Evaluating,partitioning, and mapping the spatial autocorrelation component in ecological niche modeling: a new approach based on environmentally equidistant records

Most species data display spatial autocorrelation that can affect ecological niche models (ENMs) accuracy‐statistics, affecting its ability to infer geographic distributions. Here we evaluate whether the spatial autocorrelation underlying species data affects accuracy‐statistics and map the uncertainties due to spatial autocorrelation effects on species range predictions under past and future climate models. As an example, ENMs were fitted to Qualea grandiflora (Vochysiaceae), a widely distributed plant from Brazilian Cerrado. We corrected for spatial autocorrelation in ENMs by selecting sampling sites equidistant in geographical (GEO) and environmental (ENV) spaces. Distributions were modelled using 13 ENMs evaluated by two accuracy‐statistics (TSS and AUC), which were compared with uncorrected ENMs. Null models and the similarity statistics I were used to evaluate the effects of spatial autocorrelation. Moreover, we applied a hierarchical ANOVA to partition and map the uncertainties from the time (across last glacial maximum, pre‐insustrial, and 2080 time periods) and methodological components (ENMs and autocorrelation corrections). The GEO and ENV models had the highest accuracy‐statistics values, although only the ENV model had values higher than expected by chance alone for most of the 13 ENMs. Uncertainties from time component were higher in the core region of the Brazilian Cerrado where Q. grandiflora occurs, whereas methodological components presented higher uncertainties in the extreme northern and southern regions of South America (i.e. outside of Brazilian Cerrado). Our findings show that accounting for autocorrelation in environmental space is more efficient than doing so in geographical space. Methodological uncertainties were concentrated in outside the core region of Q. grandiflora's habitat. Conversely, uncertainty due to time component in the Brazilian Cerrado reveals that ENMs were able to capture climate change effects on Q. grandiflora distributions.     

Postglacial recolonization of North America by spadefoot toads: integrating niche and corridor modeling to study species’ range dynamics over geologic time

Understanding the factors that shape species’ distributions is a key topic in biogeography. As climates change, species can either cope with these changes through evolution, plasticity or by shifting their ranges to track the optimal climatic conditions. Ecological niche modeling (ENM) is a widespread technique in biogeography that estimates the niche of the organism by using occurrences and environmental data to estimate species’ potential distributions. ENMs are often criticized for failing to take species’ dispersal abilities into consideration. Here, we attempt to fill this gap by combining ENMs with dispersal and corridor modeling to study the range dynamics of North American spadefoot toads (Scaphiopodidae) over the Holocene. We first estimated the current and past distributions of spadefoot toads and then estimated their past distributions from the Last Glacial Maximum (LGM) to the present day. Then, we estimated how each taxon recolonized North American by using dispersal and corridor modeling. By combining these two modeling approaches we were able to 1) estimate the LGM refugia used by the North American spadefoot toads, 2) further refine these projections by estimating which of the putative LGM refugia contributed to the recolonization of North America via dispersal, and 3) estimate the relative influence of each LGM refugium to the current species’ distributions. The models were tested using previously published phylogeographic data, revealing a high degree of congruence between our models and the genetic data. These results suggest that combining ENMs and dispersal modeling over time is a promising approach to investigate both historical and future species’ range dynamics.     

Habitat differentiation among three Nigeria–Cameroon chimpanzee (Pan troglodytes ellioti) populations

Ecological niche models (ENMs) are often used to predict species distribution patterns from datasets that describe abiotic and biotic factors at coarse spatial scales. Ground‐truthing ENMs provide important information about how these factors relate to species‐specific requirements at a scale that is biologically relevant for the species. Chimpanzees are territorial and have a predominantly frugivorous diet. The spatial and temporal variation in fruit availability for different chimpanzee populations is thus crucial, but rarely depicted in ENMs. The genetic and geographic distinction within Nigeria–Cameroon chimpanzee (Pan troglodytes ellioti) populations represents a unique opportunity to understand fine scale species‐relevant ecological variation in relation to ENMs. In Cameroon, P. t. ellioti is composed of two genetically distinct populations that occupy different niches: rainforests in western Cameroon and forest–woodland–savanna mosaic (ecotone) in central Cameroon. We investigated habitat variation at three representative sites using chimpanzee‐relevant environmental variables, including fruit availability, to assess how these variables distinguish these niches from one another. Contrary to the assumption of most ENM studies that intact forest is essential for the survival of chimpanzees, we hypothesized that the ecotone and human‐modified habitats in Cameroon have sufficient resources to sustain large chimpanzee populations. Rainfall, and the diversity, density, and size of trees were higher at the rainforest. The ecotone had a higher density of terrestrial herbs and lianas. Fruit availability was higher at Ganga (ecotone) than at Bekob and Njuma. Seasonal variation in fruit availability was highest at Ganga, and periods of fruit scarcity were longer than at the rainforest sites. Introduced and secondary forest species linked with anthropogenic modification were common at Bekob, which reduced seasonality in fruit availability. Our findings highlight the value of incorporating fine scale species‐relevant ecological data to create more realistic models, which have implications for local conservation planning efforts.     

Physiology in ecological niche modeling: using zebra mussel's upper thermal tolerance to refine model predictions through Bayesian analysis

Climate change and human-mediated dispersal are increasingly influencing species’ geographic distributions. Ecological niche models (ENMs) are widely used in forecasting species’ distributions, but are weak in extrapolation to novel environments because they rely on available distributional data and do not incorporate mechanistic information, such as species’ physiological response to abiotic conditions. To improve accuracy of ENMs, we incorporated physiological knowledge through Bayesian analysis. In a case study of the zebra mussel Dreissena polymorpha, we used native and global occurrences to obtain native and global models representing narrower and broader understanding of zebra mussel’ response to temperature. We also obtained thermal limit and survival information for zebra mussel from peer-reviewed literature and used the two types of information separately and jointly to calibrate native models. We showed that, compared to global models, native models predicted lower relative probability of presence along zebra mussel's upper thermal limit, suggesting the shortcoming of native models in predicting zebra mussel's response to warm temperature. We also found that native models showed improved prediction of relative probability of presence when thermal limit was used alone, and best approximated global models when both thermal limit and survival data were used. Our result suggests that integration of physiological knowledge enhances extrapolation of ENM in novel environments. Our modeling framework can be generalized for other species or other physiological limits and may incorporate evolutionary information (e.g. evolved thermal tolerance), thus has the potential to improve predictions of species’ invasive potential and distributional response to climate change.     

Genetically informed ecological niche models improve climate change predictions

We examined the hypothesis that ecological niche models (ENMs) more accurately predict species distributions when they incorporate information on population genetic structure, and concomitantly, local adaptation. Local adaptation is common in species that span a range of environmental gradients (e.g., soils and climate). Moreover, common garden studies have demonstrated a covariance between neutral markers and functional traits associated with a species’ ability to adapt to environmental change. We therefore predicted that genetically distinct populations would respond differently to climate change, resulting in predicted distributions with little overlap. To test whether genetic information improves our ability to predict a species’ niche space, we created genetically informed ecological niche models (gENMs) using Populus fremontii (Salicaceae), a widespread tree species in which prior common garden experiments demonstrate strong evidence for local adaptation. Four major findings emerged: (i) gENMs predicted population occurrences with up to 12‐fold greater accuracy than models without genetic information; (ii) tests of niche similarity revealed that three ecotypes, identified on the basis of neutral genetic markers and locally adapted populations, are associated with differences in climate; (iii) our forecasts indicate that ongoing climate change will likely shift these ecotypes further apart in geographic space, resulting in greater niche divergence; (iv) ecotypes that currently exhibit the largest geographic distribution and niche breadth appear to be buffered the most from climate change. As diverse agents of selection shape genetic variability and structure within species, we argue that gENMs will lead to more accurate predictions of species distributions under climate change.     

Occupancy frequency distributions: patterns,artefacts and mechanisms

Numerous hypotheses have been proposed to explain the shape of occupancy frequency distributions (distributions of the numbers of species occupying different numbers of areas). Artefactual effects include sampling characteristics, whereas biological mechanisms include organismal, niche-based and meta-population models. To date, there has been little testing of these models. In addition, although empirically derived occupancy distributions encompass an array of taxa and spatial scales, comparisons between them are often not possible because of differences in sampling protocol and method of construction. In this paper, the effects of sampling protocol (grain, sample number, extent, sampling coverage and intensity) on the shape of occupancy distributions are examined, and approaches for minimising artefactual effects recommended. Evidence for proposed biological determinants of the shape of occupancy distributions is then examined. Good support exists for some mechanisms (habitat and environmental heterogeneity), little for others (dispersal ability), while some hypotheses remain untested (landscape productivity, position in geographic range, range size frequency distributions), or are unlikely to be useful explanations for the shape of occupancy distributions 'species specificity and adaptation to habitat, extinction-colonization dynamics). The presence of a core (class containing species with the highest occupancy) mode in occupancy distributions is most likely to be associated with larger sample units, and small homogenous sampling areas positioned well within and towards the range centers of a sufficient proportion of the species in the assemblage. Satellite (class with species with the lowest occupancy) modes are associated with sampling large, heterogeneous areas that incorporate a large proportion of the assemblage range. However, satellite modes commonly also occur in the presence of a core mode, and rare species effects are likely to contribute to the presence of a satellite mode at most sampling scales. In most proposed hypotheses, spatial scale is an important determinant of the shape of the observed occupancy distribution. Because the attributes of the mechanisms associated with these hypotheses change with spatial scale, their predictions for the shape of occupancy distributions also change. To understand occupancy distributions and the mechanisms underlying them, a synthesis of pattern documentation and model testing across scales is thus needed. The development of null models, comparisons of occupancy distributions across spatial scales and taxa, documentation of the movement of individual species between occupancy classes with changes in spatial scale, as well as further testing of biological mechanisms are all necessary for an improved understanding of the distribution of species and assemblages within their geographic ranges.     

Field validation supports novel niche modeling strategies in a cryptic endangered amphibian

Many studies employ ecological niche models (ENMs) to predict species’ occurrences in undersampled regions, generally without field confirmation. Here, we use field surveys to test the relative utility of four potential refinements to the standard ENM approach: 1) altering model complexity based on AIC_c, 2) selecting background points from a biologically informed region, 3) using target‐group background to account for sampling bias in existing localities, and 4) using many rangewide localities (global model) versus fewer proximal localities (local model) to construct geographically restricted range predictions. We used Maxent to predict new localities for the California tiger salamander Ambystoma californiense, an endangered species that often goes undocumented due to its cryptic lifestyle. We followed this with a field survey of 260 previously unsampled potential breeding sites in Solano County, CA and used the resulting presence/absence data to compare all factorial combinations of the four model refinements using a new application of the Kruskal–Wallis test for ENM outputs. Our field surveys led to the discovery of 81 previously undocumented breeding localities for the California tiger salamander and demonstrated that ENMs could be significantly improved by utilizing target‐group background to account for spatial sampling bias and local models to focus model output on the subregion of the range being surveyed. Our results clearly demonstrate the potential for local models to outperform global models, and we recommend supplementing traditional Maxent global models that utilize all known localities with local models, particularly when species occupy geographically structured, heterogeneous habitat types. We also recommend using target‐group background since the improvement we observed when including it in our models was significant and very similar to that documented by previous studies. Most importantly, we emphasize the importance of field verification to enable rigorous statistical comparisons among models.     

Correlation between genetic diversity and environmental suitability: taking uncertainty from ecological niche models into account

The hindcast of shifts in the geographical ranges of species as estimated by ecological niche modelling (ENM) has been coupled with phylogeographical patterns, allowing the inference of past processes that drove population differentiation and genetic variability. However, more recently, some studies have suggested that maps of environmental suitability estimated by ENM may be correlated to species' abundance, raising the possibility of using environmental suitability to infer processes related to population demographic dynamics and genetic variability. In both cases, one of the main problems is that there is a wide variation in ENM development methods and climatic models. In this study, we analyse the relationship between heterozygosity (He) and environmental suitability from multiple ENMs for 25 population estimates for Dipteryx alata, a widely distributed, endemic tree species of the Cerrado region of central Brazil. We propose a new approach for generating a statistical distribution of correlations under randomly generated ENM. The confidence intervals from these distributions indicate how model selection with different properties affects the ability to detect a correlation of interest (e.g. the correlation between He and suitability). Additionally, our approach allows us to explore which particular ensemble of ENMs produces the better result for finding an association between environmental suitability and He. Caution is necessary when choosing a method or a climatic data set for modelling geographical distributions, but the new approach proposed here provides a conservative way to evaluate the ability of ensembles to detect patterns of interest.     

Introducing BioSARN – an ecological niche model refinement tool

Environmental niche modeling outputs a biological species' potential distribution. Further work is needed to arrive at a species' realized distribution. The Biological Species Approximate Realized Niche (BioSARN) application provides the ecological modeler with a toolset to refine Environmental niche models (ENMs). These tools include soil and land class filtering, niche area quantification and novelties like enhanced temporal corridor definition, and output to a high spatial resolution land class model. BioSARN is exemplified with a study on Fraser fir, a tree species with strong land class and edaphic correlations. Soil and land class filtering caused the potential distribution area to decline 17%. Enhanced temporal corridor definition permitted distinction of current, continuing, and future niches, and thus niche change and movement. Tile quantification analysis provided further corroboration of these trends. BioSARN does not substitute other established ENM methods. Rather, it allows the experimenter to work with their preferred ENM, refining it using their knowledge and experience. Output from lower spatial resolution ENMs to a high spatial resolution land class model is a pseudo high‐resolution result. Still, it maybe the best that can be achieved until wide range high spatial resolution environmental data and accurate high precision species occurrence data become generally available.     

Ecological niche models in phylogeographic studies: applications,advances and precautions

The increased availability of spatial data and methodological developments in species distribution modelling has lead to concurrent advances in phylogeography, broadening the scope of questions studied, as well as providing unprecedented insights. Given the species‐specific nature of the information provided by ecological niche models (ENMs), whether it is on the environmental tolerances of species or their estimated distribution, today or in the past, it is perhaps not surprising that ENMs have rapidly become a common tool in phylogeographic analysis. Such information is essential to phylogeographic tests that provide important biological insights. Here, we provide an overview of the different applications of ENMs in phylogeographic studies, detailing specific studies and highlighting general limitations and challenges with each application. Given that the full potential of integrating ENMs into phylogeographic cannot be realized unless the ENMs themselves are carefully applied, we provide a summary of best practices with using ENMs. Lastly, we describe some recent advances in how quantitative information from ENMs can be integrated into genetic analyses, illustrating their potential use (and key concerns with such implementations), as well as promising areas for future development.     

Predicting the distribution of Sasquatch in western North America: anything goes with ecological niche modelling

The availability of user-friendly software and publicly available biodiversity databases has led to a rapid increase in the use of ecological niche modelling to predict species distributions. A potential source of error in publicly available data that may affect the accuracy of ecological niche models (ENMs), and one that is difficult to correct for, is incorrect (or incomplete) taxonomy. Here we remind researchers of the need for careful evaluation of database records prior to use in modelling, especially when the presence of cryptic species is suspected or many records are based on indirect evidence. To draw attention to this potential problem, we construct ENMs for the North American Sasquatch (i.e. Bigfoot). Specifically, we use a large database of georeferenced putative sightings and footprints for Sasquatch in western North America, demonstrating how convincing environmentally predicted distributions of a taxon's potential range can be generated from questionable site-occurrence data. We compare the distribution of Bigfoot with an ENM for the black bear, Ursus americanus , and suggest that many sightings of this cryptozoid may be cases of mistaken identity.     

The importance of assessing parameter sensitivity when using biophysical models: a case study using plethodontid salamanders

Landscapes are continually changing due to numerous assaults, including habitat alteration, anthropogenic disturbances, and climate change. Understanding how species will respond to these changes is of critical importance for conservation and management. Mechanistic models, such as biophysical models (BPMs), are an increasingly popular tool to predict how local population dynamics or species’ distributions may be altered in response to environmental and climate changes. By mechanistically modeling relationships between environmental conditions, physiology and behavior, it is possible to make accurate predictions about how species may respond. However, BPMs are often difficult to implement due to lack of appropriate, species-specific data that is biologically realistic or relevant. In this study, we present a BPM for the salamander Plethodon jordani and assess how adding more biological realism has potential to alter model predictions about annual energy budgets. Additionally, we conducted local and global sensitivity analyses to evaluate the importance of accurately specifying model parameter values and functional relationships. We found that the addition of biological realism resulted in greater model complexity as well as substantially different estimates of energy balance. Correct parameterization of biophysical models is also critical, as small changes in parameter values can result in disproportionately large changes in downstream model estimates. Our model highlights the overall importance of using ecologically relevant and specific data for input parameters, as well as careful assessment of parameter sensitivity. We encourage researchers to be aware of the data they are using to parameterize BPMs, and urge the collection of system-specific data that is relevant in spatial and temporal scale. We also recommend greater and more transparent use of sensitivity analyses to provide a better understanding of the model, as well as greater confidence in model predictions.     

利用最大熵模型和规则集遗传算法模型预测孑遗植物裸果木的潜在地理分布及格局

利用野外调查的16个居群分布点和7个环境因子图层, 选择最大熵模型(MAXENT)和规则集遗传算法模型(GARP), 在地理和环境空间上模拟了第三纪孑遗植物裸果木(Gymnocarpos przewalskii)在中国西北地区的潜在分布。结果表明: (1)裸果木的潜在适生区全部集中在西北荒漠区, 其中最佳适生区主要集中在3个区域, 一是河西走廊中部和玉门以西、宁夏北部及内蒙古乌拉特后旗; 二是塔里木盆地西北缘; 三是柴达木盆地西北缘两片极小的高度适生区。裸果木的生态位被确定在一个较广的干旱环境空间: 适生区极端最高气温基本上在29.2-36.8 ℃之间, 极端最低气温在-18.3至-13.4 ℃之间; 年平均降水量40-200 mm; 潜在蒸发率在3-15之间。(2) MAXENT和GARP模型都较好地预测了裸果木的潜在分布, 但GARP产生了相对较大、较连续的潜在分布区, 部分过预测了破碎化生境; 而MAXENT预测到的潜在分布区, 在不同区域具有不同的环境适生性指数, 而且成功地排除了不合理的破碎化分布, 从而更直观地展示了裸果木的潜在分布格局和生态位要求。     

Locating pleistocene refugia: comparing phylogeographic and ecological niche model predictions

Ecological niche models (ENMs) provide a means of characterizing the spatial distribution of suitable conditions for species, and have recently been applied to the challenge of locating potential distributional areas at the Last Glacial Maximum (LGM) when unfavorable climate conditions led to range contractions and fragmentation. Here, we compare and contrast ENM-based reconstructions of LGM refugial locations with those resulting from the more traditional molecular genetic and phylogeographic predictions. We examined 20 North American terrestrial vertebrate species from different regions and with different range sizes for which refugia have been identified based on phylogeographic analyses, using ENM tools to make parallel predictions. We then assessed the correspondence between the two approaches based on spatial overlap and areal extent of the predicted refugia. In 14 of the 20 species, the predictions from ENM and predictions based on phylogeographic studies were significantly spatially correlated, suggesting that the two approaches to development of refugial maps are converging on a similar result. Our results confirm that ENM scenario exploration can provide a useful complement to molecular studies, offering a less subjective, spatially explicit hypothesis of past geographic patterns of distribution.     

Incorporating spatial autocorrelation into species distribution models alters forecasts of climate‐mediated range shifts

Species distribution models (SDMs) are widely used to forecast changes in the spatial distributions of species and communities in response to climate change. However, spatial autocorrelation (SA) is rarely accounted for in these models, despite its ubiquity in broad‐scale ecological data. While spatial autocorrelation in model residuals is known to result in biased parameter estimates and the inflation of type I errors, the influence of unmodeled SA on species' range forecasts is poorly understood. Here we quantify how accounting for SA in SDMs influences the magnitude of range shift forecasts produced by SDMs for multiple climate change scenarios. SDMs were fitted to simulated data with a known autocorrelation structure, and to field observations of three mangrove communities from northern Australia displaying strong spatial autocorrelation. Three modeling approaches were implemented: environment‐only models (most frequently applied in species' range forecasts), and two approaches that incorporate SA; autologistic models and residuals autocovariate (RAC) models. Differences in forecasts among modeling approaches and climate scenarios were quantified. While all model predictions at the current time closely matched that of the actual current distribution of the mangrove communities, under the climate change scenarios environment‐only models forecast substantially greater range shifts than models incorporating SA. Furthermore, the magnitude of these differences intensified with increasing increments of climate change across the scenarios. When models do not account for SA, forecasts of species' range shifts indicate more extreme impacts of climate change, compared to models that explicitly account for SA. Therefore, where biological or population processes induce substantial autocorrelation in the distribution of organisms, and this is not modeled, model predictions will be inaccurate. These results have global importance for conservation efforts as inaccurate forecasts lead to ineffective prioritization of conservation activities and potentially to avoidable species extinctions.     

Validating and improving elastic network models with molecular dynamics simulations

Elastic network models (ENMs) are a class of simple models intended to represent the collective motions of proteins. In contrast to all‐atom molecular dynamics simulations, the low computational investment required to use an ENM makes them ideal for speculative hypothesis‐testing situations. Historically, ENMs have been validated via comparison to crystallographic B‐factors, but this comparison is relatively low‐resolution and only tests the predictions of relative flexibility. In this work, we systematically validate and optimize a number of ENM‐type models by quantitatively comparing their predictions to microsecond‐scale all‐atom simulations of three different G protein coupled receptors. We show that, despite their apparent simplicity, well‐optimized ENMs perform remarkably well, reproducing the protein fluctuations with an accuracy comparable to what one would expect from all‐atom simulations run for several hundred nanoseconds. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Different facets of the same niche: Integrating citizen science and scientific survey data to predict biological invasion risk under multiple global change drivers

Citizen science initiatives have been increasingly used by researchers as a source of occurrence data to model the distribution of alien species. Since citizen science presence-only data suffer from some fundamental issues, efforts have been made to combine these data with those provided by scientifically structured surveys. Surprisingly, only a few studies proposing data integration evaluated the contribution of this process to the effective sampling of species' environmental niches and, consequently, its effect on model predictions on new time intervals. We relied on niche overlap analyses, machine learning classification algorithms and ecological niche models to compare the ability of data from citizen science and scientific surveys, along with their integration, in capturing the realized niche of 13 invasive alien species in Italy. Moreover, we assessed differences in current and future invasion risk predicted by each data set under multiple global change scenarios. We showed that data from citizen science and scientific surveys captured similar species niches though highlighting exclusive portions associated with clearly identifiable environmental conditions. In terrestrial species, citizen science data granted the highest gain in environmental space to the pooled niches, determining an increased future biological invasion risk. A few aquatic species modelled at the regional scale reported a net loss in the pooled niches compared to their scientific survey niches, suggesting that citizen science data may also lead to contraction in pooled niches. For these species, models predicted a lower future biological invasion risk. These findings indicate that citizen science data may represent a valuable contribution to predicting future spread of invasive alien species, especially within national-scale programmes. At the same time, citizen science data collected on species poorly known to citizen scientists, or in strictly local contexts, may strongly affect the niche quantification of these taxa and the prediction of their future biological invasion risk.     

Determinants of palm species distributions across Africa: the relative roles of climate,non‐climatic environmental factors,and spatial constraints

Most of the Earth's biodiversity resides in the tropics. However, a comprehensive understanding of which factors control range limits of tropical species is still lacking. Climate is often thought to be the predominant range‐determining mechanism at large spatial scales. Alternatively, species’ ranges may be controlled by soil or other environmental factors, or by non‐environmental factors such as biotic interactions, dispersal barriers, intrinsic population dynamics, or time‐limited expansion from place of origin or past refugia. How species ranges are controlled is of key importance for predicting their responses to future global change. Here, we use a novel implementation of species distribution modelling (SDM) to assess the degree to which African continental‐scale species distributions in a keystone tropical group, the palms (Arecaceae), are controlled by climate, non‐climatic environmental factors, or non‐environmental spatial constraints. A comprehensive data set on African palm species occurrences was assembled and analysed using the SDM algorithm Maxent in combination with climatic and non‐climatic environmental predictors (habitat, human impact), as well as spatial eigenvector mapping (spatial filters). The best performing models always included spatial filters, suggesting that palm species distributions are always to some extent limited by non‐environmental constraints. Models which included climate provided significantly better predictions than models that included only non‐climatic environmental predictors, the latter having no discernible effect beyond the climatic control. Hence, at the continental scale, climate constitutes the only strong environmental control of palm species distributions in Africa. With regard to the most important climatic predictors of African palm distributions, water‐related factors were most important for 25 of the 29 species analysed. The strong response of palm distributions to climate in combination with the importance of non‐environmental spatial constraints suggests that African palms will be sensitive to future climate changes, but that their ability to track suitable climatic conditions will be spatially constrained.