Red-shifts and red herrings in geographical ecology

I draw attention to the need for ecologists to take spatial structure into account more seriously in hypothesis testing. If spatial autocorrelation is ignored, as it usually is, then analyses of ecological patterns in terms of environmental factors can produce very misleading results. This is demonstrated using synthetic but realistic spatial patterns with known spatial properties which are subjected to classical correlation and multiple regression analyses. Correlation between an autocorrelated response variable and each of a set of explanatory variables is strongly biased in favour of those explanatory variables that are highly autocorrelated - the expected magnitude of the correlation coefficient increases with autocorrelation even if the spatial patterns are completely independent. Similarly, multiple regression analysis finds highly autocorrelated explanatory variables "significant" much more frequently than it should. The chances of mistakenly identifying a "significant" slope across an autocorrelated pattern is very high if classical regression is used. Consequently, under these circumstances strongly autocorrelated environmental factors reported in the literature as associated with ecological patterns may not actually be significant. It is likely that these factors wrongly described as important constitute a red-shifted subset of the set of potential explanations, and that more spatially discontinuous factors (those with bluer spectra) are actually relatively more important than their present status suggests. There is much that ecologists can do to improve on this situation. I discuss various approaches to the problem of spatial autocorrelation from the literature and present a randomisation test for the association of two spatial patterns which has advantages over currently available methods.     

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.     

Modelling niche and neutral dynamics: on the ecological interpretation of variation partitioning results

Many studies have attempted to disentangle the effects of neutral and niche‐mediated processes on community composition using partial Mantel tests and variance partitioning on dissimilarity matrices. Recently, doubts about the reliability of these methods have emerged. Here we explore how the results are affected by three confounding factors that may affect ecological data to different degrees: spatial autocorrelation of the environmental variables, length of the compositional gradient, and sampling noise. We document that the statistical hypotheses tested in these methods may or may not correspond to the ecological hypotheses of interest. A major discrepancy emerges if a large proportion of sampling units in the analysed dataset share no species, in which case compositional dissimilarities saturate to a fixed maximum value although explanatory dissimilarities do not. With increasing dissimilarity saturation, the explanatory power of regression models decrease, which may lead to the erroneous conclusion that the ecological processes represented by the explanatory variables are not operating. A survey of recent literature suggests that there is a general lack of awareness of this problem, although it appears to affect > 10% of relevant studies. Our simulations show that if dissimilarity saturation is due to a long ecological gradient, extended dissimilarities essentially solve the problem for any degree of saturation. Using distances from a hybrid multidimensional scaling alleviates the saturation problem when the degree of saturation is < 60%. However, neither correction method can provide a solution to problems caused by insufficient sampling. How the presence of multiple explanatory gradients in combination with sampling noise affects overall analysis performance remains to be clarified.     

Water–energy,land‐cover and heterogeneity drivers of the distribution of plant species richness in a mountain region of the European Alps

Aim To evaluate the relative importance of water–energy, land‐cover, environmental heterogeneity and spatial variables on the regional distribution of Red‐Listed and common vascular plant species richness. Location Trento Province (c. 6200 km²) on the southern border of the European Alps (Italy), subdivided regularly into 228 3′ × 5′ quadrants. Methods Data from a floristic inventory were separated into two subsets, representing Red‐Listed and common (i.e. all except Red‐Listed) plant species richness. Both subsets were separately related to water–energy, land‐cover and environmental heterogeneity variables. We simultaneously applied ordinary least squares regression with variation partitioning and hierarchical partitioning, attempting to identify the most important factors controlling species richness. We combined the analysis of environmental variables with a trend surface analysis and a spatial autocorrelation analysis. Results At the regional scale, plant species richness of both Red‐Listed and common species was primarily related to energy availability and land cover, whereas environmental heterogeneity had a lesser effect. The greatest number of species of both subsets was found in quadrants with the largest energy availability and the greatest degree of urbanization. These findings suggest that the elevation range within our study region imposes an energy‐driven control on the distribution of species richness, which resembles that of the broader latitude gradient. Overall, the two species subsets had similar trends concerning the relative importance of water–energy, land cover and environmental heterogeneity, showing a few differences regarding the selection of some predictors of secondary importance. The incorporation of spatial variables did not improve the explanatory power of the environmental models and the high original spatial autocorrelation in the response variables was reduced drastically by including the selected environmental variables. Main conclusions Water–energy and land cover showed significant pure effects in explaining plant species richness, indicating that climate and land cover should both be included as explanatory variables in modelling species richness in human‐affected landscapes. However, the high degree of shared variation between the two groups made the relative effects difficult to separate. The relatively low range of variation in the environmental heterogeneity variables within our sampling domain might have caused the low importance of this complex factor.     

Incorporating spatial autocorrelation in rarefaction methods: Implications for ecologists and conservation biologists

Recently, methods for constructing Spatially Explicit Rarefaction (SER) curves have been introduced in the scientific literature to describe the relation between the recorded species richness and sampling effort and taking into account for the spatial autocorrelation in the data. Despite these methodological advances, the use of SERs has not become routine and ecologists continue to use rarefaction methods that are not spatially explicit. Using two study cases from Italian vegetation surveys, we demonstrate that classic rarefaction methods that do not account for spatial structure can produce inaccurate results. Furthermore, our goal in this paper is to demonstrate how SERs can overcome the problem of spatial autocorrelation in the analysis of plant or animal communities. Our analyses demonstrate that using a spatially-explicit method for constructing rarefaction curves can substantially alter estimates of relative species richness. For both analyzed data sets, we found that the rank ordering of standardized species richness estimates was reversed between the two methods. We strongly advise the use of Spatially Explicit Rarefaction methods when analyzing biodiversity: the inclusion of spatial autocorrelation into rarefaction analyses can substantially alter conclusions and change the way we might prioritize or manage nature reserves.     

Land-cover data improve bioclimatic models for anurans and turtles at a regional scale

Aim We investigated whether accounting for land cover could improve bioclimatic models for eight species of anurans and three species of turtles at a regional scale. We then tested whether accounting for spatial autocorrelation could significantly improve bioclimatic models after statistically controlling for the effects of land cover. Location Nova Scotia, eastern Canada. Methods Species distribution data were taken from a recent (1999–2003) herpetofaunal atlas. Generalized linear models were used to relate the presence or absence of each species to climate and land‐cover variables at a 10‐km resolution. We then accounted for spatial autocorrelation using an autocovariate or third‐order trend surface of the geographical coordinates of each grid square. Finally, variance partitioning was used to explore the independent and joint contributions of climate, land cover and spatial autocorrelation. Results The inclusion of land cover significantly increased the explanatory power of bioclimatic models for 10 of the 11 species. Furthermore, including land cover significantly increased predictive performance for eight of the 11 species. Accounting for spatial autocorrelation improved model fit for rare species but generally did not improve prediction success. Variance partitioning demonstrated that this lack of improvement was a result of the high correlation between climate and trend‐surface variables. Main conclusions The results of this study suggest that accounting for the effects of land cover can significantly improve the explanatory and predictive power of bioclimatic models for anurans and turtles at a regional scale. We argue that the integration of climate and land‐cover data is likely to produce more accurate spatial predictions of contemporary herpetofaunal diversity. However, the use of land‐cover simulations in climate‐induced range‐shift projections introduces additional uncertainty into the predictions of bioclimatic models. Further research is therefore needed to determine whether accounting for the effects of land cover in range‐shift projections is merited.     

Methods to account for spatial autocorrelation in the analysis of species distributional data: a review

Species distributional or trait data based on range map (extent‐of‐occurrence) or atlas survey data often display spatial autocorrelation, i.e. locations close to each other exhibit more similar values than those further apart. If this pattern remains present in the residuals of a statistical model based on such data, one of the key assumptions of standard statistical analyses, that residuals are independent and identically distributed (i.i.d), is violated. The violation of the assumption of i.i.d. residuals may bias parameter estimates and can increase type I error rates (falsely rejecting the null hypothesis of no effect). While this is increasingly recognised by researchers analysing species distribution data, there is, to our knowledge, no comprehensive overview of the many available spatial statistical methods to take spatial autocorrelation into account in tests of statistical significance. Here, we describe six different statistical approaches to infer correlates of species’ distributions, for both presence/absence (binary response) and species abundance data (poisson or normally distributed response), while accounting for spatial autocorrelation in model residuals: autocovariate regression; spatial eigenvector mapping; generalised least squares; (conditional and simultaneous) autoregressive models and generalised estimating equations. A comprehensive comparison of the relative merits of these methods is beyond the scope of this paper. To demonstrate each method's implementation, however, we undertook preliminary tests based on simulated data. These preliminary tests verified that most of the spatial modeling techniques we examined showed good type I error control and precise parameter estimates, at least when confronted with simplistic simulated data containing spatial autocorrelation in the errors. However, we found that for presence/absence data the results and conclusions were very variable between the different methods. This is likely due to the low information content of binary maps. Also, in contrast with previous studies, we found that autocovariate methods consistently underestimated the effects of environmental controls of species distributions. Given their widespread use, in particular for the modelling of species presence/absence data (e.g. climate envelope models), we argue that this warrants further study and caution in their use. To aid other ecologists in making use of the methods described, code to implement them in freely available software is provided in an electronic appendix.     

Environmental determinants of geographic butterfly richness pattern in eastern China

A long-standing task for ecologists and biogeographers is to reveal the underlying mechanisms accounting for the geographic pattern of species diversity. The number of hypotheses to explain geographic variation in species diversity has increased dramatically during the past half century. The oldest and the most popular one is environmental determination. However, seasonality, the intra-annual variability in climate variables has been rarely related to species richness. In this study, we assessed the relative importance of three environmental hypotheses: energy, seasonality and heterogeneity in explaining species richness pattern of butterflies in Eastern China. In addition, we also examined how environmental variables affect the relationship between species richness of butterflies and seed plants at geographic scale. All the environmental factors significantly affected butterfly richness, except sampling area and coefficient of variation of mean monthly precipitation. Energy and seasonality hypotheses explained comparable variation in butterfly richness (42.3 vs. 39.3 %), higher than that of heterogeneity hypothesis (25.9 %). Variation partitioning indicated that the independent effect of seasonality was much lower (0.0 %) than that of energy (5.5 %) and heterogeneity (6.3 %). However, seasonality performed better in explaining butterfly richness in topographically complex areas, reducing spatial autocorrelation in butterfly richness, and more strongly affect the association between butterflies and seed plants. The positive relationship between seed plant richness and butterfly richness was most likely the result of environmental variables (especially seasonality) influencing them in parallel. Insufficient sampling may partly explain the low explanatory power of environmental model (52.1 %) for geographic butterfly richness pattern. Our results have important implications for predicting the response of butterfly diversity to climate change.     

Comparison of regression methods for spatially‐autocorrelated count data on regularly‐ and irregularly‐spaced locations

It has long been known that insufficient consideration of spatial autocorrelation leads to unreliable hypothesis‐tests and inaccurate parameter estimates. Yet, ecologists are confronted with a confusing array of methods to account for spatial autocorrelation. Although Beale et al. (2010) provided guidance for continuous data on regular grids, researchers still need advice for other types of data in more flexible spatial contexts. In this paper, we extend Beale et al. (2010)‘s work to count data on both regularly‐ and irregularly‐spaced plots, the latter being commonly encountered in ecological studies. Through a simulation‐based approach, we assessed the accuracy and the type I errors of two frequentist and two Bayesian ready‐to‐use methods in the family of generalized mixed models, with distance‐based or neighbourhood‐based correlated random effects. In addition, we tested whether the methods are robust to spatial non‐stationarity, and over‐ and under‐dispersion – both typical features of species distribution count data which violate standard regression assumptions. In the simplest of our simulated datasets, the two frequentist methods gave inflated type I errors, while the two Bayesian methods provided satisfying results. When facing real‐world complexities, the distance‐based Bayesian method (MCMC with Langevin–Hastings updates) performed best of all. We hope that, in the light of our results, ecological researchers will feel more comfortable including spatial autocorrelation in their analyses of count data.     

Overlapping landscapes: A persistent,but misdirected concern when collecting and analyzing ecological data

A primary focus of wildlife ecology is studying how the arrangement, quality, and distribution of habitat influence wildlife populations at multiple spatial scales. A practical limitation of conducting wildlife–habitat investigations in the field, however, is that sampling points tend to be close to one another, resulting in spatial clustering. Consequently, when ecologists seek to quantify the effects of environmental predictors surrounding their sampling points, they encounter the issue of using landscapes that are partially or completely overlapping. A presumed problem of overlapping landscapes is that data generated from these landscapes, when used as predictors in statistical modeling, might violate the assumption of independence. However, the independence of error is the critical assumption, not the independence of predictor variables. Nonetheless, many researchers strive to avoid such overlaps through sampling design or alternative analytical procedures and specialized software programs have been created to assist with this. We present theoretical arguments and empirical evidence showing that changing the amount of overlap does not alter the degree of spatial autocorrelation. Using data derived from 2 broad-scaled avian monitoring programs, we quantified the relationship between forest cover and bird abundance and occurrence at multiple landscapes ranging from 100 m to 24 km across. We found no clear evidence that increasing overlap of landscapes increased spatial autocorrelation in model residuals. Our results demonstrate that the concern of overlapping landscapes as a potential cause of violation of spatial independency among sampling units is misdirected and represents an oversimplification of the statistical and ecological issues surrounding spatial autocorrelation. Overlapping landscapes and spatial autocorrelation are separate issues in the modeling of wildlife populations and their habitats; non-overlapping landscapes do not ensure spatial independency and overlapping landscapes do not necessarily lead to greater spatial autocorrelation in model errors. © 2011 The Wildlife Society.     

Pteridophyte richness, climate and topography in the Iberian Peninsula: comparing spatial and nonspatial models of richness patterns

Aim To describe the spatial variation in pteridophyte species richness; evaluate the importance of macroclimate, topography and within‐grid cell range variables; assess the influence of spatial autocorrelation on the significance of the variables; and to test the prediction of the mid‐domain effect. Location The Iberian Peninsula. Methods We estimated pteridophyte richness on a grid map with c. 2500 km² cell size, using published geocoded data of the individual species. Environmental data were obtained by superimposing the grid system over isoline maps of precipitation, temperature, and altitude. Mean and range values were calculated for each cell. Pteridophyte richness was related to the environmental variables by means of nonspatial and spatial generalized least squares models. We also used ordinary least squares regression, where a variance partitioning was performed to partial out the spatial component, i.e. latitude and longitude. Coastal and central cells were compared to test the mid‐domain effect. Results Both spatial and nonspatial models showed that pteridophyte richness was best explained by a second‐order polynomial of mean annual precipitation and a quadratic elevation‐range term, although the relative importance of these two variables varied when spatial autocorrelation was accounted for. Precipitation range was weakly significant in a nonspatial multiple model (i.e. ordinary regression), and did not remain significant in spatial models. Richness is significantly higher along the coast than in the centre of the peninsula. Main conclusions Spatial autocorrelation affects the statistical significance of explanatory variables, but this did not change the biological interpretation of precipitation and elevation range as the main predictors of pteridophyte richness. Spatial and nonspatial models gave very similar results, which reinforce the idea that water availability and topographic relief control species richness in relatively high‐energy regions. The prediction of the mid‐domain effect is falsified.     

Small‐scale spatial autocorrelation and the interpretation of relationships between phenological parameters

Question: Are flower production and associated phenological variables (onset, end, duration, and three measures of flowering synchrony) randomly distributed in space or, alternatively, is there a neighbourhood structure (spatial autocorrelation) in the values of these variables? To which extent does spatial autocorrelation affect the correlation tests between phenological traits? Location: A tree savanna reserve in Southeastern Brazil (22°15′S,47°08′W). Methods: The flowering season of Chromolaena odorata was followed for all (96) individuals in a completely mapped area of 3000 m². The phenological traits were estimated by counting flower heads in anthesis on individual plants every seven days for 14 weeks. Results: Flowering time was unimodally distributed, but with different peak dates depending on whether individual flower heads or plants were counted. Three phenological traits and canopy closure above the plants showed some degree of spatial autocorrelation, which caused loss of up to 35% of degrees of freedom in nine of 36 correlation tests. Such a decrease in the degrees of freedom resulted in loss of significance for correlations in three pairs of variables. Conclusions: We hypothesize that the spatial autocorrelation in phenological traits between C. odorata neighbours may be driven by genetic similarity among neighbouring plants and/or spatial structuring of environmental factors. Because location and distance between samples may affect their statistical independence, we suggest that spatial autocorrelation should be taken into account in future studies of plant phenology, e.g. by using effective sample size in statistical tests.     

Spatial autocorrelation of assemblages of benthic invertebrates and its relationship to environmental factors in two upland rivers in southeastern Australia

The nature of spatial autocorrelation of biota may reveal much about underlying ecological and biological factors responsible for producing those patterns, especially dispersal processes (drift, adult flight, etc.). We report here on assemblage‐level autocorrelation in the benthic‐invertebrate assemblages (retained in sieves of 300 µm mesh) of riffles in two adjacent, relatively pristine rivers in southeastern Victoria, Australia (40‐km reaches of the Wellington and Wonnangatta Rivers). These are related to patterns of autocorrelation in physical and catchment conditions (‘environmental variables’) in the vicinity of the sampling points. Both the invertebrate assemblages and environmental variables were autocorrelated at small scales (= 8 km) in the Wellington River in one of the sampling years (1996). Dissimilarities of invertebrate assemblages were correlated with dissimilarities of environmental variables in both sampling years (1996 and 1997) in that river. Environmental variables were autocorrelated in the Wonnangatta River, but this was not expressed as autocorrelation in the assemblages of invertebrates, which were not autocorrelated at any scale studied. Individual environmental variables showed different spatial patterns between the two rivers. These results suggest that individual rivers have their own idiosyncratic patterns and one cannot assume that even similar, geographically adjacent rivers will have the same patterns, which is a difficulty for ecological assessment and restoration.     

Incorporating ecological principles into statistical models for the prediction of species’ distribution and abundance

Understanding the determinants of species’ distributions and abundances is a central theme in ecology. The development of statistical models to achieve this has a long history and the notion that the model should closely reflect underlying scientific understanding has encouraged ecologists to adopt complex statistical methods as they arise. In this paper we describe a Bayesian hierarchical model that reflects a conceptual ecological model of multi‐scaled environmental determinants of riverine fish species’ distributions and abundances. We illustrate this with distribution and abundance data of a small‐bodied fish species, the Empire gudgeon Hypseleotris galii, in the Mary and Albert Rivers, Queensland, Australia. Specifically, the model sought to address; 1) the extent that landscape‐scale abiotic variables can explain the species’ distribution compared to local‐scale variables, 2) how local‐scale abiotic variables can explain species’ abundances, and 3) how are these local‐scale relationships mediated by landscape‐scale variables. Overall, the model accounted for around 60% of variation in the distribution and abundance of H. galii. The findings show that the landscape‐scale variables explain much of the distribution of the species; however, there was considerable improvement in estimating the species’ distribution with the addition of local‐scale variables. There were many strong relationships between abundance and local‐scale abiotic variables; however, several of these relationships were mediated by some of the landscape‐scale variables. The extent of spatial autocorrelation in the data was relatively low compared to the distances among sampling reaches. Our findings exemplify that Bayesian statistical modelling provides a robust framework for statistical modelling that reflects our ecological understanding. This allows ecologists to address a range of ecological questions with a single unified probability model rather than a series of disconnected analyses.     

Random sampling does not exclude spatial dependence: The importance of neutral models for ecological hypothesis testing

Lájer (2007) notes that, to investigate phytosociological and ecological relationships, many authors apply traditional inferential tests to sets of relevés obtained by non-random methods. Unfortunately, this procedure does not provide reliable support for hypothesis testing because non-random sampling violates the assumptions of independence required by many parametric inferential tests. Instead, a random sampling scheme is recommended. Nonetheless, random sampling will not eliminate spatial autocorrelation. For instance, a classical law of geography holds that everything in a piece of (biotic) space is interrelated, but near objects are more related than distant ones. Because most ecological processes that shape community structure and species coexistence are spatially explicit, spatial autocorrelation is a vital part of almost all ecological data. This means that, independently from the underlying sampling design, ecological data are generally spatially autocorrelated, violating the assumption of independence that is generally required by traditional inferential tests. To overcome this drawback, randomization tests may be used. Such tests evaluate statistical significance based on empirical distributions generated from the sample and do not necessarily require data independence. However, as concerns hypothesis testing, randomization tests are not the universal remedy for ecologists, because the choice of inadequate null models can have significant effects on the ecological hypotheses tested. In this paper, I emphasize the need of developing null models for which the statistical assumptions match the underlying biological mechanisms.     

Model selection and information theory in geographical ecology

Aim   Although parameter estimates are not as affected by spatial autocorrelation as Type I errors, the change from classical null hypothesis significance testing to model selection under an information theoretic approach does not completely avoid problems caused by spatial autocorrelation. Here we briefly review the model selection approach based on the Akaike information criterion (AIC) and present a new routine for Spatial Analysis in Macroecology (SAM) software that helps establishing minimum adequate models in the presence of spatial autocorrelation.
Innovation    We illustrate how a model selection approach based on the AIC can be used in geographical data by modelling patterns of mammal species in South America represented in a grid system ( n  = 383) with 2° of resolution, as a function of five environmental explanatory variables, performing an exhaustive search of minimum adequate models considering three regression methods: non-spatial ordinary least squares (OLS), spatial eigenvector mapping and the autoregressive (lagged-response) model. The models selected by spatial methods included a smaller number of explanatory variables than the one selected by OLS, and minimum adequate models contain different explanatory variables, although model averaging revealed a similar rank of explanatory variables.
Main conclusions    We stress that the AIC is sensitive to the presence of spatial autocorrelation, generating unstable and overfitted minimum adequate models to describe macroecological data based on non-spatial OLS regression. Alternative regression techniques provided different minimum adequate models and have different uncertainty levels. Despite this, the averaged model based on Akaike weights generates consistent and robust results across different methods and may be the best approach for understanding of macroecological patterns.     

Spatial heterogeneity in the determinants of woody plant invasion of lowland heath

Questions: 1. What is the scale and extent of spatial variability in factors affecting Betula invasion of heaths? 2. How much effect does each factor have on within‐patch patterns of invasion? 3. How can this understanding aid in managing Betula invasions? Location: Lowland heath of southern England. Methods: Determinants of Betula (both B. pubescens and B. pendula) invasion: biomass density, necromass density, mean vegetation height, P‐availability, soil water content and total Betula seed bank density, were measured at two sites on a 5‐ha sampling grid. Spatial pattern was assessed using geostatistics. Contributions of each determinant to within‐site heterogeneity in predicted Betula seedling densities were estimated by varying variables over their full and interquartile ranges in a statistical model derived from experimental data. Results: Salient spatial trends were revealed: strong autocorrelation over distances of < 50 m for soil factors and more extensive autocorrelation (0 to > 150 m) in vegetation variables and Betula seed bank densities. The latter resulted in single across‐site gradients, the former small, distinct patches. All patterns were overlain with variance that was present at distances of < 17.6 m. Variables displaying spatial pattern also accounted for within‐site heterogeneity in predicted Betula seedling densities but their relative contribution to this varied between sites. Conclusions: Identifiable spatial autocorrelation in factors controlling patch‐scale invasion patterns allows managers to target invasion prone patches, potentially reducing management intensities. Furthermore, management effort may be optimised by spatially de‐coupling Betula seed from safe‐sites. This plan may adaptable to the management of other weeds and open‐land ecosystems.     

Scale‐dependence of vegetation‐environment relationships in semi‐natural grasslands

Questions: Which environmental and management factors determine plant species composition in semi‐natural grasslands within a local study area? Are vegetation and explanatory factors scale‐dependent? Location: Semi‐natural grasslands in Lærdal, Sognog Fjordane County, western Norway. Methods: We recorded plant species composition and explanatory variables in six grassland sites using a hierarchically nested sampling design with three levels: plots randomly placed within blocks selected within sites. We evaluated vegetation‐environment relationships at all three levels by means of DCA ordination and split‐plot GLM analyses. Results: The most important complex gradient determining variation in grassland species composition showed a broad‐scale relationship with management. Soil moisture conditions were related to vegetation variation on block scale, whereas element concentrations in the soil were significantly related to variation in species composition on all spatial scales. Our results show that vegetation‐environment relationships are dependent on the scale of observation. We suggest that scale‐related (and therefore methodological) issues may explain the wide range of vegetation‐environment relationships reported in the literature, for semi‐natural grassland in particular but also for other ecosystems. Conclusions: Interpretation of the variation in species composition of semi‐natural grasslands requires consideration of the spatial scales on which important environmental variables vary.     

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.