A critique of statistical aspects of ecological studies in spatial epidemiology

In this article, the mathematical assumptions of a number of commonly used ecological regression models are made explicit, critically assessed, and related to ecological bias. In particular, the role and interpretation of random effects models are examined. The modeling of spatial variability is considered and related to an underlying continuous spatial field. The examination of such a field with respect to the modeling of risk in relation to a point source highlights an inconsistency in commonly used approaches. A theme of the paper is to examine how plausible individual-level models relate to those used in practice at the aggregate level. The individual-level models acknowledge confounding, within-area variability in exposures and confounders, measurement error and data anomalies and so we can examine how the area-level versions consider these aspects. We briefly discuss designs that efficiently sample individual data and would appear to be useful in environmental settings.     

Sources of bias in ecological studiesof non-rare events

Ecological studies investigate relationships at the level of the group, rather than at the level of the individual. Although such studies are a common design in epidemiology, it is well-known that estimates may be subject to ecological bias. Most discussion of ecological bias has focused on rare disease events, where the tractability of the loglinear model allows some characterization of the nature of different biases. This paper concentrates on non-rare events, where the Poisson approximation to the binomial distribution is not appropriate. We limit the discussion to bias that arises from within-area variability in exposures and confounders. Our aims are to investigate the likely sizes and directions of bias and, where possible, to suggest methods for controlling the bias or for addressing the sensitivity of inference to assumptions on the nature of the bias. We illustrate that for non-rare events it is much more difficult to characterize the direction of bias than in the rare case. A series of simple numerical examples based on a chronic study of respiratory health illustrate the ideas of the paper.     

Modelling dispersal with diffusion and habitat selection: Analytical results for highly fragmented landscapes

Quantifying dispersal is crucial both for understanding ecological population dynamics, and for gaining insight into factors that affect the genetic structure of populations. The role of dispersal becomes pronounced in highly fragmented landscapes inhabited by spatially structured populations. We consider a landscape consisting of a set of habitat patches surrounded by unsuitable matrix, and model dispersal by assuming that the individuals follow a random walk with parameters that may be specific to the habitat type. We allow for spatial variation in patch quality, and account for edge-mediated behavior, the latter meaning that the individuals bias their movement towards the patches when close to an edge between a patch and the matrix. We employ a diffusion approximation of the random walk model to derive analytical expressions for various characteristics of the dispersal process. For example, we derive formulae for the time that an individual is expected to spend in its current patch i, and for the time that it will spend in the matrix, both conditional on the individual hitting next a given patch j before hitting any of the other patches or dying. The analytical formulae are based on the assumptions that the landscape is infinitely large, that the patches are circularly shaped, and that the patches are small compared to interpatch distances. We evaluate the effect of these assumptions by comparing the analytical results to numerical results in a real patch network that violates all of the three assumptions. We then consider a landscape that fulfills the assumptions, and show that in this case the analytical results are in a very good agreement with the numerical results. The results obtained here allow the construction of computationally efficient dispersal models that can be used as components of metapopulation models.     

A Bioeconomic Model of Marine Reserve Creation

This paper employs a dynamic and spatial model of renewable resource exploitation to investigate the effects of marine reserve creation. The model combines a metapopulation model incorporating resource patch heterogeneity and dispersal with a behaviorally based spatially explicit harvesting model that assumes that fishermen choose location in a manner that eliminates spatial arbitrage opportunities. The combined spatial bioeconomic model is used to simulate the effects of reserve creation under various ecological structures. We identify parameter configurations and ecological dispersal processes that give rise to a double-payoff in which both aggregate biomass and harvest increase after an area of the fishery is set aside and protected from exploitation.     

Assumption‐versus data‐based approaches to summarizing species’ ranges

For conservation decision making, species’ geographic distributions are mapped using various approaches. Some such efforts have downscaled versions of coarse‐resolution extent‐of‐occurrence maps to fine resolutions for conservation planning. We examined the quality of the extent‐of‐occurrence maps as range summaries and the utility of refining those maps into fine‐resolution distributional hypotheses. Extent‐of‐occurrence maps tend to be overly simple, omit many known and well‐documented populations, and likely frequently include many areas not holding populations. Refinement steps involve typological assumptions about habitat preferences and elevational ranges of species, which can introduce substantial error in estimates of species’ true areas of distribution. However, no model‐evaluation steps are taken to assess the predictive ability of these models, so model inaccuracies are not noticed. Whereas range summaries derived by these methods may be useful in coarse‐grained, global‐extent studies, their continued use in on‐the‐ground conservation applications at fine spatial resolutions is not advisable in light of reliance on assumptions, lack of real spatial resolution, and lack of testing. In contrast, data‐driven techniques that integrate primary data on biodiversity occurrence with remotely sensed data that summarize environmental dimensions (i.e., ecological niche modeling or species distribution modeling) offer data‐driven solutions based on a minimum of assumptions that can be evaluated and validated quantitatively to offer a well‐founded, widely accepted method for summarizing species’ distributional patterns for conservation applications.     

Deviations from predictions of the metabolic theory of ecology can be explained by violations of assumptions

The metabolic theory of ecology (MTE) is based on models derived from the first principles of thermodynamics and biochemical kinetics. The MTE predicts that the relationship between temperature and species richness of ectotherms should show a specific slope. Testing the validity of this model, however, depends on whether empirical data do not violate assumptions and are obtained within contour conditions. When dealing with richness gradients, the MTE must be empirically tested only for ectothermic organisms at high organization levels and when their body size as well as abundance does not vary with temperature gradients. Here we evaluate whether the magnitude of the deviations in slope expected from the MTE to empirical data for New World amphibians is due to the violations of model assumptions and to lack of generality due to restricting contour conditions. We found that the MTE correctly predicted biodiversity patterns only at higher levels of organization and when assumptions of the basic model were not violated. Approximately 60% of the deviations from the MTE-predicted slope across amphibian families were due to violations of the model assumptions. The hypothesis that richness patterns are a function of environmental temperature is too restrictive and does not take complex environmental and ecological processes into account. However, our results suggest that it may be possible to obtain multiple derivations of the MTE equation if idiosyncrasies in spatial and biological/ecological issues that are essential to understanding biodiversity patterns are considered.     

Exposing ecological and economic costs of the research‐implementation gap and compromises in decision making

The frequently discussed gap between conservation science and practice is manifest in the gap between spatial conservation prioritization plans and their implementation. We analyzed the research‐implementation gap of one zoning case by comparing results of a spatial prioritization analysis aimed at avoiding ecological impact of peat mining in a regional zoning process with the final zoning plan. We examined the relatively complex planning process to determine the gaps among research, zoning, and decision making. We quantified the ecological costs of the differing trade‐offs between ecological and socioeconomic factors included in the different zoning suggestions by comparing the landscape‐level loss of ecological features (species occurrences, habitat area, etc.) between the different solutions for spatial allocation of peat mining. We also discussed with the scientists and planners the reasons for differing zoning suggestions. The implemented plan differed from the scientists suggestion in that its focus was individual ecological features rather than all the ecological features for which there were data; planners and decision makers considered effects of peat mining on areas not included in the prioritization analysis; zoning was not truly seen as a resource‐allocation process and not emphasized in general minimizing ecological losses while satisfying economic needs (peat‐mining potential); and decision makers based their prioritization of sites on site‐level information showing high ecological value and on single legislative factors instead of finding a cost‐effective landscape‐level solution. We believe that if the zoning and decision‐making processes are very complex, then the usefulness of science‐based prioritization tools is likely to be reduced. Nevertheless, we found that high‐end tools were useful in clearly exposing trade‐offs between conservation and resource utilization.     

Using the negative binomial distribution to model overdispersion in ecological count data

A Poisson process is a commonly used starting point for modeling stochastic variation of ecological count data around a theoretical expectation. However, data typically show more variation than implied by the Poisson distribution. Such overdispersion is often accounted for by using models with different assumptions about how the variance changes with the expectation. The choice of these assumptions can naturally have apparent consequences for statistical inference. We propose a parameterization of the negative binomial distribution, where two overdispersion parameters are introduced to allow for various quadratic mean-variance relationships, including the ones assumed in the most commonly used approaches. Using bird migration as an example, we present hypothetical scenarios on how overdispersion can arise due to sampling, flocking behavior or aggregation, environmental variability, or combinations of these factors. For all considered scenarios, mean-variance relationships can be appropriately described by the negative binomial distribution with two overdispersion parameters. To illustrate, we apply the model to empirical migration data with a high level of overdispersion, gaining clearly different model fits with different assumptions about mean-variance relationships. The proposed framework can be a useful approximation for modeling marginal distributions of independent count data in likelihood-based analyses.     

Locating major PM10 source areas in Seoul using multivariate receptor modeling

Identifying the major sources contributing to air pollution is a problem of fundamental importance in developing effective air quality management plans. Multivariate receptor modeling aims to achieve this goal by unfolding the air pollution data into components associated with different sources based on factor analysis models. We analyze the PM₁₀ data obtained from 17 monitoring sites in Seoul to locate the major source regions using multivariate receptor modeling. The model uncertainty caused by the unknown number of sources and identifiability conditions is assessed by posterior probability of each model. The estimated source spatial profiles seem to be consistent with our prior expectation about the PM₁₀ sources in Seoul.     

Use of Inverse Spatial Conservation Prioritization to Avoid Biological Diversity Loss Outside Protected Areas

Globally expanding human land use sets constantly increasing pressure for maintenance of biological diversity and functioning ecosystems. To fight the decline of biological diversity, conservation science has broken ground with methods such as the operational model of systematic conservation planning (SCP), which focuses on design and on‐the‐ground implementation of conservation areas. The most commonly used method in SCP is reserve selection that focuses on the spatial design of reserve networks and their expansion. We expanded these methods by introducing another form of spatial allocation of conservation effort relevant for land‐use zoning at the landscape scale that avoids negative ecological effects of human land use outside protected areas. We call our method inverse spatial conservation prioritization. It can be used to identify areas suitable for economic development while simultaneously limiting total ecological and environmental effects of that development at the landscape level by identifying areas with highest economic but lowest ecological value. Our method is not based on a priori targets, and as such it is applicable to cases where the effects of land use on, for example, individual species or ecosystem types are relatively small and would not lead to violation of regional or national conservation targets. We applied our method to land‐use allocation to peat mining. Our method identified a combination of profitable production areas that provides the needed area for peat production while retaining most of the landscape‐level ecological value of the ecosystem. The results of this inverse spatial conservation prioritization are being used in land‐use zoning in the province of Central Finland.     

Misspecification of within-area exposure distribution in ecological Poisson models

Ecological studies enable investigation of geographic variations in exposure to environmental variables, across groups, in relation to health outcomes measured on a geographic scale. Such studies are subject to ecological biases, including pure specification bias which arises when a nonlinear individual exposure-risk model is assumed to apply at the area level. Introduction of the within-area variance of exposure should induce a marked reduction in this source of ecological bias. Assuming several measurements per area of exposure and no confounding risk factors, we study the model including the within-area exposure variability when Gaussian within-area exposure distribution is assumed. The robustness is assessed when the within-area exposure distribution is misspecified. Two underlying exposure distributions are studied: the Gamma distribution and an unimodal mixture of two Gaussian distributions. In case of strong ecological association, this model can reduce the bias and improve the precision of the individual parameter estimates when the within-area exposure means and variances are correlated. These different models are applied to analyze the ecological association between radon concentration and childhood acute leukemia in France.

An application of Bayesian variable selection to spatial concurrent linear models

Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the spatial processes, but in applications the data may display strong nonstationary patterns. In this article, we propose a Bayesian variable selection approach based on wavelet tools to address this problem. The proposed approach does not involve any stationarity assumptions on the priors, and instead we impose a mixture prior directly on each wavelet coefficient. We introduce an option to control the priors such that high resolution coefficients are more likely to be zero. Computationally efficient MCMC procedures are provided to address posterior sampling, and uncertainty in the estimation is assessed through posterior means and standard deviations. Examples based on simulated data demonstrate the estimation accuracy and advantages of the proposed method. We also illustrate the performance of the proposed method for real data obtained through remote sensing.     

Movement ecology: size-specific behavioral response of an invasive snail to food availability

Immigration, emigration, migration, and redistribution describe processes that involve movement of individuals. These movements are an essential part of contemporary ecological models, and understanding how movement is affected by biotic and abiotic factors is important for effectively modeling ecological processes that depend on movement. We asked how phenotypic heterogeneity (body size) and environmental heterogeneity (food resource level) affect the movement behavior of an aquatic snail (Tarebia granifera), and whether including these phenotypic and environmental effects improves advection-diffusion models of movement. We postulated various elaborations of the basic advection diffusion model as a priori working hypotheses. To test our hypotheses we measured individual snail movements in experimental streams at high- and low-food resource treatments. Using these experimental movement data, we examined the dependency of model selection on resource level and body size using Akaike's Information Criterion (AIC). At low resources, large individuals moved faster than small individuals, producing a platykurtic movement distribution; including size dependency in the model improved model performance. In stark contrast, at high resources, individuals moved upstream together as a wave, and body size differences largely disappeared. The model selection exercise indicated that population heterogeneity is best described by the advection component of movement for this species, because the top-ranked model included size dependency in advection, but not diffusion. Also, all probable models included resource dependency. Thus population and environmental heterogeneities both influence individual movement behaviors and the population-level distribution kernels, and their interaction may drive variation in movement behaviors in terms of both advection rates and diffusion rates. A behaviorally informed modeling framework will integrate the sentient response of individuals in terms of movement and enhance our ability to accurately model ecological processes that depend on animal movement.     

Using the ECLPSS software environment to build a spatially explicit component-based model of ozone effects on forest ecosystems

We have developed a modeling framework to support grid-based simulation of ecosystems at multiple spatial scales, the Ecological Component Library for Parallel Spatial Simulation (ECLPSS). ECLPSS helps ecologists to build robust spatially explicit simulations of ecological processes by providing a growing library of reusable interchangeable components and automating many modeling tasks. To build a model, a user selects components from the library, and then writes new components as needed. Some of these components represent specific ecological processes, such as how environmental factors influence the growth of individual trees. Other components provide simulation support such as reading and writing files in various formats to allow inter-operability with other software. The framework manages components and variables, the order of operations, and spatial interactions. The framework provides only simulation support; it does not include ecological functions or assumptions. This separation allows biologists to build models without becoming computer scientists, while computer scientists can improve the framework without becoming ecologists. The framework is designed to operate on multiple platforms and be used across networks via a World Wide Web-based user interface. ECLPSS is designed for use with both single processor computers for small models, and multiple processors in order to simulate large regions with complex interactions among many individuals or ecological compartments. To test Version 1.0 of ECLPSS, we created a model to evaluate the effect of tropospheric ozone on forest ecosystem dynamics. This model is a reduced-form version of two existing models: , which represents an individual tree, and , which represents forest stand growth and succession. This model demonstrates key features of ECLPSS, such as the ability to examine the effects of cell size and model structure on model predictions.     

Selecting the best home range model: an information-theoretic approach

Choosing an appropriate home range model is important for describing space use by animals and understanding the ecological processes affecting animal movement. Traditional approaches for choosing among home range models have not resulted in general, consistent, and unambiguous criteria that can be applied to individual data sets. We present a new application of information-theoretic model selection that overcomes many of the limitations of traditional approaches, as follows. (1) It alleviates the need to know the true home range to assess home range models, thus allowing performance to be evaluated with data on individual animals. (2) The best model can be chosen from a set of candidate models with the proper balance between fit and complexity. (3) If candidate home range models are based on underlying ecological processes, researchers can use the selected model not only to describe the home range, but also to infer the importance of various ecological processes affecting animal movements within the home range.     

种群水平生态风险评价方法概述及其在环境管理中的应用

生态风险评价的目的是保护生态系统功能的完整性、稳定性和持久性,为环境风险管理提供理论依据。然而,目前常见的用于保护生物的化学污染物浓度阈值大多是以个体水平的毒性试验结果为基础,忽略了物种在时间和空间相互作用等因素,不能够完全保护生态环境安全和生态系统功能的延续性。本文从生态风险评价的概念、目的和意义引出种群水平生态风险评价在环境管理应用的重要性,综述了种群水平生态风险评价的科学问题(如密度依赖、遗传变异和空间结构等),归纳了种群水平风险评价主要模型方法及其应用(如Euler-Lotka方程、预测矩阵、个体模型、空间模型和动态能量预算模型等),列举了各国现有法律法规中关于种群水平生态风险评价的规定,以期为种群水平生态风险评价方法研究及在环境管理中的应用提供有益借鉴。     

Cross-validation of species distribution models: removing spatial sorting bias and calibration with a null model

Species distribution models are usually evaluated with cross-validation. In this procedure evaluation statistics are computed from model predictions for sites of presence and absence that were not used to train (fit) the model. Using data for 226 species, from six regions, and two species distribution modeling algorithms (Bioclim and MaxEnt), I show that this procedure is highly sensitive to "spatial sorting bias": the difference between the geographic distance from testing-presence to training-presence sites and the geographic distance from testing-absence (or testing-background) to training-presence sites. I propose the use of pairwise distance sampling to remove this bias, and the use of a null model that only considers the geographic distance to training sites to calibrate cross-validation results for remaining bias. Model evaluation results (AUC) were strongly inflated: the null model performed better than MaxEnt for 45% and better than Bioclim for 67% of the species. Spatial sorting bias and area under the receiver-operator curve (AUC) values increased when using partitioned presence data and random-absence data instead of independently obtained presence-absence testing data from systematic surveys. Pairwise distance sampling removed spatial sorting bias, yielding null models with an AUC close to 0.5, such that AUC was the same as null model calibrated AUC (cAUC). This adjustment strongly decreased AUC values and changed the ranking among species. Cross-validation results for different species are only comparable after removal of spatial sorting bias and/or calibration with an appropriate null model.     

The effect of outdoor air pollutants and greenness on allergic rhinitis incidence rates: a cross-sectional study in Seoul,Korea

Air pollution poses a serious threat to human health in Asia. This study analyzes the association of air pollutants and greenness with incidence rates of allergic rhinitis in Seoul at the administrative district level to gain insight into district-level urban policies to improve public health. A spatial regression model is constructed to investigate the correlation between allergic rhinitis incidence rates and five air pollutants measured at 128 air pollution monitoring stations around Seoul: sulfur dioxide (SO₂), particulate matter less than 10 μm (PM₁₀), ozone (O₃), nitrogen dioxide (NO₂), and carbon monoxide (CO). The allergic rhinitis incidence data are derived from the National Health Insurance Service’s database that includes the number of allergic rhinitis-related clinic visits by the patients over 20 years of age and living in Seoul. A kriging geostatistical interpolation was used to estimate average air pollution level of 423 administrative districts. To assess pollen concentrations that can affect allergic rhinitis, the average normalized difference vegetation index (NDVI) is measured based on the urban greenness. The model, controlling for built environment and socio-economic attributes, identifies the possibility of a weak association between allergic rhinitis incidence rates and carbon monoxide levels. The NDVI value is negatively correlated with allergic rhinitis incidence rates, implying a complicated aspect in relation to the effect of urban greenness.     

Comparing network analysis methodologies for consumer–resource relations at species and ecosystems scales

This research compares two existing methodologies, mixed trophic impact analysis and utility analysis, which use network analysis to evaluate the direct, pair-wise, and indirect, holistic, ecological relations between ecosystem compartments. The two approaches have many similarities, but differ in some key assumptions which affect both the final results and interpretations. Here, we briefly introduce both methodologies through a series of two simple examples; a 3-compartment competition model and a 3-compartment food chain model, and then apply the methodologies to a 15-compartment ecosystem model of the Chesapeake Bay. This example demonstrates how implementing the various conceptual and methodological assumptions lead to differing results. Notably, the overall number of positive relations is greatly affected by the treatment of the self-interactions and the handling of detritus compartments lead to a distinction between ecological or trophic relations. We recommend slight changes to both methodologies, not necessarily in order to bring them completely together, but because each has some points which are stronger and better defensible.     

Evidence of equal maternal investment in the sexes in the polygynous and sexually dimorphic grey seal (Halichoerus grypus)

In polygynous and sexually dimorphic mammals, parents may be expected to bias their investment towards sons because variation in reproductive success is usually higher among males than among females. Moreover, male reproductive success often depends on adult body size, which, in turn, may depend on the level of parental investment. We therefore predicted that in the grey seal (Halichoerus grypus), a polygynous and sexually dimorphic phocid seal, females should invest more in individual sons than in individual daughters. We found that male pups were born heavier than female pups, but that the growth rates and suckling behaviour were similar for the two sexes. The growth rates and the birth weights were not correlated for the pups of either sex. Mothers did not behave differentially towards offspring of the two sexes, except that mothers of male pups spent more time in visual contact with their pups. Male and female pups had similar activity levels and begged at similar rates. We argue that reports of equal expenditure on the two sexes can be accepted as evidence of equal investment, provided that three assumptions are fulfilled. First, parental care must be costly to the parent. Second, energy expenditure must be the most important component of parental investment. Third, there must be no negative correlation between maternal body condition and the ratio of sons to daughters produced. We argue that these assumptions are met in our study, and that our results provide evidence of equal maternal investment in the sexes in grey seals.