Optimum search speed and activity: a dynamic game in a three-link trophic system

We analysed how a consumer should simultaneously trade-off search speed and time active in a game with predators that optimise their search speed. Both the consumers and the predators are continuously reproducing and maximise fitness by maximising the per capita growth rate. The impact of the predator's presence on consumer behaviour, and the effects of type I and II functional responses on the behaviour of both species are considered. In the analyses, consumers were allowed to co-ordinate activity or behave independently in relation to other consumers. The ESS-analysis of the game ensures that no mutant can invade the system. The independent activity was found to be optimal in all analyses, while the co-ordinated activity was only optimal at full activity where the two activity strategies coincided. The model showed that consumers should change activity to account for predation risk. Activity generally decreased with predation risk. Concerning the energetic aspects, both activity and search speed were important to account for the reproductive output. The functional responses influenced the optimum activity and search speed of consumers and predators. In general, the optimum behaviours showed complex non-linear responses in relation to the resource and the consumer density. A predator type II functional response had profound impacts on the properties of the optima, the stability and presence of alternative strategies. As a result of the optimum behaviours, the realised functional responses of both species became sigmoidal.     

Functional responses modified by predator density

Realistic functional responses are required for accurate model predictions at the community level. However, controversy remains regarding which types of dependencies need to be included in functional response models. Several studies have shown an effect of very high predator densities on per capita predation rates, but it is unclear whether this predator dependence is also important at low predator densities. We fit integrated functional response models to predation data from 4-h experiments where we had varied both predator and prey densities. Using an information theoretic approach we show that the best-fit model includes moderate predator dependence, which was equally strong even at low predator densities. The best fits of Beddington–DeAngelis and Arditi–Akçakaya functional responses were closely followed by the fit of the Arditi–Ginzburg model. A Holling type III functional response did not describe the data well. In addition, independent behavioral observations revealed high encounter rates between predators. We quantified the number of encounters between predators and the time the focal predator spent interacting with other individuals per encounter. This time “wasted” on conspecifics reduced the total time available for foraging and may therefore account for lower predation rates at higher predator densities. Our findings imply that ecological theory needs to take realistic levels of predator dependence into account.     

When is general wariness favored in avoiding multiple predator types?

Adaptive responses to predation are generally studied assuming only one predator type exists, but most prey species are depredated by multiple types. When multiple types occur, the optimal antipredator response level may be determined solely by the probability of attack by the relevant predator: "specific responsiveness." Conversely, an increase in the probability of attack by one predator type might increase responsiveness to an alternative predator type: "general wariness." We formulate a mathematical model in which a prey animal perceives a cue providing information on the probability of two predator types being present. It can perform one of two evasive behaviors that vary in their suitability as a response to the "wrong" predator type. We show that general wariness is optimal when incorrect behavioral decisions have differential fitness costs. Counterintuitively, difficulty in discriminating between predator types does not favor general wariness. We predict that where responses to predator types are mutually exclusive (e.g., referential alarm-calling), specific responsiveness will occur; we suggest that prey generalize their defensive responses based on cue similarity due to an assumption of response utility; and we predict, with relevance to conservation, that habituation to human disturbance should generalize only to predators that elicit the same antipredator response as humans.     

Biogeographic variation in behavioral and morphological responses to predation risk

The expression of prey antipredator defenses is often related to ambient consumer pressure, and prey express greater defenses under intense consumer pressure. Predation is generally greater at lower latitudes, and antipredator defenses often display a biogeographic pattern. Predation pressure may also vary significantly between habitats within latitudes, making biogeographic patterns difficult to distinguish. Furthermore, invasive predators may also influence the expression of prey defenses in ecological time. The purpose of this study was to determine how these factors influence the strength of antipredator responses. To assess patterns in prey antipredator defenses based upon geographic range (north vs. south), habitat type (wave-protected vs. wave-exposed shores), and invasive predators, we examined how native rock (Cancer irroratus) and invasive green (Carcinus maenas) crab predators influence the behavioral and morphological defenses of dogwhelk (Nucella lapillus) prey from habitats that differ in wave exposure across an ~230 km range within the Gulf of Maine. The expression of behavioral and morphological antipredatory responses varied according to wave exposure, geographic location, and predator species. Dogwhelks from areas with an established history with green crabs exhibited the largest behavioral and morphological antipredator responses to green crabs. Dogwhelk behavioral responses to rock crabs did not vary between habitats or geographic regions, although morphological responses were greater further south where predation pressure was greatest. These findings suggest that dogwhelk responses to invasive and native predators vary according to geographic location and habitat, and are strongly affected by ambient predation pressure due to the invasion history of an exotic predator.     

The effect of the Holling type II functional response on apparent competition

This article analyzes the classical 2-resource-1-consumer apparent competition community module with the Holling type II functional response. Two types of resource regulation (top-down vs. combined top-down and bottom-up) and two types of consumer behaviors (inflexible consumers with fixed preferences for resources vs. adaptive consumers) are considered. When resources grow exponentially and consumers are inflexible foragers, one resource is always outcompeted due to strong apparent competition. Density dependent resource growth relaxes apparent competition so that resources can coexist. As multiple attractors (either equilibria or limit cycles) coexist, population dynamics and community composition depend on initial population densities. Population dynamics change dramatically when consumers forage adaptively. In this case, the results both for top-down, and combined top-down and bottom-up regulation are similar and they show that species persistence occurs for a much larger set of parameter values when compared with inflexible consumers. Moreover, population dynamics will be chaotic when resource carrying capacities are high enough. This shows that adaptive consumer switching can destabilize population dynamics.     

Trait and density mediated indirect interactions in simple food webs

This article compares indirect trait-mediated interactions in simple resource–consumer–predator food webs with those that are density-mediated. It focuses on two well documented responses of consumers to predation risk: decrease in consumer activity and habitat switch. These behavioral effects are transmitted to resources and they cause similar indirect effects as those which are mediated by density changes in consumers. Two indirect interactions are studied in this article: trophic cascades, and apparent competition. Results for density only, trait only and combined density and trait mediated interactions are compared and discussed with respect to manipulation with predator density (top-down manipulation) and resource environmental capacity (bottom-up manipulation). The article shows that trait-mediated effects on species equilibrial densities are similar to those of density-mediated, but they are often highly non-linear. Thus, they may have potential for even stronger impact on food webs than those which are density mediated.     

Impacts of predation on dynamics of age-structured prey: Allee effects and multi-stability

With a series of mathematical models, we explore impacts of predation on a prey population structured into two age classes, juveniles and adults, assuming generalist, age-specific predators. Predation on any age class is either absent, or represented by types II or III functional responses, in various combinations. We look for Allee effects or more generally for multiple stable steady states in the prey population. One of our key findings is the occurrence of a predator pit (low-density ??refuge?? state of prey induced by predation; the chance of escaping predation thus increases both below and above an intermediate prey density) when only one age class is consumed and predators use a type II functional response ??this scenario is known to occur for an unstructured prey consumed via a type III functional response and can never occur for an unstructured prey consumed via a type II one. In the case where both age classes are consumed by type II generalist predators, an Allee effect occurs frequently, but some parameters give also rise to a predator pit and even three stable equilibria (one extinction equilibrium and two positive ones??Allee effect and predator pit combined). Multiple positive stable equilibria are common if one age class is consumed via a type II functional response and the other via a type III functional response??here, in addition to the behaviours mentioned above one may even observe three stable positive equilibria????double?? predator pit. Some of these results are discussed from the perspective of population management.     

Bistability and limit cycles in generalist predator–prey dynamics

Since generalist predators feed on a variety of prey species they tend to persist in an ecosystem even if one particular prey species is absent. Predation by generalist predators is typically characterized by a sigmoidal functional response, so that predation pressure for a given prey species is small when the density of that prey is low. Many mathematical models have included a sigmoidal functional response into predator–prey equations and found the dynamics to be more stable than for a Holling type II functional response. However, almost none of these models considers alternative food sources for the generalist predator. In particular, in these models, the generalist predator goes extinct in the absence of the one focal prey. We model the dynamics of a generalist predator with a sigmoidal functional response on one dynamic prey and fixed alternative food source. We find that the system can exhibit up to six steady states, bistability, limit cycles and several global bifurcations.     

Revisiting the influence of learning in predator functional response,how it can lead to shapes different from type III

Predator/parasitoid functional response is one of the main tools used to study predation behavior, and in assessing the potential of biological control candidates. It is generally accepted that predator learning in prey searching and manipulation can produce the appearance of a type III functional response. Holling proposed that in the presence of alternative prey, at some point the predator would shift the preferred prey, leading to the appearance of a sigmoid function that characterized that functional response. This is supported by the analogy between enzyme kinetics and functional response that Holling used as the basis for developing this theory. However, after several decades, sigmoidal functional responses appear in the absence of alternative prey in most of the biological taxa studied. Here, we propose modeling the effect of learning on the functional response by using the explicit incorporation of learning curves in the parameters of the Holling functional response, the attack rate (a), and the manipulation time (h). We then study how the variation in the parameters of the learning curves causes variations in the shape of the functional response curve. We found that the functional response product of learning can be either type I, II, or III, depending on what parameters act on the organism, and how much it can learn throughout the length of the study. Therefore, the presence of other types of curves should not be automatically associated with the absence of learning. These results are important from an ecological point of view because when type III functional response is associated with learning, it is generally accepted that it can operate as a stabilizing factor in population dynamics. Our results, to the contrary, suggest that depending on how it acts, it may even be destabilizing by generating the appearance of functional responses close to type I.     

Modeling changes in predator functional response to prey across spatial scales

Extrapolation of predator functional responses from laboratory observations to the field is often necessary to predict predation rates and predator-prey dynamics at spatial and temporal scales that are difficult to observe directly. We use a spatially explicit individual-based model to explore mechanisms behind changes in functional responses when the scale of observation is increased. Model parameters were estimated from a predator-prey system consisting of the predator Delphastus catalinae (Coleoptera: Coccinellidae) and Bemisia tabaci biotype B (Hemiptera: Aleyrodidae) on tomato plants. The model explicitly incorporates prey and predator distributions within single plants, the search behavior of predators within plants, and the functional response to prey at the smallest scale of interaction (within leaflets) observed in the laboratory. Validation revealed that the model is useful in scaling up from laboratory observations to predation in whole tomato plants of varying sizes. Comparing predicted predation at the leaflet scale, as observed in laboratory experiments, with predicted predation on whole plants revealed that the predator functional response switches from type II within leaflets to type III within whole plants. We found that the magnitude of predation rates and the type of functional response at the whole plant scale are modulated by (1) the degree of alignment between predator and prey distributions and (2) predator foraging behavior, particularly the effect of area-concentrated search within plants when prey population density is relatively low. The experimental and modeling techniques we present could be applied to other systems in which active predators prey upon sessile or slow-moving species.     

普通肉食螨对椭圆食粉螨的捕食功能

在6个恒温下研究普通肉食螨Cheyletus eruditus(Schrank)不同螨态对椭圆食粉螨Aleuroglyphus ovatus(Troupeau)的功能反应。结果表明,普通肉食螨不同螨态对椭圆食粉螨的功能反应均属于HollingⅡ型,其中雌成螨的捕食能力最强,其次是雄螨、若螨、幼螨;在各温度处理中,雌成螨在28℃时具有较高的捕食功能;普通肉食螨在16℃的低温状态下捕食功能很低,仅有雌螨对猎物有捕食行为;在猎物密度不变的情况下,普通肉食螨捕食猎物的数量随自身密度的增加而下降。     

Food-web connectance and predator interference dampen the paradox of enrichment

Classic consumer-resource models with hyperbolic functional responses predict that enrichment increases the average biomasses of the species, but eventually leads to species' extinction due to accelerated oscillations ("paradox of enrichment"). However, empirical studies have stressed the complexity of natural food webs and the dominance of sigmoid or predator-interference functional responses, which may dampen population oscillations due to enrichment. Using analytical and numerical methods, we study enrichment effects on simple consumer-resource pairs and complex food webs with hyperbolic Holling type II (hereafter: type II), sigmoid Holling type III (hereafter: type III) and Beddington-De Angelis predator-interference functional responses (hereafter: BDA). Consumer-resource systems with a type III or BDA functional response are highly robust against accelerated oscillations due to enrichment, and the "paradox of enrichment" is resolved under certain parameter combinations. Subsequently, we simulated complex food webs with empirically-corroborated body-size structures of consumers that are ten times larger than their average resource. Our analyses demonstrate positive connectance-stability relationships with BDA or type III functional responses. Moreover, increasing connectance of these food webs also increases the robustness against enrichment in models with a BDA functional response. These results suggest that the well-known destabilising effects of connectance and enrichment found in classic models with type II functional responses may be inverted into stabilising effects in more realistic food-web models that are based on empirically-corroborated body-size structures and BDA or type III functional responses.     

You can’t run but you can hide: refuge use in frog tadpoles elicits density-dependent predation by dragonfly larvae

The potential role of prey refuges in stabilizing predator–prey interactions is of longstanding interest to ecologists, but mechanisms underlying a sigmoidal predator functional response remain to be fully elucidated. Authors have disagreed on whether the stabilizing effect of prey refuges is driven by prey- versus predator-centric mechanisms, but to date few studies have married predator and prey behavioural observations to distinguish between these possibilities. We used a dragonfly nymph–tadpole system to study the effect of a structural refuge (leaf litter) on the predator’s functional response, and paired this with behavioural observations of both predator and prey. Our study confirmed that hyperbolic (type II) functional responses were characteristic of foraging predators when structural cover was low or absent, whereas the functional response was sigmoidal (type III) when prey were provided with sufficient refuge. Prey activity and refuge use were density independent across cover treatments, thereby eliminating a prey-centric mechanism as being the genesis for density-dependent predation. In contrast, the predator’s pursuit length, capture success, and handling time were altered by the amount of structure implying that observed shifts in density-dependent predation likely were related to predator hunting efficiency. Our study advances current theory by revealing that despite fixed-proportion refuge use by prey, presence of a prey refuge can induce density-dependent predation through its effect on predator hunting strategy. Ultimately, responses of predator foraging decisions in response to changes in prey availability and search efficiency may be more important in producing density-dependent predation than the form of prey refuge use.     

Trait‐mediated indirect interactions in a marine intertidal system as quantified by functional responses

Studies of trait‐mediated indirect interactions (TMIIs) typically focus on effects higher predators have on per capita consumption by intermediate consumers of a third, basal prey resource. TMIIs are usually evidenced by changes in feeding rates of intermediate consumers and/or differences in densities of this third species. However, understanding and predicting effects of TMIIs on population stability of such basal species requires examination of the type and magnitude of the functional responses exhibited towards them. Here, in a marine intertidal system consisting of a higher‐order fish predator, the shanny Lipophrys pholis, an intermediate predator, the amphipod Echinogammarus marinus, and a basal prey resource, the isopod Jaera nordmanni, we detected TMIIs, demonstrating the importance of habitat complexity in such interactions, by deriving functional responses and exploring consequences for prey population stability. Echinogammarus marinus reacted to fish predator diet cues by reducing activity, a typical anti‐predator response, but did not alter habitat use. Basal prey, Jaera nordmanni, did not respond to fish diet cues with respect to activity, distribution or aggregation behaviour. Echinogammarus marinus exhibited type II functional responses towards J. nordmanni in simple habitat, but type III functional responses in complex habitat. However, while predator cue decreased the magnitude of the type II functional response in simple habitat, it increased the magnitude of the type III functional response in complex habitat. These findings indicate that, in simple habitats, TMIIs may drive down consumption rates within type II responses, however, this interaction may remain de‐stabilising for prey populations. Conversely, in complex habitats, TMIIs may strengthen regulatory influences of intermediate consumers on prey populations, whilst potentially maintaining prey population stability. We thus highlight that TMIIs can have unexpected and complex ramifications throughout communities, but can be unravelled by considering effects on intermediate predator functional response types and magnitudes. Synthesis Higher‐order predators and habitat complexity can influence behaviour of intermediate species, affecting their consumption of prey through trait‐mediated indirect interactions (TMIIs). However, it is not clear how these factors interact to determine prey population stability. Using functional responses (FRs), relating predator consumption to prey density, we detected TMIIs in a marine system. In simple habitats, TMIIs reduced consumption rates, but FRs remained de‐stabilising for prey populations. In complex habitats, TMIIs strengthened prey regulation with population stabilizing FRs. We thus demonstrate that FRs can assess interactions of environmental and biological cues that result in complex and unexpected outcomes for prey populations.     

Predator occurrence and perceived predation risk determine grouping behavior in guanaco (Lama guanicoe)

Grouping behavior of social ungulates may depend on both predator occurrence and perceived predation risk associated with habitat structure, reproductive state, and density of conspecifics. Over 3 years, we studied grouping behavior of guanaco (Lama guanicoe) families in Chilean Patagonia during the birthing season and determined their response to variation in predator occurrence and perceived predation risk (habitat structure, calf/adult rate, and density of conspecifics). We considered the effect of two predators, puma (Puma concolor) and culpeo fox (Lycalopex culpaeus). We measured two common (family group size and vigilance) and one novel (family group cohesion) behavioral responses of guanaco. Our results show that guanaco family groups adapted their grouping behavior to both predator occurrence and perceived predation risk. Larger family groups were found in open habitats and areas with high puma occurrence, while guanacos stayed in small family groups in areas with high shrub cover or low visibility. Group cohesion increased in areas with higher occurrence of pumas and culpeo foxes, and also increased in smaller family groups and in areas with low guanaco density. Vigilance (number of vigilant adults) was mainly related to group size and visibility, increasing in areas with low visibility, while residual vigilance (vigilance after removing the group‐size effect) did not vary with the explanatory variables examined. Our results suggest that a mix of predator occurrence and perceived predation risk influences guanaco grouping behavior and highlights the importance of evaluating different antipredator responses together and considering all predator species in studies aimed at understanding ungulate behavior.     

Threshold levels of generalist predation determine consumer response to resource pulses

Many ecological systems are characterized by brief periods of increased resource availability called resource pulses. Empirical studies suggest that some populations of primary consumers grow rapidly in response to resource pulses, but others instead remain at low abundance despite increases in resource availability. Previous theory suggests that the lack of increase in primary consumers might be due to predators, which can respond to increased prey density both numerically, by increasing their own population, and functionally, by killing prey at a faster rate. The complexity of potential population responses to resource pulses can be assessed with simulations, but analytical conditions determining when one observes qualitatively distinct dynamics have yet to be identified. Here we use a graphical method based on a bifurcation diagram to derive the conditions leading to qualitatively distinct steady state and transient prey population dynamics as levels of predation (abundance and diversity) vary. When predation thresholds are crossed, consumer populations respond numerically to increases in their resources and provide a secondary resource pulse to their predators and parasites. These community dynamics have broad implications for the impact of changing predator communities on insect and rodent population outbreaks, which are economically and epidemiologically important.     

Should "handled" prey be considered? Some consequences for functional response, predator-prey dynamics and optimal foraging theory

Predator-prey models consider those prey that are free. They assume that once a prey is captured by a predator it leaves the system. A question arises whether in predator-prey population models the variable describing prey population shall consider only those prey which are free, or both free and handled prey together. In the latter case prey leave the system after they have been handled. The classical Holling type II functional response was derived with respect to free prey. In this article we derive a functional response with respect to prey density which considers also handled prey. This functional response depends on predator density, i.e., it accounts naturally for interference. We study consequences of this functional response for stability of a simple predator-prey model and for optimal foraging theory. We show that, qualitatively, the population dynamics are similar regardless of whether we consider only free or free and handled prey. However, the latter case may change predictions in some other cases. We document this for optimal foraging theory where the functional response which considers both free and handled prey leads to partial preferences which are not observed when only free prey are considered.     

Predator–prey naïveté, antipredator behavior,and the ecology of predator invasions

We present a framework for explaining variation in predator invasion success and predator impacts on native prey that integrates information about predator–prey naïveté, predator and prey behavioral responses to each other, consumptive and non‐consumptive effects of predators on prey, and interacting effects of multiple species interactions. We begin with the ‘naïve prey’ hypothesis that posits that naïve, native prey that lack evolutionary history with non‐native predators suffer heavy predation because they exhibit ineffective antipredator responses to novel predators. Not all naïve prey, however, show ineffective antipredator responses to novel predators. To explain variation in prey response to novel predators, we focus on the interaction between prey use of general versus specific cues and responses, and the functional similarity of non‐native and native predators. Effective antipredator responses reduce predation rates (reduce consumptive effects of predators, CEs), but often also carry costs that result in non‐consumptive effects (NCEs) of predators. We contrast expected CEs versus NCEs for non‐native versus native predators, and discuss how differences in the relative magnitudes of CEs and NCEs might influence invasion dynamics. Going beyond the effects of naïve prey, we discuss how the ‘naïve prey’, ‘enemy release’ and ‘evolution of increased competitive ability’ (EICA) hypotheses are inter‐related, and how the importance of all three might be mediated by prey and predator naïveté. These ideas hinge on the notion that non‐native predators enjoy a ‘novelty advantage’ associated with the naïveté of native prey and top predators. However, non‐native predators could instead suffer from a novelty disadvantage because they are also naïve to their new prey and potential predators. We hypothesize that patterns of community similarity and evolution might explain the variation in novelty advantage that can underlie variation in invasion outcomes. Finally, we discuss management implications of our framework, including suggestions for managing invasive predators, predator reintroductions and biological control.     

Predictable changes in predation mortality as a consequence of changes in food availability and predation risk

Theory predicts that animals will have lower activity levels when either the risk of predation is high or the availability of resources in the environment is high. If encounter rates with predators are proportional to activity level, then we might expect predation mortality to be affected by resource availability and predator density independent of the number of effective predators. In a factorial experiment, we tested whether predation mortality of larval wood frogs, Rana sylvatica, caused by a single larval dragonfly, Anax junius, was affected by the presence of additional caged predators and elevated resource levels. Observations were consistent with predictions. The survival rate of the tadpoles increased when additional caged predators were present and when additional resources were provided. There was no significant interaction term between predator density and food concentration. Lower predation rates at higher predator density is a form of interference competition. Reduced activity of prey at higher predator density is a potential general mechanism for this widespread phenomenon. Higher predation rates at low food levels provides an indirect mechanism for density-dependent predation. When resources are depressed by elevated consumer densities, then the higher activity levels associated with low resource levels can lead to a positive association between consumer density and consumer mortality due to predation. These linkages between variation in behaviour and density-dependent processes argue that variation in behaviour may contribute to the dynamics of the populations. Because the capture rate of predators depends on the resources available to prey, the results also argue that models of food-web dynamics will have to incorporate adaptive variation in behaviour to make accurate predictions.     

How to model the local interaction in the predator–prey system at slow diffusion in a heterogeneous environment?

We examine the nonlinear reaction–diffusion–advection equations to modeling of the predator–prey system under heterogeneous carrying capacity of the prey, and Holling type II functional response. When advection and diffusion fluxes are absent or small, we detect the discrepancy between the resource (carrying capacity) and species distributions. The large diffusion eliminates this effect. We propose a modification of the functional response coefficients to provide the correlation between species distribution and resource in both cases. The numerical simulation of several models both under small and moderate advection–diffusion fluxes is carried out.