Joint evolution of predator body size and prey-size preference

We studied the joint evolution of predator body size and prey-size preference based on dynamic energy budget theory. The predators’ demography and their functional response are based on general eco-physiological principles involving the size of both predator and prey. While our model can account for qualitatively different predator types by adjusting parameter values, we mainly focused on ‘true’ predators that kill their prey. The resulting model explains various empirical observations, such as the triangular distribution of predator–prey size combinations, the island rule, and the difference in predator–prey size ratios between filter feeders and raptorial feeders. The model also reveals key factors for the evolution of predator–prey size ratios. Capture mechanisms turned out to have a large effect on this ratio, while prey-size availability and competition for resources only help explain variation in predator size, not variation in predator–prey size ratio. Predation among predators is identified as an important factor for deviations from the optimal predator–prey size ratio.     

Lyapunov functions for Lotka–Volterra predator–prey models with optimal foraging behavior

 The theory of optimal foraging predicts abrupt changes in consumer behavior which lead to discontinuities in the functional response. Therefore population dynamical models with optimal foraging behavior can be appropriately described by differential equations with discontinuous right-hand sides. In this paper we analyze the behavior of three different Lotka–Volterra predator–prey systems with optimal foraging behavior. We examine a predator–prey model with alternative food, a two-patch model with mobile predators and resident prey, and a two-patch model with both predators and prey mobile. We show that in the studied examples, optimal foraging behavior changes the neutral stability intrinsic to Lotka–Volterra systems to the existence of a bounded global attractor. The analysis is based on the construction and use of appropriate Lyapunov functions for models described by discontinuous differential equations. Received: 23 March 1999     

Self-organised spatial patterns and chaos in a ratio-dependent predator–prey system

Mechanisms and scenarios of pattern formation in predator–prey systems have been a focus of many studies recently as they are thought to mimic the processes of ecological patterning in real-world ecosystems. Considerable work has been done with regards to both Turing and non-Turing patterns where the latter often appears to be chaotic. In particular, spatiotemporal chaos remains a controversial issue as it can have important implications for population dynamics. Most of the results, however, were obtained in terms of ‘traditional’ predator–prey models where the per capita predation rate depends on the prey density only. A relatively new family of ratio-dependent predator–prey models remains less studied and still poorly understood, especially when space is taken into account explicitly, in spite of their apparent ecological relevance. In this paper, we consider spatiotemporal pattern formation in a ratio-dependent predator–prey system. We show that the system can develop patterns both inside and outside of the Turing parameter domain. Contrary to widespread opinion, we show that the interaction between two different type of instability, such as the Turing–Hopf bifurcation, does not necessarily lead to the onset of chaos; on the contrary, the emerging patterns remain stationary and almost regular. Spatiotemporal chaos can only be observed for parameters well inside the Turing–Hopf domain. We then investigate the relative importance of these two instability types on the onset of chaos and show that, in a ratio-dependent predator–prey system, the Hopf bifurcation is indeed essential for the onset of chaos whilst the Turing instability is not.     

The role of noise in a predator–prey model with Allee effect

The existence and implications of alternative stable states in ecological systems have been investigated extensively within deterministic models. However, it is known that natural systems are undeniably subject to random fluctuations, arising from either environmental variability or internal effects. Thus, in this paper, we study the role of noise on the pattern formation of a spatial predator–prey model with Allee effect. The obtained results show that the spatially extended system exhibits rich dynamic behavior. More specifically, the stationary pattern can be induced to be a stable target wave when the noise intensity is small. As the noise intensity is increased, patchy invasion emerges. These results indicate that the dynamic behavior of predator–prey models may be partly due to stochastic factors instead of deterministic factors, which may also help us to understand the effects arising from the undeniable susceptibility to random fluctuations of real ecosystems.     

From pattern to process: identifying predator–prey models from time-series data

Fitting nonlinear models to time-series is a technique of increasing importance in population ecology. In this article, we apply it to assess the importance of predator dependence in the predation process by comparing two alternative models of equal complexity (one with and one without predator dependence) to predator–prey time-series. Stochasticities in such data come from both observation error and process error. We consider how these errors must be taken into account in the fitting process, and we develop eight different model selection criteria. Applying these criteria to laboratory data on simple protozoan and arthropod predator–prey systems shows that little predator dependence is present, with one interesting exception. Field data are more ambiguous (either selection depends on the particular criterion or no significant differences can be detected), and we show that both models fit reasonably well. We conclude that, within our modeling framework, predator dependence is in general insignificant in simple systems in homogeneous environments. Relatively complex systems show significant predator dependence more often than simple ones but the data are also often inconclusive. The analysis of such systems should rely on several models to detect predictions that are sensitive to predator dependence and to direct further research if necessary. Received: July 13, 2000 / Accepted: September 25, 2001     

Influence of consumer mutual interference on the stabilization of a three-level trophic system

In this paper, we present a three-level (food–prey–predator) trophic food chain which includes consumer mutual interference (MIF). In contrast with other analyses, we consider the effect of both prey and predator MIF on the dynamics of a three-level trophic system. MIF is generally considered to exert a stabilizing effect on population dynamics based on the predator–prey model. However, results from analytical and numerical simulations utilizing a simple three-species food chain model suggest that while the addition of prey MIF to the model provides a stabilizing influence, as the chaotic dynamics collapse to a stable steady state, adding only predator MIF to the model can only stabilize the system at intermediate MIF values. The three-species trophic food chain is also stabilized when combination of both prey and predator MIF is added to the model. Our work serves to provide insight into the effects of MIF in the real world.     

Extinction of top-predator in a three-level food-chain model

 In this paper we extend the Lyapunov functions, constructed by A. Ardito and P. Ricciardi for predator–prey system [1], to the three level food chain models. We first consider a general three-level food-chain model. A criterion for the extinction of top predator will be given. Then we restrict our attentions to the case in which the prey is of logistic growth and predators have Holling’s type II functional responses. Received: 10 October 1997     

Bayesian Inference for Functional Response in a Stochastic Predator–Prey System

We present a Bayesian method for functional response parameter estimation starting from time series of field data on predator–prey dynamics. Population dynamics is described by a system of stochastic differential equations in which behavioral stochasticities are represented by noise terms affecting each population as well as their interaction. We focus on the estimation of a behavioral parameter appearing in the functional response of predator to prey abundance when a small number of observations is available. To deal with small sample sizes, latent data are introduced between each pair of field observations and are considered as missing data. The method is applied to both simulated and observational data. The results obtained using different numbers of latent data are compared with those achieved following a frequentist approach. As a case study, we consider an acarine predator–prey system relevant to biological control problems.     

Pattern formation in a space- and time-discrete predator–prey system with a strong Allee effect

The spatiotemporal dynamics of a space- and time-discrete predator–prey system is considered theoretically using both analytical methods and computer simulations. The prey is assumed to be affected by the strong Allee effect. We reveal a rich variety of pattern formation scenarios. In particular, we show that, in a predator–prey system with the strong Allee effect for prey, the role of space is crucial for species survival. Pattern formation is observed both inside and outside of the Turing domain. For parameters when the local kinetics is oscillatory, the system typically evolves to spatiotemporal chaos. We also consider the effect of different initial conditions and show that the system exhibits a spatiotemporal multistability. In a certain parameter range, the system dynamics is not self-organized but remembers the details of the initial conditions, which evokes the concept of long-living ecological transients. Finally, we show that our findings have important implications for the understanding of population dynamics on a fragmented habitat.     

Water turbidity affects predator–prey interactions in a fish–damselfly system

Community structure may differ dramatically between clear-water and turbid lakes. These differences have been attributed to differences in the cascading effect of fish on prey populations, owing to the reduced efficiency of fish predation in the presence of macrophytes. However, recent theoretical ideas suggest that water turbidity may shape predator–prey interactions, and it is predicted that prey will relax its antipredation behaviour in turbid water (H1). As a result, the nature of predator–prey interactions is expected to shift from both direct and indirect in clear water to dominantly direct in turbid water (H2). We tested these ideas in a fish–damselfly predator–prey system. In a first behavioural experiment, we looked at antipredation behaviour of damselfly larvae isolated from habitats that differ in turbidity, in the presence of fish in clear and turbid water. As predicted in H1, the larvae were more active in turbid than in clear water. In a complementary enclosure experiment, we reared larvae in a clear-water pond and a turbid pond, respectively, and manipulated the origin of the larvae (clear-water, turbid pond), fish presence (absent, present), and vegetation density (sparse, abundant). In both ponds, fish had a direct negative effect on survival of the larvae, which was mitigated in the presence of vegetation. In the fish treatment, the change in average body mass tended to be higher in the turbid pond than in the clear-water pond, suggesting indirect effects of fish were mitigated in the turbid pond. This was supported by a negative effect of fish on the effective growth rate of larvae in the clear pond, but not in the turbid pond. These results are compatible with the idea that predator–prey relationships are mainly governed by direct effects in turbid water, and by direct and indirect effects in clear water.     

Self-optimization, community stability, and fluctuations in two individual-based models of biological coevolution

We compare and contrast the long-time dynamical properties of two individual-based models of biological coevolution. Selection occurs via multispecies, stochastic population dynamics with reproduction probabilities that depend nonlinearly on the population densities of all species resident in the community. New species are introduced through mutation. Both models are amenable to exact linear stability analysis, and we compare the analytic results with large-scale kinetic Monte Carlo simulations, obtaining the population size as a function of an average interspecies interaction strength. Over time, the models self-optimize through mutation and selection to approximately maximize a community potential function, subject only to constraints internal to the particular model. If the interspecies interactions are randomly distributed on an interval including positive values, the system evolves toward self-sustaining, mutualistic communities. In contrast, for the predator–prey case the matrix of interactions is antisymmetric, and a nonzero population size must be sustained by an external resource. Time series of the diversity and population size for both models show approximate 1/f noise and power-law distributions for the lifetimes of communities and species. For the mutualistic model, these two lifetime distributions have the same exponent, while their exponents are different for the predator–prey model. The difference is probably due to greater resilience toward mass extinctions in the food-web like communities produced by the predator–prey model.      

Role of Quantity of Additional Food to Predators as a Control in Predator–Prey Systems with Relevance to Pest Management and Biological Conservation

Necessity to understand the role of additional food as a tool in biological control programs is being increasingly felt, particularly due to its eco-friendly nature. A thorough mathematical analysis in this direction revealed the vital role of quality and quantity of the additional food in the controllability of the predator–prey systems. In this article controllability of the additional food—provided predator–prey system is studied from perspectives of pest eradication and biological conservation. Time optimal paths have been constructed to drive the state of the system to a desired terminal state by choosing quantity of the additional food as control variable. The theory developed in this article has been illustrated by solving problems related to pest eradication and biological conservation.     

Predator–prey relationships in a Mediterranean vertebrate system: Bonelli’s eagles,rabbits and partridges

How predators impact on prey population dynamics is still an unsolved issue for most wild predator–prey communities. When considering vertebrates, important concerns constrain a comprehensive understanding of the functioning of predator–prey relationships worldwide; e.g. studies simultaneously quantifying ‘functional’ and ‘numerical responses’ (i.e., the ‘total response’) are rare. The functional, the numerical, and the resulting total response (i.e., how the predator per capita intake, the population of predators and the total of prey eaten by the total predators vary with prey densities) are fundamental as they reveal the predator’s ability to regulate prey population dynamics. Here, we used a multi-spatio-temporal scale approach to simultaneously explore the functional and numerical responses of a territorial predator (Bonelli’s eagle Hieraaetus fasciatus) to its two main prey species (the rabbit Oryctolagus cuniculus and the red-legged partridge Alectoris rufa) during the breeding period in a Mediterranean system of south Spain. Bonelli’s eagle responded functionally, but not numerically, to rabbit/partridge density changes. Type II, non-regulatory, functional responses (typical of specialist predators) offered the best fitting models for both prey. In the absence of a numerical response, Bonelli’s eagle role as a regulating factor of rabbit and partridge populations seems to be weak in our study area. Simple (prey density-dependent) functional response models may well describe the short-term variation in a territorial predator’s consumption rate in complex ecosystems.     

Predator–prey encounter rates in freshwater piscivores: effects of prey density and water transparency

One of the most fundamental components of predator–prey models is encounter rate, modelled as the product of prey density and search efficiency. Encounter rates have, however, rarely been measured in empirical studies. In this study, we used a video system approach to estimate how encounter rates between piscivorous fish that use a sit-and-wait foraging strategy and their prey depend on prey density and environmental factors such as turbidity. We first manipulated prey density in a controlled pool and field enclosure experiments where environmental factors were held constant. In a correlative study of 15 freshwater lakes we then estimated encounter rates in natural habitats and related the results to both prey fish density and environmental factors. We found the expected positive dependence of individual encounter rates on prey density in our pool and enclosure experiments, whereas the relation between school encounter rate and prey density was less clear. In the field survey, encounter rates did not correlate with prey density but instead correlated positively with water transparency. Water transparency decreases with increasing prey density along the productivity gradient and will reduce prey detection distance and thus predator search efficiency. Therefore, visual predator–prey encounter rates do not increase, and may even decrease, with increasing productivity despite increasing prey densities.     

Tadpole–odonate larvae interactions: influence of body size and diel rhythm

Several studies have shown that prey and predator body size may affect the outcome of predator–prey interactions. However, few studies have taken in account the changes on predator–prey interactions over 24 h. In a tropical freshwater system I evaluated how predator and prey size, and their diel rhythm in activity influenced the interaction between Physalaemus pustulosus tadpoles and dragonfly larvae. Tadpoles of different size classes were exposed to two size classes of the dragonfly larvae Rhionaeschna spec. Feeding trials were conducted during day and night. Tadpole activity showed a diel rhythm and affected size-selective predation of the smallest dragonfly larvae, but not of the larger ones. Predator and prey size had a significant effect on the prey survivorship and prey size had a significant effect on the preference of the predator. The interaction between both factors was significant, indicating that they did not operate independently. I conclude that the predator–prey interactions between odonate larvae and anuran tadpoles were mainly affected by the size of the prey and the predator, and less by the diel activity pattern of the prey.     

Scaling up population dynamic processes in a ladybird–aphid system

Here, we study how scaling up to the metapopulation level affects predictions of a population dynamics model motivated by an aphidophagous predator–aphid system. The model incorporates optimization of egg distribution in predatory females, cannibalism among their offspring, and self-regulation of the prey population. These factors determine the within-year dynamics of the system and translate the numbers of prey and predator individuals at the beginning of the season into their numbers at the end of the season at the level of one patch—one suitable host plant or a group of these. At the end of each season, all populations of prey and all populations of predators are mixed (this simulates aphid host-alternation and ladybird migration to hibernation sites), and then redistributed at the beginning of the next season. Prey individuals are distributed at random among the patches as a “prey rain”, while adult predators that survived from the previous season optimize the distribution of their offspring, in that they prefer patches with sufficient amount of prey and absence of other predators. This redistribution followed by within-season dynamics is then iterated over many seasons. We look at whether small-scale trends in population dynamics predicted by this model are consistent with large-scale outcomes. Specifically, we show that even on the metapopulation scale, the impact of predators on prey metapopulation is relatively low. We further show how the dates of predator arrival to and departure from the system affect the qualitative behaviour of the model predictions.     

Evolutionary ecology of inducible morphological plasticity in predator–prey interaction: toward the practical links with population ecology

The outcome of species interactions is often strongly influenced by variation in the functional traits of the individuals participating. A rather large body of work demonstrates that inducible morphological plasticity in predators and prey can both influence and be influenced by species interaction strength, with important consequences for individual fitness. Much of the past research in this area has focused on the ecological and evolutionary significance of trait plasticity by studying single predator–prey pairs and testing the performance of individuals having induced and noninduced phenotypes. This research has thus been critical in improving our understanding of the adaptive value of trait plasticity and its widespread occurrence across species and community types. More recently, researchers have expanded this foundation by examining how the complexity of organismal design and community-level properties can shape plasticity in functional traits. In addition, researchers have begun to merge evolutionary and ecological perspectives by linking trait plasticity to community dynamics, with particular attention on trait-mediated indirect interactions. Here, we review recent studies on inducible morphological plasticity in predators and their prey with an emphasis on internal and external constraints and how the nature of predator–prey interactions influences the expression of inducible phenotypes. In particular, we focus on multiple-trait plasticity, flexibility and modification of inducible plasticity, and reciprocal plasticity between predator and prey. Based on our arguments on these issues, we propose future research directions that should better integrate evolutionary and population studies and thus improve our understanding of the role of phenotypic plasticity in predator–prey population and community dynamics.     

Stable isotope characterization of mammalian predator–prey relationships in a South African savanna

This paper characterizes predator–prey interactions amongst African mammals from C₄ savanna environments using stable carbon and nitrogen isotope proxies for diet. Stable carbon (δ¹³C) and nitrogen (δ¹⁵N) isotope data from hair and faeces of large African mammal carnivores, and herbivores as potential prey, are presented for a diverse range of taxa. Carbon-isotope data imply that most carnivores from the “lowveld” savanna of South Africa form part of C₄ grass-based food webs. Nitrogen isotope data show clear differences between trophic levels, although it appears that the magnitude of these differences varies between predators feeding on invertebrates and vertebrates, respectively. Whilst the number of carnivore samples for which data are available is relatively few, and data for prey are restricted mainly to large ungulate herbivores, results clearly demonstrate the potential for future applications of this technique to predator–prey food webs in African savannas. In tandem with traditional approaches, stable isotopes can help elucidate patterns of predator impacts on prey populations, domestic livestock, and resolving similar food webs in palaeoenvironmental contexts.     

The Effect of Habitat Fragmentation on Cyclic Population Dynamics: A Numerical Study

Through four spatially explicit models, we investigate how habitat fragmentation affects cyclic predator–prey population dynamics. We use a Partial Differential Equation (PDE) framework to describe the dispersal of predators and prey in a heterogeneous landscape made of high quality and low quality habitat patches, subject to increasing fragmentation through habitat separation and/or habitat loss. Our results show that habitat fragmentation decreases the amplitude of the predator–prey population cycles while average population density is not as strongly affected in general. Beyond these simple trends however, the four models show differing responses to fragmentation, indicating that when making predictions about population survival and persistence in the face of habitat fragmentation, the choice of model is important. Our results may inform conservation efforts in fragmented habitats for cyclic species such as the snowshoe hare and Canada lynx. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorised users.     

Identifying Predator–Prey Processes from Time-Series

The functional response is a key element in predator–prey models as well as in food chains and food webs. Classical models consider it as a function of prey abundance only. However, many mechanisms can lead to predator dependence, and there is increasing evidence for the importance of this dependence. Identification of the mathematical form of the functional response from real data is therefore a challenging task. In this paper we apply model-fitting to test if typical ecological predator–prey time series data, which contain both observation error and process error, can give some information about the form of the functional response. Working with artificial data (for which the functional response is known) we will show that with moderate noise levels, identification of the model that generated the data is possible. However, the noise levels prevailing in real ecological time-series can give rise to wrong identifications. We will also discuss the quality of parameter estimation by fitting differential equations to such time-series.