Statistics in disease ecology: introduction to a special issue

The three papers included in this special issue represent a set of presentations in an invited session on disease ecology at the 2005 Spring Meeting of the Eastern North American Region of the International Biometric Society. The papers each address statistical estimation and inference for particular components of different disease processes and, taken together, illustrate the breadth of statistical issues arising in the study of the ecology and public health impact of disease. As an introduction, we provide a very brief overview of the area of “disease ecology”, a variety of synonyms addressing different aspects of disease ecology, and present a schematic structure illustrating general components of the underlying disease process, data collection issues, and different disciplinary perspectives ranging from microbiology to public health surveillance.

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Alternatives to statistical hypothesis testing in ecology: a guide to self teaching.

Statistical methods emphasizing formal hypothesis testing have dominated the analyses used by ecologists to gain insight from data. Here, we review alternatives to hypothesis testing including techniques for parameter estimation and model selection using likelihood and Bayesian techniques. These methods emphasize evaluation of weight of evidence for multiple hypotheses, multimodel inference, and use of prior information in analysis. We provide a tutorial for maximum likelihood estimation of model parameters and model selection using information theoretics, including a brief treatment of procedures for model comparison, model averaging, and use of data from multiple sources. We discuss the advantages of likelihood estimation, Bayesian analysis, and meta-analysis as ways to accumulate understanding across multiple studies. These statistical methods hold promise for new insight in ecology by encouraging thoughtful model building as part of inquiry, providing a unified framework for the empirical analysis of theoretical models, and by facilitating the formal accumulation of evidence bearing on fundamental questions.     

Time: a hidden constraint on the behavioural ecology of baboons

Summary Data from wild populations of baboons are used to derive functional equations relating time budget components, day journey length and group size to environmental variables. This set of equations predicts both time budgets in an independent sample of populations and the geographical distribution of baboon populations extremely well. I then use these equations to examine the maximum ecologically tolerable group size for baboons occupying different habitats. Groups which exceed this value exhibit signs of ecological stress: they spend less time resting and in social activity than would be expected for their size and environment, they are more likely to fragment during foraging and they travel faster. Populations living in poor quality (low rainfall) habitats are more likely to live in groups that are stressed in this way.     

Model selection and model averaging in behavioural ecology: the utility of the IT-AIC framework

Behavioural ecologists often study complex systems in which multiple hypotheses could be proposed to explain observed phenomena. For some systems, simple controlled experiments can be employed to reveal part of the complexity; often, however, observational studies that incorporate a multitude of causal factors may be the only (or preferred) avenue of study. We assess the value of recently advocated approaches to inference in both contexts. Specifically, we examine the use of information theoretic (IT) model selection using Akaike’s information criterion (AIC). We find that, for simple analyses, the advantages of switching to an IT-AIC approach are likely to be slight, especially given recent emphasis on biological rather than statistical significance. By contrast, the model selection approach embodied by IT approaches offers significant advantages when applied to problems of more complex causality. Model averaging is an intuitively appealing extension to model selection. However, we were unable to demonstrate consistent improvements in prediction accuracy when using model averaging with IT-AIC; our equivocal results suggest that more research is needed on its utility. We illustrate our arguments with worked examples from behavioural experiments.     

Model averaging,missing data and multiple imputation: a case study for behavioural ecology

Model averaging, specifically information theoretic approaches based on Akaike’s information criterion (IT-AIC approaches), has had a major influence on statistical practices in the field of ecology and evolution. However, a neglected issue is that in common with most other model fitting approaches, IT-AIC methods are sensitive to the presence of missing observations. The commonest way of handling missing data is the complete-case analysis (the complete deletion from the dataset of cases containing any missing values). It is well-known that this results in reduced estimation precision (or reduced statistical power), biased parameter estimates; however, the implications for model selection have not been explored. Here we employ an example from behavioural ecology to illustrate how missing data can affect the conclusions drawn from model selection or based on hypothesis testing. We show how missing observations can be recovered to give accurate estimates for IT-related indices (e.g. AIC and Akaike weight) as well as parameters (and their standard errors) by utilizing ‘multiple imputation’. We use this paper to illustrate key concepts from missing data theory and as a basis for discussing available methods for handling missing data. The example is intended to serve as a practically oriented case study for behavioural ecologists deciding on how to handle missing data in their own datasets and also as a first attempt to consider the problems of conducting model selection and averaging in the presence of missing observations.     

Animal social networks: an introduction

Network analysis has a long history in the mathematical and social sciences and the aim of this introduction is to provide a brief overview of the potential that it holds for the study of animal behaviour. One of the most attractive features of the network paradigm is that it provides a single conceptual framework with which we can study the social organisation of animals at all levels (individual, dyad, group, population) and for all types of interaction (aggressive, cooperative, sexual etc.). Graphical tools allow a visual inspection of networks which often helps inspire ideas for testable hypotheses. Network analysis itself provides a multitude of novel statistical tools that can be used to characterise social patterns in animal populations. Among the important insights that networks have facilitated is that indirect social connections matter. Interactions between individuals generate a social environment at the population level which in turn selects for behavioural strategies at the individual level. A social network is often a perfect means by which to represent heterogeneous relationships in a population. Probing the biological drivers for these heterogeneities, often as a function of time, forms the basis of many of the current uses of network analysis in the behavioural sciences. This special issue on social networks brings together a diverse group of practitioners whose study systems range from social insects over reptiles to birds, cetaceans, ungulates and primates in order to illustrate the wide-ranging applications of network analysis. This contribution is part of the special issue “Social Networks: new perspectives” (Guest Editors: J. Krause, D. Lusseau and R. James).     

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.     

Fooled by local robustness: an applied ecology perspective

In this short discussion, we point out that it is apparently as easy to be fooled by robustness as it is to be fooled by randomness. Our objective is to bring to the attention of applied ecologists that radius-of-stability robustness models are models of local robustness. As such, these models are utterly unsuitable for the treatment/management of a severe uncertainty characterized by a vast uncertainty space and a likelihood-free quantification of the uncertainty. This observation is particularly pertinent to applications of info-gap decision theory in ecology, conservation biology, and environmental management, where the objective is to identify decisions that are robust against a severe uncertainty of this type.     

Control system approaches to ecological systems analysis: Invariants and frequency response

The steady-state assumption is a mainstay for the analysis of ecological systems with more than three or four states. However, it is well accepted in ecology that inputs to large systems come in pulses assumed to have a reasonably constant magnitude and frequency. Steady pulse inputs and the use of electro-chemical–mechanical control systems methodology enables limited short term dynamic responses of ecological systems of a scale often occurring in systems of potential engineering importance to be analyzed. This paper explores and presents a survey of multi-input–multi-output (MIMO) control systems analysis of ecosystem network models to better understand pulse frequency issues and further develop experimentally verifiable approaches to testing the MIMO concept. The analysis process is demonstrated using two network model exemplars. Two aspects of MIMO analyses appear relevant to understanding ecological systems: (1) Eigenvalue invariant analyses and singular value decomposition (SVD) analyses enable assessment of stability and relative strength of states. Eigenvalues reflect time constants and provide a check on experimentally determined system matrices. (2) Analysis of SVD versus frequency for each output indicates maximum pulse frequencies that allow system components to benefit from pulsing. As a group, MIMO analyses complement other analytical methods and provide a theoretical systems focus convenient for analyzing ecosystems from an engineering perspective.     

From individuals to ecosystem function: toward an integration of evolutionary and ecosystem ecology

An important goal in ecology is developing general theory on how the species composition of ecosystems is related to ecosystem properties and functions. Progress on this front is limited partly because of the need to identify mechanisms controlling functions that are common to a wide range of ecosystem types. We propose that one general mechanism, rooted in the evolutionary ecology of all species, is adaptive foraging behavior in response to predation risk. To support our claim, we present two kinds of empirical evidence from plant-based and detritus-based food chains of terrestrial and aquatic ecosystems. The first kind comes from experiments that explicitly trace how adaptive foraging influences ecosystem properties and functions. The second kind comes from a synthesis of studies that individually examine complementary components of particular ecosystems that together provide an integrated perspective on the link between adaptive foraging and ecosystem function. We show that the indirect effects of predators on plant diversity, plant productivity, nutrient cycling, trophic transfer efficiencies, and energy flux caused by consumer foraging shifts in response to risk are qualitatively different from effects caused by reductions in prey density due to direct predation. We argue that a perspective of ecosystem function that considers effects of consumer behavior in response to predation risk will broaden our capacity to explain the range of outcomes and contingencies in trophic control of ecosystems. This perspective also provides an operational way to integrate evolutionary and ecosystem ecology, which is an important challenge in ecology.     

The arcsine is asinine: the analysis of proportions in ecology

The arcsine square root transformation has long been standard procedure when analyzing proportional data in ecology, with applications in data sets containing binomial and non-binomial response variables. Here, we argue that the arcsine transform should not be used in either circumstance. For binomial data, logistic regression has greater interpretability and higher power than analyses of transformed data. However, it is important to check the data for additional unexplained variation, i.e., overdispersion, and to account for it via the inclusion of random effects in the model if found. For non-binomial data, the arcsine transform is undesirable on the grounds of interpretability, and because it can produce nonsensical predictions. The logit transformation is proposed as an alternative approach to address these issues. Examples are presented in both cases to illustrate these advantages, comparing various methods of analyzing proportions including untransformed, arcsine- and logit-transformed linear models and logistic regression (with or without random effects). Simulations demonstrate that logistic regression usually provides a gain in power over other methods.     

Managing organizations for sustainable development in emerging countries: an introduction

This introduction article is for the special issue ‘Managing organizations for sustainable development in emerging countries: natural resources, biodiversity, and climate change’ in the International Journal of Sustainable Development & World Ecology and presents an introduction to the topics and summarizes accepted contributions in the special issue. The accepted works may contribute with organizational management in the search for more sustainable organizations. The works focus on the challenges of managing organizations in a context of degradation of natural resources, loss of biodiversity, and climate change. Accepted papers discuss these issues, based on the reality of emerging economies (e.g. Brazil, India, and China).     

Individual deviation from behavioural correlations: a simple approach to study the evolution of behavioural syndromes

The study of correlations between different behaviours in a population—referred to as behavioural syndromes—has begun to flourish during recent years. However, the evolutionary mechanisms that cause behavioural traits to vary non-independently from each other are still poorly understood. Here, we bring behavioural syndromes into a new perspective, in which the phenomenon is regarded at the individual level and on a continuous scale instead of as a population-level presence/absence trait. As the correlation between behaviours is never perfect (i.e. r < 1), individuals are likely to vary in how consistently they behave. Therefore, we can predict that if behavioural syndromes at the population level are results of natural selection, the consistency in a suite of behaviours—and not the behavioural configuration per se—should be heritable and involve fitness advantages at the individual level. We define a variable that describes the individual deviation from the hypothetical perfect correlation predicted by the syndrome. The use of such a variable depicting the consistency of behaviours of individuals allows us to make solid evolutionary inferences about correlated behaviours from patterns of individual instead of population variation. We suggest that, by adopting the concept of syndrome deviation, understanding the evolution of behavioural syndromes and, in particular, testing competing evolutionary hypotheses about the origin of behavioural syndromes becomes possible in a more rigorous manner than before.     

The Truth About Science: A middle school curriculum teaching the scientific method and data analysis in an ecology context

The Truth About Science is a 40-lesson middle school curriculum module that teaches the process of scientific research, integrating mathematics and science concepts and skills. The goal of the curriculum is to teach students to think systematically and statistically about science inquiry. Students participate in each step of the scientific inquiry process, from asking testable research questions, designing unbiased experiments, and collecting their own data, to analyzing these data via graphical representations and statistical summaries, and communicating their research results as both poster and oral presentations. While the necessary statistical skills depend on difficult and abstract mathematical concepts, middle school students have been successful in applying them to their own research projects. The curriculum meets local and national standards in science and mathematics education and fills a gap in available educational materials. It has been piloted and revised through multiple iterations and published by the National Science Teachers Association Press. Feedback from teachers and students has been extremely positive.     

Efficient algorithms for statistical estimation in compartmental analysis: Modelling 60Co kinetics in an aquatic microcosm

A mathematical model of radionuclide kinetics in a laboratory microcosm was built by systems identification techniques. Insight into the functioning of the system was obtained from analysis of the model. Methods employed have allowed movements of radioisotopes not directly observable in the experimental system to be distinguished. Results are generalized to whole ecosystems.     

NPP列入生态统计指标体系的潜力分析——以北京地区NPP测算与空间分析为例

通过梳理目前自然资源和生态环境统计指标(简称生态统计指标)定义和使用情况,发现同内统计指标体系的内容框架有待扩展,指标体系哌待标准化.NPP是衡量生态系统对环境气候响应的重要研究指标,可以考虑作为国内生态统计指标体系的有益补充,因而在列入指标体系之前需要在数据来源和模型方面进行统一和验证.以目前最常使用的NPP光能利用率模型进行适用于研究地区的参数改进,利用RS、GIS技术手段,综合MODIS遥感数据、气象数据(每日降水量、每日气温、日照时间)、一些辅助矢量数据等多源信息,计算出北京地区2008年NPP的月度值和全年累计值,目标是为其进入生态指标体系建立一个系统的数据处理规范,以保证NPP统计的一致性、可行性和有效性.结论:从区位统计结果来看,城市核心区和城市功能拓展区NPP的季节性特征变化不明显,而生态涵养发展区的NPP随着时间变化比较大;从地貌统计结果来看,远山区的NPP值大于平原区,也大于半山区.以上结果与温度、降水的季节性变化和耕地的收种时间具有一致性,证明该处理流程可以作为北京地区NPP量化及空间评估的有效手段.表明,NPP的数据来源稳定,测量模型具有可行性和有效性,可以考虑将该指标纳入自然资源和生态环境统计体系.     

Quantitative approaches to the analysis of stable isotope food web data

Ecologists use stable isotopes (delta13C, delta15N) to better understand food webs and explore trophic interactions in ecosystems. Traditionally, delta13C vs. delta15N bi-plots have been used to describe food web structure for a single time period or ecosystem. Comparisons of food webs across time and space are increasing, but development of statistical approaches for testing hypotheses regarding food web change has lagged behind. Here we present statistical methodologies for quantitatively comparing stable isotope food web data. We demonstrate the utility of circular statistics and hypothesis tests for quantifying directional food web differences using two case studies: an arthropod salt marsh community across a habitat gradient and a freshwater fish community from Lake Tahoe, USA, over a 120-year time period. We calculated magnitude and mean angle of change (theta) for each species in food web space using mean delta13C and delta15N of each species as the x, y coordinates. In the coastal salt marsh, arthropod consumers exhibited a significant shift toward dependence on Spartina, progressing from a habitat invaded by Phragmites to a restored Spartina habitat. In Lake Tahoe, we found that all species from the freshwater fish community shifted in the same direction in food web space toward more pelagic-based production with the introduction of nonnative Mysis relicta and onset of cultural eutrophication. Using circular statistics to quantitatively analyze stable isotope food web data, we were able to gain significant insight into patterns and changes in food web structure that were not evident from qualitative comparisons. As more ecologists incorporate a food web perspective into ecosystem analysis, these statistical tools can provide a basis for quantifying directional food web differences from standard isotope data.