Bayesian non-parametric detection heterogeneity in ecological models

Environmental and Ecological Statistics - Detection heterogeneity is inherent to ecological data, arising from factors such as varied terrain or weather conditions, inconsistent sampling effort, or...     

Integrated ecological models: simulation of socio-cultural constraints on ecological dynamics

We suggest that general systems theory provides a common philosophical basis for dialog between ecological and social scientists interested in studying the reciprocal interactions of humans and their environment. We (1) provide a synopsis of the ‘systems approach' as viewed from the biological and social sciences, respectively; (2) develop a conceptual framework for the explicit linking of ecological and social variables, and (3) draw upon game theoretic results of the Prisoner's Dilemma to represent human decision-making quantitatively in a model that simulates the tragedy of the commons. The model consists of 5 submodels that represent the ‘observers world' and each of 4 ‘participant's worlds.' The observer's-world represents the decision processes, either Optimize or Tit-for-Tat, by which each of 2 users decides to add or remove animals. The 4 perceived worlds represent hypothetical situations in which (1) persons A and B both add an animal; (2) A adds and B does not; (3) B adds and A does not, and (4) neither A nor B add an animal. Simulation results indicate that net worth of the community and of each person individually under Tit-for-Tat is more than double the net worth attained under Optimize. Replacement of the static payoff matrix assumed in game theory with a dynamic quantitative model illustrates how ‘norm-based' approaches to ecosystem management can outperform optimizing approaches based on predicted outcomes. Although ‘soft systems' techniques may better help decision-makers reach norm-based agreements on ecosystem management, quantitative models have more explanatory value, and if developed sufficiently such models could incorporate complex social dimensions that would enhance further their explanatory value.     

Scaling-up spatially-explicit ecological models using graphics processors

How the properties of ecosystems relate to spatial scale is a prominent topic in current ecosystem research. Despite this, spatially explicit models typically include only a limited range of spatial scales, mostly because of computing limitations. Here, we describe the use of graphics processors to efficiently solve spatially explicit ecological models at large spatial scale using the CUDA language extension. We explain this technique by implementing three classical models of spatial self-organization in ecology: a spiral-wave forming predator-prey model, a model of pattern formation in arid vegetation, and a model of disturbance in mussel beds on rocky shores. Using these models, we show that the solutions of models on large spatial grids can be obtained on graphics processors with up to two orders of magnitude reduction in simulation time relative to normal pc processors. This allows for efficient simulation of very large spatial grids, which is crucial for, for instance, the study of the effect of spatial heterogeneity on the formation of self-organized spatial patterns, thereby facilitating the comparison between theoretical results and empirical data. Finally, we show that large-scale spatial simulations are preferable over repetitions at smaller spatial scales in identifying the presence of scaling relations in spatially self-organized ecosystems. Hence, the study of scaling laws in ecology may benefit significantly from implementation of ecological models on graphics processors.     

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.

Definition and calculation of uncertainty in ecological process models

We present a method of multi-criteria assessment for the analysis of process model uncertainty that combines analysis of model structure, parameters and data requirements. There are three components in calculation and definition of uncertainty.

(1)

Assessment criteria: Uncertainty in a process model is reduced as the model can simultaneously simulate an increased number of assessment criteria selected to test specific aspects of the theory being investigated, and within acceptable limits set for those criteria. This reduces incomplete specification of the model—the characteristic that a model may explain some, but not all, of the observed features of a phenomenon. The calculation required is computation of the Pareto set which provides the list of simultaneously achieved criteria within specified ranges.     

Uncertainty and measurement error in welfare models for risk changes

Most welfare models of environmental or mortality risk reductions assume that risks are exogenously determined and known with certainty. However, a growing body of research suggests that uncertainty about risks can affect choices over risky prospects. I present a decision-weighted random-utility model that decomposes welfare losses into those attributable to an increase in the deterministic component of risk and those attributable to uncertainty about risk. I apply the model to an illustrative dataset of subjects' perceived mortality risk and willingness to accept the risk of nuclear-waste transport. I estimate the model using Lewbel's (2000) strictly exogenous regressor approach to account for endogeneity bias and measurement error. Subjects display aversion to both risk and uncertainty about the risk of a transport accident, so that increases in either leads to social-welfare losses. Roughly 12% of the external cost of nuclear-waste transport is attributable to the public's uncertainty about transport risk.     

Testing ecological models: the meaning of validation

The ecological literature reveals considerable confusion about the meaning of validation in the context of simulation models. The confusion arises as much from semantic and philosophical considerations as from the selection of validation procedures. Validation is not a procedure for testing scientific theory or for certifying the ‘truth’ of current scientific understanding, nor is it a required activity of every modelling project. Validation means that a model is acceptable for its intended use because it meets specified performance requirements.Before validation is undertaken, (1) the purpose of the model, (2) the performance criteria, and (3) the model context must be specified. The validation process can be decomposed into several components: (1) operation, (2) theory, and (3) data. Important concepts needed to understand the model evaluation process are verification, calibration, validation, credibility, and qualification. These terms are defined in a limited technical sense applicable to the evaluation of simulation models, and not as general philosophical concepts. Different tests and standards are applied to the operational, theoretical, and data components. The operational and data components can be validated; the theoretical component cannot.The most common problem with ecological and environmental models is failure to state what the validation criteria are. Criteria must be explicitly stated because there are no universal standards for selecting what test procedures or criteria to use for validation. A test based on comparison of simulated versus observed data is generally included whenever possible. Because the objective and subjective components of validation are not mutually exclusive, disagreements over the meaning of validation can only be resolved by establishing a convention.     

Inference and model determination for temperature-driven non-linear ecological models

Environmental and Ecological Statistics - This paper is concerned with a contemporary Bayesian approach to the effect of temperature on developmental rates. We develop statistical methods using...     

Validation of ecological state space models using the Laplace approximation

Many statistical models in ecology follow the state space paradigm. For such models, the important step of model validation rarely receives as much attention as estimation or hypothesis testing, perhaps due to lack of available algorithms and software. Model validation is often based on a naive adaptation of Pearson residuals, i.e. the difference between observations and posterior means, even if this approach is flawed. Here, we consider validation of state space models through one-step prediction errors, and discuss principles and practicalities arising when the model has been fitted with a tool for estimation in general mixed effects models. Implementing one-step predictions in the R package Template Model Builder, we demonstrate that it is possible to perform model validation with little effort, even if the ecological model is multivariate, has non-linear dynamics, and whether observations are continuous or discrete. With both simulated data, and a real data set related to geolocation of seals, we demonstrate both the potential and the limitations of the techniques. Our results fill a need for convenient methods for validating a state space model, or alternatively, rejecting it while indicating useful directions in which the model could be improved.     

基于生态系统管理的湿地概念生态模型研究

湿地是地球上的一种重要生态系统,基于生态系统管理理念,进行湿地保护与管理,既是湿地科学发展的必然结果.也是当前湿地保护与管理的客观需求.湿地生态模型是以湿地生态系统作为研究对象的模型,是对湿地生态系统组成、结构、过程和功能进行简化、类比或抽象,是用来反映湿地生态系统各种过程和关系的定性或定量化工具.湿地概念生态模型是各类湿地生态模型中最基本的类型,是对湿地生态系统组成及其相互关系的一种简约的定性表达,特别是指人类活动影响下湿地生态系统因子变化及其相互关系的概念性表达.湿地概念生态模型构建的主要目的是旨在识别人类活动对湿地生态系统的驱动与胁迫,这些驱动与胁迫产生的一系列生态效应,以及湿地生态系统对此所表现出来的特征.湿地生态系统是一个多层次、多因子组成的,结构复杂、功能多样、具有多向反馈和调节机制的复杂大系统或巨系统.影响系统状态或驱动系统变化的因子众多,既有来自系统内部的、也有来自系统外部的,它们对系统造成的影响往往具有联动关系和因果效应.湿地概念生态模型就是在生态系统管理理论指导下,将这些系统因子及其关系抽象并提取出来,以"驱动-胁迫-效应-表征"为主线,判断系统变化与演化背后存在的因果关系,构建能够反映系统变化与演化特征和规律的结构性关系网络模型.湿地概念生态模型研究的意义在于在科学与决策之间架起一座桥梁,为实施湿地生态保护与管理提供指导,同时为建立湿地数量化模型奠定基础.     

Conditioning uncertainty in ecological models: Assessing the impact of fire management strategies

A simple simulation model has been used to investigate whether large fires in Mediterranean regions are a result of extreme weather conditions or the cumulative effect of a policy of fire suppression over decades. The model reproduced the fire regime characteristics for a wide variety of regions of Mediterranean climate in California, France and Spain. The Generalised Likelihood Uncertainty Estimation (GLUE) methodology was used to assess the possibility of multiple model parameter sets being consistent with the available calibration data. The resulting set of behavioural models was used to assess uncertainty in the predictions. The results suggested that (1) for a given region, the total area burned is much the same whether suppression or prescribed fire policies are used or not; however fire suppression enhances fire intensity and prescribed burning reduces it; (2) the proportion of large fires can be reduced, but not eliminated, using prescribed fires, especially in areas which have the highest proportion of large fires.     

Using global sensitivity analysis of demographic models for ecological impact assessment

Population viability analysis (PVA) is widely used to assess population‐level impacts of environmental changes on species. When combined with sensitivity analysis, PVA yields insights into the effects of parameter and model structure uncertainty. This helps researchers prioritize efforts for further data collection so that model improvements are efficient and helps managers prioritize conservation and management actions. Usually, sensitivity is analyzed by varying one input parameter at a time and observing the influence that variation has over model outcomes. This approach does not account for interactions among parameters. Global sensitivity analysis (GSA) overcomes this limitation by varying several model inputs simultaneously. Then, regression techniques allow measuring the importance of input‐parameter uncertainties. In many conservation applications, the goal of demographic modeling is to assess how different scenarios of impact or management cause changes in a population. This is challenging because the uncertainty of input‐parameter values can be confounded with the effect of impacts and management actions. We developed a GSA method that separates model outcome uncertainty resulting from parameter uncertainty from that resulting from projected ecological impacts or simulated management actions, effectively separating the 2 main questions that sensitivity analysis asks. We applied this method to assess the effects of predicted sea‐level rise on Snowy Plover (Charadrius nivosus). A relatively small number of replicate models (approximately 100) resulted in consistent measures of variable importance when not trying to separate the effects of ecological impacts from parameter uncertainty. However, many more replicate models (approximately 500) were required to separate these effects. These differences are important to consider when using demographic models to estimate ecological impacts of management actions.     

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.     

华南退化生态系统三种典型生态恢复模式的小气候效应研究

为了评价南亚热带典型退化生态系统典型生态恢复模式的小气候调节效应,从而为退化生态系统生态恢复方式和造林树种的选择提供参照,作者在广东鹤山森林生态系统国家野外科学观测研究站的3种典型生态恢复模式样地,自然恢复草坡、马尾松林（Pinus massoniana）、马占相思林（Acacia mangium）中安装了HOBO小气候仪,对光辐射、风速风向、降水、土壤含水量、地温、气温等小气候指标进行为期1年的自动观测,并进行了对比分析,结果表明,（1）华南退化生态系统3种典型生态恢复模式具有不同的小气候效应,在林间温度调节方面,人工林和草坡的平均林间温度相差不大,但草坡的最低、最高温度均比人工林低和高。人工林的林间温度变化较草坡小,具有更好的保温调节作用。对比2种人工林,不管是平均温度还是最高温度马占相思林都略大于针叶林,而二者最低温度相差不明显。针叶林的保温调节作用略优于阔叶的马占相思林;（2）在土壤温度方面,地表温度全年基本都表现为草坡〉马占相思林〉针叶林,草坡的地表温度的波动远大于2种人工林;全年20 cm土壤温度3─12月都表现为草坡〉马占相思林〉针叶林,1─2月相反,草坡20 cm土层的土壤温度波动相对较大,人工林的波动很小。（3）3种恢复模式中,自然恢复草坡的辐射强度明显高于2种人工林,年辐射总量分别马占相思林和针叶林的1.9和5.8倍,马占相思林的年辐射量为针叶林的3倍。人工林,特别是乡土的针叶林能给林下生物构建更为稳定、适中的辐射环境。（4）人工林的平均林间风速、最大阵风风速均少于草坡,针叶林的风速小于阔叶林,针叶林降低风速的效果好于相思林和草坡。（5）人工林的林间相对湿度均高于草坡,针叶林的林间空气湿度略大于相思林,针叶林的保湿效果更好。在退化生态系统恢复过程中?     

Analysis and prediction of ecological and ecosystem dynamics with response structure models

A method of directly using data concerning species' responses to various combinations of levels of environmental factors is outlined. Examples of its utilization to analyze (and predict) the dynamics of the ecological processes of population growth, interspecific competition, and predation are given for simple systems; a simulation is presented wherein all of these processes interact within a simple ecosystem. A technique of summarizing the pattern and detail of variation of levels of combination of important environmental factors is also introduced. Together these methods permit application of real world information about the components of the biological community and the environment toward the modeling of ecosystems and the making of predictions concerning them to whatever degree of accuracy which may be useful.There are several major advantages of this approach: (1) It makes maximum use of real world data; the limits of its precision are determined only by the adequacy of the data available (hypothetical values also may be used where real data are unavailable and/or where such hypothetical values may be useful in model and theory development). (2) It is powerful (and applicable to the dynamics of diverse kinds of systems), mathematically very simple, and has important advantages in that non-linearities, thresholds, etc. are automatically and accurately taken into account. (3) It can be expressed numerically or graphically, and therefore is especially helpful in permitting visualization of ecological processes and the results of their action.     

State-of-the-art of ecological modelling with emphasis on development of structural dynamic models

The paper deals with two major problems in ecological modelling today, namely how to get reliable parameters? and how to build ecosystem properties into our models? The use of new mathematical tools to answer these questions is mentioned briefly, but the main focus of the paper is on development of structural dynamic models which are models using goal functions to reflect a current change of the properties of the biological components in the models. These changes of the properties are due to the enormous adaptability of the biological components to the prevailing conditions. All species in an ecosystem attempt to obtain most biomass, i.e. to move as far away as possible from thermodynamic equilibrium which can be measured by the thermodynamic concept exergy. Consequently, exergy has been proposed as a goal function in ecological models with dynamic structure, meaning currently changed properties of the biological components and in model language currently changed parameters. An equation to compute an exergy index of a model is presented. The theoretical considerations leading to this equation are not presented here but references to literature where the basis theory can be found are given. Two case studies of structural dynamic modelling are presented: a shallow lake where the structural dynamic changes have been determined before the model was developed, and the application of biomanipulation in lake management, where the structural dynamic changes are generally known. Moreover. it is also discussed how the same idea of using exergy as a goal function in ecological modelling may be applied to facilitate the estimation of parameters.     

Evaluating the ecological benefits of wildfire by integrating fire and ecosystem simulation models

Fire managers are now realizing that wildfires can be beneficial because they can reduce hazardous fuels and restore fire-dominated ecosystems. A software tool that assesses potential beneficial and detrimental ecological effects from wildfire would be helpful to fire management. This paper presents a simulation platform called FLEAT (Fire and Landscape Ecology Assessment Tool) that integrates several existing landscape- and stand-level simulation models to compute an ecologically based measure that describes if a wildfire is moving the burning landscape towards or away from the historical range and variation of vegetation composition. FLEAT uses a fire effects model to simulate fire severity, which is then used to predict vegetation development for 1, 10, and 100 years into the future using a landscape simulation model. The landscape is then simulated for 5000 years using parameters derived from historical data to create an historical time series that is compared to the predicted landscape composition at year 1, 10, and 100 to compute a metric that describes their similarity to the simulated historical conditions. This tool is designed to be used in operational wildfire management using the LANDFIRE spatial database so that fire managers can decide how aggressively to suppress wildfires. Validation of fire severity predictions using field data from six wildfires revealed that while accuracy is moderate (30-60%), it is mostly dictated by the quality of GIS layers input to FLEAT. Predicted 1-year landscape compositions were only 8% accurate but this was because the LANDFIRE mapped pre-fire composition accuracy was low (21%). This platform can be integrated into current readily available software products to produce an operational tool for balancing benefits of wildfire with potential dangers.     

Sensitivity of ecological models to their climate drivers: statistical ensembles for forcing.

Global and regional numerical models for terrestrial ecosystem dynamics require fine spatial resolution and temporally complete historical climate fields as input variables. However, because climate observations are unevenly spaced and have incomplete records, such fields need to be estimated. In addition, uncertainty in these fields associated with their estimation are rarely assessed. Ecological models are usually driven with a geostatistical model's mean estimate (kriging) of these fields without accounting for this uncertainty, much less evaluating such errors in terms of their propagation in ecological simulations. We introduce a Bayesian statistical framework to model climate observations to create spatially uniform and temporally complete fields, taking into account correlation in time and space, spatial heterogeneity, lack of normality, and uncertainty about all these factors. A key benefit of the Bayesian model is that it generates uncertainty measures for the generated fields. To demonstrate this method, we reconstruct historical monthly precipitation fields (a driver for ecological models) on a fine resolution grid for a climatically heterogeneous region in the western United States. The main goal of this work is to evaluate the sensitivity of ecological models to the uncertainty associated with prediction of their climate drivers. To assess their numerical sensitivity to predicted input variables, we generate a set of ecological model simulations run using an ensemble of different versions of the reconstructed fields. We construct such an ensemble by sampling from the posterior predictive distribution of the climate field. We demonstrate that the estimated prediction error of the climate field can be very high. We evaluate the importance of such errors in ecological model experiments using an ensemble of historical precipitation time series in simulations of grassland biogeochemical dynamics with an ecological numerical model, Century. We show how uncertainty in predicted precipitation fields is propagated into ecological model results and that this propagation had different modes. Depending on output variable, the response of model dynamics to uncertainty in inputs ranged from uncertainty in outputs that matched that of inputs to those that were muted or that were biased, as well as uncertainty that was persistent in time after input errors dropped.     

RIVPACS models for predicting the expected macroinvertebrate fauna and assessing the ecological quality of rivers

The European Union Water Framework Directive recognises the need for and value of biological monitoring. This paper reviews the modelling approach known as River Invertebrate Prediction and Classification System (RIVPACS for assessing the ecological quality of river sites using macroinvertebrate sampling. The RIVPACS philosophy is to develop statistical relationships between the fauna and the environmental characteristics of a large set of high quality reference sites which can be used to predict the macroinvertebrate fauna to be expected at any site in the absence of pollution or other environmental stress. The observed fauna at new test sites can then be compared with their site-specific expected fauna to derive indices of ecological quality. All methodological decisions in any such model development have implications for the reliability, precision and robustness of any resulting indices for assessing the ecological quality and ecological grade (‘status’) of individual river stretches. The choice of reference sites and environmental predictor variables, the site classification and discrimination methods, the estimation of the expected fauna, and indices for comparing the agreement, or lack of it, between the observed and expected fauna, are all discussed. The indices are assessed on the reference sites and on a separate test set of 340 sites, which are subject to a wide range of types and degrees of impairment.     

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.