Time‐to‐kill: measuring attack rates in a heterogenous landscape with multiple prey types

Although spatial heterogeneity of prey and landscapes are known to contribute to variation around predator‐prey functional response models, few studies have quantified these effects. We illustrate a new approach using data from winter movement paths of GPS‐collared wolves in the Rocky Mountains of Canada and time‐to‐event models with competing risks for measuring the effect of prey and landscape characteristics on the time‐to‐kill, which is the reciprocal of attack rate (aN) in a Holling's functional response. We evaluated 13 a priori models representing hypothesized mechanisms influencing attack rates in a heterogeneous landscape with two prey types. Models ranged from variants on Holling's disc equation, including search rate and prey density, to a full model including prey density and patchiness, search rates, satiation, and landscape features, which were measured along the wolf's movement path. Movement rates of wolves while searching explained more of the variation in time‐to‐kill than prey densities. Wolves did not compensate for low prey density by increasing movement rates and there was little evidence that spatial aggregation of prey influenced attack rates in this multi‐prey system. The top model for predicting time‐to‐kill included only search rate and landscape features. Wolves killed prey more quickly in flat terrain, likely due to increased vulnerability from accumulated snow, whereas attack rates were lower when wolves hunted near human‐made features presumably due to human disturbance. Understanding the sources of variation in attack rates provides refinements to functional response models that can lead to more effective predator–prey management in human‐dominated landscapes.     

Density-dependent predation by skunks using olfactory search images

The formation of search images can create density-dependent predation. Predators have been shown to form search images when searching for many small prey items in one feeding session. This paper reports experiments that test whether striped skunks can form olfactory search images in other situations: when prey are found over several days, when prey are large, and when prey are found in certain habitats. Striped skunks were raised in captivity, and their reaction distance to food was measured outside in a natural grassy area. In experiment 1 skunks were offered many small food items for several days in a row. From one day to the next, skunks initially detected food from further away, they increased detection distance faster and their maximum detection distance increased – i.e., they formed olfactory search images faster and stronger from one day to the next. In experiment 2 skunks formed search images over several days when finding only one large food item per day. In experiment 3 skunks lost olfactory search images when they entered habitats in which they had previously searched for another type of food. These long-term search images magnify the effects of short-term search images, extend the effects of short- term search image to longer time spans, and affect different species from short-term search images. Received: 26 July 1996 / Accepted: 13 December 1996     

The detection of cryptic prey by blue jays (Cyanocitta cristata) I: the effects of travel time

The behaviour of blue jays (Cyanocitta cristata) hunting for dispersed, cryptic prey was investigated in an operant simulation in which jays were trained to search projected images for noctuid moths. Each image contained either a single moth or no moth. Each trial was structured so as to simulate travelling between patches, searching within patches, and attacking and handling each moth that was detected. In two experiments in which the travel time between patches was manipulated, increases in travel time produced increased persistence within patches. Although this qualitative effect was predicted by the marginal value theorem, quantitative analyses revealed that the blue jays were using a strategy that was more sophisticated and more efficient than the simple time-in-patch rule implied by the marginal value theorem.     

The Effects of Prey Patchiness, Predator Aggregation, and Mutual Interference on the Functional Response of Phytoseiulus persimilis Feeding on Tetranychus urticae (Acari: Phytoseiidae, Tetranychidae)

The spatial distributions of two-spotted spider mites Tetranychus urticae and their natural enemy, the phytoseiid predator Phytoseiulus persimilis, were studied on six full-grown cucumber plants. Both mite species were very patchily distributed and P. persimilis tended to aggregate on leaves with abundant prey. The effects of non-homogenous distributions and degree of spatial overlap between prey and predators on the per capita predation rate were studied by means of a stage-specific predation model that averages the predation rates over all the local populations inhabiting the individual leaves. The empirical predation rates were compared with predictions assuming random predator search and/or an even distribution of prey. The analysis clearly shows that the ability of the predators to search non-randomly increases their predation rate. On the other hand, the prey may gain if it adopts a more even distribution when its density is low and a more patchy distribution when density increases. Mutual interference between searching predators reduces the predation rate, but the effect is negligible. The stage-specific functional response model was compared with two simpler models without explicit stage structure. Both unstructured models yielded predictions that were quite similar to those of the stage-structured model.     

Searching behavior and time budgets of the predator Podisus maculiventris

Searching behavior of the predaceous insect Podisus maculiventris (Say) (Heteroptera: Pentatomidae) was investigated in the laboratory to verify assumptions made in a predator search model. Female predators were placed into an arena containing 30 lima bean plants (Phaseolus lunatus L.), each having five numbered leaflets. Prey were third-instar larvae of Mexican bean beetle (Epilachna varivestis Mulsant) at two densities. Predators were observed for 4 h periods as they searched the plant canopy. Results showed that predators searched a greater area and for longer at low prey density than at high prey density. Predators apparently searched plants without using cues, did not search areas of the canopy repeatedly after attacks, and spent approximately 1 h handling prey. Predators spent more time resting than searching, and attack rates were negatively correlated with rest time, but were not correlated with search time. Long resting periods by predators may be a result of energy conservation. The implications for using predators such as P. maculiventris against pests in crops are (i) the predators' searching behavior limits the number of prey attacked, and (ii) the predator may be able to persist at low prey densities better than species with different searching behaviors.     

Referential calls signal predator behavior in a group-living bird species

Predation is a powerful agent of natural selection, driving the evolution of antipredator calls [1]. These calls have been shown to communicate predator category [2-4] and/or predator distance to conspecifics [5-7]. However, the risk posed by predators depends also on predator behavior [8], and the ability of prey to communicate predator behavior to conspecifics would be a selective advantage reducing their predation risk. I tested this idea in Siberian jays (Perisoreus infaustus), a group-living bird species. Predation by hawks, and to a lesser extent by owls, is substantial and the sole cause of mortality in adult jays [9]. By using field data and predator-exposure experiments, I show here that jays used antipredator calls for hawks depending on predator behavior. A playback experiment demonstrated that these prey-to-prey calls were specific to hawk behavior (perch, prey search, attack) and elicited distinct, situation-specific escape responses. This is the first study to demonstrate that prey signals convey information about predator behavior to conspecifics. Given that antipredator calls in jays aim at protecting kin group members [10, 11], consequently lowering their mortality [9], kin-selected benefits could be an important factor for the evolution of predator-behavior-specific antipredator calls in such systems.     

The efficiency of adaptive search tactics for different prey distribution patterns: a simulation model based on the behaviour of juvenile plaice

Juvenile plaice Pleuronectes platessa are particularly useful for studying forager search behaviour because their search paths are essentially two dimensional, and punctuated by natural stops. Their prey occur in a range of natural distributions from highly aggregated to over‐dispersed. Juvenile plaice use area‐restricted search near aggregated prey and extensive search, consisting of longer moves and fewer turns, between aggregations and when searching for dispersed prey. They search for less conspicuous prey items mainly in the pauses between movements. This saltatory search behaviour contrasts with the continuous search that is usually assumed in search models. A simulation model of saltatory search behaviour showed that a strategy combining extensive and intensive search allows the efficient exploitation of a range of natural prey distribution patterns, and that it is particularly effective when the search behaviour is controlled by perceived prey density. This allows the predator to respond to the localized aggregations which often occur in nature. The selective use of intensive search was more efficient than the continuous use of extensive search even in prey distribution patterns that were statistically over‐dispersed.     

Bifurcation analysis of a predator-prey model with predators using hawk and dove tactics

Most classical prey-predator models do not take into account the behavioural structure of the population. Usually, the predator and the prey populations are assumed to be homogeneous, i.e. all individuals behave in the same way. In this work, we shall take into account different tactics that predators can use for exploiting a common self-reproducing resource, the prey population. Predators fight together in order to keep or to have access to captured prey individuals. Individual predators can use two behavioural tactics when they encounter to dispute a prey, the classical hawk and dove tactics. We assume two different time scales. The fast time scale corresponds to the inter-specific searching and handling for the prey by the predators and the intra-specific fighting between the predators. The slow time scale corresponds to the (logistic) growth of the prey population and mortality of the predator. We take advantage of the two time scales to reduce the dimension of the model and to obtain an aggregated model that describes the dynamics of the total predator and prey densities at the slow time scale. We present the bifurcation analysis of the model and the effects of the different predator tactics on persistence and stability of the prey-predator community are discussed.     

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.     

Individual variation in prey choice in a predator-prey community

One predator-two prey community models are studied with an emphasis on individual variation in predator behavior. The predator behaves according to a well-known prey choice model. The behavioral model predicts that predators should always attack the primary prey (more profitable prey of the two), but only attack the alternative prey (less profitable prey of the two) when the density of the primary prey is below a threshold density. The predator that accepts the alternative prey does not discriminate between the primary and alternative prey (all-or-nothing preference for the alternative prey). However, empirical studies do not result in clear all-or-nothing responses. Previous models examined the relaxation of the all-or-nothing response by assuming partial preference (e.g., predators preferentially forage on the primary prey even when they also attack the alternative prey). In this study, I consider individual variation in two predator traits (prey density perception and handling time) as the sources of the variation in the threshold density, which can make empirical data appear deviated from the expectation. I examine how community models with partial preference and individual variation differ in their dynamics and show that the differences can be substantial. For example, the dynamics of a model based on individual variation can be more stable (e.g., stable in a wider parameter region) than that of a model based on partial preference. As the general statistical property (Jensen’s inequality) is a main factor that causes the differences, the results of the study have general implications to the interpretation of models based on average per-capita rates.     

Mobbing calls signal predator category in a kin group-living bird species

Many prey species gather together to approach and harass their predators despite the associated risks. While mobbing, prey usually utter calls and previous experiments have demonstrated that mobbing calls can convey information about risk to conspecifics. However, the risk posed by predators also differs between predator categories. The ability to communicate predator category would be adaptive because it would allow other mobbers to adjust their risk taking. I tested this idea in Siberian jays Perisoreus infaustus, a group-living bird species, by exposing jay groups to mounts of three hawk and three owl species of varying risks. Groups immediately approached to mob the mount and uttered up to 14 different call types. Jays gave more calls when mobbing a more dangerous predator and when in the presence of kin. Five call types were predator-category-specific and jays uttered two hawk-specific and three owl-specific call types. Thus, this is one of the first studies to demonstrate that mobbing calls can simultaneously encode information about both predator category and the risk posed by a predator. Since antipredator calls of Siberian jays are known to specifically aim at reducing the risk to relatives, kin-based sociality could be an important factor in facilitating the evolution of predator-category-specific mobbing calls.     

Predator interference alters foraging behavior of a generalist predatory arthropod

Interactions between predators foraging in the same patch may strongly influence patch use and functional response. In particular, there is continued interest in how the magnitude of mutual interference shapes predator–prey interactions. Studies commonly focus on either patch use or the functional response without attempting to link these important components of the foraging puzzle. Predictions from both theoretical frameworks suggest that predators should modify foraging efforts in response to changes in feeding rate, but this prediction has received little empirical attention. We study the linkage between patch departure rates and food consumption by the hunting spider, Pardosa milvina, using field enclosures in which prey and predator densities were manipulated. Additionally, the most appropriate functional response model was identified by fitting alternative functional response models to laboratory foraging data. Our results show that although prey availability was the most important determinant of patch departure rates, a greater proportion of predators left enclosures containing elevated predator abundance. Functional response parameter estimation revealed significant levels of interference among predators leading to lower feeding rates even when the area allocated for each predator was kept constant. These results suggest that feeding rates determine patch movement dynamics, where interference induces predators to search for foraging sites that balance the frequency of agonistic interactions with prey encounter rates.     

Chromaticity in the UV/blue range facilitates the search for achromatically background-matching prey in birds

A large variety of predatory species rely on their visual abilities to locate their prey. However, the search for prey may be hampered by prey camouflage. The most prominent example of concealing coloration is background-matching prey coloration characterized by a strong visual resemblance of prey to the background. Even though this principle of camouflage was recognized to efficiently work in predator avoidance a long time ago, the underlying mechanisms are not very well known. In this study, we assessed whether blue tits (Cyanistes caeruleus) use chromatic cues in the search for prey. We used two prey types that were achromatically identical but differed in chromatic properties in the UV/blue range and presented them on two achromatically identical backgrounds. The backgrounds had either the same chromatic properties as the prey items (matching combination) or differed in their chromatic properties (mismatching combination). Our results show that birds use chromatic cues in the search for mismatching prey, whereupon chromatic contrast leads to a ‘pop-out’ of the prey item from the background. When prey was presented on a matching background, search times were significantly higher. Interestingly, search for more chromatic prey on the matching background was easier than search for less chromatic prey on the matching background. Our results indicate that birds use both achromatic and chromatic cues when searching for prey, and that the combination of both cues might be helpful in the search task.     

A stochastic foraging model with predator training effects. II. Optimal diets

Standard optimal diet models require that a predator's behavior while searching for food does not change in response to experiences with individual prey. There is evidence for rapid and reversible changes in feeding behavior caused by as few as one or two prey encounters. When these “training effects” occur, a given prey type is more likely to be captured next if it was the last type with which the predator had experience. This is not compatible with the standard foraging model. I present a stochastic model which incorporates predator training effects, and three types of training are explored: training in the ability to detect prey (search image formation), training in the probability of succeeding in an attempted capture, and training in the time to pursue, capture, and eat prey. The main result is that all three types of training can result in optimal diets which do not obey the standard optimal diet rules. Conditions under which these rules will suffice are discussed.     

Stochastic predation exposes prey to predator pits and local extinction

Understanding how predators affect prey populations is a fundamental goal for ecologists and wildlife managers. A well-known example of regulation by predators is the predator pit, where two alternative stable states exist and prey can be held at a low density equilibrium by predation if they are unable to pass the threshold needed to attain a high density equilibrium. While empirical evidence for predator pits exists, deterministic models of predator–prey dynamics with realistic parameters suggest they should not occur in these systems. Because stochasticity can fundamentally change the dynamics of deterministic models, we investigated if incorporating stochasticity in predation rates would change the dynamics of deterministic models and allow predator pits to emerge. Based on realistic parameters from an elk–wolf system, we found predator pits were predicted only when stochasticity was included in the model. Predator pits emerged in systems with highly stochastic predation and high carrying capacities, but as carrying capacity decreased, low density equilibria with a high likelihood of extinction became more prevalent. We found that incorporating stochasticity is essential to fully understand alternative stable states in ecological systems, and due to the interaction between top–down and bottom–up effects on prey populations, habitat management and predator control could help prey to be resilient to predation stochasticity.     

Increased turning per unit distance as an area-restricted search mechanism in a pause-travel predator, juvenile plaice, foraging for buried bivalves

During searching, discovery of a prey patch by juvenile plaice Pleuronectes platessa was associated with a change from extensive to intensive search behaviour several moves before an attack on a prey. Intensive search behaviour was characterized by reduced distance of moves, a greater rate of turning per unit distance and shorter pauses between moves. The increase in turn rate was associated with area-restricted seaching, while a decrease in distances moved suggests that plaice search more efficiently for prey when stationary than while moving. The klinokinetic mechanism that appears to regulate search behaviour in juvenile plaice should allow efficient exploitation of a range of prey distribution patterns based on localized cues alone. Such a mechanism is especially useful to a migratory predator, like plaice, whose foraging is subject to time constraints imposed by tidally available feeding areas.     

The effect of learning and search images on predator–prey interactions

In dealing with the spatial and temporal variability of prey species, predators may be able to forage optimally if they have flexible and rapid behavioral plasticity rather than predetermined responses. For predators that learn to focus attention on the cryptic prey type most frequently encountered during recent searching (termed a “search image”), rare prey types may be overlooked because of a focus on more common prey. Search imaging reflects biased searching for one of a number of available prey types, and has been studied widely in birds and mammals. Here we discuss the significant implications of this phenomenon for insect predator–prey systems, particularly with respect to parasitic wasps searching for host species using learned olfactory cues. We (1) review studies about perceptual development through individual ontogeny, (2) define the term “search image” and discuss the cognitive mechanisms involved in search-image formation, (3) discuss the role of search images and frequency-dependent predation as a proximate mechanism in the maintenance of prey diversity, (4) examine data on host–parasitoid olfactory search imaging, and (5) conclude by identifying important research areas for future studies in the field of olfactory search images.     

Prey Detection in Two Tit Species,Parus ater and P. cristatus

We studied the prey-detection response of two related tit species (Parus ater, coal tit, and P. cristatus, crested tit) which occur in similar habitats and which are separated by microhabitat use and mode of locomotion. Specifically, we tested whether the two species differ in their ability to detect cryptic prey, with the hypothesis that coal tits perform better because of their longer stays in microhabitat patches. We expected that interspecific differences and the flexible responses within species to different levels of prey crypticity both depend on search intensity. In the experiments, tits had to forage in four different prey conditions: conspicuous + small, conspicuous + large, cryptic + small, and cryptic + large. Capture success, the time needed to detect prey, and stare duration were measured. Both species were less successful with cryptic than with conspicuous prey and did worst with small and cryptic prey. They also needed more time for detection and stared longer when prey was cryptic. When prey had been overlooked, preceding stare durations were shorter than those ending in successful searches. There were clear differences between the species in performance, with the crested tit doing worse. Coal tits, on average, were more successful in detecting prey, returned less frequently to already emptied patches, detected prey faster and yet they stared more briefly. The within-species results support current notions on predator search, but the differences between species cannot be explained with the same mechanisms. We discuss these findings in the context of the foraging ecology of these species and conclude that crested tits use different cues to detect prey and/or search a larger area per unit time.     

PREY ADAPTATION AS A CAUSE OF PREDATOR-PREY CYCLES

We analyze simple models of predator-prey systems in which there is adaptive change in a trait of the prey that determines the rate at which it is captured by searching predators. Two models of adaptive change are explored: (1) change within a single reproducing prey population that has genetic variation for vulnerability to capture by the predator; and (2) direct competition between two independently reproducing prey populations that differ in their vulnerability. When an individual predator's consumption increases at a decreasing rate with prey availability, prey adaptation via either of these mechanisms may produce sustained cycles in both species' population densities and in the prey's mean trait value. Sufficiently rapid adaptive change (e.g., behavioral adaptation or evolution of traits with a large additive genetic variance), or sufficiently low predator birth and death rates will produce sustained cycles or chaos, even when the predator-prey dynamics with fixed prey capture rates would have been stable. Adaptive dynamics can also stabilize a system that would exhibit limit cycles if traits were fixed at their equilibrium values. When evolution fails to stabilize inherently unstable population interactions, selection decreases the prey's escape ability, which further destabilizes population dynamics. When the predator has a linear functional response, evolution of prey vulnerability always promotes stability. The relevance of these results to observed predator-prey cycles is discussed.     

The consequences of partially directed search effort

Search effort is undirected when a forager has a stereotypical searching behaviour that results in fixed encounter rates with its prey (e.g. diet choice models), and is directed when the forager can bias its encounter with a ‘chosen’ prey. If the bias is complete, search is totally directed (e.g. habitat selection models). When the bias is incomplete (i.e. search modes are not exclusive to a single prey type), search is partially directed. The inclusion of a prey type in the diet is then the result of two decisions: (1) which prey to search for and (2) which prey to handle. The latter decision is determined by the ratio of energy to handling time and the abundance of the preferred prey. The former decision is a function of the encounter probabilities and densities of all potential prey types in addition to their ratio of energy to handling time. Assuming two prey types, there are three distinct behavioural strategies: (1) search for the preferred prey/forage selectively; (2) search for the preferred prey/forage opportunistically; and (3) search for the non-preferred prey/forage opportunistically. If prey are depletable (i.e. prey occur in resource patches), the forager may switch search modes such that prey are depleted to the point where the marginal values of the search modes are equalized. This revised version was published online in July 2006 with corrections to the Cover Date.