A waiting game between the black-bellied plover and its fiddler crab prey

Fiddler crabs (Uca sp.) provide a good example of prey whose antipredator behaviour places them in a ‘waiting game’ contest with their predators. After visually detecting an approaching predator, fiddler crabs typically retreat into a burrow. When this occurs, a crab must decide how long to wait for the predator to depart before re-emerging and potentially exposing itself to attack. Similarly, the predator must decide how long to wait for the crab to re-emerge before departing in search of other foraging opportunities. Hugie (2003, Behavioral Ecology,14, 807-817) recently presented an analysis of such a predator-prey waiting game. The model makes various predictions, including ones about the general shape of each player's waiting distribution (the distribution of waiting times one would expect to observe for individuals in that role). I present an empirical test of the waiting game during interactions between the black-bellied plover, Pluvialis squatarola, and the fiddler crab Uca princeps. As predicted by the model, the plovers' waiting distribution resembled a negative exponential function, whereas the waiting times of crabs were more variable and followed a positively skewed distribution. As further predicted, very little overlap occurred between the two players' waiting distributions and plovers rarely outwaited crabs. I conclude that the waiting decisions of the black-bellied plover and U. princeps support the general predictions of Hugie (2003) and result from a predator-prey waiting game.     

Effect of plants on the searching efficiency of a generalist predator: the importance of predator-prey spatial association

In most studies of tritrophic interactions, the effect of plants on predators is confounded with changes in prey and predator behaviors after an encounter event. Here, we estimate how the effect of plants on prey distribution (in the absence of the predator) and on predator foraging behavior (in the absence of prey) may influence predation rate of Orius insidiosus (Say) (Heteroptera: Anthocoridae) in 11 plant by prey species combinations. The within-leaf distributions of O. insidiosus and its prey overlapped most on bean plants. The predator's foraging behavior (e.g., walking speed, turning rate) also differed among plant species. Simulations, using the prey distribution data and predator's foraging patterns on leaf surfaces of each plant species, show that, overall, the searching efficiency of O. insidiosus was higher on leaves of bean and corn than of tomato. However, the predator's searching efficiency was not consistent within plant species. Thus, the combined effect of plants directly on the predator and indirectly through the prey influenced the predator's searching efficiency.     

Habitat selection by predators and prey in communities with asymmetrical intraguild predation

Competition and predation have broad ecological consequences as they may influence individual behavior and community structure. In some cases, they are linked and predator and prey are also competitors (intraguild predation). I present a game theoretic model of habitat use by predators and prey under conditions of asymmetrical intraguild predation. This model predicts that when the diet of intraguild predators is restricted to intraguild prey and the resource for which predators and prey compete (the basal resource), co-occurrence is only stable when dietary overlap is low and productivity of the basal resource is not high. The addition of alternative resources for predators results in co-occurrence under all conditions. Variation in alternative resource productivity produces a continuum of intraguild prey distributions from matching relative habitat safety, to one that reflects both food and predation risk. When there is a substantial alternative resource for predators, the distribution of predators matches that of alternative resource availability while the distribution of prey is influenced by both habitat riskiness and food availability. The density and distribution of the predator's alternative resource thus influence habitat selection by the intraguild prey. This stresses the importance of indirect interactions in structuring habitat use in communities and the need to view habitat selection in a community context.     

Food-signal theory: population regulation and the functional response

A fully stochastic food-signal model, a function of a patchy-preyencounter sequence, and a prey-processing function is described.The model shows how prey density and its second-order statisticalproperties can sequester prey from predators, questioning theuse of only numerical abundance of predator and prey organismsas a measure of preya — predator interactions. The modelhighlights the notion that patch structure can be generatedby relative velocity of predator and prey as well as by theirspatial distribution. The model extends ideas that include the‘biological pump’ and the downwelling of carbonfrom the upper ocean, the functional response, optimal-foragingtheory, and the connections between population dynamics andvariability in the physical environment.     

Minimax strategies for a predator—Prey game

Suppose prey are distributed in patches. The predator knows the fraction of patches containing 0, 1, 2,… prey, but not how many prey a particular patch contains. It searches each patch randomly, at constant speed. It leaves a patch when the intercapture times satisfy a formula designed to maximize the number of prey eaten per unit time. We show that, if the prey distribution is Poisson, the predator should stay in each patch for the same time, regardless of what happens there. Accordingly, the prey can minimize the predator's maximum intake by choosing the Poisson distribution, and the predator can maximize its minimum intake (against a “smart” prey) by choosing the constant-time strategy.     

The evolution of rates of successful and unsuccessful predation

Summary The question, how will evolutionary change in a predator or in its prey change the ratio of the rate of successful captures to the rate of unsuccessful capture attempts is addressed. I argue that this ratio is not a good index of the predator's adaptation to prey capture, because decreased costs of capture attempts or increased assimilation efficiency (both favored by natural selection in the predator) will usually reduce the ratio. In addition, the evolution of increased ability to capture prey may lead to a reduction in the success/failure ratio. Analysis of several simple models suggests that this result is robust. The presence of unsuccessful predation does have an important influence on the evolution of predator traits that increase its rate of encounter with the prey; the presence of unsuccessful predation may cause the predator to increase its adaptations for prey detection in response to an increase in the prey's ability to avoid detection.     

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.     

Indirect cues in selecting a hunting site in a sit‐and‐wait predator

Sit‐and‐wait predators use relatively simple rules for their decisions to choose and leave a patch, such as using the direct presence of prey to select a hunting site. However, the direct presence of prey can only be used when there is a highly visited patch in the proximity of the predator. Therefore, it is plausible that sit‐and‐wait predators also exploit indirect cues of prey presence and, consequently, use associative learning to select a hunting site. The present study tests for the role of associative learning in a sit‐and‐wait predator species for which the ecology is well understood: Misumena vatia Clerck crab spiders. An ecologically relevant scenario is used by selecting flower colour as the conditioned stimulus and prey presence as the unconditioned stimulus. The results provide no evidence that M. vatia crab spiders use the association between flower colour and food presence for selecting a hunting site. After a training phase of being exposed to a colourful artificial flower highly visited by bees, spiders select a hunting site independently of its colour during the testing phase. Investigations of similar scope and ecological relevance are required with other sit‐and‐wait predators to identify the conditions promoting the use of associative learning for foraging site selection when animals face an unpredictable food supply.     

Effects of behavioral adaptation on a predator-prey model

The Volterra-Lotka predator-prey equations are modified so that the predator's ability to utilize the prey varies in proportion to the average number of encounters between the two species in the past. The behavior of this adaptive system is then described in terms of three parameters — the carrying capacity of the prey, the relative death rate of the predator, and the predator's memoryspan. The most stable situation is shown to occur when the carrying capacity of the prey is large, the predator's death rate is close to zero, and the predator is able to adapt quickly to changing levels of prey density.     

Prey and predator emigration responses in the acarine system Tetranychus urticae-Phytoseiulus persimilis

Summary Some of the processes that influence the emigration of prey and predatory mites from bean plants were investigated experimentally. The emigration of the prey depends on the damage they cause to the plants and on predator density. The predator's emigration rate is a decreasing function of prey density, and does not change (or it slightly decreases) when prey and predator numbers are increased maintaining the same prey/predator ratio. The probability of emigration of the predators is independent of their own density when prey are absent and density dependent when prey density is kep constant. Forty three per cent of the variability in the predator's instantaneous rate of emigration in the different experiments is accounted for by a two parameter negative exponential function of capture rate (number of prey eaten per predator and per unit of time).     

Spatial dynamics of communities with intraguild predation: the role of dispersal strategies

I investigate the influence of dispersal strategies on intraguild prey and predators (competing species that prey on each other). I find an asymmetry between the intraguild prey and predator in their responses to each other's dispersal. The intraguild predator's dispersal strategy and dispersal behavior have strong effects on the intraguild prey's abundance pattern, but the intraguild prey's dispersal strategy and behavior have little or no effect on the intraguild predator's abundance pattern. This asymmetry arises from the different constraints faced by the two species: the intraguild prey has to acquire resources while avoiding predation, but the intraguild predator only has to acquire resources. It leads to puzzling distribution patterns: when the intraguild prey and predator both move away from areas of high density, they become aggregated to high-density habitats, but when they both move toward areas of high resource productivity, they become segregated to resource-poor and resource-rich habitats. Aggregation is more likely when dispersal is random or less optimal, and segregation is more likely as dispersal becomes more optimal. The crucial implication is that trophic constraints dictate the fitness benefits of using dispersal strategies to sample environmental heterogeneity. A strategy that affords greater benefits to an intraguild predator can lead to a more optimal outcome for both the intraguild predator and prey than a strategy that affords greater benefits to an intraguild prey.     

Predator's invasion into an isolated patch with spatially heterogeneous prey distribution

The invasion success of a diffusing predator which changes its diffusion coefficient depending on whether the prey exists or not is investigated. The prey is assumed to be immobile and distributed in an isolated patch. The isolated patch consists of two kinds of region: prey-existing zone and prey-vacant zone. We discuss what relation a heterogeneity of prey distribution has with the predator's invasion success into the patch. Its spatial heterogeneity appears to affect significantly the predator's invasion. In an Appendix we briefly treat an analogous problem involving two competing species.     

Prey community structure affects how predators select for Mullerian mimicry

Müllerian mimicry describes the close resemblance between aposematic prey species; it is thought to be beneficial because sharing a warning signal decreases the mortality caused by sampling by inexperienced predators learning to avoid the signal. It has been hypothesized that selection for mimicry is strongest in multi-species prey communities where predators are more prone to misidentify the prey than in simple communities. In this study, wild great tits (Parus major) foraged from either simple (few prey appearances) or complex (several prey appearances) artificial prey communities where a specific model prey was always present. Owing to slower learning, the model did suffer higher mortality in complex communities when the birds were inexperienced. However, in a subsequent generalization test to potential mimics of the model prey (a continuum of signal accuracy), only birds that had foraged from simple communities selected against inaccurate mimics. Therefore, accurate mimicry is more likely to evolve in simple communities even though predator avoidance learning is slower in complex communities. For mimicry to evolve, prey species must have a common predator; the effective community consists of the predator's diet. In diverse environments, the limited diets of specialist predators could create 'simple community pockets' where accurate mimicry is selected for.     

Predation risk and the structure of freshwater zooplankton communities

Summary Many predators inflict substantial mortality on their prey. The prey respond to these selective pressures with changes in their spatial and temporal overlap with the predator (density risk responses), or with changes in their vulnerability to the predator (prey vulnerability responses). Here we develop a simple predation model that permits quantification of the basic response types of the prey in nature. We then test the hypothesis that prey response will be proportional to the intensity of the predation mortality relative to all other sources of mortality and decreased natality acting on the prey. A significant regression relationship is obtained for the prey vulnerability response but not for any of the density risk responses. The individual response values and regression statistics are used to interpret the relative importance of the different response types and to assess the predator's influence on prey community structure.Supported by Lehigh University Environmental Studies Center     

Efficiency evaluation of two competing foraging modes under different conditions

Various foraging modes are employed by predators in nature, ranging from ambush to active predation. Although the foraging mode may be limited by physiological constraints, other factors, such as prey behavior and distribution, may come into play. Using a simulation model, we tested to what extent the relative success of an ambush and an active predator changes as a function of the relative velocity and movement directionality of prey and active predator. In accordance with previous studies, we found that when both active predator and prey use nondirectional movement, the active mode is advantageous. However, as movement becomes more directional, this advantage diminishes gradually to 0. Previous theoretical studies assumed that animal movement is nondirectional; however, recent field observations show that in fact animal movement usually has some component of directionality. We therefore suggest that our simulation is a better predictor of encounter rates than previous studies. Furthermore, we show that as long as the active predator cannot move faster than its prey, it has little or no advantage over the ambush predator. However, as the active predator's velocity increases, its advantage increases sharply.     

An avoidance learning submodel for a general predation model

Summary This paper attempts to determine the effect on the number of prey eaten by predators of the addition of the component avoidance learning by prey to a computer model of the predation process developed by Holling. Generality was retained by concentrating upon a basic aspect of the prey's behaviour, its distance of reaction to an approaching predator. The zebra danio (Brachydanio rerio), a small freshwater fish, was used as an analogue of a general vertebrate prey. The predator used was the largemouth bass (Micropterus salmoides).Previous work (Dill, 1973b) showed that prey reactive distance increased with increasing experience with the predator. In the present study, this increased prey reactive distance is shown to increase predator pursuit time and hypothesized to decrease predator pursuit success. These relationships were expressed mathematically and built into Holling's (1965, 1966) model of the predation process, along with an equation describing the way in which reactive distance increases following an unsuccessful attack. Other changes necessitated in the model by the addition of the avoidance learning component included: a) Modifications of the calculation of search time to remove a previously implicit time spent unsuccessfully pursuing prey, and to correct the density of prey to account for those whose reactive distances exceed that of the predator and are therefore not susceptible to discovery; b) Addition of a new subroutine (CHASE) to calculate pursuit time, unsuccessful pursuit time, pursuit success, and strike success; c) Changes in subroutine ADCOM to assign prey to different classes (with different reactive distances) according to the number of times they have been unsuccessfully attacked; and d) Addition of a stochastic element via random numbers to determine the class to which an attacked prey belongs, the time to refuge, and the predator's strike success.Simulation was used to explore the consequences of these additions. The capability of learning substantially increased the prey's probability of surviving subsequent attack. Addition of an avoidance learning component caused declines in the predator's functional responses to both prey and predator density. The new component was also suggested to decrease the predator's numerical response to prey density and to increase the probability of stability in a predator-prey interaction.From a thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, University of British Columbia.     

The dynamics of prey choice in fish: the importance of prey size and satiation

Over a number of decades the process of prey choice has been investigated using fishes as model predators. Using fishes for the model has allowed the proximate factors that determine how a mobile predator finds and chooses to eat the prey encountered within a variable 3‐D environment to be estimated. During prey choice a number of constraints exist, in particular most fish predators will eat their prey whole thus their jaws and gut create functional limitations once a prey has been attacked. By considering the relationship between the size of the prey and the predator's feeding apparatus and feeding motivation this study explores the link between mechanistic studies and theoretical, optimal foraging based predictions. How the prediction of prey choices made by the fish following prey encounter can be reconciled with what is likely to be found in the fish's stomach is discussed. This study uses a progression of empirical examples to illustrate how the limits of functional constraints and prey choice at different stages of motivation to feed can be taken into account to improve predictions of predator prey choice.     

Alternative prey can change model–mimic dynamics between parasitism and mutualism

Classical (conventional) Müllerian mimicry theory predicts that two (or more) defended prey sharing the same signal always benefit each other despite the fact that one species can be more toxic than the other. The quasi‐Batesian (unconventional) mimicry theory, instead, predicts that the less defended partner of the mimetic relationship may act as a parasite of the signal, causing a fitness loss to the model. Here we clarify the conditions for parasitic or mutualistic relationships between aposematic prey, and build a model to examine the hypothesis that the availability of alternative prey is crucial to Müllerian and quasi‐Batesian mimicry. Our model is based on optimal behaviour of the predator. We ask if and when it is in the interest of the predator to learn to avoid certain species as prey when there is alternative (cryptic) prey available. Our model clearly shows that the role of alternative prey must be taken into consideration when studying model–mimic dynamics. When food is scarce it pays for the predator to test the models and mimics, whereas if food is abundant predators should leave the mimics and models untouched even if the mimics are quite edible. Dynamics of the mimicry tend to be classically Müllerian if mimics are well defended, while quasi‐Batesian dynamics are more likely when they are relatively edible. However, there is significant overlap: in extreme cases mimics can be harmful to models (a quasi‐Batesian case) even if the species are equally toxic. A crucial parameter explaining this overlap is the search efficiency with which indiscriminating vs. discriminating predators find cryptic prey. Quasi‐Batesian mimicry becomes much more likely if discrimination increases the efficiency with which the specialized predator finds cryptic prey, while the opposite case tends to predict Müllerian mimicry. Our model shows that both mutualistic and parasitic relationship between model and mimic are possible and the availability of alternative prey can easily alter this relationship.     

How weird can mimicry get?

Classical mimicry theory distinguishes clearly between the mutualistic resemblance between two or more defended species (muellerian mimicry), and the parasitic resemblance of a palatable species to a defended species (batesian mimicry). Modelling the behaviour of predators, without initially taking ecological complications into account, is a good strategy for exploring whether this division is valid. Two such behavioural models are described: conditioning theory, which simulates changes in motivational attack levels according to the norms of current learning theory; and saturation theory, which considers how a predator may become saturated with a particular toxic compound, and then cease feeding on the prey species that delivers it. This effect is to be clearly distinguished from simple satiation. Most formulations of the conditioning model allow the direction of reinforcement produced by a particular prey to change according the predator's current state of motivation: this leads to the existence of quasi-batesian mimicry, a parasitic mimicry between two species that could both be described as defended. At high densities, two prey species that share a chemical defense will be ‘muellerian mutualists’, mutually protecting each other against predators that have been saturated with the defensive compound. This mutualism may be accompanied by true muellerian mimicry of the colour patterns, or the patterns may be completely different. This can therefore be regarded as a form of mimicry in a non-visual communication channel. Even an apparently palatable prey species may be effectively unavailable to predators if its density is such as to deliver a particular nutrient in excess of the predator's need for a balanced diet. Such a nutrient in effect becomes a toxin, and such an abundant prey species would be partly defended and potentially able to act as the model in a mimicry system. Thus there might be protective mimicry between ‘palatable’ species, and a ‘palatable’ species might even function as the model for a ‘defended’ mimic. These unorthodox kinds of mimicry probably exist transiently during fluctuations of prey populations. It is less likely that these conditions persist for long enough to induce the evolution of mimicry, and the relationships perhaps usually occur when mimicry already exists for other reasons. Mimicry rings may be mutually stabilised by a combination of toxic mutualism and the exchange of species between the rings. Colour polymorphism in a defended species is strictly neutral whenever the population is dense enough to saturate the predator. This, as well as quasi-batesian mimicry, may help to explain the minority of warningly coloured species that are polymorphic. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effects of predator behavior and proximity on risk assessment by Columbian black-tailed deer

In predator-prey encounters, many factors influence risk perceptionby prey and their decision to flee. Previous studies indicatethat prey take flight at longer distances when they detect predatorsat longer distances and when the predator's behavior indicatesthe increased likelihood of attack. We examined the flight decisionsof Columbian black-tailed deer (Odocoileus hemionus columbianus)using an approaching human whose speed, directness of approach,directness of gaze, and simulated gun carrying varied. Deerfled at greater distances when approached more quickly and directly,and there was a concave-down quadratic trend in the relationshipbetween the distances at which the predator began its approachand at which the deer became alert (alert distance [AD]), indicatingthat deer have a zone of awareness beyond which there is a delayin detecting an approaching predator. Time spent assessing theapproacher (assessment time) was shorter during faster approachesand was positively related with AD. Deer fled at longer distancesand had shorter assessment times when they were already alertto the predator at the initiation of approach. Males fled atshorter distances than females when approached during the gun-holdingcondition, and males had shorter assessment times than femaleswhen the approacher averted his gaze. Such sex differences inrisk assessment might reflect male motivation during the matingseason as well as exposure to human hunting. We suggest thatrisk assessment is affected the by the predator's behavior,the state of awareness of the prey, and the distance at whichthey detect the predator.