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1. Environmental temperature has systematic effects on rates of species interactions, primarily through its influence on organismal physiology. 2. We present a mechanistic model for the thermal response of consumer–resource interactions. We focus on how temperature affects species interactions via key traits – body velocity, detection distance, search rate and handling time – that underlie per capita consumption rate. The model is general because it applies to all foraging strategies: active-capture (both consumer and resource body velocity are important), sit-and-wait (resource velocity dominates) and grazing (consumer velocity dominates). 3. The model predicts that temperature influences consumer–resource interactions primarily through its effects on body velocity (either of the consumer, resource or both), which determines how often consumers and resources encounter each other, and that asymmetries in the thermal responses of interacting species can introduce qualitative, not just quantitative, changes in consumer–resource dynamics. We illustrate this by showing how asymmetries in thermal responses determine equilibrium population densities in interacting consumer–resource pairs. 4. We test for the existence of asymmetries in consumer–resource thermal responses by analysing an extensive database on thermal response curves of ecological traits for 309 species spanning 15 orders of magnitude in body size from terrestrial, marine and freshwater habitats. We find that asymmetries in consumer–resource thermal responses are likely to be a common occurrence. 5. Overall, our study reveals the importance of asymmetric thermal responses in consumer–resource dynamics. In particular, we identify three general types of asymmetries: (i) different levels of performance of the response, (ii) different rates of response (e.g. activation energies) and (iii) different peak or optimal temperatures. Such asymmetries should occur more frequently as the climate changes and species' geographical distributions and phenologies are altered, such that previously noninteracting species come into contact. 6. By using characteristics of trophic interactions that are often well known, such as body size, foraging strategy, thermy and environmental temperature, our framework should allow more accurate predictions about the thermal dependence of consumer–resource interactions. Ultimately, integration of our theory into models of food web and ecosystem dynamics should be useful in understanding how natural systems will respond to current and future temperature change.

Consumer attitudes and behaviors are fundamentally dynamic processes; thus, understanding consumer dynamics is crucial for truly understanding consumer behaviors and for firms to formulate appropriate actions. Recent history in empirical marketing research has enjoyed increasingly richer consumer data as the result of technology and firms’ conscious data collection efforts. Richer data, in turn, have propelled the development and application of quantitative methods in modeling consumer dynamics, and have contributed to the understanding of complex dynamic behaviors across many domains. In this paper, we discuss the sources of consumer dynamics and how our understanding in this area has improved over the past four decades. Accordingly, we discuss several commonly used empirical methods for conducting dynamics research. Finally, as the data evolution continues into new forms and new environments, we identify cutting-edge trends and domains, and offer directions for advancing the understanding of consumer dynamics in these emerging areas.

The curvature of generalized Holling type functional response curves is controlled by a shape parameter b yielding hyperbolic type II (b = 1) to increasingly sigmoid type III (b > 1) responses. Empirical estimates of b vary considerably across taxa. Larger consumer–resource body mass ratios have been suggested to generate more pronounced type III responses and therefore to promote dynamic stability. The dependence of consumer–resource stability on b has, however, not been systematically explored, and the accurate empirical determination of b is challenging. Specifically, the shape of the functional response of the pelagic grazer Daphnia feeding on phytoplankton, and its consequences for stability, remain controversial. We derive a novel analytical condition relating b to local stability of consumer–resource interactions and use it to predict stability of empirically parameterized models of Daphnia and phytoplankton under enrichment. Functional response parameters were experimentally derived for two species of Daphnia feeding separately on single cultures of two different phytoplankton species. All experimentally studied Daphnia–algae systems exhibited type III responses. Parameterized type III responses are predicted to stabilize the modeled Daphnia–phytoplankton dynamics in some species pairs but not in others. Remarkably, stability predictions differ depending on whether functional response parameters are derived from clearance vs. ingestion rates. Accurate parameter estimation may therefore require fitting to both rates. In addition, our estimates of b for filter‐feeding Daphnia are much smaller than predicted for actively hunting predators at similar consumer–resource body mass ratios. This suggests that the relationship between functional response shape and body mass ratios may vary with predation mode.

The chironomids of Lake Mývatn show extreme population fluctuations that affect most aspects of the lake ecosystem. During periods of high chironomid densities, chironomid larvae comprise over 90% of aquatic secondary production. Here, we show that chironomid larvae substantially stimulate benthic gross primary production (GPP) and net primary production (NPP), despite consuming benthic algae. Benthic GPP in experimental mesocosms with 140,000 larvae/m2 was 71% higher than in mesocosms with no larvae. Similarly, chlorophyll a concentrations in mesocosms increased significantly over the range of larval densities. Furthermore, larvae showed increased growth rates at higher densities, possibly due to greater benthic algal availability in these treatments. We investigated the hypothesis that larvae promote benthic algal growth by alleviating nutrient limitation, and found that (1) larvae have the potential to cycle the entire yearly external loadings of nitrogen and phosphorus during the growing season, and (2) chlorophyll a concentrations were significantly greater in close proximity to larvae (on larval tubes). The positive feedback between chironomid larvae and benthic algae generated a net mutualism between the primary consumer and primary producer trophic levels in the benthic ecosystem. Thus, our results give an example in which unexpected positive feedbacks can lead to both high primary and high secondary production.

Warming global temperatures are driving changes in species distributions, growth and timing, but much uncertainty remains regarding how climate change will alter species interactions. Consumer–Resource interactions in particular can be strongly impacted by changes to the relative performance of interacting species. While consumers generally gain an advantage over their resources with increasing temperatures, nonlinearities can change this relation near temperature extremes. We use an experimental approach to determine how temperature changes between 5 and 30 °C will alter the growth of the algae Scenedesmus obliquus and the functional responses of the small‐bodied Daphnia ambigua and the larger Daphnia pulicaria. The impact of warming generally followed expectations, making both Daphnia species more effective grazers, with the increase in feeding rates outpacing the increases in algal growth rate. At the extremes of our temperature range, however, warming resulted in a decrease in Daphnia grazing effectiveness. Between 25 and 30 °C, both species of Daphnia experienced a precipitous drop in feeding rates, while algal growth rates remained high, increasing the likelihood of algal blooms in warming summer temperatures. Daphnia pulicaria performed significantly better at cold temperatures than D. ambigua, but by 20 °C, there was no significant difference between the two species, and at 25 °C, D. ambigua outperformed D. pulicaria. Warming summer temperatures will favour the smaller D. ambigua, but only over a narrow temperature range, and warming beyond 25 °C could open D. ambigua to invasion from tropical species. By fitting our results to temperature‐dependent functions, we develop a temperature‐ and density‐dependent model, which produces a metric of grazing effectiveness, quantifying the grazer density necessary to halt algal growth. This approach should prove useful for tracking the transient dynamics of other density‐dependent consumer–resource interactions, such as agricultural pests and biological‐control agents.

Ecologists have long been fascinated by cyclic population fluctuations, because they suggest strong interactions between exploiter and victim species. Nonetheless, even for populations showing high‐amplitude fluctuations, it is often hard to identify which species are the key drivers of the dynamics, because data are generally only available for a single species. Here, we use a paleoecological approach to investigate fluctuations in the midge population in Lake Mývatn, Iceland, which ranges over several orders of magnitude in irregular, multigeneration cycles. Previous circumstantial evidence points to consumer–resource interactions between midges and their primary food, diatoms, as the cause of these high‐amplitude fluctuations. Using a pair of sediment cores from the lake, we reconstructed 26 years of dynamics of midges using egg remains and of algal groups using diagnostic pigments. We analyzed these data using statistical methods that account for both the autocorrelated nature of paleoecological data and measurement error caused by the mixing of sediment layers. The analyses revealed a signature of consumer–resource interactions in the fluctuations of midges and diatoms: diatom abundance (as inferred from biomarker pigment diatoxanthin) increased when midge abundance was low, and midge abundance (inferred from egg capsules) decreased when diatom abundance was low. Similar patterns were not found for pigments characterizing the other dominant primary producer group in the lake (cyanobacteria), subdominant algae (cryptophytes), or ubiquitous but chemically unstable biomarkers of total algal abundance (chlorophyll a); however, a significant but weaker pattern was found for the chemically stable indicator of total algal populations (β‐carotene) to which diatoms are the dominant contributor. These analyses provide the first paleoecological evaluation of specific trophic interactions underlying high amplitude population fluctuations in lakes.

Heritable trait variation is a central and necessary ingredient of evolution. Trait variation also directly affects ecological processes, generating a clear link between evolutionary and ecological dynamics. Despite the changes in variation that occur through selection, drift, mutation, and recombination, current eco‐evolutionary models usually fail to track how variation changes through time. Moreover, eco‐evolutionary models assume fitness functions for each trait and each ecological context, which often do not have empirical validation. We introduce a new type of model, Gillespie eco‐evolutionary models (GEMs), that resolves these concerns by tracking distributions of traits through time as eco‐evolutionary dynamics progress. This is done by allowing change to be driven by the direct fitness consequences of model parameters within the context of the underlying ecological model, without having to assume a particular fitness function. GEMs work by adding a trait distribution component to the standard Gillespie algorithm – an approach that models stochastic systems in nature that are typically approximated through ordinary differential equations. We illustrate GEMs with the Rosenzweig–MacArthur consumer–resource model. We show not only how heritable trait variation fuels trait evolution and influences eco‐evolutionary dynamics, but also how the erosion of variation through time may hinder eco‐evolutionary dynamics in the long run. GEMs can be developed for any parameter in any ordinary differential equation model and, furthermore, can enable modeling of multiple interacting traits at the same time. We expect GEMs will open the door to a new direction in eco‐evolutionary and evolutionary modeling by removing long‐standing modeling barriers, simplifying the link between traits, fitness, and dynamics, and expanding eco‐evolutionary treatment of a greater diversity of ecological interactions. These factors make GEMs much more than a modeling advance, but an important conceptual advance that bridges ecology and evolution through the central concept of heritable trait variation. We introduce a new type of eco‐evolutionary model that (1) incorporates changes in heritable trait variation through time; and (2) does not require the specification of fitness functions. We show that these models – Gillespie eco‐evolutionary models, or GEMs – provide a powerful tool for understanding and modeling a wide range of eco‐evolutionary processes.

Functional traits are characteristics of an organism that represents how it interacts with its environment and can influence the structure and function of ecosystems. Ecological stoichiometry provides a framework to understand ecosystem structure and function by modeling the coupled flow of elements (e.g. carbon [C], nitrogen [N], phosphorus [P]) between consumers and their environment. Animals tend to be homeostatic in their nutrient requirements and preferentially sequester the element in shortest supply relative to demand, and release relatively more of the element in excess. Tissue stoichiometry is an important functional trait that allows for predictions among the elemental composition of animals, their diet, and their waste products, with important effects on the cycling and availability of nutrients in ecosystems. Here, we examined the tissue stoichiometric niches (C:N:P) and nutrient recycling stoichiometries (N:P) of several filter-feeding freshwater mussels in the subfamily Ambleminae. Despite occupying the same functional-feeding group and being restricted to a single subfamily-level radiation, we found that species occupied distinct stoichiometric niches and that these niches varied, in part, as a function of their evolutionary history. The relationship between phylogenetic divergence and functional divergence suggests that evolutionary processes may be shaping niche complementarity and resource partitioning. Tissue and excretion stoichiometry were negatively correlated as predicted by stoichiometric theory. When scaled to the community, higher species richness and phylogenetic diversity resulted in greater functional evenness and reduced functional dispersion. Filter-feeding bivalves are an ecologically important guild in freshwater ecosystems globally, and our study provides a more nuanced view of the stoichiometric niches and ecological functions performed by this phylogenetically and ecologically diverse assemblage.

Cannibalistic and asymmetrical behavioral interactions between stages are common within stage-structured predator populations. Such direct interactions between predator stages can result in density- and trait-mediated indirect interactions between a predator and its prey. A set of structured predator—prey models is used to explore how such indirect interactions affect the dynamics and structure of communities. Analyses of the separate and combined effects of stage-structured cannibalism and behavior-mediated avoidance of cannibals under different ecological scenarios show that both cannibalism and behavioral avoidance of cannibalism can result in short- and long-term positive indirect connections between predator stages and the prey, including \"apparent mutualism.\" These positive interactions alter the strength of trophic cascades such that the system's dynamics are determined by the interaction between bottom-up and top-down effects. Contrary to the expectation of simpler models, enrichment increases both predator and prey abundance in systems with cannibalism or behavioral avoidance of cannibalism. The effect of behavioral avoidance of cannibalism, however, depends on how strongly it affects the maturation rate of the predator. Behavioral interactions between predator stages reduce the short-term positive effect of cannibalism on the prey density, but can enhance its positive long-term effects. Both interaction types reduce the destabilizing effect of enrichment. These results suggest that inconsistencies between data and simple models can be resolved by accounting for stage-structured interactions within and among species.

In many consumer—resource systems the consumer population has synchronized reproduction at regular intervals (e.g., years) but consumes the resource and dies continuously, while the resource population grows continuously or has overlapping generations that are short relative to the time between consumer reproductive events. Such systems require \"semi-discrete\" models that have both discrete and continuous components. This paper defines and analyzes a canonical, semi-discrete model for a widespread class of consumer—resource interactions in which the consumer is a discrete breeder and the resource reproduction can be described continuously. The model is the analog of the Nicholson-Bailey and Lotka-Volterra models for discrete and continuous systems, respectively. It thereby develops the basis for understanding more realistic, and hence more complex, semi-discrete models. The model can display stable equilibria, consumer—resource cycles, and single-species-like overcompensation cycles. Cycles are induced by high maximum fecundity in the consumer. If the resource grows rapidly and the consumer has high maximum fecundity, the model reduces to a single-species discrete-time model of the consumer, which can exhibit overcompensation cycles. By contrast, such cycles in discrete consumer—resource models typically occur only in the resource once the consumer is extinct. Also unlike a common class of discrete models that do not display consumer—resource cycles with periods below four years, semi-discrete models can exhibit consumer—resource cycles with periods as short as two years.