Encounters in predator-prey systems: a simple discrete model

Predator-prey systems are often described by exploitation models. These models can mimic experimental data very accurately, but it is sometimes difficult to realize the relationships between the models and the behavior of individual predator and prey animals. A simple discrete model is proposed here that tries to elucidate the connections between: the animals' movements, the predator/prey encounters; and the dynamics in the system as globally represented by the exploitation models. In these models, the term "area of discovery" plays an essential role. This term is shown to be a predictable coefficient that is composed of measurable physical properties of the analyzed predator-prey system. The model takes into account that predators and prey in experimental systems often do not search randomly but prefer some parts of the test area. The model is applied to the mite system Phytoseiulus persimilis/Tetranychus urticae under simple artificial conditions.     

Protean defence by prey animals

Summary Attention is drawn to the widespread occurrence ofprotean phenomena, in which the appearance and behaviour of prey animals are rendered variable and irregular, as a weapon in the biological arms race between predators and their prey. Protean behaviour is defined as that behaviour which is sufficiently unsystematic to prevent a reactor predicting in detail the position or actions of the actor.Single prey animals frequently flee from a predator in an irregular manner, zigzagging, spinning, looping, or bouncing. Thissingle erratic display occurs widely in the Animal Kingdom, and may also be utilised in everyday movements of potential prey as insurance against possible attack. Examples are given.In a group of prey animals the protean aspect of escape is enhanced by the effect of numbers. In scatter reactions the effect is of multiple choice and of the simultaneous operation of several single erratics. In mobbing displays there are also successive changes in the actors' behavioural role. In protean deterrence the shuffling of individuals within a tightly packed group prevents a predator from singling one out for attack.In many species the confusing effect of changes in movement and behavioural role is enhanced by rapid changes in appearance, particularly colour.It is suggested that those prey individuals which employ escape patterns unfamiliar to the predator will tend to be at a selective advantage. During phylogeny this is likely to lead to intra-specific and inter-specific increase in the number and diversity of escape behaviours. Apostatic polymorphism is seen as a special case of protean variation within populations.There is evidence that protean displays operate by arousing neurological conflict, thereby delaying the predator's reactions and reducing the effectiveness of predatory mechanisms. Also they insure against learned countermeasures by incorporating irregularities as a basic principle. It is stressed that the irregular variability of protean displays is not accidental but has been selected for in phylogeny. A number of poorly understood behavioural aspects of the ecology of predator-prey relationships are thus united in a single theory.     

Predator hunting modes and predator–prey space games

Predators and prey are often engaged in a game where their expected fitnesses are affected by their relative spatial distributions. Game models generally predict that when predators and prey move at similar temporal and spatial scales that predators should distribute themselves to match the distribution of the prey's resources and that prey should be relatively uniformly distributed. These predictions should better apply to sit-and-pursue and sit-and-wait predators, who must anticipate the spatial distributions of their prey, than active predators that search for their prey. We test this with an experiment observing the spatial distributions and estimating the causes of movements between patches for Pacific tree frog tadpoles (Pseudacris regilla), a sit-and-pursue dragonfly larvae predator (Rhionaeschna multicolor), and an active salamander larval predator (Ambystoma tigrinum mavortium) when a single species was in the arena and when the prey was with one of the predators. We find that the sit-and-pursue predator favors patches with more of the prey's algae resources when the prey is not in the experimental arena and that the prey, when in the arena with this predator, do not favor patches with more resources. We also find that the active predator does not favor patches with more algae and that prey, when with an active predator, continue to favor these higher resource patches. These results suggest that the hunting modes of predators impact their spatial distributions and the spatial distributions of their prey, which has potential to have cascading effects on lower trophic levels.     

Movement and direction of movement of a simulated prey affect the success rate in barn owl Tyto alba attack

The present study was aimed at testing a novel idea, that rather than maximizing their distance from a predator during close-distance encounters, prey species are better off moving directly or diagonally toward the predator in order to increase the relative speed and confine the attack to a single available clashing point. We used two tamed barn owls Tyto alba to measure the rate of attack success in relation to the direction of prey movement. A dead mouse or chick was used to simulate the prey, pulled to various directions by means of a transparent string during the owl's attack. Both owls showed a high success rate in catching stationary compared with moving food items (90% and 21%, respectively). Success was higher when the prey moved directly away, rather than towards the owls (50% and 18%, respectively). Strikingly, these owls had 0% success in catching food items that were pulled sideways. This failure to catch prey that move sideways may reflect constraints in postural head movements in aerial raptors that cannot move the eyes but rather move the entire head in tracking prey. So far there is no evidence that defensive behavior in terrestrial prey species takes advantage of the above escape directions to lower rates of predator success. However, birds seem to adjust their defensive tactics in the vertical domain by taking-off at a steep angle, thus moving diagonally toward the direction of an approaching aerial predator. These preliminary findings warrant further studies in barn owls and other predators, in both field and laboratory settings, to uncover fine predator head movements during hunting, the corresponding defensive behavior of the prey, and the adaptive significance of these behaviors.     

Scale dependent effects of predatory fish on stream benthos

In open predation experiments the effects of predators on prey densities can be influenced by predator consumption and by prey movements in to and out of experimental arenas. A published model predicts that the predator effects observed in such experiments are scale dependent over the scale range where there is a transition from movement control (of prey densities) to consumption control. The scale dependence follows from the assumption that per capita rate of emigration out of an experimental arena decreases with increasing arena size.
To test this model the effects of a small benthic fish ( Cottus gobio ) on densities of stream invertebrates was investigated in instream channels of different length (0.5, 2 and 8 m). The effect of fish predation was scale dependent for four prey taxa. For three of these taxa predator effects increased with experimental scale, which is in agreement with model predictions. However, this proved to be a case of "making the right prediction for the wrong reason" as the basic assumption of scale dependent emigration rate was not upheld. By analyzing the behaviour of the model, parameterized with emigration and consumption rates observed in the experimental channels, it was found that observed scale effects occurred because prey emigration in response to the predator treatment was modified by the experimental scale. Further analysis of the parameterized model suggested that the densities of most prey taxa were controlled by prey movements and not by consumption by the sculpins.     

Managing predators: The influence of kangaroo rat antipredator displays on sidewinder rattlesnake hunting behavior

Upon sensing predators in their vicinity, many prey species perform antipredator displays that are thought to provide information to the predator that deters it from attacking (predator‐deterrent signals). These displays can be complex, incorporating a variety of signaling elements as well as direct physical harassment of the predator. Although the display behaviors in these communication systems are often well characterized, evidence of the efficacy of these displays in deterring predators is limited due to the challenges associated with studying free‐ranging predators. Here, we examine how the anti‐snake signals of the desert kangaroo rat (Dipodomys deserti) influence the ambush hunting behaviors of sidewinder rattlesnakes (Crotalus cerastes). We found that, although desert kangaroo rats incorporate a number of signal elements into their antipredator display, only sand kicking behavior was a significant factor in motivating sidewinder rattlesnakes to cease hunting: high rates of sand kicking led to early abandonment of ambush coils. These results indicate that anti‐snake displays of small mammals may be especially effective at mitigating the threat posed by rattlesnakes when those displays incorporate physical harassment as well as signaling.     

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

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

Systematic deviations from linear size spectra of lake fish communities are correlated with predator–prey interactions and lake‐use intensity

Size structure of organisms at logarithmic scale (i.e. size spectrum) can often be described by a linear function with a negative slope; however, substantial deviations from linearity have often been found in natural systems. Theoretical studies suggest that greater nonlinearity in community size spectrum is associated with high predator–prey size ratios but low predator–prey abundance ratios; however, empirical evaluation of the effects of predator–prey interactions on nonlinear structures remains scarce. Here, we aim to empirically explore the pattern of the size‐specific residuals (i.e. deviations from the linear regression between the logarithmic fish abundance and the logarithmic mean fish size) by using size spectra of fish communities in 74 German lakes. We found that nonlinearity was strong in lakes with high predator–prey abundance ratios but at low predator–prey size ratios. More specifically, our results suggest that only large predators, even if occurring in low abundances, can control the density of prey fishes in a broad range of size classes in a community and thus promote linearity in the size spectrum. In turn, the lack of large predator fishes may cause high abundances of fish in intermediate size classes, resulting in nonlinear size spectra in these lakes. Moreover, these lakes were characterized by a more intense human use including high fishing pressure and high total phosphorus concentrations, which have negative impacts on the abundance of large, predatory fish. Our findings indicate that nonlinear size spectra may reflect dynamical processes potentially caused by predator–prey interactions. This opens a new perspective in the research on size spectrum, and can be relevant to further quantify the efficiency of energy transfer in aquatic food webs.     

Application of a model of scale dependence to quantify scale domains in open predation experiments

We use a model of open predation experiments to define scale domains that differ in terms of the controlling processes and scale dependence of predator impacts. For experimental arenas that are small compared to the movements of the prey (small scale domain) the model predicts that predator impacts are scale independent and controlled by prey movements. For arenas of intermediate scale we predict that predator impacts are scale dependent and controlled by both prey movements and direct predation, and for the largest scale domain we predict weak scale dependence and predation control.
We propose that the scale‐domain concept is useful when designing and interpreting field experiments. As an illustration we apply the concept to experiments examining predator effects on the stream benthos. First, we test two key assumptions of the underlying model: that area‐specific prey migration rates decrease with increasing size of experimental arenas and that predation rates are independent of arena size. For this purpose we used published estimates of prey emigration and predator consumption rates for nine studies examining the effects of stream predators on benthic prey. We found that prey per capita emigration rates but not predation rates decreased with increasing arena length.
Second, we demonstrate a method for identifying the scale domain of real experiments. The model of predation experiments was parameterized using experimental data and the expected spatial and temporal scale dependence of predator impacts on prey in these experiments was simulated. The simulations suggest that the studies conducted in the largest arenas (length 15–35 m) should be classified as large‐scale, consumption‐controlled experiments, whereas the experiments conducted in smaller arenas (length 1.5–6 m) should be classified as small or intermediate‐scale. We also attempted to determine the scale domain of the experiments in a large data set, including results from most published stream predation experiments. The majority of arenas used in these experiments (73%) were smaller than 1 m in length. Our data on the scale dependence of predation and prey migration rate suggest that experiments in this scale range (<1 m) should be classified as small‐scale, movement‐controlled experiments for most prey taxa.     

Influence of Predator Presence and Prey Density on Behavior and Growth of Damselfly Larvae (Ischnura elegans) (Odonata: Zygoptera)

Foraging behavior is often determined by the conflicting benefits of energy gain and the risk of mortality from predation or other causes. Theory predicts that animals should have lower activity levels when either the risk of predation or the availability of resources in the environment is high. We investigated the adjustment of the behavior of I. elegans larvae to predator presence (Anax imperator) and prey density (Daphnia sp.) and their interaction in a completely crossed factorial experiment in the lab and the effect of behavior on growth. The foraging activity of the I. elegans larvae was significantly reduced in the presence of a free-swimming predator but not a caged predator. Abdominal movements were significantly reduced at a low prey density. Growth was significantly reduced by the presence of a free swimming predator and low prey densities. These results provide evidence that these damselfly larvae adjust their behavior to the presence of predators to increase their survival at the expense of reduced growth and development.     

Optimal diet selection,frequency dependence and prey renewal

This paper extends existing models of frequency-dependent diet selection by considering the optimal diet selection of a predator feeding upon prey populations which can be depleted but are also capable of renewal (e.g. immigration, growth, or reproduction). This model and existing models which include prey depletion, predict partial-preference and a generic diet preference for the commonest prey types (apostatic selection). Unlike previous diet selection models, it is found that the optimal diet selection of an individual predator can be to favour the rarest prey type (anti-apostatic selection) when encounter rates are high, even if the individual prey do not differ in their nutritional value. Studies have demonstrated that predators generally show apostatic selection, even when all prey have the same nutritional value. Anti-apostatic selection has also been observed when prey are crowded, and therefore at high density, consistent with the idea of high encounter rates. This anti-apostatic diet selection has previously been proposed as evidence for the use of prey search images by a predator, or variation in individual prey preference. In this paper it is suggested that prey renewal is a further factor, often confounded in experiments, which could favour anti-apostatic selection.     

Balancing yield with resilience and conservation objectives in harvested predator–prey communities

The global overexploitation of fish stocks is endangering many marine food webs. Scientists and managers now call for an ecosystem‐based fisheries management, able to take into account the complexity of marine ecosystems and the multiple ecosystem services they provide. By contrast, many fishery management plans only focus on maximizing the productivity of harvested stocks. Such practices are suggested to affect other ecosystem services, altering the integrity and resilience of natural communities. Here we show that while yield‐maximizing policies can allow for coexistence and resilience in predator–prey communities, they are not optimal in a multi‐objective context. We find that although total prey and predator maximum yields are higher with a prey‐oriented harvest, focusing on the predator improves species coexistence. Also, moderate harvesting of the predator can enhance resilience. Furthermore, increasing maximum yields by changing catchabilities improves resilience in predator‐oriented systems, but reduces it in prey‐oriented systems. In a multi‐objective context, optimal harvesting strategies involve a general tradeoff between yield and resilience. Resilience‐maximizing strategies are however compatible with quite high yields, and should often be favored. Our results further suggest that balancing harvest between trophic levels is often best at maintaining simultaneously species coexistence, resilience and yield.     

Effect of temperature extremes on the spatial dynamics of predator–prey interactions: A case study with dragonfly nymphs and newt larvae

Theory predicts that predators are more vulnerable to increasing temperature than prey. Despite huge variations in the magnitude and duration of thermally-extreme episodes in nature, most empirical studies on predator–prey interactions consider conditions induced by a climatic shift in mean temperature. We asked whether the increased vulnerability of predators holds under daily thermal extremes occurring during heat waves, using dragonfly nymphs and newt larvae as the predator–prey model system. Direct exposure of predator to prey in heated and non-heated aquaria under semi-natural conditions revealed that predator movements increased with rising temperature, whereas prey activity decreased. In contrast to the theory of predator–prey space use, the spatial co-occurrence of predator and prey individuals increased with temperature, while predation rates diminished. We conclude that daily thermal extremes affect trophic interactions in the same way, i.e. through the increased vulnerability of predators, as do long-term shifts in mean environmental temperature. Our results highlight the importance of behavioral studies for understanding mechanisms mediating the effect of extreme thermal events on species interactions.     

You can run--or you can hide: optimal strategies for cryptic prey against pursuit predators

We consider the optimal behavior of a cryptic prey individualas it is approached by a predator searching for prey. Althoughthe predator has not yet discovered the prey, it has an increasinglikelihood of doing so as it gets closer to the prey. Further,the closer the predator is to the prey when it discovers it,the more likely the predator will be to capture the prey. Thesearguments suggest that the prey should flee before the predatordiscovers it. However, the act of fleeing will alert the predatorto the presence of the prey and trigger an attack that mightnot have occurred otherwise. We capture these conflicting outcomesin a mathematical model, which we then use to predict the optimalbehavior of the prey and predator. We argue that the optimalstrategy for the prey is either to run as soon as they detecta predator approaching or to only flee in response to havingbeen detected by the predator. Running as soon as the predatoris detected is associated with low predator search speeds, alow nonpredation cost to running, a large advantage to the preyin initiating chases rather than reacting, limited ability tospot the predator at distance, a high ability to spot prey bythe predator, and a high probability that chases will be successful.The optimal strategy for the predator depends on whether itscurrent trajectory is taking it closer to or further from theprey. In the latter case, the predator should attack immediatelyon discovering the prey; in the former case, it should delayits attack until it reaches the point on its current trajectorywhere distance to the prey is minimized.     

Hydrodynamic mediation of predator-prey interactions: differential patterns of prey susceptibility and predator success explained by variation in water flow

In most shallow water marine systems, fluid movements vary on scales that may influence local community dynamics both directly, through changes in the abundance of species, and indirectly, by modifying important behaviors of organisms. We examined how differences in current speed affect the outcome of predator-prey interactions for two species of marine benthic predators (knobbed whelks, Busycon carica, and blue crabs, Callinectes sapidus) foraging on two common prey species (bay scallops, Argopecten irradians, and hard clams, Mercenaria mercenaria). The predators differ in their foraging strategies and prey in their potential escape responses. Predation by blue crabs, highly mobile predators/scavengers that rely upon chemical odors transported in the water column to locate prey, could be strongly affected by changes in current speed and turbulent mixing because their foraging strategy relies on a high degree of spatial integration of prey odor plumes. Whelks, slow moving, predatory gastropods that often forage with their bodies buried in the sediment, may be less susceptible to flow-induced distortion of prey odor plumes because their sluggish movements result in a high degree of temporal integration of prey odors. Bay scallops, relatively mobile bivalves capable of rapid short-distance swimming burst, and hard clams, sedentary bivalves, have been shown to respond to varying degrees to predator odors that are dispersed in the water column. Flow regime for the predator-prey experiments was manipulated in situ using large channels. Predation by blue crabs on both juvenile hard clams and bay scallops decreased with increases in water flow (0-12 vs. 0-30 cm s⁻¹). Whelk predation on bay scallops increased with increases in water flow, whereas predation by whelks on hard clams did not differ between flow regimes. For blue crabs movement decreased at periods of high water flow. Because blue crabs locate prey through chemolocation of water-borne cues, which are diluted rapidly at higher flows, decreases in foraging may result from the inability to successfully detect prey at enhanced flows. Differences in predation by whelks could not be explained by a similar mechanism. Visual observations of foraging whelks revealed no differences in whelk behavior between the two flow regimes. The pattern of higher whelk predation on scallops at enhanced flow is likely to be related to a flow-inhibiting ability of scallops to detect predator approach. Thus, flow enhancement interferes with three of the predator-prey systems but the effect on predator success depends on whether the predator or prey is most affected.     

Dragonfly larvae and tadpole frog space use games in varied light conditions

Predators and prey often engage in a game where predators attemptto be in areas with higher prey densities and prey attempt tobe in areas with lower predator densities. A few models havepredicted the resulting distributions of predators and prey,but little empirical data exist to test these predictions andto examine how abiotic and biotic factors shape the distributions.Thus, we observed how Anax dragonfly nymphs and Pacific treefrog tadpoles (Pseudacris regilla) either together or separatelydistributed themselves in an arena with a high- and a low-preyresource patch. Trials were conducted in high- and low-lightconditions to manipulate predation risk and to view the effectsof this abiotic factor. Counter to the model predictions, wefound that predators were not more abundant in high-resource(HR) patches, and they thus did not force prey toward beinguniformly distributed. Using a model selection approach to assesswhat factors affected predator and prey patch-switching movement,we found that prey more often left patches that had more predatorspresent, but predators surprisingly more often left patcheswith more prey present. Light levels did not affect predationrisk; however, in the dark with the associated reduction invisual information predators preferred HR patches. This causeda lower coincidence of prey and predators in patches. Predatorsalso switched patches less often when they occupied the samepatch as the other predator. This suggests that predator distributions,and indirectly prey distributions, are affected by the riskof intraguild predation.     

Predicting krill swarm characteristics important for marine predators foraging off East Antarctica

Open ocean predator‐prey interactions are often difficult to interpret because of a lack of information on prey fields at scales relevant to predator behaviour. Hence, there is strong interest in identifying the biological and physical factors influencing the distribution and abundance of prey species, which may be of broad predictive use for conservation planning and evaluating effects of environmental change. This study focuses on a key Southern Ocean prey species, Antarctic krill Euphausia superba, using acoustic observations of individual swarms (aggregations) from a large‐scale survey off East Antarctica. We developed two sets of statistical models describing swarm characteristics, one set using underway survey data for the explanatory variables, and the other using their satellite remotely sensed analogues. While survey data are in situ and contemporaneous with the swarm data, remotely sensed data are all that is available for prediction and inference about prey distribution in other areas or at other times. The fitted models showed that the primary biophysical influences on krill swarm characteristics included daylight (solar elevation/radiation) and proximity to the Antarctic continental slope, but there were also complex relationships with current velocities and gradients. Overall model performance was similar regardless of whether underway or remotely sensed predictors were used. We applied the latter models to generate regional‐scale spatial predictions using a 10‐yr remotely‐sensed time series. This retrospective modelling identified areas off east Antarctica where relatively dense krill swarms were consistently predicted during austral mid‐summers, which may underpin key foraging areas for marine predators. Spatiotemporal predictions along Antarctic predator satellite tracks, from independent studies, illustrate the potential for uptake into further quantitative modelling of predator movements and foraging. The approach is widely applicable to other krill‐dependent ecosystems, and our findings are relevant to similar efforts examining biophysical linkages elsewhere in the Southern Ocean and beyond.     

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

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

Predator response to the coloured eyespots and defensive posture of Colombian four-eyed frogs

Deimatic displays, where sudden changes in prey appearance elicit aversive predator reactions, have been suggested to occur in many taxa. These (often only putative) displays frequently involve different components that may also serve antipredator functions via other mechanisms (e.g., mimicry, warning signalling, body inflation). The Colombian four-eyed frog, Pleurodema brachyops, has been suggested to gain protection against predation through putative deimatic displays where they inflate and elevate the posterior part of their body revealing eye-like colour markings. We exposed stationary artificial frogs to wild predators to test whether the two components (eyespot/colour markings, defensive posture) of their putative deimatic display, and their combination, provide protection from predation without the sudden change in appearance. We did not detect any obvious additive effect of defensive posture and eyespots/colour markings on predation risk, but found a marginally significant trend for model frogs in the resting posture to be less attacked when displaying eyespots/colour markings than when they were not, suggesting that the presence of colour markings/eyespots may provide some protection on its own. Additionally, we found that models in a resting posture were overall more frequently attacked on the head than models in a defensive posture, indicating that a defensive posture alone could help redirect predator attacks to non-vital parts of the body. The trends found in our study suggest that the different components of P. brachyops' coloration may serve different functions during a deimatic display, but further research is needed to elucidate the role of each component when accompanied by sudden prey movement.