Reversed predator–prey cycles are driven by the amplitude of prey oscillations

Ecoevolutionary feedbacks in predator–prey systems have been shown to qualitatively alter predator–prey dynamics. As a striking example, defense–offense coevolution can reverse predator–prey cycles, so predator peaks precede prey peaks rather than vice versa. However, this has only rarely been shown in either model studies or empirical systems. Here, we investigate whether this rarity is a fundamental feature of reversed cycles by exploring under which conditions they should be found. For this, we first identify potential conditions and parameter ranges most likely to result in reversed cycles by developing a new measure, the effective prey biomass, which combines prey biomass with prey and predator traits, and represents the prey biomass as perceived by the predator. We show that predator dynamics always follow the dynamics of the effective prey biomass with a classic ¼‐phase lag. From this key insight, it follows that in reversed cycles (i.e., ¾‐lag), the dynamics of the actual and the effective prey biomass must be in antiphase with each other, that is, the effective prey biomass must be highest when actual prey biomass is lowest, and vice versa. Based on this, we predict that reversed cycles should be found mainly when oscillations in actual prey biomass are small and thus have limited impact on the dynamics of the effective prey biomass, which are mainly driven by trait changes. We then confirm this prediction using numerical simulations of a coevolutionary predator–prey system, varying the amplitude of the oscillations in prey biomass: Reversed cycles are consistently associated with regions of parameter space leading to small‐amplitude prey oscillations, offering a specific and highly testable prediction for conditions under which reversed cycles should occur in natural systems.     

Impacts of consumer–resource interaction transitions on persistence and long‐term interaction outcomes of random ecological networks

Despite the prevalence of context‐dependent interaction transitions in ecological systems, their impacts on persistence and interaction diversity have scarcely been explored in complex ecological networks. By using multispecies bi‐directional and unidirectional consumer–resource models, representing a continuum of interaction transitions (sign change of interaction outcomes), we investigated the effects of structural interaction transitions on persistence (the fraction of remaining species) and long‐term interaction outcomes in random ecological networks. We found that high interaction strength of exploiting resources generally decreased persistence, and high strength of providing resources increased persistence when the strength of exploiting resources was low in more complex networks; also, the networks with high persistence had a high proportion of mutualistic interactions relative to antagonistic interactions present initially and over the long term. The shifting of interaction strengths shaped the long‐term interaction compositions. Meanwhile, population dynamics, especially species extinction, affected the difference between initial and long‐term interactions. Based on classical consumer–resource theory, these results establish a transitional continuum of interaction outcomes in ecological networks and imply a theoretical association among interaction transition, community persistence and interaction diversity.     

CONSUMER–RESOURCE INTERACTIONS AND THE EVOLUTION OF MIGRATION

Theoretical studies have demonstrated that selection will favor increased migration when fitnesses vary both temporally and spatially, but it is far from clear how pervasive those theoretical conditions are in nature. Although consumer–resource interactions are omnipresent in nature and can generate spatial and temporal variation, it is unknown even in theory whether these dynamics favor the evolution of migration. We develop a mathematical model to address whether and how migration evolves when variability in fitness is determined at least in part by consumer–resource coevolutionary interactions. Our analyses show that such interactions can drive the evolution of migration in the resource, consumer, or both species and thus supplies a general explanation for the pervasiveness of migration. Over short time scales, we show the direction of change in migration rate is determined primarily by the state of local adaptation of the species involved: rates increase when a species is locally maladapted and decrease when locally adapted. Our results reveal that long‐term evolutionary trends in migration rates can differ dramatically depending on the strength or weakness of interspecific interactions and suggest an explanation for the evolutionary divergence of migration rates among interacting species.     

Modelling inducible defences in predator–prey interactions: assumptions and dynamical consequences of three distinct approaches

Inducible defences against predation are widespread in the natural world, allowing prey to economise on the costs of defence when predation risk varies over time or is spatially structured. Through interspecific interactions, inducible defences have major impacts on ecological dynamics, particularly predator–prey stability and phase lag. Researchers have developed multiple distinct approaches, each reflecting assumptions appropriate for particular ecological communities. Yet, the impact of inducible defences on ecological dynamics can be highly sensitive to the modelling approach used, making the choice of model a critical decision that affects interpretation of the dynamical consequences of inducible defences. Here, we review three existing approaches to modelling inducible defences: Switching Function, Fitness Gradient and Optimal Trait. We assess when and how the dynamical outcomes of these approaches differ from each other, from classic predator–prey dynamics and from commonly observed eco‐evolutionary dynamics with evolving, but non‐inducible, prey defences. We point out that the Switching Function models tend to stabilise population dynamics, and the Fitness Gradient models should be carefully used, as the difference with evolutionary dynamics is important. We discuss advantages of each approach for applications to ecological systems with particular features, with the goal of providing guidelines for future researchers to build on.     

Not attackable or not crackable—How pre‐ and post‐attack defenses with different competition costs affect prey coexistence and population dynamics

It is well‐known that prey species often face trade‐offs between defense against predation and competitiveness, enabling predator‐mediated coexistence. However, we lack an understanding of how the large variety of different defense traits with different competition costs affects coexistence and population dynamics. Our study focusses on two general defense mechanisms, that is, pre‐attack (e.g., camouflage) and post‐attack defenses (e.g., weaponry) that act at different phases of the predator—prey interaction. We consider a food web model with one predator, two prey types and one resource. One prey type is undefended, while the other one is pre‐ or post‐attack defended paying costs either by a higher half‐saturation constant for resource uptake or a lower maximum growth rate. We show that post‐attack defenses promote prey coexistence and stabilize the population dynamics more strongly than pre‐attack defenses by interfering with the predator's functional response: Because the predator spends time handling “noncrackable” prey, the undefended prey is indirectly facilitated. A high half‐saturation constant as defense costs promotes coexistence more and stabilizes the dynamics less than a low maximum growth rate. The former imposes high costs at low resource concentrations but allows for temporally high growth rates at predator‐induced resource peaks preventing the extinction of the defended prey. We evaluate the effects of the different defense mechanisms and costs on coexistence under different enrichment levels in order to vary the importance of bottom‐up and top‐down control of the prey community.     

Eco‐evolutionary feedback promotes Red Queen dynamics and selects for sex in predator populations

Although numerous hypotheses exist to explain the overwhelming presence of sexual reproduction across the tree of life, we still cannot explain its prevalence when considering all inherent costs involved. The Red Queen hypothesis states that sex is maintained because it can create novel genotypes with a selective advantage. This occurs when the interactions between species induce frequent environmental change. Here, we investigate whether coevolution and eco‐evolutionary feedback dynamics in a predator‐prey system allows for indirect selection and maintenance of sexual reproduction in the predator. Combining models and chemostat experiments of a rotifer‐algae system we show a continuous feedback between population and trait change along with recurrent shifts from selection by predation and competition for a limited resource. We found that a high propensity for sex was indirectly selected and was maintained in rotifer populations within environments containing these eco‐evolutionary dynamics; whereas within environments under constant conditions, predators evolved rapidly to lower levels of sex. Thus, our results indicate that the influence of eco‐evolutionary feedback dynamics on the overall evolutionary change has been underestimated.     

Moving forward in circles: challenges and opportunities in modelling population cycles

Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer–resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non‐intuitive ways, the high‐dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco‐evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem‐level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research.     

Natural enemy specialization and the period of population cycles

The dynamical consequences of multiple‐species interactions remain an elusive and fiercely debated topic. Recently, Murdoch and colleagues proposed a general rule for the dynamics of generalist natural enemies: when periodic, they exhibit single generation cycles (SGCs), similar to single species systems. This contrasts markedly with specialists, which tend to show classic (longer period) consumer–resource cycles. Using a well‐studied laboratory system, we show that this general rule is contradicted when we consider resource age‐structure.     

Testing the validity of functional response models using molecular gut content analysis for prey choice in soil predators

Analysis of predator–prey interactions is a core concept of animal ecology, explaining structure and dynamics of animal food webs. Measuring the functional response, i.e. the intake rate of a consumer as a function of prey density, is a powerful method to predict the strength of trophic links and assess motives of prey choice, particularly in arthropod communities. However, due to their reductionist set‐up, functional responses, which are based on laboratory feeding experiments, may not display field conditions, possibly leading to skewed results. Here, we tested the validity of functional responses of centipede predators and their prey by comparing them with empirical gut content data from field‐collected predators. Our predator–prey system included lithobiid and geophilomorph centipedes, abundant and widespread predators of forest soils and their soil‐dwelling prey. First, we calculated the body size‐dependent functional responses of centipedes using a published functional response model in which we included natural prey abundances and animal body masses. This allowed us to calculate relative proportions of specific prey taxa in the centipede diet. In a second step, we screened field‐collected centipedes for DNA of eight abundant soil‐living prey taxa and estimated their body size‐dependent proportion of feeding events. We subsequently compared empirical data for each of the eight prey taxa, on proportional feeding events with functional response‐derived data on prey proportions expected in the gut, showing that both approaches significantly correlate in five out of eight predator–prey links for lithobiid centipedes but only in one case for geophilomorph centipedes. Our findings suggest that purely allometric functional response models, which are based on predator–prey body size ratios are too simple to explain predator–prey interactions in a complex system such as soil. We therefore stress that specific prey traits, such as defence mechanisms, must be considered for accurate predictions.     

Effects of warming on predator–prey interactions – a resource‐based approach and a theoretical synthesis

We theoretically explore consequences of warming for predator–prey dynamics, broadening previous approaches in three ways: we include beyond‐optimal temperatures, predators may have a type III functional response, and prey carrying capacity depends on explicitly modelled resources. Several robust patterns arise. The relationship between prey carrying capacity and temperature can range from near‐independence to monotonically declining/increasing to hump‐shaped. Predators persist in a U‐shaped region in resource supply (=enrichment)‐temperature space. Type II responses yield stable persistence in a U‐shaped band inside this region, giving way to limit cycles with enrichment at all temperatures. In contrast, type III responses convey stability at intermediate temperatures and confine cycles to low and high temperatures. Warming‐induced state shifts can be predicted from system trajectories crossing stability and persistence boundaries in enrichment‐temperature space. Results of earlier studies with more restricted assumptions map onto this graph as special cases. Our approach thus provides a unifying framework for understanding warming effects on trophic dynamics.     

Eco‐evolutionary dynamics in a coevolving host–virus system

Eco‐evolutionary dynamics have been shown to be important for understanding population and community stability and their adaptive potential. However, coevolution in the framework of eco‐evolutionary theory has not been addressed directly. Combining experiments with an algal host and its viral parasite, and mathematical model analyses we show eco‐evolutionary dynamics in antagonistic coevolving populations. The interaction between antagonists initially resulted in arms race dynamics (ARD) with selective sweeps, causing oscillating host–virus population dynamics. However, ARD ended and populations stabilised after the evolution of a general resistant host, whereas a trade‐off between host resistance and growth then maintained host diversity over time (trade‐off driven dynamics). Most importantly, our study shows that the interaction between ecology and evolution had important consequences for the predictability of the mode and tempo of adaptive change and for the stability and adaptive potential of populations.     

Fitness minimization and dynamic instability as a consequence of predator–prey coevolution

We analyse dynamic models of the coevolution of continuous traits that determine the capture rate of a prey species by a predator. The goal of the analysis is to determine conditions when the coevolutionary dynamics will be unstable and will generate population cycles. We use a simplified model of the evolutionary dynamics of quantitative traits in which the rate of change of the mean trait value is proportional to the rate of increase of individual fitness with trait value. Traits that increase ability in the predatory interaction are assumed to have negative effects on another component of fitness. We concentrate on the role of equilibrial fitness minima in producing cycles. In this case, the mean trait of a rapidly evolving species minimizes its fitness and it is chased around this equilibrium by adaptive evolution in the other species. Such cases appear to be most likely if the capture rate of prey by predators is maximal when predator and prey phenotypes match each other. They are possible, but less likely when traits in each species determine a one-dimensional axis of ability related to the interaction. Population dynamics often increase the range of parameter values for which cycles occur, relative to purely evolutionary models, although strong prey self-regulation may stabilize an evolutionarily unstable subsystem.     

Hot spots become cold spots: coevolution in variable temperature environments

Antagonistic coevolution between hosts and parasites is a key process in the genesis and maintenance of biological diversity. Whereas coevolutionary dynamics show distinct patterns under favourable environmental conditions, the effects of more realistic, variable conditions are largely unknown. We investigated the impact of a fluctuating environment on antagonistic coevolution in experimental microcosms of Pseudomonas fluorescens SBW25 and lytic phage SBWΦ2. High‐frequency temperature fluctuations caused no deviations from typical coevolutionary arms race dynamics. However, coevolution was stalled during periods of high temperature under intermediate‐ and low‐frequency fluctuations, generating temporary coevolutionary cold spots. Temperature variation affected population density, providing evidence that eco‐evolutionary feedbacks act through variable bacteria–phage encounter rates. Our study shows that environmental fluctuations can drive antagonistic species interactions into and out of coevolutionary cold and hot spots. Whether coevolution persists or stalls depends on the frequency of change and the environmental optima of both interacting players.     

Top–down limits on prey populations may be more severe in larger prey species,despite having fewer predators

Variation in the vulnerability of herbivore prey to predation is linked to body size, yet whether this relationship is size‐nested or size‐partitioned remains debated. If size‐partitioned, predators would be focused on prey within their preferred prey size range. If size‐nested, smaller prey species should become increasingly more vulnerable because increasingly more predators are capable of catching them. Yet, whether either of these strategies manifests in top–down prey population limitation would depend both on the number of potential predator species as well as the total mortality imposed. Here we use a rare ecosystem scale ‘natural experiment’ comparing prey population dynamics between a period of intense predator persecution and hence low predator densities and a period of active predator protection and population recovery. We use three decades of data on herbivore abundance and distribution to test the role of predation as a mechanism of population limitation among prey species that vary widely in body size. Notably, we test this within one of the few remaining systems where a near‐full suite of megaherbivores occur in high density and are thus able to include a thirtyfold range in herbivore body size gradient. We test whether top–down limitation on prey species of particular body size leads to compositional shifts in the mammalian herbivore community. Our results support both size‐nested and size‐partitioning predation but suggest that the relative top–down limiting impact on prey populations may be more severe for intermediate sized species, despite having fewer predators than small species. In addition we show that the gradual recovery of predator populations shifted the herbivore community assemblage towards large‐bodied species and has led to a community that is strongly dominated by large herbivore biomass.     

Declining body size in an endangered large mammal

Body size affects almost every aspect of the biology of a species. According to the ‘resource rule’, decreasing resource availability (e.g. prey density) will lead to a reduction in body size or, alternatively, a decline in mass‐independent energy expenditure. In the present study, we provide a test of this hypothesis, assessing the effect of significantly decreasing prey density on endangered African wild dog (Lycaon pictus) body size and energy expenditure over a 20‐year period. As predicted from the ‘resource rule’, decreasing resource availability resulted in energetic re‐allocation: wild dogs' body size decreased significantly (both shorter and slimmer), whereas our fitness‐related measure of energy expenditure (i.e. litter size) remained constant over time. A phenotypic change of up to 17% within 20 years, as found in the present study, appears to be unprecedented in a nonharvested large mammal, thus advancing the emerging field of eco‐evolutionary dynamics. © 2011 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, 105 , 8–12.     

Exploring context dependency in eco‐evolutionary patterns with the stick insect Timema cristinae

Rapid evolution can influence the ecology of populations, communities, and ecosystems, but the importance of evolution for ecological dynamics remains unclear, largely because the contexts in which evolution is powerful are poorly resolved. Here, we carry out a large observational study to test hypotheses about context dependency of eco‐evolutionary patterns previously identified on the stick insect Timema cristinae. Experiments and observations conducted in 2011 and 2012 documented predator‐mediated negative effects of camouflage maladaptation (i.e., evolutionary dynamics) on: (a) T. cristinae abundance and, (b) species richness and abundance of other arthropods. Here we show that camouflage maladaptation does not correlate with T. cristinae abundance and, instead, is associated with increased abundance and species richness of cohabitating arthropods. We furthermore find that plants with high levels of Timema maladaptation tend to have higher foliar nitrogen, that is, higher nutritional value, and more positive mass‐abundance slopes in the coexisting arthropod communities. We propose explanations for the observed contrasting results, such as negative density‐ and frequency‐dependent selection, feedbacks between herbivore abundance and plant nutritional quality, and common effects of predation pressure on selection and prey abundance. Our results demonstrate the utility of observational studies to assess the context dependency of eco‐evolutionary dynamics patterns and provide testable hypotheses for future work.     

Coevolutionary alternation in antagonistic interactions

Coevolution between parasites and hosts or predators and prey often involves multiple species with similar kinds of defenses and counter-defenses. Classic examples include the interactions between phytophagous insects and their host plants, thick-shelled invertebrates and their shell-crushing predators, and ungulates and their predators. There are three major hypotheses for the nonequilibrium coevolutionary dynamics of these multispecific trophic interactions: escalation in traits, cycles in traits leading to fluctuating polymorphisms, and coevolutionary alternation. The conditions under which cycles and escalation are likely to occur have been well developed theoretically. In contrast, the conditions favoring coevolutionary alternation-evolutionary fluctuations in predator or prey preference driven by evolutionary shifts in relative levels of prey defense and vice versa-have yet to be identified. Using a set of quantitative coevolutionary models, we demonstrate that coevolutionary alternation can occur across a wide range of biologically plausible conditions. The result is often repeated, and potentially rapid, evolutionary shifts in patterns of specialization within networks of interacting species.     

A synthesis of subdisciplines: predator–prey interactions, and biodiversity and ecosystem functioning

The last 15 years has seen parallel surges of interest in two research areas that have rarely intersected: biodiversity and ecosystem functioning (BEF), and multispecies predator–prey interactions (PPI). Research addressing role of biodiversity in ecosystem functioning has focused primarily on single trophic‐level systems, emphasizing additive effects of diversity that manifest through resource partitioning and the sampling effect. Conversely, research addressing predator–prey interactions has focused on two trophic‐level systems, emphasizing indirect and non‐additive interactions among species. Here, we use a suite of consumer‐resource models to organize and synthesize the ways in which consumer species diversity affects the densities of both resources and consumer species. Specifically, we consider sampling effects, resource partitioning, indirect effects caused by intraguild interactions and non‐additive effects. We show that the relationship between consumer diversity and the density of resources and consumer species are broadly similar for systems with one vs. two trophic levels, and that indirect and non‐additive interactions generally do little more than modify the impacts of diversity established by the sampling effect and resource partitioning. The broad similarities between systems with one vs. two trophic levels argue for greater communication between researchers studying BEF, and researchers studying multispecies PPI.     

Transient dynamics limit the effectiveness of keystone predation in bringing about coexistence

We analyze the transient dynamics of simple models of keystone predation, in which a predator preferentially consumes the dominant of two (or more) competing prey species. We show that coexistence is unlikely in many systems characterized both by successful invasion of either prey species into the food web that lacks it and by a stable equilibrium with high densities of all species. Invasion of the predator-resistant consumer species often causes the resident, more vulnerable prey to crash to such low densities that extinction would occur for many realistic population sizes. Subsequent transient cycles may entail very low densities of the predator or of the initially successful invader, which may also preclude coexistence of finite populations. Factors causing particularly low minimum densities during the transient cycles include biotic limiting resources for the prey, limited resource partitioning between the prey, a highly efficient predator with relatively slow dynamics, and a vulnerable prey whose population dynamics are rapid relative to the less vulnerable prey. Under these conditions, coexistence of competing prey via keystone predation often requires that the prey's competitive or antipredator characteristics fall within very narrow ranges. Similar transient crashes are likely to occur in other food webs and food web models.     

The virtues and limitations of exploring the eco‐evolutionary dynamics of sexually selected traits

Most studies on eco‐evolutionary feedbacks concern the influence of abiotic factors, or predator–prey and host–parasite interactions, while studies involving sexual interactions are lagging behind. This is at odds with the potential of these interactions to engage in such processes. Indeed, there is now ample evidence that sexual selection is affected by ecological change and that sexually selected traits can evolve rapidly, which may modify the ecological context of populations, and thus the selection pressures they will be exposed to. Here we review evidence for such eco‐evolutionary processes. We discuss examples of eco‐evolutionary change in an attempt to understand the challenges related with identifying and characterizing such processes. In particular, we focus on the challenges associated with accurately identifying the components of the feedback as well as their causal relation. Finally, we evaluate scenarios where understanding eco‐evolutionary feedbacks of sexual selection may help us appreciate the effects of sexual selection in shaping evolutionary processes.