Foraging behavior in stochastic environments

How do temporally stochastic environments affect risk sensitivity in foraging behavior? We build a simple model of foraging under predation risks in stochastic environments, where the environments change over generations. We analyze the effects of stochastic environments on risk sensitivity of foraging animals by means of the difference between the geometric mean fitness and the arithmetic mean fitness. We assume that foraging is associated with predation risks whereas resting in the nest is safe because it is free of predators. In each generation, two different environments with given food amounts and predation risks occur with a certain probability. The geometric mean optimum is independent of food amounts. In most cases of stochastic environments, risk-averse tendency is increased, but in some limited conditions, more risk-prone behavior is favored. Specifically, risk-prone tendency is increased when the variation in food amount increases. Our results imply that the optimal behavior depends on the probability distribution of environmental effects under all selection regimes.     

State-dependent ideal free distributions

Summary The standard ideal free distribution (IFD) states how animals should distribute themselves at a stable competitive equilibrium. The equilibrium is stable because no animal can increase its fitness by changing its location. In applying the IFD to choice between patches of food, fitness has been identified with the net rate of energetic gain. In this paper we assess fitness in terms of survival during a non-reproductive period, where the animal may die as a result of starvation or predation. We find the IFD when there is a large population that can distribute itself between two patches of food. The IFD in this case is state-dependent, so that an animal's choice of patch depends on its energy reserves. Animals switch between patches as their reserves change and so the resulting IFD is a dynamic equilibrium. We look at two cases. In one there is no predation and the patches differ in their variability. In the other, patches differ in their predation risk. In contrast to previous IFDs, it is not necessarily true that anything is equalized over the two patches.     

Assessing predation risk: optimal behaviour and rules of thumb

We look at a simple model in which an animal makes behavioural decisions over time in an environment in which all parameters are known to the animal except predation risk. In the model there is a trade-off between gaining information about predation risk and anti-predator behaviour. All predator attacks lead to death for the prey, so that the prey learns about predation risk by virtue of the fact that it is still alive. We show that it is not usually optimal to behave as if the current unbiased estimate of the predation risk is its true value. We consider two different ways to model reproduction; in the first scenario the animal reproduces throughout its life until it dies, and in the second scenario expected reproductive success depends on the level of energy reserves the animal has gained by some point in time. For both of these scenarios we find results on the form of the optimal strategy and give numerical examples which compare optimal behaviour with behaviour under simple rules of thumb. The numerical examples suggest that the value of the optimal strategy over the rules of thumb is greatest when there is little current information about predation risk, learning is not too costly in terms of predation, and it is energetically advantageous to learn about predation. We find that for the model and parameters investigated, a very simple rule of thumb such as 'use the best constant control' performs well.     

THE EFFECTS OF PREDATION ON THE AGE AND SIZE OF MATURITY OF PREY

The effects of nonselective predation on the optimal age and size of maturity of their prey are investigated using mathematical models of a simple life history with juvenile and adult stages. Fitness is measured by the product of survival to the adult stage and expected adult reproduction, which is usually an increasing function of size at maturity. Size is determined by both age at maturity and the value of costly traits that increase mean growth rate (growth effort). The analysis includes cases with fixed size but flexible time to maturity, fixed time but flexible size, and adaptively flexible values of both variables. In these analyses, growth effort is flexible. For comparison with previous theory, models with a fixed growth effort are analyzed. In each case, there may be indirect effects of predation on the prey's food supply. The effect of increased predation depends on (1) which variables are flexible; (2) whether increased growth effort requires increased exposure to predators; and (3) how increased predator density affects the abundance of food for juvenile prey. If there is no indirect effect of predators on prey food supply, size at maturity will generally decrease in response to increased predation. However, the indirect effect from increased food has the opposite effect, and the net result of predation is often increased size. Age at maturity may either increase or decrease, depending on functional forms and parameter values; this is true regardless of the presence of indirect effects. The results are compared with those of previous theoretical analyses. Observed shifts in life history in response to predation are reviewed, and the role of size-selective predation is reassessed.     

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.     

Determining the fitness consequences of antipredation behavior

Any animal whose form or behavior facilitates the avoidanceof predators or escape when attacked by predators will havea greater probability of surviving to breed and therefore greaterprobability of producing offspring (i.e., fitness). Althoughin theory the fitness consequences of any antipredation behaviorcan simply be measured by the resultant probability of survivalor death, determining the functional significance of antipredationbehavior presents a surprising problem. In this review we drawattention to the problem that fitness consequences of antipredationbehaviors cannot be determined without considering the potentialfor reduction of predation risk, or increased reproductive output,through other compensatory behaviors than the behaviors understudy. We believe we have reached the limits of what we canever understand about the ecological effects of antipredationbehavior from empirical studies that simply correlate a singlebehavior with an apparent fitness consequence. Future empiricalstudies must involve many behaviors to consider the range ofpotential compensation to predation risk. This is because antipredationbehaviors are a composite of many behaviors that an animal canadjust to accomplish its ends. We show that observed variationin antipredation behavior does not have to reflect fitness andwe demonstrate that few studies can draw unambiguous conclusionsabout the fitness consequences of antipredation behavior. Lastly,we provide suggestions of how future research should best betargeted so that, even in the absence of death rates or changesin reproductive output, reasonable inferences of the fitnessconsequences of antipredation behaviors can be made.     

动物觅食行为对捕食风险的反应

动物进行任何活动时均面临被捕食的风险 ,分析捕食风险与猎物觅食行为的关系 ,有助于揭示捕食者与猎物的协同进化机制。捕食风险具有限制或调节猎物种群数量的功能。在进化时间内 ,对猎物形态和行为特征的进化是潜在的选择压力之一 ,可利用环境因子作为信息源估测食物可利用性和捕食风险大小的动物 ,具有更大的适合度。信息源可分为包括视觉的、听觉的和化学的。动物进行觅食活动时 ,依据信息源的变化确定环境中捕食风险的大小 ,并根据自身的质量在捕食风险的大小之间做出权衡 ,通过食物选择、活动格局和栖息地利用等行为的变化降低捕食风险     

Vigilance and fitness in grey partridges Perdix perdix: the effects of group size and foraging-vigilance trade-offs on predation mortality

1. Vigilance increases fitness by improving predator detection but at the expense of increasing starvation risk. We related variation in vigilance among 122 radio-tagged overwintering grey partridges Perdix perdix (L.) across 20 independent farmland sites in England to predation risk (sparrowhawk Accipiter nisus L., kill rate), use of alternative antipredation behaviours (grouping and use of cover) and survival. 2. Vigilance was significantly higher when individuals fed in smaller groups and in taller vegetation. In the covey period (in early winter when partridges are in flocks), vigilance and use of taller vegetation was significantly higher at sites with higher sparrowhawk predation risk, but tall vegetation was used less by larger groups. Individuals were constrained in reducing individual vigilance by group size and habitat choice because maximum group size was determined by overall density in the area during the covey period and by the formation of pairs at the end of the winter (pair period), when there was also a significant twofold increase in the use of tall cover. 3. Over the whole winter individual survival was higher in larger groups and was lower in the pair period. However, when controlling for group size, mean survival decreased as vigilance increased in the covey period. This result, along with vigilance being higher at sites with increasing with raptor risk, suggests individual vigilance increases arose to reduce short-term predation risk from raptors but led to long-term fitness decreases probably because high individual vigilance increased starvation risk or indicated longer exposure to predation. The effect of raptors on survival was less when there were large groups in open habitats, where individual partridges can probably both detect predators and feed efficiently. 4. Our study suggests that increasing partridge density and modifying habitat to remove the need for high individual vigilance may decrease partridge mortality. It demonstrates the general principle that antipredation behaviours may reduce fitness long-term via their effects on the starvation-predation risk trade-off, even though they decrease predation risk short-term, and that it may be ecological constraints, such as poor habitat (that lead to an antipredation behaviour compromising foraging), that cause mortality, rather than the proximate effect of an antipredation behaviour such as vigilance.     

Life-history plasticity and inbreeding depression under mate limitation and predation risk: cumulative lifetime fitness dissected with a life table response experiment

Environmental effects on the evolution of mating systems are increasingly discussed, but we lack many examples of how environmental conditions affect the expression and consequences of alternative mating systems. Variation in mate availability sets up a trade-off between reproductive assurance and inbreeding depression, but the consequences of both mate limitation and inbreeding may depend on other environmental conditions. Predation risk is common under natural conditions, and known to affect allocation to reproduction, but we know little about the effects of isolation and inbreeding under predation risk. We reared selfed and outcrossed hermaphroditic freshwater snails (Physa acuta) in four environments (predator cues present or absent crossed with mating partners available or not) and quantified life-history traits and cumulative lifetime fitness. Our results confirm that isolation from mates can increase longevity and growth, resulting in higher lifetime fecundity. Thus, we observed no evidence for mate limitation of reproduction. However, reproduction under isolation (i.e., selfing) resulted in inbreeding depression, which should counteract the benefits of selfing. Inbreeding depression in fitness occurred in both predator and no-predator environments, but there was no overall change in inbreeding depression with predator cues. This represents, to our knowledge, the first empirical estimate of the effect of predation risk on inbreeding depression in an animal. Cumulative fitness was most influenced by early survival and especially early fecundity. As predation risk and inbreeding (both ancestral and due to a lack of mates) reduced early fecundity, these effect are predicted to have important contributions to population growth under natural conditions. Therefore life-history plasticity (e.g., delayed reproduction) is likely to be very important to overall fitness.     

Anti-predation behaviour during bird migration; the benefit of studying multiple behavioural dimensions

Predation and predation risk have recently been shown to have profound effects on bird migration, but we still know relatively little about how birds respond to predation risk en route and how this is translated into fundamental aspects of optimal migration. Here, we make the case that to understand the fitness consequences of foraging and anti-predation behaviour en route we cannot rely on single behaviour relationships but must take many aspects of behaviour into account, because of predation risk compensation. We show this in a case study of fat and vigilant birds feeding close to cover, which emphasises the importance and potential of predation risk compensation. Another reason for taking many aspects of behaviour into account is that different behaviours need not contribute equally to individual fitness. Birds faced with an increased predation risk during migration can compensate for increased predation risk in different ways. This implies that the adaptive value of a behavioural trait can still be ambiguous even if a survival cost can be correlated with particular behaviour where all other things are equal (e.g. in an experiment). That is because in natural systems there may frequently be many other ways for animals to compensate, because all other things are never equal, so that the particular behaviour can actually be of little consequence to individual fitness. In conclusion, when studying foraging decisions and anti-predation behaviour during stopover potential compensatory mechanisms should be incorporated. This knowledge is also critical for improving future models of optimal migration.     

Patch choice under predation hazard

In this paper we study optimal animal movement in heterogeneous environments consisting of several food patches in which animals trade-off energy gain versus predation risk. We derive a myopic optimization rule describing optimal animal movements by fitness maximization assuming an animal state is described by a single quantity (such as weight, size, or energy reserves). This rule predicts a critical state at which an animal should switch from a more dangerous and more profitable patch to a less dangerous and less profitable patch. Qualitatively, there are two types of behavior: either the animal switches from one patch to another and stays in the new patch for some time before it switches again, or the animal switches between two patches instantaneously. The former case happens if animal state growth is positive in all patches, while the latter case happens if animal state growth is negative in one patch. In particular, this happens if one patch is a refuge. We consider in detail two special cases. The first one assumes a linear animal state growth while the second assumes a saturating animal state growth described by the von Bertalanffy curve. For the first model the proportion of time spent in the more profitable and more risky patch increases with profitability of this patch when state growth is positive in both patches. On contrary, if state growth is negative in the less profitable and safer patch, animals spend proportionally less time in the more profitable and more risky patch as its profitability increases. As a function of the predation risk in the more profitable patch the time spent there proportionally decreases. When animal state growth is described by the saturating curve, time spent in the more risky patch is a hump-shaped curve if state growth is positive in both patches. Our results extend the mu/f rule, which predicts that animals should behave in such a way as to minimize mortality risk to resource intake ratio.     

Resource levels and prey state influence antipredator behavior and the strength of nonconsumptive predator effects

The risk of predation can drive trophic cascades by causing prey to engage in antipredator behavior (e.g. reduced feeding), but these behaviors can be energetically costly for prey. The effects of predation risk on prey (nonconsumptive effects, NCEs) and emergent indirect effects on basal resources should therefore depend on the ecological context (e.g. resource abundance, prey state) in which prey manage growth/predation risk tradeoffs. Despite an abundance of behavioral research and theory examining state‐dependent responses to risk, there is a lack of empirical data on state‐dependent NCEs and their impact on community‐level processes. We used a rocky intertidal food chain to test model predictions for how resources levels and prey state (age/size) shape the magnitude of NCEs. Risk cues from predatory crabs Carcinus maenas caused juvenile and sub‐adult snails Nucella lapillus to increase their use of refuge habitats and decrease their growth and per capita foraging rates on barnacles Semibalanus balanoides. Increasing resource levels (high barnacle density) and prey state (sub‐adults) enhanced the strength of NCEs. Our results support predictions that NCEs will be stronger in resource‐rich systems that enhance prey state and suggest that the demographic composition of prey populations will influence the role of NCEs in trophic cascades. Contrary to theory, however, we found that resources and prey state had little to no effect on snails in the presence of predation risk. Rather, increases in NCE strength arose because of the strong positive effects of resources and prey state on prey foraging rates in the absence of risk. Hence, a common approach to estimating NCE strength – integrating measurements of prey traits with and without predation risk into a single metric – may mask the underlying mechanisms driving variation in the strength and relative importance of NCEs in ecological communities.     

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.     

On the evolution of group-escape strategies of selfish prey

The phenomenon of group escape cannot be explained by an argument of risk dilution, applied to gregarious behaviour of passive prey whose risk of predation is equally shared by all group members (Hamilton, 1971). Instead, individuals at the tail of an escaping group suffer the bulk of the group’s predation risk, and thus have the highest incentive to desert it. Just because of this, desertion, in this case, may serve as a signal of vulnerability for the pursuing predator. Under wide conditions, it is therefore shown that the predator is always expected to prefer the chasing of a deserter, whenever it is observed. Consequently, an individual who finds himself at the tail of the herd must compare the risk of remaining there with that of deserting the herd and thereby becoming a likely target for predation. If the first risk is higher than the latter, the herd disperses; if the latter is higher, the herd cohesively follows the fastest individuals in its lead (we deal also with cases in which only part of the herd disperses). We see, however, that the question which risk is higher depends not only on the terrain, but also on the route of escape that is decided by the fastest members at the lead of the herd, those that are least likely to be caught. Concentrating on herds without family structure, we assume that the route of escape is selfishly chosen by these ad hoc leaders to minimize their own predation risk, regardless of the others’ welfare. However, the predation risk of the leader depends very much on the willingness of other herd members to follow him, thus providing a buffer between him and the pursuing predator. Consequently, when choosing an escape route, the leader has also to consider the cohesion of the herd, i.e., the reaction of slower individuals to his choice. Under some plausible conditions, this choice may force the herd to follow, while other conditions may lead to its dispersal. In some cases the leader may choose a route that serves the needs of the entire group, and sometime only those of its more vulnerable members. In other cases the leader may choose a route that sacrifices the weakest members, thereby improving the survival probability of the others.We employ a model of a k+1 players game, a single predator, and k heterogeneous prey individuals. The predator aims to maximize the probability of a successful catch, and each individual aims to minimize his probability of being caught.     

Foraging-efficiency-predation-risk trade-off in the grey squirrel

Many animals must often respond to environmental patterns that simulatneously influence both foraging efficiency and predation risk. We noted that grey squirrels (Sciurus carolinensis) sometimes immediately consume food items in areas of relatively great exposure to predators, and at other times carry food items to the safety of a tree prior to consumption. We outlined a hypothesis that the squirrels were somehow trading-off energy intake rate against predation risk. A simple model shows that maximal energetic efficiency is associated with immediate consumption, whereas (under the field conditions studied) carrying items to the safety of trees provides for minimal exposure to predation. Our analysis of the model predicts that the tendency to carry a food item should decrease with distance of food from cover (travel time) and increase with item size (handling time). To test our predictions, we presented free-roaming grey squirrels with patches containing a fixed number of identical food items. We estimated the proportion of items carried to trees before consumption for 12 different combinations of distance to the nearest tree and item size. The results support our hypothesis and indicate that a simple behavioural criterion based solely on foraging rate or time exposed to predators is insufficient to explain the variation in the data.     

Nongenetic inheritance and the evolution of costly female preference

In species where males provide neither direct benefits nor paternal care, it is typically assumed that female preferences are maintained by indirect selection reflecting genetic benefits to offspring of preferred males. However, it remains unclear whether populations harbour sufficient genetic variation in fitness to support costly female preferences – a problem called the ‘lek paradox’. Here, we ask whether indirect selection on female preferences can be maintained by nongenetic inheritance. We construct a general model that can be used to represent either genetic or nongenetic inheritance, depending on the choice of parameter values. Interestingly, we find that costly preference is most likely to evolve and persist when fitness depends on an environmentally induced factor that can be transmitted over a single generation only, such as an environment‐dependent paternal effect. Costly preference can also be supported when fitness depends on a highly mutable factor that can persist over multiple generations, such as an epigenetic mark, but the necessary conditions are more restrictive. Our findings show that nongenetic inheritance provides a plausible hypothesis for the maintenance of costly female preferences in species where males provide no direct benefits to females. Nongenetic paternal inheritance of fitness can occur in species lacking conventional forms of paternal care. Indeed, transmission of paternal condition via sperm‐borne nongenetic factors may be more likely to evolve than conventional forms of paternal investment because sperm‐borne effects are protected from cuckoldry. Our results furnish a novel example of an interaction between genetic and nongenetic inheritance that can lead to otherwise unexpected evolutionary outcomes.     

Climate change enhances the negative effects of predation risk on an intermediate consumer

Predators are a major source of stress in natural systems because their prey must balance the benefits of feeding with the risk of being eaten. Although this ‘fear’ of being eaten often drives the organization and dynamics of many natural systems, we know little about how such risk effects will be altered by climate change. Here, we examined the interactive consequences of predator avoidance and projected climate warming in a three‐level rocky intertidal food chain. We found that both predation risk and increased air and sea temperatures suppressed the foraging of prey in the middle trophic level, suggesting that warming may further enhance the top‐down control of predators on communities. Prey growth efficiency, which measures the efficiency of energy transfer between trophic levels, became negative when prey were subjected to predation risk and warming. Thus, the combined effects of these stressors may represent an important tipping point for individual fitness and the efficiency of energy transfer in natural food chains. In contrast, we detected no adverse effects of warming on the top predator and the basal resources. Hence, the consequences of projected warming may be particularly challenging for intermediate consumers residing in food chains where risk dominates predator‐prey interactions.     

Titrating the cost of plant toxins against predators: determining the tipping point for foraging herbivores

1. Foraging herbivores must deal with plant characteristics that inhibit feeding and they must avoid being eaten. Principally, toxins limit food intake, while predation risk alters how long animals are prepared to harvest resources. Each of these factors strongly affects how herbivores use food patches, and both constraints can pose immediate proximate costs and long-term consequences to fitness. 2. Using a generalist mammalian herbivore, the common brushtail possum (Trichosurus vulpecula), our aim was to quantitatively compare the influence of plant toxin and predation risk on foraging decisions. 3. We performed a titration experiment by offering animals a choice between non-toxic food at a risky patch paired with food with one of five toxin concentrations at a safe patch. This allowed us to identify the tipping point, where the cost of toxin in the safe food patch was equivalent to the perceived predation risk in the alternative patch. 4. At low toxin concentration, animals ate more from the safe than the risky patch. As toxin concentration increased at the safe patch, intake shifted until animals ate mainly from the risky patch. This shift was associated with behavioural changes: animals spent more time and fed longer at the risky patch, while vigilance increased at both risky and safe patches. 5. Our results demonstrate that the variation in toxin concentration, which occurs intraspecifically among plants, can critically influence the relative cost of predation risk on foraging. We show that herbivores quantify, compare and balance these two different but proximate costs, altering their foraging patterns in the process. This has potential ecological and evolutionary implications for the production of plant defence compounds in relation to spatial variation in predation risk to herbivores.     

The impact of predation on burrow use by arctic ground squirrels in the boreal forest

In sedentary animals, the choice of a suitable home site is critical to survival and reproductive fitness. However, habitat suitability may vary with predation risk. We compared habitat use of Arctic ground squirrels (Spermophilus parryii plesius) living in the boreal forest under conditions of fluctuating predation pressure. In our study area, predators show ten-year cycles in numbers that track that of their primary prey, the snowshoe hare (Lepus americanus). In 1993, we compared burrows that continued to be occupied following the period of intense predation during the hare decline of 1990-1992 with those that became vacant, and with random locations. We contrasted these sites to those in a predator exclosure where predation pressure was minimized. Burrows on control sites were located on sloped sites with high visibility. Burrows that remained occupied during the period of intense predation were more likely to be in open areas with fewer fallen trees than burrows that became vacant. We used discriminant functions derived from the control sites and found that 89% of the burrows on the predator exclosure were classified as being similar to the random locations on control sites. We conclude that the distribution of Arctic ground squirrels in the boreal forest is a direct function of predator presence.