Life-history decisions under predation risk: Importance of a game perspective

We model ontogenetic shifts (e.g. in food or habitat use) during development under predation risk. We ask whether inclusion of state and frequency dependence will provide new insights when compared with game-free life-history theory. We model a simple biological scenario in which a prey animal must switch from a low-predation, low-growth habitat to a high-predation, high-growth habitat. To assess the importance of frequency dependence, we compare the results of four scenarios of increasing complexity: (1) no predation; (2) constant predation; (3) frequency-dependent predation (predation risk diluted at high prey density); and (4) frequency-dependent predation as in (3) but with predators allowed to respond adaptively to prey behaviour. State dependence is included in all scenarios through initial size, assumed to be environmental. A genetic algorithm is used to search for optimal solutions to the scenarios. We find substantially different results in the four different scenarios and suggest a decision tree by which biological systems could be tested to ascertain which scenario is most applicable.     

Ontogenetic differences of herbivory on woody and herbaceous plants: a meta-analysis demonstrating unique effects of herbivory on the young and the old, the slow and the fast

Defensive modifications in prey traits that reduce predation risk can also have negative effects on prey fitness. Such nonconsumptive effects (NCEs) of predators are common, often quite strong, and can even dominate the net effect of predators. We develop an intuitive graphical model to identify and explore the conditions promoting strong NCEs. The model illustrates two conditions necessary and sufficient for large NCEs: (1) trait change has a large cost, and (2) the benefit of reduced predation outweighs the costs, such as reduced growth rate. A corollary condition is that potential predation in the absence of trait change must be large. In fact, the sum total of the consumptive effects (CEs) and NCEs may be any value bounded by the magnitude of the predation rate in the absence of the trait change. The model further illustrates how, depending on the effect of increased trait change on resulting costs and benefits, any combination of strong and weak NCEs and CEs is possible. The model can also be used to examine how changes in environmental factors (e.g., refuge safety) or variation among predator–prey systems (e.g., different benefits of a prey trait change) affect NCEs. Results indicate that simple rules of thumb may not apply; factors that increase the cost of trait change or that increase the degree to which an animal changes a trait, can actually cause smaller (rather than larger) NCEs. We provide examples of how this graphical model can provide important insights for empirical studies from two natural systems. Implementation of this approach will improve our understanding of how and when NCEs are expected to dominate the total effect of predators. Further, application of the models will likely promote a better linkage between experimental and theoretical studies of NCEs, and foster synthesis across systems.     

Predator and Prey Models with Flexible Individual Behavior and Imperfect Information

To begin identifying what behavioral details might be needed to characterize community dynamics and stability, we examined the effect of prey behavioral responses to predation risk on community dynamics and stability. We considered the case of prey altering their foraging effort to trade off energy gain and predation risk. We used state-dependent dynamic optimization to calculate the optimal trade-off for four models of prey behaviorally responding to predation risk. We consider a fixed behavior model in which prey use constant levels of foraging effort and three flexible behavior models in which prey change their foraging effort according to their physiological state and their perceived level of predation risk. Flexible behavior was destabilizing at the community level as evidenced by higher predator-prey oscillations and lower community persistence times. The mechanisms by which prey estimated predation risk also affected community stability. We found that community dynamics resulting from prey with flexible behavior and fixed perception of risk approximated community dynamics resulting from prey with flexible behavior and perfect information about predation risk, however neither approximated the community dynamics resulting from prey with flexible behavior and flexible perception of risk. Thus, whether it might be possible to abstract complex behavior with simpler rules when modeling community dynamics depends on the prey's behavioral mechanisms, which are empirically poorly known.     

Frequency-dependent predation and maintenance of prey polymorphism

In positive frequency-dependent predation, predation risk of an individual prey correlates positively with the frequency of that prey type. In a number of small-scale experiments individual predators have shown frequency-dependent behaviour, often leading to the conclusion that a population of such predators could maintain prey polymorphism. Using simulations, I studied the dynamics of frequency-dependent predation and prey polymorphism. The model suggests that persistence of prey polymorphism decreases with increasing number of predators that show frequency-dependent behaviour, questioning conclusions about polymorphism based on experiments with few predators. In addition, prey population size, prey crypsis, difference in crypsis between prey morphs and the way the behaviour was adjusted affected the persistence of polymorphism. Under some circumstances prey population remained polymorphic for a shorter time under frequency-dependent than under frequency-independent predation. This suggests that although positive frequency-dependent predator behaviour may maintain prey polymorphism, it is not a sufficient condition for persistent prey polymorphism.     

Dying from the lesser of three evils: facilitation and non‐consumptive effects emerge in a model with multiple predators

Prey modify their behaviour to avoid predation, but dilemmas arise when predators vary in hunting style. Behaviours that successfully evade one predator sometimes facilitate exposure to another predator, forcing the prey to choose the lesser of two evils. In such cases, we need to quantify behavioural strategies in a mix of predators. We model optimal behaviour of Atlantic cod Gadus morhua larvae in a water column, and find the minimal vulnerability from three common predator groups with different hunting modes; 1) ambush predators that sit‐and‐wait for approaching fish larvae; 2) cruising invertebrates that eat larvae in their path; and 3) fish which are visually hunting predators. We use a state‐dependent model to find optimal behaviours (vertical position and swimming speed over a diel light cycle) under any given exposure to the three distinct modes of predation. We then vary abundance of each predator and quantify direct and indirect effects of predation. The nature and strength of direct and indirect effects varied with predator type and abundance. Larvae escaped about half the mortality from fish by swimming deeper to avoid light, but their activity level and cumulative predation from ambush predators increased. When ambush invertebrates dominated, it was optimal to be less active but in more lit habitats, and predation from fish increased. Against cruising predators, there was no remedy. In all cases, the shift in behaviour allowed growth to remain almost the same, while total predation were cut by one third. In early life stages with high and size‐dependent mortality rates, growth rate can be a poor measure of the importance of behavioural strategies.     

Optimal harvesting of prey–predator system with interval biological parameters: A bioeconomic model

The paper presents the study of one prey one predator harvesting model with imprecise biological parameters. Due to the lack of precise numerical information of the biological parameters such as prey population growth rate, predator population decay rate and predation coefficients, we consider the model with imprecise data as form of an interval in nature. Many authors have studied prey–predator harvesting model in different form, here we consider a simple prey–predator model under impreciseness and introduce parametric functional form of an interval and then study the model. We identify the equilibrium points of the model and discuss their stabilities. The existence of bionomic equilibrium of the model is discussed. We study the optimal harvest policy and obtain the solution in the interior equilibrium using Pontryagin’s maximum principle. Numerical examples are presented to support the proposed model.     

Geometry for mutualistic and selfish herds: the limited domain of danger

We present a two-dimensional individual-based model of aggregation behaviour in animals by introducing the concept of a "limited domain of danger", which represents either a limited detection range or a limited attack range of predators. The limited domain of danger provides a suitable framework for the analysis of individual movement rules under real-life conditions because it takes into account the predator's prey detection and capture abilities. For the first time, a single geometrical construct can be used to analyse the predation risk of both peripheral and central individuals in a group. Furthermore, our model provides a conceptual framework that can be equally applied to aggregation behaviour and refuge use and thus presents a conceptual advance on current theory that treats these antipredator behaviours separately. An analysis of individual movement rules using limited domains of danger showed that the time minimization strategy outcompetes the nearest neighbour strategy proposed by Hamilton's (J. Theor. Biol. 31 (1971) 295) selfish herd model, whereas a random strategy confers no benefit and can even be disadvantageous. The superior performance of the time minimization strategy highlights the importance of taking biological constraints, such as an animal's orientation relative to its neighbours, into account when searching for efficient movement rules underlying the aggregation process.     

Dynamic state-dependent modelling predicts optimal usage patterns of responsive defences

Chemical defences against predation often involve responses to specific predation events where the prey expels fluids, such as haemolymph or gut contents, which are aversive to the predator. The common link is that each predation attempt that is averted results in an energetic cost and a reduction in the chemical defences of the prey, which might leave the prey vulnerable if the next predation attempt occurs soon afterwards. Since prey appear to be able to control the magnitude of their responses, we should expect them to trade-off the need to repel the current threat against the need to preserve defences against future threats and conserve energy for other essential activities. Here we use dynamic state-dependent models to predict optimal strategies of defence deployment in the juvenile stage of an animal that has to survive to maturation. We explore the importance of resource level, predator density, and the costs of making defences on the magnitude of the responses and optimal age and size at maturation. We predict the patterns of investment and the magnitude of the deployment of defences to potentially multiple attacks over the juvenile period, and show that responses should be smaller when the costs of defences and/or predation risk are higher. The model enables us to predict that animals in which defences benefit the adult stage will employ different strategies than those that do not use the same defences as adults, and thereby experience a smaller reduction in body size as a result of repeated attacks. We also explore the effect of the importance of adult size, and find that the sex and mating system of the prey should also affect defensive strategies. Our work provides the first predictive theory of the adaptive use of responsive defences across taxa.     

Trophic cascades: the primacy of trait-mediated indirect interactions

Trophic cascades are textbook examples of predator indirect effects on ecological systems. Yet there is considerable debate about their nature, strength and overall importance. This debate stems in part from continued uncertainty about the ultimate mechanisms driving cascading effects. We present a synthesis of empirical evidence in support of one possible ultimate mechanism: the foraging‐predation risk trade‐offs undertaken by intermediary species. We show that simple trade‐off behaviour can lead to both positive and negative indirect effects of predators on plant resources and hence can explain considerable contingency on the nature and strength of cascading effects among systems. Thus, predicting the sign and strength of indirect effect simply requires knowledge of habitat and resource use by prey with regard to predators’ presence, habitat use and hunting mode. The synthesis allows us to postulate a hypothesis for new conceptualization of trophic cascades which is to be viewed as an ultimate trade‐off between intervening species. In this context, different predators apply different rules of engagement based on their hunting mode and habitat use. These different rules then determine whether behavioural effects persist or attenuate at the level of the food chain.     

Animal camouflage: compromise or specialize in a 2 patch-type environment?

Many animals possess camouflage markings that reduce the riskof detection by visually hunting predators. A key aspect ofcamouflage involves mimicking the background against which theanimal is viewed. However, most animals experience a wide varietyof backgrounds and cannot change their external appearance tomatch each selectively. We investigate whether such animalsshould adopt camouflage specialized with respect to one backgroundor adopt a compromise between the attributes of multiple backgrounds.We do this using a model consisting of predators that hunt preyin patches of 2 different types, where prey adopt the camouflagethat minimizes individual risk of predation. We show that theoptimal strategy of the prey is affected by a number of factors,including the relative frequencies of the patch types, the traveltime of predators between patches, the mean prey number in eachpatch type, and the trade-off function between the levels ofcrypsis in the patch types. We find evidence that both specialistand compromise strategies of prey camouflage are favored underdifferent model parameters, indicating that optimal concealmentmay not be as straightforward as previously thought.     

Simple heuristics and rules of thumb: where psychologists and behavioural biologists might meet

The Centre for Adaptive Behaviour and Cognition (ABC) has hypothesised that much human decision-making can be described by simple algorithmic process models (heuristics). This paper explains this approach and relates it to research in biology on rules of thumb, which we also review. As an example of a simple heuristic, consider the lexicographic strategy of Take The Best for choosing between two alternatives: cues are searched in turn until one discriminates, then search stops and all other cues are ignored. Heuristics consist of building blocks, and building blocks exploit evolved or learned abilities such as recognition memory; it is the complexity of these abilities that allows the heuristics to be simple. Simple heuristics have an advantage in making decisions fast and with little information, and in avoiding overfitting. Furthermore, humans are observed to use simple heuristics. Simulations show that the statistical structures of different environments affect which heuristics perform better, a relationship referred to as ecological rationality. We contrast ecological rationality with the stronger claim of adaptation. Rules of thumb from biology provide clearer examples of adaptation because animals can be studied in the environments in which they evolved. The range of examples is also much more diverse. To investigate them, biologists have sometimes used similar simulation techniques to ABC, but many examples depend on empirically driven approaches. ABC's theoretical framework can be useful in connecting some of these examples, particularly the scattered literature on how information from different cues is integrated. Optimality modelling is usually used to explain less detailed aspects of behaviour but might more often be redirected to investigate rules of thumb.     

Prey scan at random to evade observant predators

Anti-predator scans by animals occur with very irregular timing, so that the initiation of scans resembles a random, Poisson-like, process. At first sight, this seems both dangerous (predators could exploit the long intervals) and wastefull (scans after very short intervals are relatively uninformative). We explored vigilance timing using a new model that allows both predators and prey to vary their behaviour. Given predators that attack at random with respect to prey behaviour, constant inter-scan intervals minimize predation risk. However, if prey scan regularly to minimize their risk from randomly attacking predators, they become more vulnerable to predators that initiate attacks when the inter-scan intervals begin. If, in order to defeat this tactic, prey choose extremely variable inter-scan intervals, they become more vulnerable to predators who wait for long intervals before launching attacks. Only if predators can monitor the variability of inter-scan intervals and either attack immediately (if variability is too low) or wait for long intervals to attack (if variability is too high) does the empirically observed pattern of Poisson-like scanning become the optimal prey strategy.     

Sex‐Specific Parental Care in Response to Predation Risk in the European Roller,Coracias garrulus

Sublethal effects of predation constitute an important part of predation effects, which may modulate prey population and community dynamics. In birds, the risk of nest predation may cause a reduction in parental activity in the care of offspring to reduce the chance of being detected by predators. In addition, parents may modify their parental food allocation preferences within the brood in response to predation risk. Our aim in this study was to evaluate the effects of risk of nest predation on parental care and within‐nest food allocation in the European Roller (Coracias garrulus), an asynchronously hatching bird. We manipulated brood predation risk by placing a snake model near the nests that simulates the most common nest predator in the Mediterranean region. Our results show that males but not females increased their provisioning rate when they were exposed to the model and that despite this, nestlings’ body mass decreased in response to this temporary increase in predation risk. We did not find evidence that parents changed their food allocation strategy towards senior or junior nestlings in their nests in response to predation risk. These results show that the European roller modifies parental care in response to their perception of predation risk in the nest and a sex‐specific sensitivity to the threat, which suggests a different perception of offspring reproductive value by parents. Finally, our results show that changes in parental behaviour in response to nest predation risk might have consequences for nestling fitness prospects.     

Investment into Defensive Traits by Anuran Prey (Lithobates pipiens) Is Mediated by the Starvation-Predation Risk Trade-Off

Prey can invest in a variety of defensive traits when balancing risk of predation against that of starvation. What remains unknown is the relative costs of different defensive traits and how prey reconcile investment into these traits when energetically limited. We tested the simple allocation model of prey defense, which predicts an additive effect of increasing predation risk and resource availability, resulting in the full deployment of defensive traits under conditions of high risk and resource saturation. We collected morphometric, developmental, and behavioural data in an experiment using dragonfly larvae (predator) and Northern leopard frog tadpoles (prey) subject to variable levels of food availability and predation risk. Larvae exposed to food restriction showed limited response to predation risk; larvae at food saturation altered behaviour, development, and growth in response to predation risk. Responses to risk varied through time, suggesting ontogeny may affect the deployment of particular defensive traits. The observed negative correlation between body size and activity level for food-restricted prey – and the absence of a similar response among adequately-fed prey – suggests that a trade-off exists between behavioural and growth responses when energy budgets are limited. Our research is the first to demonstrate how investment into these defensive traits is mediated along gradients of both predation risk and resource availability over time. The interactions we demonstrate between resource availability and risk level on deployment of inducible defenses provide evidence that both internal condition and extrinsic risk factors play a critical role in the production of inducible defenses over time.     

Predator-prey shell games: large-scale movement and its implications for decision-making by prey

Many classical models of food patch use under predation risk assume that predators impose patch-specific predation risks independent of prey behavior. These models predict that prey should leave a chosen patch only if and when the food depletes below some critical level. In nature, however, prey individuals may regularly move among food patches, even in the apparent absence of food depletion. We suggest that such prey movement is part of a predator-prey "shell game", in which predators attempt to learn prey location, and the prey attempt to be unpredictable in space. We investigate this shell game using an individual-based model that allows predators to update information about prey location, and permits prey to move with some random component among patches, but with reduced energy intake. Our results show the best prey strategy depends on what the predator does. A non-learning (randomly moving) predator favors non-moving prey – moving prey suffer higher starvation and predation. However, a learning predator favors prey movement. In general, the best prey strategy involves movement biased toward, but not completely committed to, the richer food patch. The strategy of prey movement remains beneficial even in combination with other anti-predator defenses, such as prey vigilance.     

Predation risk and the evolutionary ecology of reproductive behaviour

A large literature exists on the effects of predation risk on foraging and survival-related behaviours. In contrast, with some notable exceptions, relatively few theoretical or experimental studies have examined the effects of predation risk on reproductive behaviours. Existing literature on risk and reproductive behaviour and suggestion directions for future study are reviewed. In particular: (1) effects on predation risk on mating behaviour; (2) the influence of spatial patchiness on interactions between risk and reproductive behaviour; (3) the potential influence of multi-species interactions on the effects of predation risk on mating dynamics; (4) the importance of looking at sets of inter-related antipredator traits; and (5) some effects of predation risk on prey population patterns due to changes in prey reproductive behaviour are discussed. To illustrate various points examples involving fish and other aquatic organisms are used.     

Foraging strategy switching in an antlion larva

Antlion larvae are typically considered as trap-building predators, but some species of antlions always forage without using pits or only sometimes use pits to capture prey; they can ambush prey without pits. This study examined a species that switches its strategy between pit-trapping and ambushing and asked the mechanism behind the switching behaviour. A dynamic optimization model incorporating tradeoffs between the two strategies was built. The tradeoffs were prey capture success and predation risk (both are higher when pit-trapping). The model predicted that antlions should use the trap-building strategy when their energy status is low and should use the ambush strategy when their energy status is high. These predictions as well as an assumption (i.e., predation risk associated with pit-trapping is higher than that associated with ambushing) of the model were empirically confirmed. The results suggest that antlions flexibly switch between pit-trapping and ambushing to maximize their fitness by balancing the costs and benefits of the two strategies.     

A theoretical investigation into the direct and indirect effects of state on the risk of predation

As well as there being a direct physical effect of the state (for example fat reserves, or size) of an animal on the risk of being caught by a predator, state also has an effect on predation risk indirectly through changes in behaviour. We present a mathematical model which looks at these two components of the effect of state on predation risk. We focus on two different models, (i) where the animal must achieve a fixed state and its fitness depends on the time at which this state is reached and (ii) where the animal must survive until a fixed time and its fitness depends on its final state. We investigate conditions under which the indirect effect of increased state is to increase or decrease predation risk, and give some numerical illustrations. Under certain conditions in the fixed-state model, the indirect effect of state is to increase predation risk, whereas under certain conditions in the fixed-time model the indirect effect of state is to decrease predation risk. We discuss the implications of our results for empirical investigations into the effect of state on predation risk.     

Protective parenting may have population-level consequences

In many animal species, recruitment is facilitated by adults’ efforts to protect offspring from predation. Theoretical studies of this phenomenon have usually focused on resolving the conflict between an individual's self-preservation and its attempts to successfully reproduce. While the decision to protect is made at the level of a single individual, the aggregation of these decisions may affect population density and structure. This idea motivates the development of a functional response for predators that is compatible with the protective behaviour of prey. We use this functional response to study the long-term behaviour of a protective prey population under different levels of predation. We find that contribution of protective effort may promote or inhibit population density depending on the riskiness associated with interference. Moreover, our results suggest that, in environments characterised by intense predation, a protection-driven Allee effect allows sufficiently large populations to persist. We interpret these results in the context of different strategies for newborn defence.     

Heterogeneous landscapes and the role of refuge on the population dynamics of a specialist predator and its prey

How, and where, a prey species survives predation by a specialist predator during low phases of population fluctuations or a cycle, and how the increase phase of prey population is initiated, are much-debated questions in population and theoretical ecology. The persistence of the prey species could be due mainly to habitats that act as refuges from predation and/or due to anti-predatory behaviour of individuals. We present models for the former conjecture in two (and three) habitat systems with a specialist predator and its favoured prey. The model is based on dispersal of prey between habitats with high reproductive output but high risk of predation, and less productive habitats with relatively low risk of predation. We illustrate the predictions of our model using parameters from one of the most intriguing vertebrate predator–prey systems, the multi-annual population cycles of boreal voles and their predators. We suggest that cyclic population dynamics could result from a sequence of extinction and re–colonization events. Field voles (Microtus agrestis), a key vole species in the system, can be hunted to extinction in their preferred meadow habitat, but persist in sub-optimal wet habitats where their main predator, the least weasel (Mustela nivalis nivalis) has a low hunting efficiency. Re–colonization of favourable habitats would occur after the predator population crashes. At the local scale, the model suggests that the periodicity and amplitude of population cycles can be strongly influenced by the relative availability of risky and safe habitats for the prey. Furthermore, factors like intra-guild predation may lead to reduced predation pressure on field voles in sub-optimal habitats, which would act as a refuge for voles during the low phase of their population cycles. Elasticity analysis suggested that our model is quite robust to changes in most parameters but sensitive to changes in the population dynamics of field voles in the optimal grassland habitat, and to the maximum predation rate of weasels.