Coevolution-driven predator-prey cycles: predicting the characteristics of eco-coevolutionary cycles using fast-slow dynamical systems theory

Predation drives complex eco-evolutionary dynamics in sexually selected traits

Predation plays a role in preventing the evolution of ever more complicated sexual displays, because such displays often increase an individual's predation risk. Sexual selection theory, however, omits a key feature of predation in modeling costs to sexually selected traits: Predation is density dependent. As a result of this density dependence, predator-prey dynamics should feed back into the evolution of sexual displays, which, in turn, feeds back into predator-prey dynamics. Here, we develop both population and quantitative genetic models of sexual selection that explicitly link the evolution of sexual displays with predator-prey dynamics. Our primary result is that predation can drive eco-evolutionary cycles in sexually selected traits. We also show that mechanistically modeling the cost to sexual displays as predation leads to novel outcomes such as the maintenance of polymorphism in sexual displays and alters ecological dynamics by muting prey cycles. These results suggest predation as a potential mechanism to maintain variation in sexual displays and underscore that short-term studies of sexual display evolution may not accurately predict long-run dynamics. Further, they demonstrate that a common verbal model (that predation limits sexual displays) with widespread empirical support can result in unappreciated, complex dynamics due to the density-dependent nature of predation.

Evolutionarily stable strategies in stable and periodically fluctuating populations: The Rosenzweig-MacArthur predator-prey model

An evolutionarily stable strategy (ESS) is an evolutionary strategy that, if adapted by a population, cannot be invaded by any deviating (mutant) strategy. The concept of ESS has been extensively studied and widely applied in ecology and evolutionary biology [M. Smith, On Evolution (1972)] but typically on the assumption that the system is ecologically stable. With reference to a Rosenzweig-MacArthur predator-prey model [M. Rosenzweig, R. MacArthur, Am. Nat. 97, 209-223 (1963)], we derive the mathematical conditions for the existence of an ESS when the ecological dynamics have asymptotically stable limit points as well as limit cycles. By extending the framework of Reed and Stenseth [J. Reed, N. C. Stenseth, J. Theoret. Biol. 108, 491-508 (1984)], we find that ESSs occur at values of the evolutionary strategies that are local optima of certain functions of the model parameters. These functions are identified and shown to have a similar form for both stable and fluctuating populations. We illustrate these results with a concrete example.

How (co)evolution alters predator responses to increased mortality: extinction thresholds and hydra effects

Population responses to environmental change depend on both the ecological interactions between species and the evolutionary responses of all species. In this study, we explore how evolution in prey, predators, or both species affect the responses of predator populations to a sustained increase in mortality. We use an eco-evolutionary predator-prey model to explore how evolution alters the predator extinction threshold (defined as the minimum mortality rate that prevents population growth at low predator densities) and predator hydra effects (increased predator abundance in response to increased mortality). Our analysis identifies how evolutionary responses of prey and predators individually affect the predator extinction threshold and hydra effects, and how those effects are altered by interactions between the evolutionary responses. Based on our theoretical results, we predict that it is common in natural systems for evolutionary responses in one or both species to allow predators to persist at higher mortality rates than would be possible in the absence of evolution (i.e., evolution increases the predator mortality extinction threshold). We also predict that evolution-driven hydra effects occur in a minority of natural systems, but are not rare. We revisited published eco-evolutionary models and found that evolution causes hydra effects and increases the predator extinction threshold in many studies, but those effects have been overlooked. We discuss the implications of these results for species conservation, predicting population responses to environmental change, and the possibility of evolutionary rescue.

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.

Evolutionary contribution to coexistence of competitors in microbial food webs

The theory of species coexistence is a key concept in ecology that has received much attention. The role of rapid evolution for determining species coexistence is still poorly understood although evolutionary change on ecological time-scales has the potential to change almost any ecological process. The influence of evolution on coexistence can be especially pronounced in microbial communities where organisms often have large population sizes and short generation times. Previous work on coexistence has assumed that traits involved in resource use and species interactions are constant or change very slowly in terms of ecological time-scales. However, recent work suggests that these traits can evolve rapidly. Nevertheless, the importance of rapid evolution to coexistence has not been tested experimentally. Here, we show how rapid evolution alters the frequency of two bacterial competitors over time when grown together with specialist consumers (bacteriophages), a generalist consumer (protozoan) and all in combination. We find that consumers facilitate coexistence in a manner consistent with classic ecological theory. However, through disentangling the relative contributions of ecology (changes in consumer abundance) and evolution (changes in traits mediating species interactions) on the frequency of the two competitors over time, we find differences between the consumer types and combinations. Overall, our results indicate that the influence of evolution on species coexistence strongly depends on the traits and species interactions considered.

Disentangling eco-evolutionary dynamics of predator-prey coevolution: the case of antiphase cycles

The impact of rapid predator-prey coevolution on predator-prey dynamics remains poorly understood, as previous modelling studies have given rise to contradictory conclusions and predictions. Interpreting and reconciling these contradictions has been challenging due to the inherent complexity of model dynamics, defying mathematical analysis and mechanistic understanding. We develop a new approach here, based on the Geber method for deconstructing eco-evolutionary dynamics, for gaining such understanding. We apply this approach to a co-evolutionary predator-prey model to disentangle the processes leading to either antiphase or ¼-lag cycles. Our analysis reveals how the predator-prey phase relationship is driven by the temporal synchronization between prey biomass and defense dynamics. We further show when and how prey biomass and trait dynamics become synchronized, resulting in antiphase cycles, allowing us to explain and reconcile previous modelling and empirical predictions. The successful application of our proposed approach provides an important step towards a comprehensive theory on eco-evolutionary feedbacks in predator-prey systems.

Stability of A Coevolving Host-parasite System Peaks at Intermediate Productivity

Habitat productivity may affect the stability of consumer-resource systems, through both ecological and evolutionary mechanisms. We hypothesize that coevolving consumer-resource systems show more stable dynamics at intermediate resource availability, while very low-level resource supply cannot support sufficiently large populations of resource and consumer species to avoid stochastic extinction, and extremely resource-rich environments may promote escalatory arms-race-like coevolution that can cause strong fluctuations in species abundance and even extinction of one or both trophic levels. We tested these ideas by carrying out an experimental evolution study with a model bacterium-phage system (Pseudomonas fluorescens SBW25 and its phage SBW25Φ2). Consistent with our hypothesis, this system was most stable at intermediate resource supply (fewer extinction events and smaller magnitude of population fluctuation). In our experiment, the rate of coevolution between bacterial resistance and phage infectivity was correlated with the magnitude of population fluctuation, which may explain the different in stability between levels of resource supply. Crucially, our results are consistent with a suggestion that, among the two major modes of antagonistic coevolution, arms race is more likely than fluctuation selection dynamics to cause extinction events in consumer-resource systems. This study suggests an important role of environment-dependent coevolutionary dynamics for the stability of consumer-resource species systems, therefore highlights the importance to consider contemporaneous evolutionary dynamics when studying the stability of ecosystems, particularly those under environmental changes.