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.     

Spatial optimization of protected area placement incorporating ecological, social and economical criteria

We describe two approaches for spatial optimization of protected area placement, both based on maximizing an objective function that incorporates ecological, social, and economical criteria. Of these, a seed cell selection procedure works by evaluating potential cells for protection one by one, picking the one that maximizes the objective function, adding seed cells. This continues to full protection of the project area. The other is a Monte Carlo approach, which uses a likelihood sampling procedure based on weighted importance layers of conservation interest to evaluate alternative protected area sizing and placement. This is similar to the objective function of Marxan, a priority-selection decision-support tool based on optimization algorithms using geographic information system data. The two approaches are alternative options in a common spatial optimization module, which uses the time- and spatial-dynamic Ecospace model for the evaluations. The optimizations are implemented as components of the Ecopath with Ecosim approach and software. In a case study, we find that there can be protected area zoning that will accommodate economical and social factors, without causing ecological deterioration. We also find a tradeoff between including cells of special conservation interest, and the economic and social interests. While this does not need to be a general feature, it emphasizes the need to use modeling techniques to evaluate the tradeoff.     

Multiscale codependence analysis: an integrated approach to analyze relationships across scales

The spatial and temporal organization of ecological processes and features and the scales at which they occur are central topics to landscape ecology and metapopulation dynamics, and increasingly regarded as a cornerstone paradigm for understanding ecological processes. Hence, there is need for computational approaches which allow the identification of the proper spatial or temporal scales of ecological processes and the explicit integration of that information in models. For that purpose, we propose a new method (multiscale codependence analysis, MCA) to test the statistical significance of the correlations between two variables at particular spatial or temporal scales. Validation of the method (using Monte Carlo simulations) included the study of type I error rate, under five statistical significance thresholds, and of type II error rate and statistical power. The method was found to be valid, in terms of type I error rate, and to have sufficient statistical power to be useful in practice. MCA has assumptions that are met in a wide range of circumstances. When applied to model the river habitat of juvenile Atlantic salmon, MCA revealed that variables describing substrate composition of the river bed were the most influential predictors of parr abundance at 0.4-4.1 km scales whereas mean channel depth was more influential at 200-300 m scales. When properly assessed, the spatial structuring observed in nature may be used purposefully to refine our understanding of natural processes and enhance model representativeness.     

基于空间信息技术的城市环境时空调控范式研究

城市环境－生态系统是高度复杂的时空复合动力学系统。通过对城市环境问题的空间动力学机制分析后,提出城市环境可持续发展时空调控的层次途径,并构造了融合遥感、地理信息系统等空间信息技术、环境建模技术、决策支持系统、人工智能等技术的城市生态－环境系统时空调控的体系框架,为城市环境管理及环境空间决策提供新的理论范。     

Variation partitioning of species data matrices: estimation and comparison of fractions

Establishing relationships between species distributions and environmental characteristics is a major goal in the search for forces driving species distributions. Canonical ordinations such as redundancy analysis and canonical correspondence analysis are invaluable tools for modeling communities through environmental predictors. They provide the means for conducting direct explanatory analysis in which the association among species can be studied according to their common and unique relationships with the environmental variables and other sets of predictors of interest, such as spatial variables. Variation partitioning can then be used to test and determine the likelihood of these sets of predictors in explaining patterns in community structure. Although variation partitioning in canonical analysis is routinely used in ecological analysis, no effort has been reported in the literature to consider appropriate estimators so that comparisons between fractions or, eventually, between different canonical models are meaningful. In this paper, we show that variation partitioning as currently applied in canonical analysis is biased. We present appropriate unbiased estimators. In addition, we outline a statistical test to compare fractions in canonical analysis. The question addressed by the test is whether two fractions of variation are significantly different from each other. Such assessment provides an important step toward attaining an understanding of the factors patterning community structure. The test is shown to have correct Type I. error rates and good power for both redundancy analysis and canonical correspondence analysis.     

Appreciating Ecological Complexity: Habitat Contours as a Conceptual Landscape Model

Abstract:  Organisms respond to their surroundings at multiple spatial scales, and different organisms respond differently to the same environment. Existing landscape models, such as the "fragmentation model" (or patch-matrix-corridor model) and the "variegation model," can be limited in their ability to explain complex patterns for different species and across multiple scales. An alternative approach is to conceptualize landscapes as overlaid species-specific habitat contour maps. Key characteristics of this approach are that different species may respond differently to the same environmental conditions and at different spatial scales. Although similar approaches are being used in ecological modeling, there is much room for habitat contours as a useful conceptual tool. By providing an alternative view of landscapes, a contour model may stimulate more field investigations stratified on the basis of ecological variables other than human-defined patches and patch boundaries. A conceptual model of habitat contours may also help to communicate ecological complexity to land managers. Finally, by incorporating additional ecological complexity, a conceptual model based on habitat contours may help to bridge the perceived gap between pattern and process in landscape ecology. Habitat contours do not preclude the use of existing landscape models and should be seen as a complementary approach most suited to heterogeneous human-modified landscapes.     

Investigating cumulative effects across ecological scales

Species, habitats, and ecosystems are increasingly exposed to multiple anthropogenic stressors, fueling a rapidly expanding research program to understand the cumulative impacts of these environmental modifications. Since the 1970s, a growing set of methods has been developed through two parallel, sometimes connected, streams of research within the applied and academic realms to assess cumulative effects. Past reviews of cumulative effects assessment (CEA) methods focused on approaches used by practitioners. Academic research has developed several distinct and novel approaches to conducting CEA. Understanding the suite of methods that exist will help practitioners and academics better address various ecological foci (physiological responses, population impacts, ecosystem impacts) and ecological complexities (synergistic effects, impacts across space and time). We reviewed 6 categories of methods (experimental, meta-analysis, single-species modeling, mapping, qualitative modeling, and multispecies modeling) and examined the ability of those methods to address different levels of complexity. We focused on research gaps and emerging priorities. We found that no single method assessed impacts across the 4 ecological foci and 6 ecological complexities considered. We propose that methods can be used in combination to improve understanding such that multimodel inference can provide a suite of comparable outputs, mapping methods can help prioritize localized models or experimental gaps, and future experiments can be paired from the outset with models they will inform.     

The representation of the environment in the context of individual-based modeling

Individual-based modeling includes the explicit representation of the environment, to which individual organisms interact. From the perspective of spatial representation, spatially extended environment is different from discrete individual organisms, thus the success of object-orientation in the representation of individual organisms may not be applicable to the representation of the environment. Over the past few years, the attempt to adopt object-orientation in the representation of the environment has stimulated interesting discussions over what space is and how it may be represented in ecological modeling. The objective of this paper is to evaluate the merit of two traditional approaches used to represent the environment, i.e., the grid model and the patch model, and, in particular, the object-oriented versions of the two approaches in the representation of the environment. Two case studies are provided in support of the discussions of how the environment may be represented. One case study concerns individual fish growth and movement in an aquatic environment and the other concerns the movement of calving elk in a short-grass prairie. The discussion stresses the importance of two issues in the context of individual-based modeling: (1) the distinction between object-orientation used as a programming technique and as a representation means, and (2) the conceptual compatibility between a perceived phenomenon and the approach used to represent the phenomenon. It is suggested that caution be exercised in the practice of treating cells as objects. The paper concludes that two approaches may be appropriate for individual-based modeling. One is a hybrid approach that incorporates the traditional grid model of the environment and an object-oriented model of individual organisms. The other is the all-object approach that combines the object-oriented patches of the environment and the object-oriented individual organisms.     

Analyzing or explaining beta diversity? Understanding the targets of different methods of analysis

It has been actively discussed recently what statistical methods are appropriate when one is interested in testing hypotheses about the origin of beta diversity, especially whether one should use the raw-data approach (e.g., canonical analysis such as RDA and CCA) or the distance approach (e.g., Mantel test and multiple regression on distance matrices). Most of the confusion seems to stem from uncertainty as to what is the response variable in the different approaches. Here our aim is to clarify this issue. We also show that, although both the raw-data approach and the distance approach can often be used to address the same ecological hypothesis, they target fundamentally different predictions of those hypotheses. As the two approaches shed light on different aspects of the ecological hypotheses, they should be viewed as complementary rather than alternative ways of analyzing data. However, in some cases only one of the approaches may be appropriate. We argue that S. P. Hubbell's neutral theory can only be tested using the distance approach, because its testable predictions are stated in terms of distances, not in terms of raw data. In all cases, the decision on which method is chosen must be based on which addresses the question at hand, it cannot be based on which provides the highest proportion of explained variance in simulation studies.     

Efficient statistical mapping of avian count data

We develop a spatial modeling framework for count data that is efficient to implement in high-dimensional prediction problems. We consider spectral parameterizations for the spatially varying mean of a Poisson model. The spectral parameterization of the spatial process is very computationally efficient, enabling effective estimation and prediction in large problems using Markov chain Monte Carlo techniques. We apply this model to creating avian relative abundance maps from North American Breeding Bird Survey (BBS) data. Variation in the ability of observers to count birds is modeled as spatially independent noise, resulting in over-dispersion relative to the Poisson assumption. This approach represents an improvement over existing approaches used for spatial modeling of BBS data which are either inefficient for continental scale modeling and prediction or fail to accommodate important distributional features of count data thus leading to inaccurate accounting of prediction uncertainty.     

Rethinking receiver operating characteristic analysis applications in ecological niche modeling

The area under the curve (AUC) of the receiver operating characteristic (ROC) has become a dominant tool in evaluating the accuracy of models predicting distributions of species. ROC has the advantage of being threshold-independent, and as such does not require decisions regarding thresholds of what constitutes a prediction of presence versus a prediction of absence. However, we show that, comparing two ROCs, using the AUC systematically undervalues models that do not provide predictions across the entire spectrum of proportional areas in the study area. Current ROC approaches in ecological niche modeling applications are also inappropriate because the two error components are weighted equally. We recommend a modification of ROC that remedies these problems, using partial-area ROC approaches to provide a firmer foundation for evaluation of predictions from ecological niche models. A worked example demonstrates that models that are evaluated favorably by traditional ROC AUCs are not necessarily the best when niche modeling considerations are incorporated into the design of the test.     

Sensitivity Analyses of Spatial Population Viability Analysis Models for Species at Risk and Habitat Conservation Planning

Abstract:  Population viability analysis (PVA) is an effective framework for modeling species- and habitat-recovery efforts, but uncertainty in parameter estimates and model structure can lead to unreliable predictions. Integrating complex and often uncertain information into spatial PVA models requires that comprehensive sensitivity analyses be applied to explore the influence of spatial and nonspatial parameters on model predictions. We reviewed 87 analyses of spatial demographic PVA models of plants and animals to identify common approaches to sensitivity analysis in recent publications. In contrast to best practices recommended in the broader modeling community, sensitivity analyses of spatial PVAs were typically ad hoc, inconsistent, and difficult to compare. Most studies applied local approaches to sensitivity analyses, but few varied multiple parameters simultaneously. A lack of standards for sensitivity analysis and reporting in spatial PVAs has the potential to compromise the ability to learn collectively from PVA results, accurately interpret results in cases where model relationships include nonlinearities and interactions, prioritize monitoring and management actions, and ensure conservation-planning decisions are robust to uncertainties in spatial and nonspatial parameters. Our review underscores the need to develop tools for global sensitivity analysis and apply these to spatial PVA.     

Defining an ecological thermodynamics using discrete simulation approaches

New insights into interdisciplinary engineering endeavors, from classical modeling to nano–macroscale extrapolation and critical evaluation, weigh heavily on the pervasive nature of thermodynamics in the physical world. Just as statistical thermodynamic approaches provide a beneficial complement to a process-based macroscale thermodynamic approaches with physical systems, a Lagrangian approach to energetics in biological systems can, we believe, provide a beneficial complement to popular Eulerian approaches. Statistical thermodynamics is used as a springboard for some analogies that are similarly used to leap into the ecological scale. The Lagrangian simulation, a discrete simulation, is implemented with a spreadsheet approach, a discrete simulation approach, and a new stochastic differential equation solution approach. The Lagrangian approach complements the more widely used continuous (or Eulerian) simulation approaches such as STELLA or Environ theory approaches. The Lagrangian approach decomposes energy into small packets or ecological quanta. An ecological entropy is computed based on nodal contacts in the network, with the notion that nodal contact is analogous to molecular speed. In the cases shown, the results of ecological entropy appear generally consistent with thermodynamic entropy. A newly available simulation package (ECONET) enabled an easy Lagrangian approach to analyzing the Cone Springs and Oyster ecological models. An analogy between nodal contact numbers and molecular speed was developed to enable computation of an ecological entropy. There is a similarity between classical and ecological entropy based on similarity in shape of the Maxwell–Boltzmann distributions to the packet-nodal contact numbers. An ecological temperature can be defined based on this similarity. Selected ratios of ecological entropy versus classical macroscopic entropy appeared to have some degree of robustness. Other aspects of ecological thermodynamics remain to be developed. It is felt that the ecological thermodynamics approach presented offers an improved way to combine biochemical and ecological entropy. A sound combination of entropies at multiple scales will help bring together measurements at disparate scales.     

Intertype mark correlation function: A new tool for the analysis of species interactions

The spatial pattern of the different species in complex ecosystems reflects the underlying ecological processes. In this paper a second order moment function is proposed and tested to analyse the spatial distribution of a mark, which could be a tree characteristic such as diameter or height, between two different types of points, which could be two different tree species. The proposed function was a conditional density function based on the intertype K_rs(d) function, incorporating as test function the correlation of the marks between pairs composed of points of different types. The results obtained in simulated and real plots prove that the function is capable of revealing the scale at which spatial correlation of the mark between two types of points exists. The proposed function allows the spatial association between individuals of different species at different life stages to be identified. This analysis may reveal information on species ecology and interspecific interactions in forest ecosystems.     

Habitat selection predicts genetic relatedness in an alpine ungulate

Landscape heterogeneity plays an integral role in shaping ecological and evolutionary processes. Despite links between the two disciplines, ecologists and population geneticists have taken different approaches to evaluating habitat selection, animal movement, and gene flow across the landscape. Ecologists commonly use statistical models such as resource selection functions (RSFs) to identify habitat features disproportionately selected by animals, whereas population genetic approaches model genetic differentiation according to the distribution of habitat variables. We combined ecological and genetic approaches by using RSFs to predict genetic relatedness across a heterogeneous landscape. We constructed sex- and season-specific resistance surfaces based on RSFs estimated using data from 102 GPS (global positioning system) radio-collared mountain goats (Oreamnos americanus) in southeast Alaska, USA. Based on mountain goat ecology, we hypothesized that summer and male surfaces would be the best predictors of relatedness. All individuals were genotyped at 22 microsatellite loci, which we used to estimate genetic relatedness. Summer resistance surfaces derived from RSFs were the best predictors of genetic relatedness, and winter models the poorest. Mountain goats generally selected for areas close to escape terrain and with a high heat load (a metric related to vegetative productivity and snow depth), while avoiding valleys. Male- and female-specific surfaces were similar, except for winter, for which male habitat selection better predicted genetic relatedness. The null models of isolation-by-distance and barrier only outperformed the winter models. This study merges high-resolution individual locations through GPS telemetry and genetic data, that can be used to validate and parameterize landscape genetics models, and further elucidates the relationship between landscape heterogeneity and genetic differentiation.     

Modelling directional spatial processes in ecological data

Distributions of species, animals or plants, terrestrial or aquatic, are influenced by numerous factors such as physical and biogeographical gradients. Dominant wind and current directions cause the appearance of gradients in physical conditions whereas biogeographical gradients can be the result of historical events (e.g. glaciations). No spatial modelling technique has been developed to this day that considers the direction of an asymmetric process controlling species distributions along a gradient or network. This paper presents a new method that can model species spatial distributions generated by a hypothesized asymmetric, directional physical process. This method is an eigenfunction-based spatial filtering technique that offers as much flexibility as the Moran's eigenvector maps (MEM) framework; it is called asymmetric eigenvector maps (AEM) modelling. Information needed to construct eigenfunctions through the AEM framework are the spatial coordinates of the sampling or experimental sites, a connexion diagram linking the sites to one another, prior information about the direction of the hypothesized asymmetric process influencing the response variable(s), and optionally, weights attached to the edges (links). To illustrate how this new method works, AEM is compared to MEM analysis through simulations and in the analysis of an ecological example where a known asymmetric forcing is present. The ecological example reanalyses the dietary habits of brook trout (Salvelinus fontinalis) sampled in 42 lakes of the Mastigouche Reserve, Québec.     

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.     

Dealing with collinearity in behavioural and ecological data: model averaging and the problems of measurement error

There has been a great deal of recent discussion of the practice of regression analysis (or more generally, linear modelling) in behaviour and ecology. In this paper, I wish to highlight two factors that have been under-considered, collinearity and measurement error in predictors, as well as to consider what happens when both exist at the same time. I examine what the consequences are for conventional regression analysis (ordinary least squares, OLS) as well as model averaging methods, typified by information theoretic approaches based around Akaike’s information criterion. Collinearity causes variance inflation of estimated slopes in OLS analysis, as is well known. In the presence of collinearity, model averaging reduces this variance for predictors with weak effects, but also can lead to parameter bias. When collinearity is strong or when all predictors have strong effects, model averaging relies heavily on the full model including all predictors and hence the results from this and OLS are essentially the same. I highlight that it is not safe to simply eliminate collinear variables without due consideration of their likely independent effects as this can lead to biases. Measurement error is also considered and I show that when collinearity exists, this can lead to extreme biases when predictors are collinear, have strong effects but differ in their degree of measurement error. I highlight techniques for dealing with and diagnosing these problems. These results reinforce that automated model selection techniques should not be relied on in the analysis of complex multivariable datasets.     

Exploring the risks and benefits of flexibility in biodiversity offset location in a case study of migratory shorebirds

Biodiversity offsets aim to counterbalance the residual impacts of development on species and ecosystems. Guidance documents explicitly recommend that biodiversity offset actions be located close to the location of impact because of higher potential for similar ecological conditions, but allowing greater spatial flexibility has been proposed. We examined the circumstances under which offsets distant from the impact location could be more likely to achieve no net loss or provide better ecological outcomes than offsets close to the impact area. We applied a graphical model for migratory shorebirds in the East Asian–Australasian Flyway as a case study to explore the problems that arise when incorporating spatial flexibility into offset planning. Spatially flexible offsets may alleviate impacts more effectively than local offsets; however, the risks involved can be substantial. For our case study, there were inadequate data to make robust conclusions about the effectiveness and equivalence of distant habitat-based offsets for migratory shorebirds. Decisions around offset placement should be driven by the potential to achieve equivalent ecological outcomes; however, when considering more distant offsets, there is a need to evaluate the likely increased risks alongside the potential benefits. Although spatially flexible offsets have the potential to provide more cost-effective biodiversity outcomes and more cobenefits, our case study showed the difficulty of demonstrating these benefits in practice and the potential risks that need to be considered to ensure effective offset placement.     

A geostatistical approach for mapping thematic classification accuracy and evaluating the impact of inaccurate spatial data on ecological model predictions

Spatial information in the form of geographical information system coverages and remotely sensed imagery is increasingly used in ecological modeling. Examples include maps of land cover type from which ecologically relevant properties, such as biomass or leaf area index, are derived. Spatial information, however, is not error-free: acquisition and processing errors, as well as the complexity of the physical processes involved, make remotely sensed data imperfect measurements of ecological attributes. It is therefore important to first assess the accuracy of the spatial information being used and then evaluate the impact of such inaccurate information on ecological model predictions. In this paper, the role of geostatistics for mapping thematic classification accuracy through integration of abundant image-derived (soft) and sparse higher accuracy (hard) class labels is presented. Such assessment leads to local indices of map quality, which can be used for guiding additional ground surveys. Stochastic simulation is proposed for generating multiple alternative realizations (maps) of the spatial distribution of the higher accuracy class labels over the study area. All simulated realizations are consistent with the available pieces of information (hard and soft labels) up to their validated level of accuracy. The simulated alternative class label representations can be used for assessing joint spatial accuracy, i.e., classification accuracy regarding entire spatial features read from the thematic map. Such realizations can also serve as input parameters to spatially explicit ecological models; the resulting distribution of ecological responses provides a model of uncertainty regarding the ecological model prediction. A case study illustrates the generation of alternative land cover maps for a Landsat Thematic Mapper (TM) subscene, and the subsequent construction of local map quality indices. Simulated land cover maps are then input into a biogeochemical model for assessing uncertainty regarding net primary production (NPP).