Residual Spatial Autocorrelation Research Articles

Investigating the Existence of Second Order Spatial Autocorrelation in Crash Frequency across Adjacent Freeway Segments

This study developed spatial Poisson model to incorporate spatial autocorrelation in crash frequency across contagious freeway segments. Spatial autocorrelation is the presence of spatial pattern in crash frequency over space due to geographic proximity. Usually crash caused congestion on a freeway segment propagates upstream and creates chance of occurring secondary crashes. This phenomenon makes the crash frequency on the contiguous freeway segments correlated. This correlation makes the distributional assumption of independence of crash frequency invalid. The existence of spatial autocorrelation is investigated by using Conditional autoregressive models (CAR models). The models are set up in a Bayesian modeling framework, to include terms which help to identify and quantify residual spatial autocorrelation for neighboring observation units. Models which recognize the presence of spatial dependence help to obtain unbiased estimates of parameters quantifying safety levels since the effects of spatial autocorrelation are accounted for in the modeling process. Based on CAR models, approximately 51% of crash frequencies across contiguous freeway segments are spatially auto-correlated. The incident rate ratios revealed that wider shoulder and weaving segments decreased crash frequency by factors of 0.84 and 0.75 respectively. The marginal impacts graphs showed that an increase in longitudinal space for segments with two lanes decreased crash frequency. However, an increase of facility width above three lanes results in more crashes, which indicates an increase in traffic flows and driving behavior leading to crashes. These results call an important step of analyzing contagious freeway segments simultaneously to account for the existence of spatial autocorrelation.

Volunteer-based surveys offer enhanced opportunities for biodiversity monitoring across broad spatial extent

The growing public interest in biodiversity projects provides great opportunities to monitor biodiversity across broad geographic areas at low cost. Such volunteer-based surveys should however need careful consideration during statistical analysis since the presence of residual spatial autocorrelation and over-heterogeneity can lead to misguided inference. The recent development of new statistical tools allows accounting for these problems in all steps of the statistical analysis. Especially, the spatial leave-one-out method allows accounting for spatial autocorrelation in the variable selection step while the R-INLA tool box provides a useful way to estimate complex spatial hierarchical models in a minimum computation time. We applied such tools on a dataset collected by volunteers between 2000 and 2013 giving the relative abundance of 12 raptors breeding in France. We then estimated their spatial distribution, population sizes and trends with a particular emphasis in quantifying the uncertainty of our estimations. Our results suggest that broad-scale volunteer-based surveys offer enhanced opportunities for monitoring widespread species but may fail in giving accurate information for less common species, especially when sampling is too scattered. Providing uncertainty of estimations helps in identifying species and areas from which estimations are the more reliable and thus gives more powerful information for conservation practitioners.

Spatial autocorrelation in fitness affects the estimation of natural selection in the wild

Summary Natural selection is typically estimated in the wild using Lande and Arnold's multiple regression approach. Despite its utility for evolutionary ecologists, this method is subject to the classical assumptions of multiple regressions, which could result in potential analytical problems. In particular, spatial autocorrelation in fitness violates the assumption of residuals independence. Although widespread in the wild, the consequences of this effect have yet to be investigated in the context of Lande and Arnold's regression and resulting selection estimation. Here we first described four spatially explicit models that allow to control for spatial autocorrelation in residuals of the Lande and Arnold's regression: a generalized least square (GLS) model with a distance‐based exponential covariance function, two simultaneous autoregressive models (SAR, the lagged‐response model (SAR‐lag) and the spatial error model (SAR‐err)) and a 5‐step procedure using the principal coordinates of neighbour matrices (PCNM) method based on the extraction of spatial descriptors. We then compared the four spatially explicit models of selection to non‐spatial models for three life‐history traits recorded over 6 years in a wild blue tit (Cyanistes caeruleus) population. We also compared the performance of the four spatially explicit models of selection using a simulation approach. Our analyses revealed strong spatial autocorrelation in residuals of selection models, which was completely described by the two SAR and the PCNM models, while only partially described by the GLS model. The magnitude of selection gradients and differentials decreased systematically in the 4 spatially explicit models while the degree of fit of these models increased (except for the GLS model). Moreover, we showed using simulations that the selection coefficients extracted from the SAR‐lag model were systematically biased compared to those extracted from the GLS, SAR‐err and PCNM models. We hereby showed that spatial autocorrelation in fitness can severely affect selection differentials and gradients, even at a relatively small spatial scale. By using geostatistical models such as PCNM or SAR‐err models, it is possible to control for this spatial autocorrelation. Finally, since spatial autocorrelation is closely linked to spatial environmental variation, this approach can also be used to explore environmental components of covariance between fitness and traits.

A test for robust detection of residual spatial autocorrelation with application to mortality rates in Sweden

Background: When analyzing data collected with a geographical dimension it is important to be able to test for spatial autocorrelation. The presence of spatial autocorrelation might unveil ignored explanatory variables or just be a factor necessary to consider when further analyzing the data.Objectives: The aim of this paper is to propose a new test that works well for detecting spatial autocorrelation, which is robust against heteroscedasticity and useful regardless of the underlying distribution. The new test is then used to investigate if the mortality rates in the aging Swedish population show spatial autocorrelation as an example of its use.Methods: We derive such a test assuming the mean function for the model is known and perform simulations for this case and for residuals to investigate its finite sample performance, especially how the nominal rejection size is kept.Results: In the simulations we show that our test works well if there is no heteroscedasticity and also under difficult situations such as heteroscedasticity with structure, given that sufficient number of observations are available. This study finds no autocorrelation of mortality rates in Swedish municipalities in the age group 64–75 in year 2006.

Where are the electric vehicles? A spatial model for vehicle-choice count data

Electric vehicles (EVs) are predicted to increase in market share as auto manufacturers introduce more fuel efficient vehicles to meet stricter fuel economy mandates and fossil fuel costs remain unpredictable. Reflecting spatial autocorrelation while controlling for a variety of demographic and locational (e.g., built environment) attributes, the zone-level spatial count model in this paper offers valuable information for power providers and charging station location decisions. By anticipating over 745,000 personal-vehicle registrations across a sample of 1000 census block groups in the Philadelphia region, a trivariate Poisson-lognormal conditional autoregressive (CAR) model anticipates Prius hybrid EV, other EV, and conventional vehicle ownership levels.Initial results signal higher EV ownership rates in more central zones with higher household incomes, along with significant residual spatial autocorrelation, suggesting that spatially-correlated latent variables and/or peer (neighbor) effects on purchase decisions are present. Such data sets will become more comprehensive and informative as EV market shares rise. This work’s multivariate Poisson-lognormal CAR modeling approach offers a rigorous, behaviorally-defensible framework for spatial patterns in choice behavior.

Multi‐scale spatial controls of understory vegetation in Douglas‐fir–western hemlock forests of western Oregon, USA

Forest understory vegetation is influenced by broad‐scale variation in climate, intermediate‐scale variation in topography, disturbance and neighborhood interactions. However, little is known about how these multi‐scale controls interact to influence observed spatial patterns. We examined relationships between the aggregated cover of understory plant species (%CU) and multi‐scale controls using a large‐scale experiment including treatments of low (LS), moderate (MS) and variable (VS) disturbance severity replicated in second‐growth Douglas‐fir (Pseudotsuga meziesii)–western hemlock (Tsuga heterophylla) forests spanning climate and topographic gradients. We developed hierarchical models using a multi‐step selection process, assessing changes residual spatial autocorrelation associated with progressively broader spatial scales of influence and interaction. To examine the role of plant traits in mediating multi‐scale controls, we contrasted effects for early‐ (%CES) and late‐seral (%CLS) species cover.At neighborhood scales, decreases in %CU with overstory density were accelerated with increases in the relative importance of hemlock in the overstory in the in all but the LS treatment. At intermediate scales, %CU was lower in areas with higher potential radiation in undisturbed control treatments but that trend was reversed in the harvested, disturbed areas. When separated, effects of multi‐scale controls differed between %CES and %CLS. Rates of increases in %CES with reductions in density increased with disturbance severity and decreased with increases in %CLS. At broader scales, %CES increased with climatic moisture deficit where potential radiation was high, and %CLS low. Similarly to %CU, %CLS was related to a three‐way interaction between overstory density, disturbance and hemlock abundance. %CLS declined with increases in climatic moisture deficit where overstory density and the relative abundance of hemlock was high, and decreased with local increases in %CES. Multi‐scale controls explained a portion of the observed spatial autocorrelation for %CES but not %CLS, suggesting the spatial patterning of %CLS is related primarily to unmeasured processes. Results show how understory responses to overstory density and disturbance severity vary across the landscape with moisture and potential radiation, at fine scales with neighborhood structure, and with species traits. Hence, understory responses to climate change likely depend on overstory composition and structure, disturbance and species traits.

Predicting the geographical distribution of two invasive termite species from occurrence data.

Predicting the potential habitat of species under both current and future climate change scenarios is crucial for monitoring invasive species and understanding a species' response to different environmental conditions. Frequently, the only data available on a species is the location of its occurrence (presence-only data). Using occurrence records only, two models were used to predict the geographical distribution of two destructive invasive termite species, Coptotermes gestroi (Wasmann) and Coptotermes formosanus Shiraki. The first model uses a Bayesian linear logistic regression approach adjusted for presence-only data while the second one is the widely used maximum entropy approach (Maxent). Results show that the predicted distributions of both C. gestroi and C. formosanus are strongly linked to urban development. The impact of future scenarios such as climate warming and population growth on the biotic distribution of both termite species was also assessed. Future climate warming seems to affect their projected probability of presence to a lesser extent than population growth. The Bayesian logistic approach outperformed Maxent consistently in all models according to evaluation criteria such as model sensitivity and ecological realism. The importance of further studies for an explicit treatment of residual spatial autocorrelation and a more comprehensive comparison between both statistical approaches is suggested.

Estimating soil organic carbon stocks of Swiss forest soils by robust external-drift kriging

Abstract. Accurate estimates of soil organic carbon (SOC) stocks are required to quantify carbon sources and sinks caused by land use change at national scale. This study presents a novel robust kriging method to precisely estimate regional and national mean SOC stocks, along with truthful standard errors. We used this new approach to estimate mean forest SOC stock for Switzerland and for its five main ecoregions. Using data of 1033 forest soil profiles, we modelled stocks of two compartments (0–30, 0–100 cm depth) of mineral soils. Log-normal regression models that accounted for correlation between SOC stocks and environmental covariates and residual (spatial) auto-correlation were fitted by a newly developed robust restricted maximum likelihood method, which is insensitive to outliers in the data. Precipitation, near-infrared reflectance, topographic and aggregated information of a soil and a geotechnical map were retained in the models. Both models showed weak but significant residual autocorrelation. The predictive power of the fitted models, evaluated by comparing predictions with independent data of 175 soil profiles, was moderate (robust R2 = 0.34 for SOC stock in 0–30 cm and R2 = 0.40 in 0–100 cm). Prediction standard errors (SE), validated by comparing point prediction intervals with data, proved to be conservative. Using the fitted models, we mapped forest SOC stock by robust external-drift point kriging at high resolution across Switzerland. Predicted mean stocks in 0–30 and 0–100 cm depth were equal to 7.99 kg m−2 (SE 0.15 kg m−2) and 12.58 kg m−2 (SE 0.24 kg m−2), respectively. Hence, topsoils store about 64% of SOC stocks down to 100 cm depth. Previous studies underestimated SOC stocks of topsoil slightly and those of subsoils strongly. The comparison further revealed that our estimates have substantially smaller SE than previous estimates.

Improving forest soil carbon models using spatial data and geostatistical approaches

Forest soils store large amounts of carbon (C), and stock changes in this C pool may significantly increase the CO2 concentration in the atmosphere. However, estimation of soil organic carbon (SOC) stocks and stock changes following land use transition to forestry is subject to large uncertainty. Many currently used geochemical modelling approaches, such as YASSO, are used to estimate regional changes in forest SOC stocks, but these are difficult to calibrate to reflect regional conditions because of limited availability of sufficient SOC data. In addition, most model frameworks give little consideration regarding the appropriate use of geospatial climatic and topographical data, as dependent variables in the model. As a result, many regional models may exhibit spatial autocorrelation (SAC) of residuals, which contributes to overall model error. In this paper, we develop a method for assessing SOC stock changes in Irish forests by compiling a spatial SOC database and using these data to calibrate and improve on an existing YASSO model. Careful consideration was given to the use of available climatic and digital elevation GIS data in YASSO with the aim of reducing SAC of model residuals and to more precisely predict soil- and site-specific variations in SOC stock changes following transition to forestry.Analysis of the complied national SOC database shows that stock changes in afforested mineral soils may increase or decrease depending on previous land use and soil type. During refinement of the YASSO model, conventional statistical approaches confirmed that model performance can be improved by using climatic GIS data at the appropriate scale (resolution), together with additional use of novel topographical spatial data. The current YASSO model does not use these topographical factors as dependent variables, nor is there any consideration given to the spatial or temporal resolution of GIS datasets used. Use of GIS geo-statistical approaches to determine if SAC was reduced, as the YASSO model accuracy was improved on, produced conflicting results. We suggest that the use of Anselin Local Moran's I outlier analysis may not be suitable for this purpose because it may falsely detect spatial outliers due to the presence of neighbouring points with very high or low residual values. In contrast, semi-variogram analysis appeared to be the most useful geo-statistical measure of the spatial dependency, distribution and scale at which residual SAC occurs. Use of fine resolution (50m) slope and topographical position index (TPI) raster datasets to predict forest SOC stocks significantly improved the final YASSO model accuracy and precision. In addition, semi-variogram analysis confirmed that the final YASSO model residuals exhibited no spatial dependency and residual error was uniformly distributed over the entire sample area, from which the SOC database was derived. However, the final YASSO model we describe requires considerable refinement using more intensive sampling studies and independent validation before it can be applied at a national level. In the future, particular emphasis should be directed to sampling forest brown earth soils, which are suggested to result in a net emission of C following transition from grassland to forest land.

“The Glasgow effect?”– The result of the geographical patterning of deprived areas?

The aim of this research was to examine whether the excess mortality found in Glasgow, compared to other cities in the UK (“Glasgow effect”), could be attributed to patterns of the distribution of deprived neighbourhoods within the cities. Data on mortality and deprivation at a neighbourhood scale were used to examine the impact of the patterning of neighbourhood deprivation on mortality in Glasgow, Liverpool and Manchester. Analysis using a combination of GIS and statistical approaches, including a Moran׳s I test and Conditional Auto Regressive models to capture residual spatial autocorrelation, was carried out. The pattern of deprivation was found to be more dispersed in Glasgow compared to the other cities. The impact of surrounding deprivation at two different scales shows strong impact on neighbourhood health outcomes in Glasgow and Liverpool but not in Manchester, suggesting that patterning is not a major contribution to the excess mortality in Glasgow.

Lupus nephritis associated with placental site trophoblastic tumor: A case report and review of the literature

•An improved YASSO model is proposed by considering residual spatial autocorrelation.•Model prediction errors are minimised using GIS data at the appropriate spatial scale.•Topographical factors describe 24-49% of variation in soil carbon.

A quality assessment of eigenvector spatial filtering based parameter estimates for the normal probability model

Eigenvector spatial filtering, which introduces a subset of eigenvectors extracted from a spatial weights matrix as synthetic control variables in a regression model specification, furnishes a solution to extraordinarily intricate statistical modeling problems involving spatial dependences. It accounts for spatial autocorrelation in standard specifications of regression models. But the quality of the resulting regression parameter estimates has yet to be ascertained. The estimator properties to establish include unbiasedness, efficiency, and consistency. The purpose of this paper is to demonstrate these estimator properties for linear regression parameters based on eigenvector spatial filtering, including a comparison with the simultaneous autoregressive (SAR) model. Eigenvector spatial filtering methodology requires the judicious selection of eigenvectors, whose number tends to increase with both level of linear regression residual spatial autocorrelation and the number of areal units. A logistic regression description of the number of eigenvectors selected in a simulation pilot study suggests estimator consistency.

Spatial leave‐one‐out cross‐validation for variable selection in the presence of spatial autocorrelation

AbstractAimProcesses and variables measured in ecology are almost always spatially autocorrelated, potentially leading to the choice of overly complex models when performing variable selection. One way to solve this problem is to account for residual spatial autocorrelation (RSA) for each subset of variables considered and then use a classical model selection criterion such as the Akaike information criterion (AIC). However, this method can be laborious and it raises other concerns such as which spatial model to use or how to compare different spatial models. To improve the accuracy of variable selection in ecology, this study evaluates an alternative method based on a spatial cross‐validation procedure. Such a procedure is usually used for model evaluation but can also provide interesting outcomes for variable selection in the presence of spatial autocorrelation.InnovationWe propose to use a special case of spatial cross‐validation, spatial leave‐one‐out (SLOO), giving a criterion equivalent to the AIC in the absence of spatial autocorrelation. SLOO only computes non‐spatial models and uses a threshold distance (equal to the range of RSA) to keep each point left out spatially independent from the others. We first provide some simulations to evaluate how SLOO performs compared with AIC. We then assess the robustness of SLOO on a large‐scale dataset. R software codes are provided for generalized linear models.Main conclusionsThe AIC was relevant for variable selection in the presence of RSA if the independent variables considered were not spatially autocorrelated. It otherwise failed because highly spatially autocorrelated variables were more often selected than others. Conversely, SLOO had similar performances whether the variables were themselves spatially autocorrelated or not. It was particularly useful when the range of RSA was small, which is a common property of spatial tools. SLOO appears to be a promising solution for selecting relevant variables from most ecological spatial datasets.

Spatial eigenvector filtering for spatiotemporal crime mapping and spatial crime analysis

Spatial and spatiotemporal analyses are exceedingly relevant to determine criminogenic factors. The estimation of Poisson and negative binomial models (NBM) is complicated by spatial autocorrelation. Therefore, first, eigenvector spatial filtering (ESF) is introduced as a method for spatiotemporal mapping to uncover time-invariant crime patterns. Second, it is demonstrated how ESF is effectively used in criminology to invalidate model misspecification, i.e., residual spatial autocorrelation, using a nonviolent crime dataset for the metropolitan area of Houston, Texas, over the period 2005–2010. The results suggest that local and regional geography significantly contributes to the explanation of crime patterns. Furthermore, common space-time eigenvectors selected on an annual basis indicate striking spatiotemporal patterns persisting over time. The findings about the driving forces behind Houston’s crime show that linear and nonlinear, spatially filtered, NBMs successfully absorb latent autocorrelation and, therefore, prevent parameter estimation bias. The consideration of a spatial filter also increases the explanatory power of the regressions. It is concluded that ESF can be highly recommended for the integration in spatial and spatiotemporal modeling toolboxes of law enforcement agencies.

Improvement of fire danger modelling with geographically weighted logistic model

Global models dominate historical documents on fire danger modelling. However, local variations may exist in the relationships between fire presence and fire-influencing factors. In this study, 50 fire danger models (10 global logistic models and 40 geographically weighted logistic models, i.e. local models), were developed to model daily fire danger in Heilongjiang province in north-east China and cross-validation was performed to evaluate the predictive performance of the various developed models. In modelling, multi-temporal spatial sampling and repeated random sub-sampling were applied to obtain 10 groups of training sub-samples and inner testing sub-samples. For each of the 10 groups of training sub-samples, principal component analysis, in which muticollinearity among variables can be removed, was used to create nine principal components that were then employed as covariates to develop one global logistic model and four geographically weighted logistic models. Compared to global models, all local models showed better model fitting, less spatial autocorrelation of residuals and more desirable modelling of fire presence. In particular, not only was local spatial variation in fire–environment relationships accounted for in the adaptive Gaussian geographically weighted logistic models, but spatial autocorrelation of residuals was significantly reduced to acceptable levels, indicating strong inferential performance.

Disease Mapping and Regression with Count Data in the Presence of Overdispersion and Spatial Autocorrelation: A Bayesian Model Averaging Approach

This paper applies the generalised linear model for modelling geographical variation to esophageal cancer incidence data in the Caspian region of Iran. The data have a complex and hierarchical structure that makes them suitable for hierarchical analysis using Bayesian techniques, but with care required to deal with problems arising from counts of events observed in small geographical areas when overdispersion and residual spatial autocorrelation are present. These considerations lead to nine regression models derived from using three probability distributions for count data: Poisson, generalised Poisson and negative binomial, and three different autocorrelation structures. We employ the framework of Bayesian variable selection and a Gibbs sampling based technique to identify significant cancer risk factors. The framework deals with situations where the number of possible models based on different combinations of candidate explanatory variables is large enough such that calculation of posterior probabilities for all models is difficult or infeasible. The evidence from applying the modelling methodology suggests that modelling strategies based on the use of generalised Poisson and negative binomial with spatial autocorrelation work well and provide a robust basis for inference.

Evaluating area-level spatial clustering of SalmonellaEnteritidis infections and their socioeconomic determinants in the greater Toronto area, Ontario, Canada (2007 – 2009): a retrospective population-based ecological study

BackgroundThere have been only a few region-level ecological studies conducted in Canada investigating enteric infections in humans. Our study objectives were to 1) assess the spatial clustering of Salmonella enterica serotype Enteritidis (S. Enteritidis) human infections in the Greater Toronto Area, and 2) identify underlying area-level associations between S. Enteritidis infection rates and socioeconomic status (SES) indicators that might explain the clustering of infections.MethodsRetrospective data on S. Enteritidis infections from 2007 to 2009 were obtained from Ontario’s reportable disease surveillance database and were grouped at the forward sortation area (FSA) - level. A spatial scan statistic was employed to identify FSA-level spatial clusters of high infection rates. Negative binomial regression was used to identify FSA-level associations between S. Enteritidis infection rates and SES indicators obtained from the 2006 Census of Canada. Global Moran’s I statistic was used to evaluate the final model for residual spatial clustering.ResultsA spatial cluster that included nine neighbouring FSAs was identified in downtown Toronto. A significant positive curvilinear relationship was observed between S. Enteritidis infection rates and FSA-level average number of children at home per census family. Areas with high and areas with low average median family income had higher infection rates than FSAs with medium average median family income. Areas with a high proportion of visible minority population had lower infection rates than FSAs with a medium proportion of visible minority population. The Moran’s I statistic was not significant, indicating that no residual spatial autocorrelation was present after accounting for the SES variables in the final model.ConclusionsOur study demonstrated that FSAs with high and low average median family income, medium proportion of visible minority population, and high average number of children at home per census family had the highest S. Enteritidis infection rates. These areas should be targeted when designing disease control and prevention programs. Future studies are needed in areas with high S. Enteritidis infection rates to identify sources of environmental contamination of the local food supply, to assess food safety practices at local food markets, retail stores, and restaurants, and to identify novel individual-level risk factors.

Predicting socioeconomic conditions from satellite sensor data in rural developing countries: A case study using female literacy in Assam, India

Social data from census and household surveys provide key information for monitoring the status of populations, but the data utility can be limited by temporal gaps between surveys. Recent studies have pointed to the potential for remotely sensed satellite sensor data to be used as proxies for social data. Such an approach could provide valuable information for the monitoring of populations between enumeration periods. Field observations in Assam, north-east India suggested that socioeconomic conditions could be related to patterns in the type and abundance of local land cover dynamics prompting the development of a more formal approach. This research tested if environmental data derived from remotely sensed satellite sensor data could be used to predict a socioeconomic outcome using a generalised autoregressive error (GARerr) model. The proportion of female literacy from the 2001 Indian National Census was used as an indicator of socioeconomic conditions. A significant positive correlation was found with woodland and a significant negative correlation with winter cropland (i.e., additional cropping beyond the normal cropping season). The dependence of female literacy on distance to nearest road was very small. The GARerr model reduced residual spatial autocorrelation and revealed that the logistic regression model over-estimated the significance of the explanatory covariates. The results are promising, while also revealing the complexities of population–environment interactions in rural, developing world contexts. Further research should explore the prediction of socioeconomic conditions using fine spatial resolution satellite sensor data and methods that can account for such complexities.

Multiscale, presence‐only habitat suitability models: fine‐resolution maps for eight bat species

Summary To manage anthropogenic environmental change for the benefit of biodiversity, we must improve our understanding of the complex relationships between organisms and their environment. We have developed multiscale habitat suitability models (HSMs) for bats, a mobile group of mammals, for a geographically varied region of the UK. We ask whether the models have sufficient accuracy to contribute to informed decision‐making in habitat management and in minimizing the impact of climate change and human infrastructural development. We used acoustic surveys supplemented by catching to gather presence data for eight species from 30 sites across the south of the Lake District National Park in NW England. Species were identified by manual and automated extraction and analysis of echolocation calls. Fine‐resolution (50 and 100 m) habitat maps were generated at twelve spatial scales by calculating the variables across squares of increasing size, from 100 to 6000 m, around each focal 50 or 100 m square. Presence‐only HSM software, MaxEnt, was used to determine the predictive power of each habitat variable at each scale. Multiscale models included data for each variable at the scale at which it had the strongest relationship with the presence of each species. The best multiscale models were selected using fivefold cross‐validation, with backwards, stepwise variable removal, whilst minimizing residual spatial autocorrelation and sampling bias. Further tests with independent field data indicated good model transferability across the entire National Park. Foraging bats were generally most strongly associated with variables measured at small spatial scales and distance measures. However, each species responded differently across the range of scales, and strong associations were also found at the largest scale of analysis (6000 m). Synthesis and applications. The best models for determining habitat suitability had few variables, making them easy to interpret and use in practical conservation planning. The approach is applicable to any taxa for which reliable presence records are available, providing insight into the potential impacts of land‐use and environmental change. Maps identify areas of conservation concern, such as hot spots for diversity, rare or vulnerable species and potential or threatened network corridors, making them useful for ecological impact assessment of proposed developments, and to conservation managers planning habitat creation or improvement.

Landscape‐scale patterns in tree occupancy and abundance in subarctic Alaska

Recent studies suggest that climate warming in interior Alaska may result in major shifts from spruce‐dominated forests to broadleaf‐dominated forests or even grasslands. To quantify patterns in tree distribution and abundance and to investigate the potential for changes in forest dynamics through time, we initiated a spatially extensive vegetation monitoring program covering 1.28 million ha in Denali National Park and Preserve (DNPP). Using a probabilistic sampling design, we collected field measurements throughout the study area to develop spatially explicit Bayesian hierarchical models of tree occupancy and abundance. These models demonstrated a strong partitioning of the landscape among the six tree species in DNPP, and allowed us to account for and examine residual spatial autocorrelation in our data. Tree distributions were governed by two primary ecological gradients: (1) the gradient from low elevation, poorly drained, permafrost‐influenced sites with shallow active layers and low soil pH (dominated by Picea mariana) to deeply thawed and more productive sites at mid‐elevation with higher soil pH on mineral substrate (dominated by Picea glauca); and (2) the gradient from older, less recently disturbed sites dominated by conifers to those recently affected by disturbance in the form of fire and flooding with increased occupancy and abundance of broadleaf species. We found that the establishment of broadleaf species was largely dependent on disturbance, and mixed forests and pure stands of broadleaf trees were relatively rare and occurred in localized areas. Contrary to recent work in nearby areas of interior Alaska, our results suggest that P. glauca distribution may actually increase in DNPP under warming conditions rather than decline as previously predicted, as P. glauca expands into areas formerly underlain by permafrost. We found no evidence of a shift to broadleaf forests in DNPP, particularly in the poorly drained basin landscape positions that may be resistant to such changes. Overall, our results indicate that probabilistic sampling conducted at a landscape scale can improve inference relative to the habitat associations driving the distribution and abundance of trees in the boreal forest and the potential effects of climate change on them.