental process that influences the response of species to landscape change and habitat fragmentation. In an attempt to better understand dispersal in the Australian bush rat, Rattus fuscipes, we have combined a new multilocus autocorrelation method with hypervariable microsatellite genetic markers to investigate fine-scale (< or = 1 km) patterns of spatial distribution and spatial genetic structure. The study was conducted across eight trapping transects at four sites, with a total of 270 animals sampled. Spatial autocorrelation analysis of bush rat distribution revealed that, in general, animals occurred in groups or clusters of higher density (< or = 200 m across), with intervening gaps or lower density areas. Spatial genetic autocorrelation analysis, based on seven hypervariable microsatellite loci (He = 0.8) with a total of 80 alleles, revealed a consistent pattern of significant positive local genetic structure. This genetic pattern was consistent for all transects, and for adults and sub-adults, males and females. By testing for autocorrelation at multiple scales from 10 to 800 m we found that the extent of detectable positive spatial genetic structure exceeded 500 m. Further analyses detected significantly weaker spatial genetic structure in males compared with females, but no significant differences were detected between adults and sub adults. Results from Mantel tests and hierarchical AMOVA further support the conclusion that the distribution of bush rat genotypes is not random at the scale of our study. Instead, proximate bush rats are more genetically alike than more distant animals. We conclude that in bush rats, gene flow per generation is sufficiently restricted to generate the strong positive signal of local spatial genetic structure. Although our results are consistent with field data on animal movement, including the reported tendency for males to move further than females, we provide the first evidence for restricted gene flow in bush rats. Our study appears to be the first microsatellite-based study of fine-scale genetic variation in small mammals and the first to report consistent positive local genetic structure across sites, age-classes, and sexes. The combination of new forms of autocorrelation analyses, hypervariable genetic markers and fine-scale analysis (< 1 km) may thus offer new evolutionary insights that are overlooked by more traditional larger scaled (> 10 km) population genetic studies.     

海南岛东北部土地利用与生态系统服务价值空间自相关格局分析

土地利用/覆被变化是全球环境变化的重要原因,对生态系统服务价值空间分布格局有直接影响。以海南岛东北部为研究对象,基于遥感影像数据,应用空间自相关理论定量探讨了土地利用与生态系统服务价值的空间自相关格局和分布特征,并运用双变量空间自相关分析两者之间的空间响应规律。结果表明:2016年海南岛东北部生态系统服务功能总价值为132.09亿元,其中林地构成生态系统服务功能价值的主体,而湿地的单位生态系统服务价值最高。土地利用类型具有显著的空间自相关性(P0.05),不同土地利用类型所表现的空间聚集或异常的区域及范围明显不同,以建设用地和林地的空间聚集性最强。研究区生态系统服务价值在空间上呈显著的正相关性(P0.05),高值区明显聚集于海岸带、东寨港和清澜港红树林一带,低值区集中在海口城区、文昌北部农耕区域;土地利用程度与生态系统服务价值呈空间负相关关系(P0.05),且具有明显的空间溢出效应。根据研究结论建议继续实施生态修复与保护政策,优化土地利用结构,提升生态核心的服务价值,实现区域可持续发展和维护生态安全。     

Spatial autocorrelation as a tool for identifying the geographical patterns of aphid annual abundance

Abstract 1 A spatial autocorrelation analysis was undertaken to investigate the spatial structure of annual abundance for the pest aphid Myzus persicae collected in suction traps distributed across north‐west Europe. 2 The analysis was applied at two different scales. The Moran index was used to estimate the degree of spatial autocorrelation at all sites within the study area (global level). The contributions of each site to the global index were identified by the use of a local indicator of spatial autocorrelation (LISA). A hierarchical cluster analysis was undertaken to highlight differences between groups of resulting correlograms. 3 Similarity between traps was shown to occur over large geographical distances, suggesting an impact of phenomena such as climatic gradients or land use types. 4 The presence of outliers and zones of similarity (hot‐spots) and of dissimilarity (cold‐spots) were identified indicating a strong impact of local effects. 5 Several groups of traps characterized by similarities in their local spatial structure (correlograms, value of Moran's I_i) also had similar values for land use variables (the area occupied by agricultural zones, forest and sea). 6 It is concluded that trap data can provide information about Myzus persicae that is representative of large geographical areas. Thus, trap data can be used to estimate the aerial abundance of this species, even if the suction traps are not regularly and densely distributed.     

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.     

Spatial autocorrelation patterns of stream invertebrates: exogenous and endogenous factors

Aim To investigate spatial autocorrelation of taxonomic stream invertebrate groups (richness and composition) at a large geographical scale and to analyse the importance of exogenous and endogenous factors. Location The Mediterranean Basin. Methods For exogenous factors, we used large‐scale factors related to climate, geology and river zonation; for endogenous factors, we used the dispersal mode of each taxonomic group. After describing and analysing spatial patterns of genus richness and genus composition of stream invertebrate groups in the Mediterranean Basin, we computed Moran’s I before and after accounting for the exogenous factors and related it to the endogenous factors. Results In relation to genus richness, most of the taxonomic groups did not show significant spatial autocorrelation, suggesting that no main large‐scale exogenous or endogenous factors were important and that local‐scale factors were probably controlling taxonomic richness. In contrast, for genus composition, all taxonomic groups except Odonata had significant spatial autocorrelation before accounting for the environment. After accounting for the environment, most taxonomic groups still had a significant spatial autocorrelation, but it decreased with their increasing dispersal ability (from Crustacea to Coleoptera). Thus, spatial taxonomic composition of groups with the strongest dispersal potential is mainly related to exogenous factors, whereas that of groups with weaker dispersal potential is related to a combination of exogenous and endogenous factors. Main conclusions Our results illustrate the importance of dispersal as an endogenous factor causing spatial autocorrelation and suggest that ignoring endogenous factors can lead to misunderstandings when explaining large‐scale community patterns.     

Effects of multiple founder populations on spatial genetic structure of reintroduced American martens

Reintroductions and translocations are increasingly used to repatriate or increase probabilities of persistence for animal and plant species. Genetic and demographic characteristics of founding individuals and suitability of habitat at release sites are commonly believed to affect the success of these conservation programs. Genetic divergence among multiple source populations of American martens (Martes americana) and well documented introduction histories permitted analyses of post‐introduction dispersion from release sites and development of genetic clusters in the Upper Peninsula (UP) of Michigan <50 years following release. Location and size of spatial genetic clusters and measures of individual‐based autocorrelation were inferred using 11 microsatellite loci. We identified three genetic clusters in geographic proximity to original release locations. Estimated distances of effective gene flow based on spatial autocorrelation varied greatly among genetic clusters (30–90 km). Spatial contiguity of genetic clusters has been largely maintained with evidence for admixture primarily in localized regions, suggesting recent contact or locally retarded rates of gene flow. Data provide guidance for future studies of the effects of permeabilities of different land‐cover and land‐use features to dispersal and of other biotic and environmental factors that may contribute to the colonization process and development of spatial genetic associations.     

The imprint of Quaternary glaciers on the present-day distribution of the obligate groundwater amphipod Niphargus virei (Niphargidae)

Aim A plausible yet untested biogeographical scenario suggests that Quaternary glaciers shaped the present‐day distribution of the groundwater amphipod Niphargus virei. This study was designed to test two hypotheses pertaining to this scenario: (1) the probability of occurrence of N. virei in ice‐free areas decreases in the vicinity of the Würm glacier; and (2) dispersal is sufficiently low for the historical record of glacial effects to persist over time. Location The study area was located in the southern Jura Mountains, France. Methods A total of 497 sites were sampled to ascertain the distribution of N. virei in the southern Jura. Amplified fragment length polymorphism was analysed from a subset of 24 sites. The relationships between the probability of occurrence of N. virei and distance to the Würm glacier or elevation were investigated using a logistic regression. Spatial autocorrelation analyses were performed on both the residuals of the logistic regression and genetic distance to test the significance of dispersal and barriers to post‐glacial recolonization. The influence of catchment boundaries as barriers to dispersal was examined using different neighbouring relationships between sites. We tested the statistical significance of the reduction in deviance and gain in precision of an autologistic regression that took into consideration the influence of dispersal constraints on the distribution of N. virei. Results Niphargus virei rarely occurred in formerly glaciated areas, and its probability of occurrence in ice‐free areas decreased in the vicinity of the Würm glacier. Combined autocorrelation analyses of spatial distribution and spatial genetic structure showed that: (1) the distance at which spatial autocorrelation was no longer significantly positive did not exceed 16 km; (2) genetic differentiation fitted a model of isolation by distance; and (3) catchment boundaries acted as barriers to dispersal. The autologistic regression with dispersal constraints significantly increased our capacity to predict the distribution of N. virei. Maps of probabilities of occurrence suggested that post‐glacial recolonization was impeded by the extension of glacial outwash. Main conclusions The present distribution of N. virei in southern Jura is probably the result of a historical range reduction driven by glaciation coupled with restricted dispersal and isolation by distance.     

Fine scale genetic structure in the wild ancestor of maize (Zea mays ssp. parviglumis)

Analysis of fine scale genetic structure in continuous populations of outcrossing plant species has traditionally been limited by the availability of sufficient markers. We used a set of 468 SNPs to characterize fine‐scale genetic structure within and between two dense stands of the wild ancestor of maize, teosinte (Zea mays ssp. parviglumis). Our analyses confirmed that teosinte is highly outcrossing and showed little population structure over short distances. We found that the two populations were clearly genetically differentiated, although the actual level of differentiation was low. Spatial autocorrelation of relatedness was observed within both sites but was somewhat stronger in one of the populations. Using principal component analysis, we found evidence for significant local differentiation in the population with stronger spatial autocorrelation. This differentiation was associated with pronounced shifts in the first two principal components along the field. These shifts corresponded to changes in allele frequencies, potentially due to local topographical features. There was little evidence for selection at individual loci as a contributing factor to differentiation. Our results demonstrate that significant local differentiation may, but need not, co‐occur with spatial autocorrelation of relatedness. The present study represents one of the most detailed analyses of local genetic structure to date and provides a benchmark for future studies dealing with fine scale patterns of genetic diversity in natural plant populations.     

Modelling geographical patterns in species richness using eigenvector-based spatial filters

Aim To test the mechanisms driving bird species richness at broad spatial scales using eigenvector‐based spatial filtering. Location South America. Methods An eigenvector‐based spatial filtering was applied to evaluate spatial patterns in South American bird species richness, taking into account spatial autocorrelation in the data. The method consists of using the geographical coordinates of a region, based on eigenanalyses of geographical distances, to establish a set of spatial filters (eigenvectors) expressing the spatial structure of the region at different spatial scales. These filters can then be used as predictors in multiple and partial regression analyses, taking into account spatial autocorrelation. Autocorrelation in filters and in the regression residuals can be used as stopping rules to define which filters will be used in the analyses. Results Environmental component alone explained 8% of variation in richness, whereas 77% of the variation could be attributed to an interaction between environment and geography expressed by the filters (which include mainly broad‐scale climatic factors). Regression coefficients of environmental component were highest for AET. These results were unbiased by short‐scale spatial autocorrelation. Also, there was a significant interaction between topographic heterogeneity and minimum temperature. Conclusion Eigenvector‐based spatial filtering is a simple and suitable statistical protocol that can be used to analyse patterns in species richness taking into account spatial autocorrelation at different spatial scales. The results for South American birds are consistent with the climatic hypothesis, in general, and energy hypothesis, in particular. Habitat heterogeneity also has a significant effect on variation in species richness in warm tropical regions.     

Genetic spatial autocorrelation can readily detect sex-biased dispersal

Sex-biased dispersal is expected to generate differences in the fine-scale genetic structure of males and females. Therefore, spatial analyses of multilocus genotypes may offer a powerful approach for detecting sex-biased dispersal in natural populations. However, the effects of sex-biased dispersal on fine-scale genetic structure have not been explored. We used simulations and multilocus spatial autocorrelation analysis to investigate how sex-biased dispersal influences fine-scale genetic structure. We evaluated three statistical tests for detecting sex-biased dispersal: bootstrap confidence intervals about autocorrelation r values and recently developed heterogeneity tests at the distance class and whole correlogram levels. Even modest sex bias in dispersal resulted in significantly different fine-scale spatial autocorrelation patterns between the sexes. This was particularly evident when dispersal was strongly restricted in the less-dispersing sex (mean distance <200 m), when differences between the sexes were readily detected over short distances. All tests had high power to detect sex-biased dispersal with large sample sizes (n ≥ 250). However, there was variation in type I error rates among the tests, for which we offer specific recommendations. We found congruence between simulation predictions and empirical data from the agile antechinus, a species that exhibits male-biased dispersal, confirming the power of individual-based genetic analysis to provide insights into asymmetries in male and female dispersal. Our key recommendations for using multilocus spatial autocorrelation analyses to test for sex-biased dispersal are: (i) maximize sample size, not locus number; (ii) concentrate sampling within the scale of positive structure; (iii) evaluate several distance class sizes; (iv) use appropriate methods when combining data from multiple populations; (v) compare the appropriate groups of individuals.     

Spatial distribution of communal nests in a colonial breeding bird: benefits without costs?

Abstract The spatial organization of individuals, or groups of individuals, within a population can provide valuable information about social organization and population dynamics. We analysed the spatial distribution of nests of the sociable weaver (Philetairus socius) on two farms in the Kalahari. Sociable weavers build large communal nests on big savannah trees, forming a pattern of trees with and without nests. We used two spatial statistics, Ripley's K and the pair correlation function, to describe characteristics of the point patterns over a range of distances. (i) At distances of 200 and 300 m, communal nests were clustered. (ii) At distances greater than 1000 m, communal nests were regularly distributed. These findings are independent of the spatial distribution of trees. Furthermore, we used Moran's I to analyse spatial autocorrelation of nest sizes. We expected negative autocorrelation because of competition between nests. But on both farms there was no significant autocorrelation of nest sizes for any distance class. The regular distribution observed at larger distances may indicate competition and/or territoriality among different nests, but the lack of spatial autocorrelation between nest sizes suggests that these interactions may happen between nest clusters rather than between single nests. This was confirmed by significant clustering of nests on small scales. We thus suggest, that colonies of P. socius consist of several nests on adjacent trees forming a cluster of subcolonies. The question why sociable weavers establish subcolonies instead of adding more chambers to the natal nest, could not simply be answered by limitation of nesting space. We suggest a strategy to avoid costs due to increasing colony size.     

Application of a geographically-weighted regression analysis to estimate net primary production of Chinese forest ecosystems

Aim The objective of this paper is to obtain a net primary production (NPP) regression model based on the geographically weighted regression (GWR) method, which includes spatial non‐stationarity in the parameters estimated for forest ecosystems in China. Location We used data across China. Methods We examine the relationships between NPP of Chinese forest ecosystems and environmental variables, specifically altitude, temperature, precipitation and time‐integrated normalized difference vegetation index (TINDVI) based on the ordinary least squares (OLS) regression, the spatial lag model and GWR methods. Results The GWR method made significantly better predictions of NPP in simulations than did OLS, as indicated both by corrected Akaike Information Criterion (AIC_c) and R². GWR provided a value of 4891 for AIC_c and 0.66 for R², compared with 5036 and 0.58, respectively, by OLS. GWR has the potential to reveal local patterns in the spatial distribution of a parameter, which would be ignored by the OLS approach. Furthermore, OLS may provide a false general relationship between spatially non‐stationary variables. Spatial autocorrelation violates a basic assumption of the OLS method. The spatial lag model with the consideration of spatial autocorrelation had improved performance in the NPP simulation as compared with OLS (5001 for AIC_c and 0.60 for R²), but it was still not as good as that via the GWR method. Moreover, statistically significant positive spatial autocorrelation remained in the NPP residuals with the spatial lag model at small spatial scales, while no positive spatial autocorrelation across spatial scales can be found in the GWR residuals. Conclusions We conclude that the regression analysis for Chinese forest NPP with respect to environmental factors and based alternatively on OLS, the spatial lag model, and GWR methods indicated that there was a significant improvement in model performance of GWR over OLS and the spatial lag model.