The ecology of fear and inverted biomass pyramids

In inverted biomass pyramids (IBPs) prey are outnumbered by their predators when measured by biomass. We investigate how prey should behave in the face of danger from higher predator biomass, and how anti-predator behavior (in the form of vigilance) can, in turn, affect the predator–prey system. In this study, we incorporate anti-predator behaviors into a Lotka–Volterra predator–prey model in the form of fixed and facultative vigilance. Facultative vigilance models behavior as a dynamic foraging game, allowing us to assess optimal behavioral responses in the context of IBPs using a dynamical fitness optimization approach. We model vigilance as a tradeoff between safety and either the prey's maximum growth rate or its carrying capacity. We assess the population dynamics of predators and prey with fear responses, and investigate the role fear plays on trophic structure. We found that the ecology of fear plays an important role in predator–prey systems, impacting trophic structure and the occurrence of IBPs. Fixed vigilance works against IBP structure by always reducing the predator–prey biomass ratio at equilibrium with increasing levels of vigilance. Facultative vigilance can actually promote IBPs, as prey can now adjust their vigilance levels to cope with increased predation and the costs associated with vigilance. This is especially true when the effectiveness of vigilance is low and predators are very lethal. In general, these trends are true whether the costs of vigilance are felt on the prey's maximum growth rate or its carrying capacity. Just as the ecology of fear, when first introduced, was used to explain why top carnivores are rare in terrestrial systems, it can also be used to understand how big fierce predators can be common in IBPs.     

The effect of group size on vigilance in Ruddy Turnstones Arenaria interpres varies with foraging habitat

Foraging birds can manage time spent vigilant for predators by forming groups of various sizes. However, group size alone will not always reliably determine the optimal level of vigilance. For example, variation in predation risk or food quality between patches may also be influential. In a field setting, we assessed how simultaneous variation in predation risk and intake rate affects the relationship between vigilance and group size in foraging Ruddy Turnstones Arenaria interpres. We compared vigilance, measured as the number of ‘head‐ups’ per unit time, in habitat types that differed greatly in prey energy content and proximity to cover from which predators could launch surprise attacks. Habitats closer to predator cover provided foragers with much higher potential net energy intake rates than habitats further from cover. Foragers formed larger and denser flocks on habitats closer to cover. Individual vigilance of foragers in all habitats declined with increasing flock size and increased with flock density. However, vigilance by foragers on habitats closer to cover was always higher for a given flock size than vigilance by foragers on habitats further from cover, and habitat remained an important predictor of vigilance in models including a range of potential confounding variables. Our results suggest that foraging Ruddy Turnstones can simultaneously assess information on group size and the general likelihood of predator attack when determining their vigilance contribution.     

Multi-behavioral strategies in a predator–prey game: an evolutionary algorithm analysis

Behavioral games between predators and prey often involve two sub-games: 'pre-encounter' games affecting the rate of encounter between predators and prey (e.g. predator–prey space games, Sih 2005 ), and 'post-encounter' games that influence the outcome of encounters (e.g. waiting games at prey refugia, Hugie 2003 , and games of vigilance, Brown et al. 1999 ). Most models, however, focus on only one or the other of these two sub-games.
I investigated a multi-behavioral game between predators and prey that integrated both pre-encounter and post-encounter behaviors. These behaviors included landscape-scale movements by predators and prey, a type of prey vigilance that increases immediately after an encounter and then decays over time ('ratcheting vigilance'), and predator management of prey vigilance. I analyzed the game using a computer-based evolutionary algorithm. This algorithm embedded an individual-based model of ecological interactions within a dynamic adaptive process of mutation and selection. I investigated how evolutionarily stable strategies (ESS) varied with the predators' learning ability, killing efficiency, density and rate of movement. I found that when predators learn prey location, random prey movement can be an ESS. Increased predator killing efficiency reduced prey movement, but only if the rate of predator movement was low. Predators countered ratcheting vigilance by delaying their follow-up attacks; however, this delay was reduced in the presence of additional predators. The interdependence of pre-and post-encounter behaviors revealed by the evolutionary algorithm suggests an intricate co-evolution of multi-behavioral predator–prey behavioral strategies.     

Does an opportunistic predator preferentially attack nonvigilant prey?

The dilution effect as an antipredation behaviour is the main theoretical reason for grouping in animals and states that all individuals in a group have an equal risk of being predated if equally spaced from each other and the predator. Stalking predators, however, increase their chance of attack success by preferentially targeting nonvigilant individuals, potentially making relative vigilance rates in a group relatively important in determining predation compared with the dilution effect. Many predators, however, attack opportunistically without stalking, when targeting of nonvigilant individuals may be less likely, so that the dilution effect will then be a relatively more important antipredation reason for grouping. We tested whether an opportunistically hunting predator, the sparrowhawk, Accipiter nisus, preferentially attacked vigilant or feeding prey models presented in pairs. We found that sparrowhawks attacked vigilant and feeding mounts at similar frequencies. Our results suggest that individuals should prioritize maximizing group size or individual vigilance dependent on the type of predator from which they are at risk. When the most likely predator is a stalker, individuals should aim to have the highest vigilance levels in a group, and there may be relatively little selective advantage to being in the largest group. In contrast, if the most likely predator is an opportunist, then individuals should simply aim to be in the largest group and can also spend more time foraging without compromising predation risk. For most natural systems this will mean a trade-off between the two strategies dependent on the frequency of attack of each predator type. Copyright 2003 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.     

The influence of vigilance on intraguild predation

Theoretical work on intraguild predation suggests that if a top predator and an intermediate predator share prey, the system will be stable only if the intermediate predator is better at exploiting the prey, and the top predator gains significantly from consuming the intermediate predator. In mammalian carnivore systems, however, there are examples of top predator species that attack intermediate predator species, but rarely or never consume the intermediate predator. We suggest that top predators attacking intermediate predators without consuming them may not only reduce competition with the intermediate predators, but may also increase the vigilance of the intermediate predators or alter the vigilance of their shared prey, and that this behavioral response may help to maintain the stability of the system. We examine two models of intraguild predation, one that incorporates prey vigilance, and a second that incorporates intermediate predator vigilance. We find that stable coexistence can occur when the top predator has a very low consumption rate on the intermediate predator, as long as the attack rate on the intermediate predator is relatively large. However, the system is stable when the top predator never consumes the intermediate predator only if the two predators share more than one prey species. If the predators do share two prey species, and those prey are vigilant, increasing top predator attack rates on the intermediate predator reduces competition with the intermediate predator and reduces vigilance by the prey, thereby leading to higher top predator densities. These results suggest that predator and prey behavior may play an important dynamical role in systems with intraguild predation.     

Dilution games: use of protective cover can cause a reduction in vigilance for prey in groups

Antipredatory vigilance usually decreases in groups. The generallyaccepted "collective detection" explanation implies that becausethere are more eyes to scan the surroundings for predators,individuals in a group can lower their personal investment invigilance without increasing their predation risk. The roleof other factors, such as numerical risk dilution caused bythe mere presence of companions, has been neglected. In a model,we explore a dilution game when foragers in groups have accessto protective cover. We show that foragers can take advantageof risk dilution and that this leads to changes in vigilancewith group size without the need to invoke collective detection.We identify a cost to maintaining high levels of vigilance asless vigilant foragers gather food faster and so depart thegroup sooner (to reach cover) leaving more vulnerable stragglersbehind. In groups, there is a scramble to reach safe sites thatcan induce a reduction in vigilance levels. Such a mechanismoperates less forcefully in large groups because individualsin these groups are less vulnerable to the departure of an individual.We also demonstrate that individuals should adopt lower levelsof vigilance, to reach safe sites sooner, when predator evasionis compromised or when the rate of food intake is high. Themodel provides new insights into the mechanisms underlying changesin vigilance with group size in animals.     

Temporary intermissions in capturing prey (<Emphasis Type="Italic">Daphnia</Emphasis>) by planktivorous fish (<Emphasis Type="Italic">Rutilus</Emphasis><Emphasis Type="Italic">rutilus</Emphasis>): Are they due to scramble competition or the need for antipredation vigilance?

Capture rates in planktivorous fish may differ in individuals foraging alone or in a group, and this may result either from the altered risk of predation due to vigilance sharing in the group, or from a difference in the intensity of scramble competition for encountered prey items. Changes in capture frequency and the feeding pattern observed in young roach (Rutilus rutilus) feeding alone and in a group of three on a high density prey (Daphnia), in the presence and in the absence of predator odor, were used to determine which of these two alternate explanations is more likely. Earlier studies revealed that a foraging roach captures Daphnia prey in uninterrupted sequences of captures occurring every 1–3 s. Such multiple captures are separated by intermissions of 10–20 s, with their duration being likely to determine the overall capture rate. An experiment was performed to examine whether feeding in a group of three permits higher capture rates (hypothesis 1), and whether the intermittent foraging pattern is due to the need to invest more time for vigilance when foraging alone (hypothesis 2). Video recordings were made of many series of subsequent prey captures by roach feeding on high Daphnia densities, alone or in a group, and in the presence or absence of predator odor. Analysis of these data revealed that the mean duration of intermissions between bursts of feeding activity was significantly greater in the presence of predator odor, which resulted in a significant decrease in the capture rate. Furthermore, when the roach were feeding in a group, these intermissions were reduced to a greater extent in the presence of predator odor than in its absence, implying that the intermission intervals represent an investment for vigilance as an effective antipredation defense that permits increased food intake regardless of whether or not it is enhanced by the resource or the interference competition.     

Density-dependent prey behaviours and mutable predator foraging modes induce Allee effects and over-prediction of prey mortality rates

1. Predator–prey models are often used to represent consumptive interactions between species but, typically, are derived using simple experimental systems with little plasticity in prey or predator behaviours. However, many prey and predators exhibit a broad suite of behaviours. Here, we experimentally tested the effect of density-dependent prey and predator behaviours on per capita relative mortality rates using Florida bass (Micropterus floridanus) consuming juvenile Bluegill (Lepomis macrochirus).
2. Experimental ponds were stocked with a factorial design of low, medium, and high prey and predator densities. Prey mortality, prey–predator behaviours, and predator stomach contents were recorded over or after 7 days. We assumed the mortality dynamics followed foraging arena theory. This pathologically flexible predator–prey model separates prey into invulnerable and vulnerable pools where predators can consume prey in the latter. As this approach can represent classic Lotka–Volterra and ratio-dependent dynamics, we fit a foraging arena predator–prey model to the number of surviving prey.
3. We found that prey exhibited density-dependent prey behaviours, hiding at low densities, shoaling at medium densities, and using a provided refuge at high densities. Predators exhibited ratio-dependent behaviours, using an ambush foraging mode when one predator was present, hiding in the shadows at low prey–high predator densities, and shoaling at medium and high prey–high predator densities. The foraging arena model predicted the mortality rates well until the high prey–high predator treatment where group vigilance prey behaviours occurred and predators probably interfered with one another resulting in the model predicting higher mortality than observed.
4. This is concerning given the ubiquity of predator–prey models in ecology and natural resource management. Furthermore, as Allee effects engender instability in population regulation, it could lead to inaccurate predictions of conservation status, population rebuilding or harvest rates.

     

The effectiveness of short‐term fox control in protecting a seasonally vulnerable species,the Eastern Long‐necked Turtle (Chelodina longicollis)

Reducing predation by introduced predators on seasonally vulnerable prey is of interest to biodiversity and game managers around the world. In Australia, the Red Fox (Vulpes vulpes) is a significant predator of freshwater turtle nests, destroying up to 93% of nests. We used a nonrandomized intervention study to assess the effectiveness of a short‐term (3‐week) but broad‐scale baiting operation in reducing the level of nest predation on artificial turtle nests around a complex lake system during a major flooding event in north‐western Victoria. Estimates of fox occupancy declined from 0.58 (0.44–0.70 95% CI) to 0.34 (0.21–0.46 95% CI) following fox control. Modelling of nest‐survival rates indicated there was no significant change in survival rates. Effective short‐term predator control to protect seasonally vulnerable prey is desirable and achievable. Knowledge of underlying predator density, predator–bait encounter and consumption rates, and the optimal duration of short‐term control is needed to reduce the risk to prey.     

Diel vertical migration arising in a habitat selection game

Predator and prey react to each other, adjusting their behavior to maximize their fitness and optimizing their food intake while keeping their predation risk as low as possible. In a pelagic environment, prey reduce their predation mortality by adopting a diel vertical migration (DVM) strategy, avoiding their predator during their peak performance by finding refuge in deep layers during daylight hours and feeding at the surface during the night. Due to the duality of the interaction between prey and predator, we used a game theory approach to investigate whether DVM can be a suitable strategy for the predator as well as the prey. We formulated three scenarios in plankton ecology in order to address this question. A novel finding is that mixed strategies emerge as optimal over a range of the parameter space, where part of the predator or prey population adopts a DVM while the rest adopt one or other “sit and wait” strategies.     

Investigating Differences in Vigilance Tactic Use within and between the Sexes in Eastern Grey Kangaroos

Aggregation is thought to enhance an animal’s security through effective predator detection and the dilution of risk. A decline in individual vigilance as group size increases is commonly reported in the literature and called the group size effect. However, to date, most of the research has only been directed toward examining whether this effect occurs at the population level. Few studies have explored the specific contributions of predator detection and risk dilution and the basis of individual differences in the use of vigilance tactics. We tested whether male and female (non-reproductive or with young) eastern grey kangaroos (Macropus giganteus) adopted different vigilance tactics when in mixed-sex groups and varied in their reliance on predator detection and/or risk dilution as group size changed. This species exhibits pronounced sexual dimorphism with females being much smaller than males, making them differentially vulnerable toward predators. We combined field observations with vigilance models describing the effects of detection and dilution on scanning rates as group size increased. We found that females with and without juveniles relied on predator detection and risk dilution, but the latter adjusted their vigilance to the proportion of females with juveniles within their group. Two models appeared to equally support the data for males suggesting that males, similarly to females, relied on predator detection and risk dilution but may also have adjusted their vigilance according to the proportion of mothers within their group. Differential vulnerability may cause sex differences in vigilance tactic use in this species. The presence of males within a group that do not, or only partially, contribute to predator detection and are less at risk may cause additional security costs to females. Our results call for reexamination of the classical view of the safety advantages of grouping to provide a more detailed functional interpretation of gregariousness.     

Spatial dynamics of communities with intraguild predation: the role of dispersal strategies

I investigate the influence of dispersal strategies on intraguild prey and predators (competing species that prey on each other). I find an asymmetry between the intraguild prey and predator in their responses to each other's dispersal. The intraguild predator's dispersal strategy and dispersal behavior have strong effects on the intraguild prey's abundance pattern, but the intraguild prey's dispersal strategy and behavior have little or no effect on the intraguild predator's abundance pattern. This asymmetry arises from the different constraints faced by the two species: the intraguild prey has to acquire resources while avoiding predation, but the intraguild predator only has to acquire resources. It leads to puzzling distribution patterns: when the intraguild prey and predator both move away from areas of high density, they become aggregated to high-density habitats, but when they both move toward areas of high resource productivity, they become segregated to resource-poor and resource-rich habitats. Aggregation is more likely when dispersal is random or less optimal, and segregation is more likely as dispersal becomes more optimal. The crucial implication is that trophic constraints dictate the fitness benefits of using dispersal strategies to sample environmental heterogeneity. A strategy that affords greater benefits to an intraguild predator can lead to a more optimal outcome for both the intraguild predator and prey than a strategy that affords greater benefits to an intraguild prey.     

Theory and method in studies of vigilance and aggregation

Predation is considered one of the most important selective pressures on free-ranging animals. Our understanding of it derives mainly from studies of individual vigilance (visual scanning of the surroundings beyond the immediate vicinity) and aggregation in prey. Vigilance bears a direct relationship to aggregation, because animals in groups may rely on associates for early warning of danger. This review addresses the relationship between vigilance and aggregation with particular attention to the prediction that individual vigilance declines with increasing group size. Contrary to most other animals studied, primates do not support the prediction. Exploring this, I examined the assumptions underlying vigilance theory in the light of primate behaviour. First I tested whether manual harvesting and upright processing of food as seen among primates might permit them to feed and scan simultaneously. I found no support for this idea. Next I examined the targets of primate vigilance and found that one component (within-group vigilance) might explain the differences between primates and other animals. Finally, I evaluated whether individual primates in large groups face a lower risk of predation than those in small groups. A conclusion was impossible, but by separating group-level from individual-level risk, I was able to identify several common circumstances in which group size would not predict individual risk or vigilance. These circumstances arose for primates and nonprimates alike. I concluded that the relationship of vigilance to aggregation is not straightforward. The absence of a group-size effect on vigilance among primates is probably due to functional differences in vigilance behaviour or safety in groups, not to methodological differences. Furthermore, future work on animal vigilance and aggregation must fully consider both the targets of glances, and the assumption that larger groups are safer from predators. I predict that animals will not relax vigilance in larger groups if conspecific threat increases with group size. Group size will not predict individual risk of predation nor individual vigilance rates when predators do not rely on surprise, or when predators select a small subset of highly vulnerable group members. Copyright 2000 The Association for the Study of Animal Behaviour.     

Influence of intra‐ and interspecific variation in predator–prey body size ratios on trophic interaction strengths

1. Predation is a pervasive force that structures food webs and directly influences ecosystem functioning. The relative body sizes of predators and prey may be an important determinant of interaction strengths. However, studies quantifying the combined influence of intra‐ and interspecific variation in predator–prey body size ratios are lacking.
2. We use a comparative functional response approach to examine interaction strengths between three size classes of invasive bluegill and largemouth bass toward three scaled size classes of their tilapia prey. We then quantify the influence of intra‐ and interspecific predator–prey body mass ratios on the scaling of attack rates and handling times.
3. Type II functional responses were displayed by both predators across all predator and prey size classes. Largemouth bass consumed more than bluegill at small and intermediate predator size classes, while large predators of both species were more similar. Small prey were most vulnerable overall; however, differential attack rates among prey were emergent across predator sizes. For both bluegill and largemouth bass, small predators exhibited higher attack rates toward small and intermediate prey sizes, while larger predators exhibited greater attack rates toward large prey. Conversely, handling times increased with prey size, with small bluegill exhibiting particularly low feeding rates toward medium–large prey types. Attack rates for both predators peaked unimodally at intermediate predator–prey body mass ratios, while handling times generally shortened across increasing body mass ratios.
4. We thus demonstrate effects of body size ratios on predator–prey interaction strengths between key fish species, with attack rates and handling times dependent on the relative sizes of predator–prey participants.
5. Considerations for intra‐ and interspecific body size ratio effects are critical for predicting the strengths of interactions within ecosystems and may drive differential ecological impacts among invasive species as size ratios shift.

     

Predator–prey interactions and metabolic rates are altered in stable and unstable groups in a social fish

Understanding the determinants and consequences of predation effort, success and prey responses is important since these factors affect the fitness of predators and prey. When predators are also invasive species, the impacts on prey can be particularly far-reaching with ultimate ecosystem-level consequences. However, predators are typically viewed as behaviourally fixed within this interaction and it is unclear how variation in predator social dynamics affects predator–prey interactions. Using the invasive eastern mosquitofish Gambusia holbrooki and a native glass shrimp Paratya australiensis in Australia, we investigated how varying levels of social conflict within predator groups influences predator–prey interactions. By experimentally manipulating group stability of G. holbrooki, we show that rates of social conflict were lower in groups with large size differences, but that routine metabolic rates were higher in groups with large size differences. Predation effort and success did not vary depending on group stability, but in stable groups predation effort by aggressive dominants was greater than subordinates. The anti-predator responses of prey to the stability of predator groups were mixed. While more prey utilized shelters when exposed to stable compared to unstable groups of predators, a greater proportion were sedentary when predator groups were unstable. Overall, this study demonstrates predator group stability is modulated by differences in body size and can influence prey responses. Further, it reveals a hidden metabolic cost of living in stable groups despite reduced overt social conflict. For invasive species management, it is therefore important to consider the behavioural and physiological plasticity of the invasive predators, whose complex social interactions and metabolic demands can modulate patterns of predator–prey interactions.     

Faced with a choice, sparrowhawks more often attack the more vulnerable prey group

Whether predators always attack the most vulnerable prey or simply attack prey that exceeds a minimum vulnerability level is an important question to answer in furthering our understanding of predator and antipredation behaviour. Predators may attack any reasonably vulnerable prey rather than waste time identifying the most vulnerable prey, particularly when prey can respond quickly to alter their vulnerability in response to a predator. We tested whether sparrowhawks always choose to attack the group of prey that maximises their capture probability, or whether they simply attack any group above a minimum vulnerability. We modelled sparrowhawk attack success when hunting redshanks using data from three winters and found that probability of capture increased when group size or distance to predator-concealing cover decreased. We then used this model to predict the relative vulnerability to capture of redshank groups occurring in pairs in a fourth winter and found that sparrowhawks attacked the most vulnerable prey group twice as often as not (66% n=59 pairs). When sparrowhawks attacked the less vulnerable group, there was no tendency for both groups to be particularly vulnerable or for the difference in the vulnerability between the two groups to be relatively small. This suggests that, while sparrowhawks do on average attack the most vulnerable group available, they consider other factors that affect vulnerability or that additional factors lead them to also attack opportunistically. This suggests that there will be selection for the predator to monitor a large number of prey individuals and groups and for prey to have the ability to monitor the behaviour of conspecifics in the same and different groups so that they can assess relative vulnerability.     

Costs and Benefits of Sociality Differ Between Female Guanacos Living in Contrasting Ecological Conditions

According to current theory, anti‐predator benefits promote group formation in open‐dwelling ungulates. An inverse relationship between vigilance effort and group size has been documented frequently and thought to reflect the consequent decrease in perceived predation risk as group size increases. In contrast, competition costs are supposed to set the upper limit to the number of individuals that can forage together. As anti‐predator behavior is no longer functional in the absence of predation and competition costs might be affected by resource distribution, the net benefit of aggregation will depend on the particular combination of predation risk and habitat structure experienced by the individual. To test this hypothesis, group‐size effects on female time allocation and within‐group aggression rate were compared between two guanaco populations exposed to contrasting levels of puma predation. Habitat structure within both sites consisted of mosaics of shrublands and grasslands, and group‐size effects were also compared between these habitat types. Females under predation risk showed a strong reduction in vigilance as the number of adults in the group increased, whereas females from the predator‐free population showed overall low levels of vigilance, regardless of group size. These results emphasize the anti‐predator significance of the group‐size effect on female vigilance, as well as guanaco plasticity to adjust time allocation to local conditions. On the other hand, within‐group aggression rate increased with the number of adults in the group. Aggression rate was almost null within groups located in grasslands but was significantly higher in shrublands, regardless of predation risk, suggesting that the more heterogeneous distribution of shrubs increases the interference competition level. These results strengthen the notion of predation pressure and habitat structure as major determinants of the balance between costs and benefits of group living, and highlight the potential of individual behavioral patterns to make qualitative predictions about group‐size variation within territorial ungulates.     

The evolution of traits affecting resource acquisition and predator vulnerability: character displacement under real and apparent competition

This article investigates some simple models of the evolutionary interaction between two prey species that share a common resource and a common predator. Each prey species is characterized by a trait that determines both the rate of resource capture and vulnerability to a predator. In a simple model of a three-species food chain, such traits usually increase in response to an imposed reduction in resource density. When the per capita growth rates of each of two prey species depend linearly on resource density, such traits will change in opposite directions when the two prey come into sympatry. In addition, the ratio of the effect of the predator on prey fitness to the effect of the resource on prey fitness will diverge from the corresponding ratio in a second prey species when those species coexist in sympatry. These simple predictions need not hold under several alternative assumptions, which may be more common in biological systems. Parallel changes in sympatry may occur if the relationship between resource consumption and prey growth is nonlinear, if the prey species have partial overlap in the set of resources used or in the set of predators that consume them, or if prey experience direct intraspecific competition. The responses to a second prey can also differ significantly from those predicted by the simplest model if separate traits affect vulnerability to predators and resource acquisition rate. It is important to determine whether examples of character displacement previously interpreted as responses to competition for resources might also reflect responses to altered predation risks in sympatry.     

No evidence of nonlinear effects of predator density,refuge availability,or body size of prey on prey mortality rates

Predator density, refuge availability, and body size of prey can all affect the mortality rate of prey. We assume that more predators will lead to an increase in prey mortality rate, but behavioral interactions between predators and prey, and availability of refuge, may lead to nonlinear effects of increased number of predators on prey mortality rates. We tested for nonlinear effects in prey mortality rates in a mesocosm experiment with different size classes of western mosquitofish (Gambusia affinis) as the prey, different numbers of green sunfish (Lepomis cyanellus) as the predators, and different levels of refuge. Predator number and size class of prey, but not refuge availability, had significant effects on the mortality rate of prey. Change in mortality rate of prey was linear and equal across the range of predator numbers. Each new predator increased the mortality rate by about 10% overall, and mortality rates were higher for smaller size classes. Predator–prey interactions at the individual level may not scale up to create nonlinearity in prey mortality rates with increasing predator density at the population level.     

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.