Explore the vast range of titles available.

In this paper we derive sufficient conditions for the permanence and ergodicity of a stochastic predator–prey model with a Beddington–DeAngelis functional response. The conditions obtained are in fact very close to the necessary conditions. Both nondegenerate and degenerate diffusions are considered. One of the distinctive features of our results is that they enable the characterization of the support of a unique invariant probability measure. It proves the convergence in total variation norm of the transition probability to the invariant measure. Comparisons to the existing literature and matters related to other stochastic predator–prey models are also given.

In this paper, we provide efficient estimators and honest confidence bands for a variety of treatment effects including local average (LATE) and local quantile treatment effects (LQTE) in data-rich environments. We can handle very many control variables, endogenous receipt of treatment, heterogeneous treatment effects, and function-valued outcomes. Our framework covers the special case of exogenous receipt of treatment, either conditional on controls or unconditionally as in randomized control trials. In the latter case, our approach produces efficient estimators and honest bands for (functional) average treatment effects (ATE) and quantile treatment effects (QTE). To make informative inference possible, we assume that key reduced-form predictive relationships are approximately sparse. This assumption allows the use of regularization and selection methods to estimate those relations, and we provide methods for postregularization and post-selection inference that are uniformly valid (honest) across a wide range of models. We show that a key ingredient enabling honest inference is the use of orthogonal or doubly robust moment conditions in estimating certain reducedform functional parameters. We illustrate the use of the proposed methods with an application to estimating the effect of 401(k) eligibility and participation on accumulated assets. The results on program evaluation are obtained as a consequence of more general results on honest inference in a general moment-condition framework, which arises from structural equation models in econometrics. Here, too, the crucial ingredient is the use of orthogonal moment conditions, which can be constructed from the initial moment conditions. We provide results on honest inference for (function-valued) parameters within this general framework where any high-quality, machine learning methods (e.g., boosted trees, deep neural networks, random forest, and their aggregated and hybrid versions) can be used to learn the nonparametric/high-dimensional components of the model. These include a number of supporting auxiliary results that are of major independent interest: namely, we (1) prove uniform validity of a multiplier bootstrap, (2) offer a uniformly valid functional delta method, and (3) provide results for sparsitybased estimation of regression functions for function-valued outcomes.

Although classical ecological theory (e.g., on ideal free consumers) recognizes the potential effect of population density on the spatial distribution of animals, empirical species distribution models assume that species-habitat relationships remain unchanged across a range of population sizes. Conversely, even though ecological models and experiments have demonstrated the importance of spatial heterogeneity for the rate of population change, we still have no practical method for making the connection between the makeup of real environments, the expected distribution and fitness of their occupants, and the long-term implications of fitness for population growth. Here, we synthesize several conceptual advances into a mathematical framework using a measure of fitness to link habitat availability/selection to (density-dependent) population growth in mobile animal species. A key feature of this approach is that it distinguishes between apparent habitat suitability and the true, underlying contribution of a habitat to fitness, allowing the statistical coefficients of both to be estimated from multiple observation instances of the species in different environments and stages of numerical growth. Hence, it leverages data from both historical population time series and snapshots of species distribution to predict population performance under environmental change. We propose this framework as a foundation for building more realistic connections between a population's use of space and its subsequent dynamics (and hence a contribution to the ongoing efforts to estimate a species' critical habitat and fundamental niche). We therefore detail its associated definitions and simplifying assumptions, because they point to the framework's future extensions. We show how the model can be fit to data on species distributions and population dynamics, using standard statistical methods, and we illustrate its application with an individual-based simulation. When contrasted with nonspatial population models, our approach is better at fitting and predicting population growth rates and carrying capacities. Our approach can be generalized to include a diverse range of biological considerations. We discuss these possible extensions and applications to real data.

Knowledge of feeding rates is the basis to understand interaction strength and subsequently the stability of ecosystems and biodiversity. Feeding rates, as all biological rates, depend on consumer and resource body masses and environmental temperature. Despite five decades of research on functional responses as quantitative models of feeding rates, a unifying framework of how they scale with body masses and temperature is still lacking. This is perplexing, considering that the strength of functional responses (i.e. interaction strengths) is crucially important for the stability of simple consumer–resource systems and the persistence, sustainability and biodiversity of complex communities. Here, we present the largest currently available database on functional response parameters and their scaling with body mass and temperature. Moreover, these data are integrated across ecosystems and metabolic types of species. Surprisingly, we found general temperature dependencies that differed from the Arrhenius terms predicted by metabolic models. Additionally, the body-mass-scaling relationships were more complex than expected and differed across ecosystems and metabolic types. At local scales (taxonomically narrow groups of consumer–resource pairs), we found hump-shaped deviations from the temperature and body-mass-scaling relationships. Despite the complexity of our results, these body-mass- and temperature-scaling models remain useful as a mechanistic basis for predicting the consequences of warming for interaction strengths, population dynamics and network stability across communities differing in their size structure.

1. In community and population ecology, there is a chronic gap between the classic Eltonian ecology describing patterns in abundance and body mass across species and ecosystems and the more process oriented foraging ecology addressing interactions and quantitative population dynamics. However, this dichotomy is arbitrary, because body mass also determines most species traits affecting foraging interactions and population dynamics. 2. In this review, allometric (body-mass dependent) scaling of handling times and attack rates are documented, whereas body-mass effects on Hill exponents (varying between hyperbolic type II and sigmoid type III functional responses) and predator interference coefficients are lacking. This review describes how these allometric relationships define a biological plausible parameter space for population dynamic models. 3. Consistent with the classic Eltonian description, species co-existence in consumer-resource models and tri-trophic food chains is restricted to intermediate consumer-resource body-mass ratios. Allometric population dynamic models allow understanding the processes of energy limitation and unstable dynamics leading to this restriction. Complex food webs are stabilized by high predator-prey body-mass ratios, which are consistent with those found in natural ecosystems. These high body-mass ratios yield positive diversity-stability and complexity-stability relationships thus supporting the classic picture of ecosystem stability. 4. Allometric-trophic network models, based on body mass and trophic information from ecosystems, bridge the gap between Eltonian community patterns and process-oriented foraging ecology and provide a new means to describe the dynamics and functioning of natural ecosystems.

Models of habitat preference are widely used to quantify animal–habitat relationships, to describe and predict differential space use by animals, and to identify habitat that is important to an animal (i.e. that is assumed to influence fitness). Quantifying habitat preference involves the statistical comparison of samples of habitat use and availability. Preference is therefore contingent upon both of these samples. The inferences that can be made from use versus availability designs are influenced by subjectivity in defining what is available to the animal, the problem of quantifying the accessibility of available resources and the framework in which preference is modelled. Here, we describe these issues, document the conditional nature of preference and establish the limits of inferences that can be drawn from these analyses. We argue that preference is not interpretable as reflecting the intrinsic behavioural motivations of the animal, that estimates of preference are not directly comparable among different samples of availability and that preference is not necessarily correlated with the value of habitat to the animal. We also suggest that preference is context-dependent and that functional responses in preference resulting from changing availability are expected. We conclude by describing advances in analytical methods that begin to resolve these issues.

Temperature is one of the most important environmental parameters influencing all the biological processes and functions of poikilothermic organisms. Although extensive research has been carried out to evaluate the effects of temperature on animal life histories and to determine the upper and lower temperature thresholds as well as the optimal temperatures for survival, development, and reproduction, few studies have investigated links between thermal window, metabolism, and trophic interactions such as predation. We developed models and conducted laboratory experiments to investigate how temperature influences predator-prey interaction strengths (i.e., functional response) using a ladybeetle larva feeding on aphid prey. As predicted by the metabolic theory of ecology, we found that handling time exponentially decreases with warming, but—in contrast with this theory—search rate follows a hump-shaped relationship with temperature. An examination of the model reveals that temperature thresholds for predation depend mainly on search rate, suggesting that predation rate is primarily determined by searching activities and secondly by prey handling. In contrast with prior studies, our model shows that per capita short-term predator-prey interaction strengths and predator energetic efficiency (per capita feeding rate relative to metabolism) generally increase with temperature, reach an optimum, and then decrease at higher temperatures. We conclude that integrating the concept of thermal windows in short- and long-term ecological studies would lead to a better understanding of predator-prey population dynamics at thermal limits and allow better predictions of global warming effects on natural ecosystems.

The predator functional response (i.e. per capita consumption rate as a function of prey density) is central to our understanding of predator–prey population dynamics. This response is behavioural, depending on the rate of attack and time it takes to handle prey. Consistent behavioural differences among conspecific individuals, termed behavioural types, are a widespread feature of predator and prey populations but the effects of behavioural types on the functional response remain unexplored. We tested the effects of crab (Panopeus herbstii) behavioural type, specifically individual activity level, on the crab functional response to mussel (Brachidontes exustus) prey. We further tested whether the effects of activity level on the response are mediated by the presence of toadfish (Opsanus tau) predation threat in the form of waterborne chemical cues known to reduce crab activity level. The effects of crab activity level on the functional response were dependent on crab body size. Individual activity level increased the magnitude (i.e. slope and asymptote) of the type II functional response of small crabs, potentially through an increase in time spent foraging, but had no effect on the functional response of large crabs. Predation threat did not interact with activity level to influence mussel consumption, but independently reduced the slope of the type II functional response. Overall, this study demonstrates size‐specific effects of a behavioural type on a predator–prey interaction, as well as a general pathway (modification of the functional response) by which the effects of individual behavioural types can scale up to influence predator–prey population dynamics.

1. The selection for particular habitat patches can vary as a function of local and regional levels of anthropogenic disturbance. Although such functional responses can better reveal habitat loss for species of precarious status faced with dwindling resources, they remain rarely used in conservation planning. We show that functional responses can occur at multiple levels, even as nested hierarchies, and that they can explain the plasticity in habitat selection observed in threatened forest-dwelling caribou Rangifer tarandus caribou, within and among home-ranges. 2. Twenty-seven caribou were followed with global positioning system collars between 2005 and 2010. Generalized linear mixed models served as the basis from which we built multi-level functional responses characterizing how caribou alter their selection for closed-canopy conifer forests, depending upon the availability of these forests and the amount of cutovers and roads. 3. Caribou increased their selection for closed-canopy conifer forests in areas of their home-range that were comprised of a high proportion of recent cutovers during calving and summer and of high closed-canopy conifer forests during winter. Also, caribou that were established in highly disturbed areas displayed an overall stronger selection for conifer forests. These individuals further adjusted their selection for conifer forests in areas of their home-ranges that were largely comprised of recent cutovers. This concurrent response to local and global anthropogenic disturbances provides evidence of nested-hierarchical functional responses. 4. Synthesis and applications. Reliable characterization of disturbance effects on animals is necessary for conservation planning. Multi-level functional responses can accurately describe animal distribution, and we provided a framework for modelling these responses. Our multi-level functional responses indicate that fixing habitat requirements based on patterns of habitat selection for the average amount of disturbance can be misleading because it overlooks plasticity in the response of animals to habitat heterogeneity. For example, selection of closed-canopy conifer forests by caribou generally became stronger with increasing disturbance levels. Anthropogenic disturbance thus could not only lead to the functional loss of residual habitat, but it can also increase the 'relative value' of residual patches. Our study provides a tool for more thorough assessments of spatial variation in the attractiveness of resource patches and, presumably, in the fitness benefits.

Invasion ecology urgently requires predictive methodologies that can forecast the ecological impacts of existing, emerging and potential invasive species. We argue that many ecologically damaging invaders are characterised by their more efficient use of resources. Consequently, comparison of the classical ‘functional response’ (relationship between resource use and availability) between invasive and trophically analogous native species may allow prediction of invader ecological impact. We review the utility of species trait comparisons and the history and context of the use of functional responses in invasion ecology, then present our framework for the use of comparative functional responses. We show that functional response analyses, by describing the resource use of species over a range of resource availabilities, avoids many pitfalls of ‘snapshot’ assessments of resource use. Our framework demonstrates how comparisons of invader and native functional responses, within and between Type II and III functional responses, allow testing of the likely population-level outcomes of invasions for affected species. Furthermore, we describe how recent studies support the predictive capacity of this method; for example, the invasive ‘bloody red shrimp’ Hemimysis anomala shows higher Type II functional responses than native mysids and this corroborates, and could have predicted, actual invader impacts in the field. The comparative functional response method can also be used to examine differences in the impact of two or more invaders, two or more populations of the same invader, and the abiotic (e.g. temperature) and biotic (e.g. parasitism) context-dependencies of invader impacts. Our framework may also address the previous lack of rigour in testing major hypotheses in invasion ecology, such as the ‘enemy release’ and ‘biotic resistance’ hypotheses, as our approach explicitly considers demographic consequences for impacted resources, such as native and invasive prey species. We also identify potential challenges in the application of comparative functional responses in invasion ecology. These include incorporation of numerical responses, multiple predator effects and trait-mediated indirect interactions, replacement versus non-replacement study designs and the inclusion of functional responses in risk assessment frameworks. In future, the generation of sufficient case studies for a meta-analysis could test the overall hypothesis that comparative functional responses can indeed predict invasive species impacts.