Information-theoretic approaches to statistical analysis in behavioural ecology: an introduction

Scientific thinking may require the consideration of multiple hypotheses, which often call for complex statistical models at the level of data analysis. The aim of this introduction is to provide a brief overview on how competing hypotheses are evaluated statistically in behavioural ecological studies and to offer potentially fruitful avenues for future methodological developments. Complex models have traditionally been treated by model selection approaches using threshold-based removal of terms, i.e. stepwise selection. A recently introduced method for model selection applies an information-theoretic (IT) approach, which simultaneously evaluates hypotheses by balancing between model complexity and goodness of fit. The IT method has been increasingly propagated in the field of ecology, while a literature survey shows that its spread in behavioural ecology has been much slower, and model simplification using stepwise selection is still more widespread than IT-based model selection. Why has the use of IT methods in behavioural ecology lagged behind other disciplines? This special issue examines the suitability of the IT method for analysing data with multiple predictors, which researchers encounter in our field. The volume brings together different viewpoints to aid behavioural ecologists in understanding the method, with the hope of enhancing the statistical integration of our discipline.     

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.     

城市化与生态环境响应研究综述

城市化是学者们一直比较关注的重点问题,他们从不同视角对城市化及其过程进行了大量而富有创新的研究,并取得了丰硕的成果。伴随着城市化进程的加快,人们对生态环境问题的关注,城市化与生态环境的响应关系是城市地理新的关注点。文章分别就国内外学者对城市化、城市生态环境、城市化与生态环境响应的研究进行了综述,认为国内外学者对城市化、城市生态环境的研究起步早,成果多,近年来研究范围日益拓展,研究程度日益加深,并加强了新技术新方法的应用。国内学者对城市化的研究集中于城市化道路选择问题的探讨、城市化水平测度以及城市化的动力机制三个方面。对城市生态环境的研究多集中于社会—经济—自然复合生态系统及生态城市的研究。对于城市化与生态环境响应关系的研究则多见于生态学家、经济学家及地理学家的成果中,主要集中在单方面的城市化对生态环境的影响研究,而对于生态环境是怎样反过来影响城市化进程的研究则比较少见。另外,学者们的研究以微观单个影响因子的研究居多,从宏观综合角度出发进行的研究较少。这将是今后研究的一个重点问题。     

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.     

Round your numbers in rank tests: exact and asymptotic inference and ties

Non-parametric statistical tests are commonly used in the behavioral sciences. Researchers need to be aware that non-parameteric methods involving ranks can perform unreliably as a result of very small amounts of noise added in the storage and manipulation of values by computers, causing spurious reduction in the number of ties. In order to avoid this problem, researchers should round values to an appropriate number of decimal places prior to the ranking procedure to ensure that data points whose values cannot be separated according to the precision of their measurement are recorded as having identical rank. We also recommend exact rather than asymptotic evaluation of p values in non-parametric statistical tests.     

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.     

Imperfectly optimal animals

Summary We consider models of behavior that apply to two different problems: when a predator should leave a foraging site and how a female should choose the best available male. In each case we derive rules for an optimal solution to the problem. We also derive models based on very simple, plausible rules of behavior that we suspect animals may actually use. Although the expected payoffs from optimality models always exceed the expected payoffs from our simpler behavioral models, under certain conditions the difference is not large. When good foraging sites last but a short time and when females' mobility in their habitat is limited, the results of simple models and optimal models are very close indeed.Because of the difficulty of distinguishing between the results of each type of model and because natural selection will presumably provide a best mix of solutions to a range of problems rather than a best solution to any one problem, we suggest that behavioral ecologists expend more effort on simple, plausible models of animal behavior. Such models provide ready-made testable hypotheses about the animal's approximation to optimality and about the actual mechanisms of behavior.     

Prey risk allocation in a grazing ecosystem.

Understanding the behaviorally mediated indirect effects of predators in ecosystems requires knowledge of predator-prey behavioral interactions. In predator-ungulate-plant systems, empirical research quantifying how predators affect ungulate group sizes and distribution, in the context of other influential variables, is particularly needed. The risk allocation hypothesis proposes that prey behavioral responses to predation risk depend on background frequencies of exposure to risk, and it can be used to make predictions about predator-ungulate-plant interactions. We determined non-predation variables that affect elk (Cervus elaphus) group sizes and distribution on a winter range in the Greater Yellowstone Ecosystem (GYE) using logistic and log-linear regression on surveys of 513 1-km2 areas conducted over two years. Employing model selection techniques, we evaluated risk allocation and other a priori hypotheses of elk group size and distributional responses to wolf (Canis lupus) predation risk while accounting for influential non-wolf-predation variables. We found little evidence that wolves affect elk group sizes, which were strongly influenced by habitat type and hunting by humans. Following predictions from the risk allocation hypothesis, wolves likely created a more dynamic elk distribution in areas that they frequently hunted, as elk tended to move following wolf encounters in those areas. This response should dilute elk foraging pressure on plant communities in areas where they are frequently hunted by wolves. We predict that this should decrease the spatial heterogeneity of elk impacts on grasslands in areas that wolves frequently hunt. We also predict that this should decrease browsing pressure on heavily browsed woody plant stands in certain areas, which is supported by recent research in the GYE.     

A case for quantile regression in behavioral ecology: getting more out of flight initiation distance data

A central goal of behavioral ecology is to quantify and explain variation in behavior. While much previous work has focused on the differences in mean behavior across groups or treatments, we present a complementary approach studying changes in the distribution of the response variable. This is important because changes in the edges of a distribution may be more informative than changes in the mean if behavior at the edges of a distribution better reflects behavioral constraints. Quantile regression estimates the rate of change of conditional quantiles of a response variable and thus allows the study of changes in any part of its distribution. Although quantile regression is gaining popularity in the ecological literature, it is strikingly unused in behavioral ecology. Here, we demonstrate the usefulness of this method by analyzing the relationship between the starting distance (SD) at which an observer approach a focal animal and its flight initiation distance (FID, the distance between the observer and the animal when it decides to flee). In particular, we used a simple model of flight initiation distance to show that in most situations ordinary least-square regression cannot be used to analyse the SD–FID relationship. Quantile regression conducted on the lowest quantiles appears more robust and we applied this approach to data from four bird species. Overall, changes in the lowest FID values appeared to be the most informative to determine if a species displays a “flush early” strategy, a strategy which has been hypothesized to be a general rule. We hope this example will bring quantile regression to the attention of behavioral ecologists as a valuable tool to add to their statistical toolbox.     

Why have birds got multiple sexual ornaments?

Summary Males of many animals have more than a single exaggerated secondary sexual character, but inter-specific variability in the number of ornaments has never been explained. We examine three hypotheses that may account for the presence of multiple ornaments. First, the multiple message hypothesis proposes that each display reflects a single property of the overall quality of an animal. This is likely to be the case for ornaments that respond to condition on different time scales. Second, the redundant signal hypothesis suggests that each ornament gives a partial indication of condition. Females pay attention to several sex traits because in combination they provide a better estimate of general condition than does any single ornament. The redundant signal hypothesis predicts that (i) multiple ornaments should be particularly common among taxa with relatively uncostly and fine-tuned female choice, and (ii) females pay equal attention to the expression of all the secondary sex traits in order to obtain an estimate of overall male condition. Finally, the unreliable signal hypothesis argues that some ornaments are unreliable indicators of overall condition and are only maintained because they are relatively uncostly to produce and there is a weak female preference for them. This predicts that (i) multiple sexual ornaments should be particularly common in taxa with the most intense sexual selection (i.e. lekking and other polygynous taxa), and (ii) there should be more evidence for condition dependence in ornaments of species with single as opposed to multiple ornaments. Both the latter predictions are supported by data on feather ornaments in birds.Correspondence to: A. Pomiankowski     

Egg coloration in ring-billed gulls (<Emphasis Type="Italic">Larus delawarensis</Emphasis>): a test of the sexual signaling hypothesis

Although many avian eggs appear to be cryptically colored, many species also lay vibrant blue green eggs. This seemingly conspicuous coloration has puzzled biologists since Wallace, as natural selection should favor reduced egg visibility to minimize predation pressure. The sexual signaling hypothesis posits that blue green egg coloration serves as a signal of female quality and that males exert post-mating sexual selection on this trait by investing more in the nests of females laying more intensely blue green eggs. This hypothesis has received mixed support to date, and most previous studies have been conducted in cavity-nesting species where male evaluation of his partner’s egg coloration, relative to that of other females, may be somewhat limited. In this study, we test the sexual signaling hypothesis in colonially nesting ring-billed gulls (Larus delawarensis) where males have ample opportunity to assess their mate’s egg coloration relative to that of other females. We used correlational data and an experimental manipulation to test four assumptions and predictions of the sexual signaling hypothesis: (1) blue green pigmentation should be limiting to females; (2) extent of blue green egg coloration should relate to female quality; (3) extent of blue green egg coloration should relate to offspring quality; and (4) males should provide more care to clutches with higher blue green chroma. Our data provide little support for these predictions of the sexual signaling hypothesis in ring-billed gulls. In light of this and other empirical data, we encourage future studies to consider additional hypotheses for the evolution of blue green egg coloration.     

Using information theory as a substitute for stepwise regression in ecology and behavior

In ecological and behavioral research, drawing reliable conclusions from statistical models with multiple predictors is usually difficult if all predictors are simultaneously in the model. The traditional way of handling multiple predictors has been the use of threshold-based removal-introduction algorithms, that is, stepwise regression, which currently receives considerable criticism. A more recent and increasingly propagated modelling method for multiple predictors is the information theoretic (IT) approach that quantifies the relative suitability of multiple, potentially non-nested models based on a balance of model fit and the accuracy of estimates. Here, we examine three shortcomings of stepwise regression, subjective critical values, model uncertainty, and parameter estimation bias, which have been suggested to be avoided by applying information theory. We argue that, in certain circumstances, the IT approach may be sensitive to these issues as well. We point to areas where further testing and development could enhance the performance of IT methods and ultimately lead to robust inferences in behavioral ecology.     

Demonstration as a Means to Translate Conservation Science into Practice

Abstract:  To be relevant to societal interests and needs, conservation science must explicitly lend itself to solving real-world problems. Failure to evaluate under field conditions how a new technology or method performs or the cost of its implementation can prevent its acceptance by end users. Demonstration, defined here as the translation of scientific understanding into metrics of performance and cost of implementation under real-world conditions, is a logical step in the challenging progression from fundamental research to application. Demonstration reduces scientific uncertainty and validates the hypothesis that a management approach is both effective and financially sustainable. Much like adaptive management, demonstration enables researchers and resource managers to avoid trial-and-error approaches and instead conduct unbiased assessment of management interventions. The participation of end users and regulators in the development and execution of demonstration projects ensures that performance measures are credible and increases the probability that successful innovations will be adopted. Four actions might better connect science to the needs of resource managers via demonstration. First, we recommend that demonstration be conducted as a formal process that documents successes and failures. Second, demonstration should be budgeted as an integral component of government agencies' science programs and executed as a partnership between researchers and managers. Third, public and private funders should increase the opportunities and incentives for academics to engage in demonstration. Fourth, social influences on adoption of new technologies and methods should be further explored. When end users can evaluate explicitly whether a new approach is likely to achieve management objectives, save money, and reduce risk under uncertainty, the professional community successfully has bridged a chasm between research and application .     

Assessing the components of adaptive capacity to improve conservation and management efforts under global change

Natural‐resource managers and other conservation practitioners are under unprecedented pressure to categorize and quantify the vulnerability of natural systems based on assessment of the exposure, sensitivity, and adaptive capacity of species to climate change. Despite the urgent need for these assessments, neither the theoretical basis of adaptive capacity nor the practical issues underlying its quantification has been articulated in a manner that is directly applicable to natural‐resource management. Both are critical for researchers, managers, and other conservation practitioners to develop reliable strategies for assessing adaptive capacity. Drawing from principles of classical and contemporary research and examples from terrestrial, marine, plant, and animal systems, we examined broadly the theory behind the concept of adaptive capacity. We then considered how interdisciplinary, trait‐ and triage‐based approaches encompassing the oft‐overlooked interactions among components of adaptive capacity can be used to identify species and populations likely to have higher (or lower) adaptive capacity. We identified the challenges and value of such endeavors and argue for a concerted interdisciplinary research approach that combines ecology, ecological genetics, and eco‐physiology to reflect the interacting components of adaptive capacity. We aimed to provide a basis for constructive discussion between natural‐resource managers and researchers, discussions urgently needed to identify research directions that will deliver answers to real‐world questions facing resource managers, other conservation practitioners, and policy makers. Directing research to both seek general patterns and identify ways to facilitate adaptive capacity of key species and populations within species, will enable conservation ecologists and resource managers to maximize returns on research and management investment and arrive at novel and dynamic management and policy decisions.     

Diagnosing Units of Conservation Management

Species-oriented conservation programs attempt to analyze and maintain intra-specific variation in order to maximally preserve biological diversity. The "evolutionarily significant unit" has become an operational term for a group of organisms that should be the minimial unit for conservation management. No generally accepted definition for this term exists that would be the basis for the evaluation of these units in practical conservation situations. Currently, taxonomic decisions in species conservation are mostly based on the biological species concept. But the universal application of criteria of reproductive isolation or phenetic similarity to delimit conservation units is problematical. We favor a definition for evolutionarily significant units based on patterns of variation. In the theoretical framework of the phylogenetic species concept, conservation units are delimited by characters that diagnose clusters of individuals or populations to the exclusion of other such clusters. Characters are used for cladistic analysis to infer hypotheses of the phylogenetic relationships of individuals, and differentiated populations are diagnosed using population aggregation analysis. Characters can be based on genetic, morphological, ecological, or behavioral information, provided they are inferred to be heritable. The use of cladistics and population aggregation analysis has the potential to make the evaluation of evoluntionarily significant units objective and testable, an important consideration in politically controversial cases. Our cladistic approach is demonstrated by the evaluation of potential conservation units in the endangered tiger beetles Cicindela dorsalis and C. puritana .     

Reconciling competing ecological explanations for sexual segregation in ungulates

Sexual segregation in ungulates has important conservation and theoretical implications, but despite numerous studies, the impetus for this behavioral pattern remains a topic of debate. Sexual segregation hypotheses can be broadly grouped into social and ecological explanations, but only ecological explanations can adequately describe why sexes use different areas and habitats. The reproductive strategy hypothesis (RSH) and forage selection hypothesis (FSH) are leading ecological explanations, and although both have received support in the literature, neither the collective basis for that support nor overlap between these hypotheses has been adequately evaluated. This review analyzed seasonal sex comparisons of habitat forage quantity (n=66), quality (n=67), and diet (n=63) from peer-reviewed studies of north temperate ruminants to test predictions of each hypothesis. Empirical data supported predictions of the RSH, but did not support two of three key predictions of the FSH. Males used habitats with greater forage quantity significantly more than females. But, contrary to predictions of the FSH, females did not use habitats with superior forage quality nor consume higher-quality diets more than males. Sexes typically used habitats and consumed diets of similar quality, and when differences were reported, males used higher-quality habitats significantly more than females. Results refute FSH arguments that differences in dietary requirements associated with sexual dimorphism are a universal explanation for sexual segregation in ungulates, but the physiological mechanism on which the FSH is predicated may explain why males consume poorer-quality diets when high-quality forage is scarce. The FSH, therefore, operates at a proximate level because it explains diet and habitat selection by males under certain environmental conditions, but multiple environmental factors may influence sexual segregation, and no single proximate explanation adequately describes this behavioral pattern. The RSH explains sexual segregation as the evolutionary response to differences in reproductive strategies: males choose habitats to maximize energy gains in preparation for rut, and females select habitats with combinations of resources that contribute to offspring survival. Consequently, the RSH provides an ultimate explanation that can be used to explain and interpret studies of sexual segregation in ungulates.     

Advancing the Integration of History and Ecology for Conservation

Abstract: The important role of humans in the development of current ecosystems was recognized decades ago; however, the integration of history and ecology in order to inform conservation has been difficult. We identified four issues that hinder historical ecological research and considered possible solutions. First, differences in concepts and methods between the fields of ecology and history are thought to be large. However, most differences stem from miscommunication between ecologists and historians and are less substantial than is usually assumed. Cooperation can be achieved by focusing on the features ecology and history have in common and through understanding and acceptance of differing points of view. Second, historical ecological research is often hampered by differences in spatial and temporal scales between ecology and history. We argue that historical ecological research can only be conducted at extents for which sources in both disciplines have comparable resolutions. Researchers must begin by clearly defining the relevant scales for the given purpose. Third, periods for which quantitative historical sources are not easily accessible (before AD 1800) have been neglected in historical ecological research. Because data from periods before 1800 are as relevant to the current state of ecosystems as more recent data, we suggest that historical ecologists actively seek out data from before 1800 and apply analytic methods commonly used in ecology to these data. Fourth, humans are not usually considered an intrinsic ecological factor in current ecological research. In our view, human societies should be acknowledged as integral parts of ecosystems and societal processes should be recognized as driving forces of ecosystem change.     

The importance of white on black: unmelanized plumage proportion predicts display complexity in birds

Animal ritualized displays have been classically viewed as behavioral characters that decrease signal ambiguity or that facilitate the evaluation of costly exhibitions. It has been shown that their prevalence and level of complexity across species can reflect phylogenetic relationships between them, but the adaptive function of these behavioral traits is poorly known. Here, I hypothesize that, given that the efficacy of visual displays basically depends on conspicuousness and level of performance, species with low levels of conspicuousness may be forced to perform more complex varieties of a given display to get the same signal efficiency than other more conspicuous species. Thus, the evolution of display complexity, considered as the level of exaggeration of ritualized movements, may be explained as an adaptive trait and not only by phylogenetic inertia. I illustrate and test this hypothesis with the case of black-and-white plumage patches of pelecaniform birds. As predicted, there was a negative correlation between level of complexity and species conspicuousness (proportion of unmelanized plumage) for two different social displays. This indicates that classical ideas on the adaptiveness of ritualized displays should be considered to understand the present variation in signal form across species, which sheds light on the evolution of multiple signals.     

Worker senescence and the sociobiology of aging in ants

Senescence, the decline in physiological and behavioral function with increasing age, has been the focus of significant theoretical and empirical research in a broad array of animal taxa. Preeminent among invertebrate social models of aging are ants, a diverse and ecologically dominant clade of eusocial insects characterized by reproductive and sterile phenotypes. In this review, we critically examine selection for worker life span in ants and discuss the relationship between functional senescence, longevity, task performance, and colony fitness. We did not find strong or consistent support for the hypothesis that demographic senescence in ants is programmed, or its corollary prediction that workers that do not experience extrinsic mortality die at an age approximating their life span in nature. We present seven hypotheses concerning how selection could favor extended worker life span through its positive relationship to colony size and predict that large colony size, under some conditions, should confer multiple and significant fitness advantages. Fitness benefits derived from long worker life span could be mediated by increased resource acquisition, efficient division of labor, accuracy of collective decision-making, enhanced allomaternal care and colony defense, lower infection risk, and decreased energetic costs of workforce maintenance. We suggest future avenues of research to examine the evolution of worker life span and its relationship to colony fitness and conclude that an innovative fusion of sociobiology, senescence theory, and mechanistic studies of aging can improve our understanding of the adaptive nature of worker life span in ants.