Distance-based eigenvector maps (DBEM) to analyse metapopulation structure with irregular sampling

Characterizing spatial patterns due to ecological processes is a major issue for analysing and predicting species distributions. Grasping the non-linear nature of population dynamics over networks of discrete suitable sites is here central, as very specific signatures are expected. In the line of promising results from Fourier analysis of metapopulation maps, we found distance-based eigenvector maps (DBEM) to help disentangle the respective signatures of habitat and metapopulation structuring, with the great advantage of being applicable to irregular sampling schemes, a common feature of ecological surveys. A smoothing procedure was required to obtain the distinguishable signatures, and this may be a critical issue for investigating non-contingent and reliable patterns in spatial ecology.     

Variation partitioning involving orthogonal spatial eigenfunction submodels

When partitioning the variation of univariate or multivariate ecological data with respect to several submodels of spatial eigenfunctions (e.g., Moran's eigenvector maps, MEM) acting as explanatory data, a problem occurs: although the submodels are constructed to be orthogonal to one another, the partitioning based on adjusted R2 statistics produces nonzero values in the intersections between spatial submodels. This phenomenon is described and two solutions are proposed. The first solution is to apportion the intersection fractions proportionally to the variation explained by each submodel. The second solution consists in creating a hierarchy among the spatial submodels, in accordance with hierarchy theory. These solutions lead to new partitioning equations that are described in the Appendix. R functions are provided to carry out partitioning with respect to environmental variables and spatial eigenfunction submodels. This development is important for the correct interpretation of spatial modeling results implying explanatory environmental data as well as submodels of spatial eigenfunctions involving two or more spatial scales.     

The spatial links tool: Automated mapping of habitat linkages in variegated landscapes

The removal, alteration and fragmentation of habitat in many parts of the world has led to a loss of biodiversity. Within the prevailing societal limitations the process is not easily reversed. Attempts are being made to minimise the fragmentation of remaining habitat by strategically reversing or managing habitat loss. Although their relative usefulness is a topic of debate among ecologists, habitat corridors are seen as one way of maintaining spatially dependent ecological processes within landscapes where habitat has been seriously depleted. Corridors can only be effective if they significantly contribute to the species sustaining processes of gene flow, resource access or the colonisation of vacant patches. We present a spatial habitat modelling methodology for evaluating the contribution and potential contribution of connecting paths to landscape connectivity. We have developed the spatial links tool (SLT), which maps link value across a region. The SLT combines connectivity measures from metapopulation ecology with the least cost path algorithm from graph theory, and can be applied to continuously variable landscape data. Combined with expert judgement, link value maps can be used to delineate habitat corridors. The approach capitalises on some synergies between ecological relevance and computational efficiency to produce an easily applied heuristic tool that has been successfully applied in NSW Australia.     

The performance of state-of-the-art modelling techniques depends on geographical distribution of species

We explored the effects of prevalence, latitudinal range and clumping (spatial autocorrelation) of species distribution patterns on the predictive accuracy of eight state-of-the-art modelling techniques: Generalized Linear Models (GLMs), Generalized Boosting Method (GBM), Generalized Additive Models (GAMs), Classification Tree Analysis (CTA), Artificial Neural Network (ANN), Multivariate Adaptive Regression Splines (MARS), Mixture Discriminant Analysis (MDA) and Random Forest (RF). One hundred species of Lepidoptera, selected from the Distribution Atlas of European Butterflies, and three climate variables were used to determine the bioclimatic envelope for each butterfly species. The data set consisting of 2620 grid squares 30′ × 60′ in size all over Europe was randomly split into the calibration and the evaluation data sets. The performance of different models was assessed using the area under the curve (AUC) of a receiver operating characteristic (ROC) plot. Observed differences in modelling accuracy among species were then related to the geographical attributes of the species using GAM. The modelling performance was negatively related to the latitudinal range and prevalence, whereas the effect of spatial autocorrelation on prediction accuracy depended on the modelling technique. These three geographical attributes accounted for 19–61% of the variation in the modelling accuracy. Predictive accuracy of GAM, GLM and MDA was highly influenced by the three geographical attributes, whereas RF, ANN and GBM were moderately, and MARS and CTA only slightly affected. The contrasting effects of geographical distribution of species on predictive performance of different modelling techniques represent one source of uncertainty in species spatial distribution models. This should be taken into account in biogeographical modelling studies and assessments of climate change impacts.     

Modelling plant species richness using functional groups

Conservation biologists increasingly rely on spatial predictive models of biodiversity to support decision-making. Therefore, highly accurate and ecologically meaningful models are required at relatively broad spatial scales. While statistical techniques have been optimized to improve model accuracy, less focus has been given to the question: How does the autecology of a single species affect model quality? We compare a direct modelling approach versus a cumulative modelling approach for predicting plant species richness, where the latter gives more weight to the ecology of functional species groups. In the direct modelling approach, species richness is predicted by a single model calibrated for all species. In the cumulative modelling approach, the species were partitioned into functional groups, with each group calibrated separately and species richness of each group was cumulated to predict total species richness. We hypothesized that model accuracy depends on the ecology of individual species and that the cumulative modelling approach would predict species richness more accurately. The predictors explained plant species richness by ca. 25%. However, depending on the functional group the deviance explained varied from 3 to 67%. While both modelling approaches performed equally well, the models of the different functional groups highly varied in their quality and their spatial richness pattern. This variability helps to improve our understanding on how plant functional groups respond to ecological gradients.     

Incorporating consumer–resource spatial interactions in reserve design

The persistence of species in reserves depends in large part on the persistence of functional ecological interactions. Despite their importance, however, ecological interactions have not yet been explicitly incorporated into conservation prioritization methods. We develop here a general method for incorporating consumer–resource interactions into spatial reserve design. This method protects spatial consumer–resource interactions by protecting areas that maintain the connectivity between the distribution of consumers and resources. We illustrate our method with a conservation planning case study of a mammalian predator, American marten (Martes americana), and its two primary prey species, Red-backed vole (Clethrionomys rutilus) and Deer mouse (Peromyscus maniculatus). The conservation goal was to identify a reserve for marten that comprised 12% of a forest management unit in the boreal forest in Québec, Canada. We compared reserves developed using analysis variants that utilized different levels of information about predator and prey habitat distributions, species-specific connectivity requirements, and interaction connectivity requirements. The inclusion of consumer–resource interactions in reserve-selection resulted in spatially aggregated reserves that maintained local habitat quality for the species. This spatial aggregation was not induced by applying a qualitative penalty for the boundary length of the reserve, but rather was a direct consequence of modelling the spatial needs of the interacting consumer and resources. Our method for maintaining connectivity between consumers and their resources within reserves can be applied even under the most extreme cases of either complete spatial overlap or complete spatial segregation of consumer–resource distributions. The method has been made available via public software.     

Hierarchical analysis of species distributions and abundance across environmental gradients

Abiotic and biotic processes operate at multiple spatial and temporal scales to shape many ecological processes, including species distributions and demography. Current debate about the relative roles of niche-based and stochastic processes in shaping species distributions and community composition reflects, in part, the challenge of understanding how these processes interact across scales. Traditional statistical models that ignore autocorrelation and spatial hierarchies can result in misidentification of important ecological covariates. Here, we demonstrate the utility of a hierarchical modeling framework for testing hypotheses about the importance of abiotic factors at different spatial scales and local spatial autocorrelation for shaping species distributions and abundances. For the two orchid species studied, understory light availability and soil moisture helped to explain patterns of presence and abundance at a microsite scale (<4 m2), while soil organic content was important at a population scale (<400 m2). The inclusion of spatial autocorrelation is shown to alter the magnitude and certainty of estimated relationships between abundance and abiotic variables, and we suggest that such analysis be used more often to explore the relationships between species life histories and distributions. The hierarchical modeling framework is shown to have great potential for elucidating ecological relationships involving abiotic and biotic processes simultaneously at multiple scales.     

The effect of species response form on species distribution model prediction and inference

Ecological theory and current evidence support the validity of various species response curves according to a variety of environmental gradients. Various methods have been developed for building species distribution models but it is not well known how these methods perform under various assumptions about the form of the underlying species response. It is also not well known how spatial correlation in species occurrence affects model performance. These effects were investigated by applying an environmental envelope method (BIOCLIM) and three regression-based methods: logistic regression (LR), generalized additive modelling (GAM), and classification and regression tree (CART) to simulated species occurrence data. Each simulated species was constructed as a sum of responses with varying weights. Three basic species response curves were assumed: Gaussian (bell-shaped), Beta (skew) and linear. The two non-linear responses conform to standard ecological niche theory. All three responses were applied in turn to three simulated environmental variables, each with varying degrees of spatial autocorrelation. GAM produced the most consistent model performance over all forms of simulated species response. BIOCLIM and CART were inclined to underrate the performance of variables with a linear response. BIOCLIM was less sensitive to data density. LR was susceptible to model misspecification. The use of a linear function in LR underestimated the performance of variables with non-linear species response and contributed to increased spatial autocorrelation in model residuals. Omission of important environmental variables with non-linear species response also contributed to increased spatial autocorrelation in model residuals. Adding a spatial autocovariate term to the LR model (autologistic model) reduced the spatial autocorrelation and improved model performance, but did not correct the misidentification of the dominant environmental determinant. This is to be expected since the autologistic approach was designed primarily for prediction and not for inference. Given that various forms of species response to environmental determinants arise commonly in nature: (1) higher order functions should always be tested when applying LR in modelling species distribution; (2) spatial autocorrelation in species distribution model residuals can indicate that environmental determinants with non-linear response are missing from the model; and (3) deficiencies in LR model performance due to model misspecification can be addressed by adding a spatial autocovariate to the model, but care should be taken when interpreting the coefficients of the model parameters.     

Species distribution models and ecological theory: A critical assessment and some possible new approaches

Given the importance of knowledge of species distribution for conservation and climate change management, continuous and progressive evaluation of the statistical models predicting species distributions is necessary. Current models are evaluated in terms of ecological theory used, the data model accepted and the statistical methods applied. Focus is restricted to Generalised Linear Models (GLM) and Generalised Additive Models (GAM). Certain currently unused regression methods are reviewed for their possible application to species modelling.A review of recent papers suggests that ecological theory is rarely explicitly considered. Current theory and results support species responses to environmental variables to be unimodal and often skewed though process-based theory is often lacking. Many studies fail to test for unimodal or skewed responses and straight-line relationships are often fitted without justification.Data resolution (size of sampling unit) determines the nature of the environmental niche models that can be fitted. A synthesis of differing ecophysiological ideas and the use of biophysical processes models could improve the selection of predictor variables. A better conceptual framework is needed for selecting variables.Comparison of statistical methods is difficult. Predictive success is insufficient and a test of ecological realism is also needed. Evaluation of methods needs artificial data, as there is no knowledge about the true relationships between variables for field data. However, use of artificial data is limited by lack of comprehensive theory.Three potentially new methods are reviewed. Quantile regression (QR) has potential and a strong theoretical justification in Liebig's law of the minimum. Structural equation modelling (SEM) has an appealing conceptual framework for testing causality but has problems with curvilinear relationships. Geographically weighted regression (GWR) intended to examine spatial non-stationarity of ecological processes requires further evaluation before being used.Synthesis and applications: explicit theory needs to be incorporated into species response models used in conservation. For example, testing for unimodal skewed responses should be a routine procedure. Clear statements of the ecological theory used, the nature of the data model and sufficient details of the statistical method are needed for current models to be evaluated. New statistical methods need to be evaluated for compatibility with ecological theory before use in applied ecology. Some recent work with artificial data suggests the combination of ecological knowledge and statistical skill is more important than the precise statistical method used. The potential exists for a synthesis of current species modelling approaches based on their differing ecological insights not their methodology.     

Modeling freshwater fish distributions using multiscale landscape data: A case study of six narrow range endemics

Species distribution models (SDMs) have become integral tools in scientific research and conservation planning. Despite progress in the assessment of various statistical models for use in SDMs, little has been done in way of evaluating appropriate ecological models. In this paper, we evaluate the multiscale filter framework as a suitable theoretical model for predicting freshwater fish distributions in the upper Green River system (Ohio River drainage), USA. The spatial distributions of six fishes with contrasting biogeographies were modeled using boosted regression trees and multiscale landscape data. Species biogeography did not appear to affect predictive performance and all models performed well statistically with receiver operating characteristic area under the curve (AUC) ranging from 0.87 to 0.98. Predictive maps show accurate estimations of ranges for five of six species based on historical collections. The relative influence of each type of environmental feature and spatial scale varied markedly with between species. A hierarchical effect was detected for narrowly distributed species. These species were highly influenced by soil composition at larger spatial scales and land use/land cover (LULC) patterns at more proximal scales. Conversely, LULC pattern was the most influential feature for widely distributed at all spatial scales. Using multiscale data capable of capturing hierarchical landscape influences allowed production of accurate predictive models and provided further insight into factors controlling freshwater fish distributions.     

Application of a Random Forest algorithm to predict spatial distribution of the potential yield of Ruditapes philippinarum in the Venice lagoon, Italy

We present a modelling framework that combines machine learning techniques and Geographic Information Systems to support the management of an important aquaculture species, Manila clam (Ruditapes philippinarum). We use the Venice lagoon (Italy), the first site in Europe for the production of R. philippinarum, to illustrate the potential of this modelling approach. To investigate the relationship between the yield of R. philippinarum and a set of environmental factors, we used a Random Forest (RF) algorithm. The RF model was tuned with a large data set (n = 1698) and validated by an independent data set (n = 841). Overall, the model provided good predictions of site-specific yields and the analysis of marginal effect of predictors showed substantial agreement among the modelled responses and available ecological knowledge for R. philippinarum. The most influent environmental factors for yield estimation were percentage of sand in the sediment, salinity, and water depth. Our results agree with findings from other North Adriatic lagoons. The application of the fitted RF model to continuous maps of all the environmental variables allowed estimates of the potential yield for the whole basin. Such a spatial representation enabled site-specific estimates of yield in different farming areas within the lagoon. We present a possible management application of our model by estimating the potential yield under the current farming distribution and comparing it to a proposed re-organization of the farming areas. Our analysis suggests a reduction of total yield is likely to result from the proposed re-organization.     

Temporal limits to simulating the future spread pattern of invasive species: Buddleja davidii in Europe and New Zealand

The spread of invasive species is a major ecological and economic problem. Dynamic spread modelling is a potentially valuable tool to assist regional and central government authorities to monitor and control invasive species. To date a lack of suitable data has meant that most broad scale dispersal models have not been validated with independent datasets, and so their predictive ability and reliability has remained unscrutinised. A dynamic, stochastic dispersal model of the widely invasive plant Buddleja davidii was calibrated on European spread data and then used to project the temporal progression of B. davidii's distribution in New Zealand, starting from several different historical distributions. To assess the model's performance, we constructed an occupancy map based on the average number of simulation realisations that have a population present. The application of Receiver Operating Characteristic (ROC) curves to occupancy maps is introduced, but with specificity substituted by the proportion of available area used in a realisation. A derivative measure, the partial area under these curves when assessed through time (pAUC), is introduced and used to assess overall performance of the spread model. The model was able to attain a high level of model sensitivity, encompassing all of the known locations within the occupancy envelope. However, attempting to simulate the spread of this invasive species beyond a decade had very low model specificity. This is due to several factors, including the exponential process of spread (the further a population spreads the more sites exist from which it can spread stochastically), and the Markovian chain property of the stochastic system whereby differences between realisations compound through time. These features are seen in many reports of spread models, without being explicitly acknowledged. Our measure of pAUC through time allows a model's temporal performance and its specificity to be simultaneously assessed. While the rapid deterioration in model performance limits the utility of this type of modelling for forecasting long-term broad-scale strategic management of biological invasions, it does not necessarily limit its attractiveness for informing smaller scale and shorter term invasion management activities such as surveillance, containment and local eradication.     

Uncertainty propagation in vegetation distribution models based on ensemble classifiers

Ensemble learning techniques are increasingly applied for species and vegetation distribution modelling, often resulting in more accurate predictions. At the same time, uncertainty assessment of distribution models is gaining attention. In this study, Random Forests, an ensemble learning technique, is selected for vegetation distribution modelling based on environmental variables. The impact of two important sources of uncertainty, that is the uncertainty on spatial interpolation of environmental variables and the uncertainty on species clustering into vegetation types, is quantified based on sequential Gaussian simulation and pseudo-randomization tests, respectively. An empirical assessment of the uncertainty propagation to the distribution modelling results indicated a gradual decrease in performance with increasing input uncertainty. The test set error ranged from 30.83% to 52.63% and from 30.83% to 83.62%, when the uncertainty ranges on spatial interpolation and on vegetation clustering, respectively, were fully covered. Shannon’s entropy, which is proposed as a measure for uncertainty of ensemble predictions, revealed a similar increasing trend in prediction uncertainty. The implications of these results in an empirical distribution modelling framework are further discussed with respect to monitoring setup, spatial interpolation and species clustering.     

Spatial modeling in ecology: the flexibility of eigenfunction spatial analyses

Recently, analytical approaches based on the eigenfunctions of spatial configuration matrices have been proposed in order to consider explicitly spatial predictors. The present study demonstrates the usefulness of eigenfunctions in spatial modeling applied to ecological problems and shows equivalencies of and differences between the two current implementations of this methodology. The two approaches in this category are the distance-based (DB) eigenvector maps proposed by P. Legendre and his colleagues, and spatial filtering based upon geographic connectivity matrices (i.e., topology-based; CB) developed by D. A. Griffith and his colleagues. In both cases, the goal is to create spatial predictors that can be easily incorporated into conventional regression models. One important advantage of these two approaches over any other spatial approach is that they provide a flexible tool that allows the full range of general and generalized linear modeling theory to be applied to ecological and geographical problems in the presence of nonzero spatial autocorrelation.     

Spatial connectivity in a large river system: resolving the sources and fate of dissolved organic matter

Large rivers are generally heterogeneous and productive systems that receive important inputs of dissolved organic matter (DOM) from terrestrial and in situ sources. Thus, they are likely to play a significant role in the biogeochemical cycling of the DOM flowing to the oceans. The asymmetric spatial gradient driven by directional flow and environmental heterogeneity contributes to the fate of DOM flowing downstream. Yet, the relative effects of spatial connectivity and environmental heterogeneity on DOM dynamics are poorly understood. For example, since environmental variables show spatial heterogeneity, the variation explained by environmental and spatial variables may be redundant. We used the St. Lawrence River (SLR) as a representative large river to resolve the unique influences of environmental heterogeneity and spatial connectivity on DOM dynamics. We used three-dimensional fluorescence matrices combined with parallel factor analysis (PARAFAC) to characterize the DOM pool in the SLR. Seven fluorophores were modeled, of which two were identified to be of terrestrial origin and three from algal exudates. We measured a set of environmental variables that are known to drive the fate of DOM in aquatic systems. Additionally, we used asymmetric eigenvector map (AEM) modeling to take spatial connectivity into account. The combination of spatial and environmental models explained 85% of the DOM variation. We show that spatial connectivity is an important driver of DOM dynamics, as a large fraction of environmental heterogeneity was attributable to the asymmetric spatial gradient. Along the longitudinal axis, we noted a rapid increase in dissolved organic carbon (DOC), mostly controlled by terrestrial input of DOM originating from the tributaries. Variance partitioning demonstrated that freshly produced protein-like DOM was found to be the preferential substrate for heterotrophic bacteria undergoing rapid proliferation, while humic-like DOM was more correlated to the diffuse attenuation coefficient of UVA radiation.     

Social dominance,seasonal movements,and spatial segregation in African elephants: a contribution to conservation behavior

The structure of dominance relationships among individuals in a population is known to influence their fitness, access to resources, risk of predation, and even energy budgets. Recent advances in global positioning system radio telemetry provide data to evaluate the influence of social relationships on population spatial structure and ranging tactics. Using current models of socio-ecology as a framework, we explore the spatial behaviors relating to the maintenance of transitive (i.e., linear) dominance hierarchies between elephant social groups despite the infrequent occurrence of contests over resources and lack of territorial behavior. Data collected from seven families of different rank demonstrate that dominant groups disproportionately use preferred habitats, limit their exposure to predation/conflict with humans by avoiding unprotected areas, and expend less energy than subordinate groups during the dry season. Hence, our data provide strong evidence of rank derived spatial partitioning in this migratory species. These behaviors, however, were not found during the wet season, indicating that spatial segregation of elephants is related to resource availability. Our results indicate the importance of protecting preexisting social mechanisms for mitigating the ecological impacts of high density in this species. This analysis provides an exemplar of how behavioral research in a socio-ecological framework can serve to identify factors salient to the persistence and management of at risk species or populations. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Are Swiss birds tracking climate change?: Detecting elevational shifts using response curve shapes

Climate change is affecting biodiversity worldwide inducing species to either “move, adapt or die”. In this paper we propose a conceptual framework for analysing range shifts, namely a catalogue of the possible patterns of change in the distribution of a species along elevational or other environmental gradients and an improved quantitative methodology to identify and objectively describe these patterns. Patterns are defined in terms of changes occurring at the leading, trailing or both edges of the distribution: (a) leading edge expansion, (b) trailing edge retraction, (c) range expansion, (d) optimum shift, (e) expansion, (f) retraction, and (g) shift. The methodology is based on the modelling of species distributions along a gradient using generalized additive models (GAMs). Separate models are calibrated for two distinct periods of assessment and response curves are compared over five reference points. Changes occurred at these points are formalized into a code that ultimately designates the corresponding change pattern. We tested the proposed methodology using data from the Swiss national common breeding bird survey. The elevational distributions of 95 bird species were modelled for the periods 1999-2002 and 2004-2007 and significant upward shifts (all patterns confounded) were identified for 35% of the species. Over the same period, an increase in mean temperature was registered for Switzerland. In consideration of the short period covered by the case study, assessed change patterns are considered to correspond to intermediate patterns in an ongoing shifting process. However, similar patterns can be determined by habitat barriers, land use/land cover changes, competition with concurrent or invasive species or different warming rates at different elevations.     

Connectivity Planning to Address Climate Change

As the climate changes, human land use may impede species from tracking areas with suitable climates. Maintaining connectivity between areas of different temperatures could allow organisms to move along temperature gradients and allow species to continue to occupy the same temperature space as the climate warms. We used a coarse‐filter approach to identify broad corridors for movement between areas where human influence is low while simultaneously routing the corridors along present‐day spatial gradients of temperature. We modified a cost–distance algorithm to model these corridors and tested the model with data on current land‐use and climate patterns in the Pacific Northwest of the United States. The resulting maps identified a network of patches and corridors across which species may move as climates change. The corridors are likely to be robust to uncertainty in the magnitude and direction of future climate change because they are derived from gradients and land‐use patterns. The assumptions we applied in our model simplified the stability of temperature gradients and species responses to climate change and land use, but the model is flexible enough to be tailored to specific regions by incorporating other climate variables or movement costs. When used at appropriate resolutions, our approach may be of value to local, regional, and continental conservation initiatives seeking to promote species movements in a changing climate. Planificación de Conectividad para Atender el Cambio Climático