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.     

Gregarious behaviour of evasive prey

Gregarious behavior of potential prey was explained by Hamilton (1971) on the basis of risk-sharing: The probability of being picked up by a predator is small when one makes part of a large aggregate of prey. This argument holds only if the predator chooses its victims at random. It is not the case for herds of evasive prey in the open, where prey's gregarious behavior, favorable for the fast group members, makes it easier for the predator to home in on the slowest ones. We show conditions under which gregarious behavior of the relatively fast prey individuals leaves slowest prey with no other choice but to join the group. Failing to do so would signal their vulnerability, making them a preferred target for the predator. Analysis of an n+1 player game of a predator and n unequal prey individuals clarifies conditions for fully gregarious, partially gregarious, or solitary behavior of the prey.     

Theoretical dynamics of competitors under predation

Summary Continuous population models of two prey species and a predator were explored by isocline analysis. When predator satiation and substitution between prey (with or without switching) are introduced in the models, many qualitatively different kinds of dynamic behaviour become possible. These depend in a complex but predictable way on competitive relations between prey and on predator feeding behaviour and efficiency. Under constant predation many cases of threshold responses between two or more alternate stable states are possibly; the numerical response of the predator population reduces some of the possibilities.Apparently contradictory community phenomena previously proposed, e.g. prey coexistence versus exclusion by addition of predator, exclusion versus stabilization by addition of alternate prey, are all possible as special cases. A prey which is relatively tolerant to predation can act as a keystone species, on which the existence of other prey species in the community depends, in either a positive or a negative sense. In certain conditions predator-induced obligatory mutualism between two prey species is theoretically possible.To Michael Evenari, pioneer, teacher and friend     

Evolution of a predator-prey Volterra-Lotka ecosystem with saturation effect

This paper has studied the evolution of a predator-prey Volterra-Lotka ecosystem with saturation effect for the general case where both predator and prey evolve. We have interesting results under the evolutional condition, as follows: (1) the predator population and the ratio of predator to prey populations increase; (2) the parameters of the prey drift in the direction of increasing multiplication rate and saturation level, while the parameters of the predator drift in the direction of decreasing death rate.     

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.     

Behavioural and life history effects of predator diet cues during ontogeny in damselfly larvae

A central issue in predator–prey interactions is how predator associated chemical cues affect the behaviour and life history of prey. In this study, we investigated how growth and behaviour during ontogeny of a damselfly larva (Coenagrion hastulatum) in high and low food environments was affected by the diet of a predator (Aeshna juncea). We reared larvae in three different predator treatments; no predator, predator feeding on conspecifics and predator feeding on heterospecifics. We found that, independent of food availability, larvae displayed the strongest anti-predator behaviours where predators consumed prey conspecifics. Interestingly, the effect of predator diet on prey activity was only present early in ontogeny, whereas late in ontogeny no difference in prey activity between treatments could be found. In contrast, the significant effect of predator diet on prey spatial distribution was unaffected by time. Larval size was affected by both food availability and predator diet. Larvae reared in the high food treatment grew larger than larvae in the low food treatment. Mean larval size was smallest in the treatment where predators consumed prey conspecifics, intermediate where predators consumed heterospecifics and largest in the treatment without predators. The difference in mean larval size between treatments is probably an effect of reduced larval feeding, due to behavioural responses to chemical cues associated with predator diet. Our study suggests that anti-predator responses can be specific for certain stages in ontogeny. This finding shows the importance of considering where in its ontogeny a study organism is before results are interpreted and generalisations are made. Furthermore, this finding accentuates the importance of long-term studies and may have implications for how results generated by short-term studies can be used.     

Conditions for the spread of conspicuous warning signals: a numerical model with novel insights

The initial evolution of conspicuous warning signals presents an evolutionary problem because selection against rare conspicuous signals is presumed to be strong, and new signals are rare when they first arise. Several possible solutions have been offered to solve this apparent evolutionary paradox, but disagreement persists over the plausibility of some of the proposed mechanisms. In this paper, we construct a deterministic numerical simulation model that allows us to derive the strength of selection on novel warning signals in a wide range of biologically relevant situations. We study the effects of predator psychology (learning, rate of mistaken attacks, and neophobia) on selection. We also study the how prey escape, predation intensity, number of predators, and abundance of different prey types affects selection. The model provides several important results. Selection on novel warning signals is number rather than frequency dependent. In most cases, there exists a threshold number of aposematic individuals below which aposematism is selected against and above which aposematism is selected for. Signal conspicuousness (which increases detection rate) and distinctiveness (which allows predator to distinguish defended from nondefended prey) have opposing effects on evolution of warning signals. A more conspicuous warning signal cannot evolve unless it makes the prey more distinctive from palatable prey, reducing mistaken attacks by predators. A novel warning signal that is learned quickly can spread from lower abundance more easily than a signal that is learned more slowly. However, the relative rate at which the resident signal and the novel signal are learned is irrelevant for the spread of the novel signal. Long-lasting neophobia can facilitate the spread of novel warning signals. Individual selection via the ability of defended prey to escape from predator is not likely to facilitate evolution of conspicuous warning signals if both the resident (cryptic) morph and the novel morph have the same escape probability. Predation intensity (defined as the proportion of palatable prey eaten by the predator) has a strong effect on selection. More intense predation results in strong selection against rare signals, but also strong selective advantage to common signals. The threshold number of aposematic individuals is lower when predation is intense. Thus, the evolution of warning signals may be more likely in environments where predation is intense. The effect of numbers of predators depends on whether predation intensity also changes. When predation intensity is constant, increasing numbers of predators raises the threshold number of aposematic individuals, and thus makes evolution of aposematism more difficult. If predation intensity increases in parallel with number of predators, the threshold number of aposematic individuals does not change much, but selection becomes more intense on both sides of the threshold.     

The role of prey taxis in biological control: a spatial theoretical model

We study a reaction-diffusion-advection model for the dynamics of populations under biological control. A control agent is assumed to be a predator species that has the ability to perceive the heterogeneity of pest distribution. The advection term represents the predator density movement according to a basic prey taxis assumption: acceleration of predators is proportional to the prey density gradient. The prey population reproduces logistically, and the local population interactions follow the Holling Type II trophic function. On the scale of the population, our spatially explicit approach subdivides the predation process into random movement represented by diffusion, directed movement described by prey taxis, local prey encounters, and consumption modeled by the trophic function. Thus, our model allows studying the effects of large-scale predator spatial activity on population dynamics. We show under which conditions spatial patterns are generated by prey taxis and how this affects the predator ability to maintain the pest population below some economic threshold. In particular, intermediate taxis activity can stabilize predator-pest populations at a very low level of pest density, ensuring successful biological control. However, very intensive prey taxis destroys the stability, leading to chaotic dynamics with pronounced outbreaks of pest density.     

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.     

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.     

Nonconsumptive effects in a multiple predator system reduce the foraging efficiency of a keystone predator

Many studies have demonstrated that the nonconsumptive effect (NCE) of predators on prey traits can alter prey demographics in ways that are just as strong as the consumptive effect (CE) of predators. Less well studied, however, is how the CE and NCE of multiple predator species can interact to influence the combined effect of multiple predators on prey mortality. We examined the extent to which the NCE of one predator altered the CE of another predator on a shared prey and evaluated whether we can better predict the combined impact of multiple predators on prey when accounting for this influence. We conducted a set of experiments with larval dragonflies, adult newts (a known keystone predator), and their tadpole prey. We quantified the CE and NCE of each predator, the extent to which NCEs from one predator alters the CE of the second predator, and the combined effect of both predators on prey mortality. We then compared the combined effect of both predators on prey mortality to four predictive models. Dragonflies caused more tadpoles to hide under leaf litter (a NCE), where newts spend less time foraging, which reduced the foraging success (CE) of newts. Newts altered tadpole behavior but not in a way that altered the foraging success of dragonflies. Our study suggests that we can better predict the combined effect of multiple predators on prey when we incorporate the influence of interactions between the CE and NCE of multiple predators into a predictive model. In our case, the threat of predation to prey by one predator reduced the foraging efficiency of a keystone predator. Consequently, the ability of a predator to fill a keystone role could be compromised by the presence of other predators.     

A predator–prey refuge system: Evolutionary stability in ecological systems

A refuge model is developed for a single predator species and either one or two prey species where no predators are present in the prey refuge. An individual’s fitness depends on its strategy choice or ecotype (predators decide which prey species to pursue and prey decide what proportion of their time to spend in the refuge) as well as on the population sizes of all three species. It is shown that, when there is a single prey species with a refuge or two prey species with no refuge compete only indirectly (i.e. there is only apparent competition between prey species), that stable resident systems where all individuals in each species have the same ecotype cannot be destabilized by the introduction of mutant ecotypes that are initially selectively neutral. In game-theoretic terms, this means that stable monomorphic resident systems, with ecotypes given by a Nash equilibrium, are both ecologically and evolutionarily stable. However, we show that this is no longer the case when the two indirectly-competing prey species have a refuge. This illustrates theoretically that two ecological factors, that are separately stabilizing (apparent competition and refuge use), may have a combined destabilizing effect from the evolutionary perspective. These results generalize the concept of an evolutionarily stable strategy (ESS) to models in evolutionary ecology. Several biological examples of predator–prey systems are discussed from this perspective.     

Predation in multi-prey communities

We consider the effect of a top predator on the stability of a system of competing prey species. In the first instance, this is done in detail for two prey species where the predators either behave in a completely random way, interfere with each other or switch to the more abundant prey at any time. The analysis is then extended to the case of n similar prey species, either competing equally or competing with their two nearest neighbours in exploiting a one-dimensional resource spectrum. It is found that predator switching can produce local stability when the prey species overlap completely and even when the competition coefficients are greater than one. This, however, is more difficult to attain for nearest neighbour competition. In either case switching is advantageous to the predators, since it allows them to coexist successfully with their prey over a wider range of conditions.     

Hunting‐mediated predator facilitation and superadditive mortality in a European ungulate

Predator‐prey theory predicts that in the presence of multiple types of predators using a common prey, predator facilitation may result as a consequence of contrasting prey defense mechanisms, where reducing the risk from one predator increases the risk from the other. While predator facilitation is well established in natural predator‐prey systems, little attention has been paid to situations where human hunters compete with natural predators for the same prey. Here, we investigate hunting‐mediated predator facilitation in a hunter‐predator‐prey system. We found that hunter avoidance by roe deer (Capreolus capreolus) exposed them to increase predation risk by Eurasian lynx (Lynx lynx). Lynx responded by increasing their activity and predation on deer, providing evidence that superadditive hunting mortality may be occurring through predator facilitation. Our results reveal a new pathway through which human hunters, in their role as top predators, may affect species interactions at lower trophic levels and thus drive ecosystem processes.     

Two-Species Migration and Clustering in Two-Dimensional Domains

We extend two-species models of individual aggregation or clustering to two-dimensional spatial domains, allowing for more realistic movement of the populations compared with one spatial dimension. We assume that the domain is bounded and that there is no flux into or out of the domain. The motion of the species is along fitness gradients which allow the species to seek out a resource. In the case of competition, species which exploit the resource alone will disperse while avoiding one another. In the case where one of the species is a predator or generalist predator which exploits the other species, that species will tend to move toward the prey species, while the prey will tend to avoid the predator. We focus on three primary types of interspecies interactions: competition, generalist predator–prey, and predator–prey. We discuss the existence and stability of uniform steady states. While transient behaviors including clustering and colony formation occur, our stability results and numerical evidence lead us to believe that the long-time behavior of these models is dominated by spatially homogeneous steady states when the spatial domain is convex. Motivated by this, we investigate heterogeneous resources and hazards and demonstrate how the advective dispersal of species in these environments leads to asymptotic steady states that retain spatial aggregation or clustering in regions of resource abundance and away from hazards or regions or resource scarcity.     

Interspecific infanticide deters predators

It is well known that young, small predator stages are vulnerable to predation by conspecifics, intra-guild competitors or hyperpredators. It is less known that prey can also kill vulnerable predator stages that present no danger to the prey. Since adult predators are expected to avoid places where their offspring would run a high predation risk, this opens the way for potential prey to deter dangerous predator stages by killing vulnerable predator stages. We present an example of such a complex predator–prey interaction. We show that (1) the vulnerable stage of an omnivorous arthropod prey discriminates between eggs of a harmless predator species and eggs of a dangerous species, killing more eggs of the latter; (2) prey suffer a minor predation risk from newly hatched predators; (3) adult predators avoid ovipositing near killed predator eggs, and (4) vulnerable prey near killed predator eggs experience an almost fourfold reduction of predation. Hence, by attacking the vulnerable stage of their predator, prey deter adult predators and thus reduce their own predation risk. This provides a novel explanation for the killing of vulnerable stages of predators by prey and adds a new dimension to anti-predator behaviour.     

Increased susceptibility to predation and altered anti-predator behaviour in an acanthocephalan-infected amphipod

According to the 'parasitic manipulation hypothesis', phenotypic changes induced by parasites in their intermediate hosts are effective means of increasing trophic transmission to final hosts. One obvious prediction, although seldom tested, is that increased vulnerability of infected prey to an appropriate predator should be achieved by the parasite altering the anti-predator behaviour of its intermediate host. In this study, we tested this prediction using the fish acanthocephalan Pomphorhynchus tereticollis and the freshwater amphipod Gammarus pulex. Firstly, we estimated the relative vulnerability of infected and uninfected gammarids to predation by the bullhead Cottus gobio in the field. Second, we investigated under experimental conditions how two common anti-predator behaviours of aquatic invertebrates, refuge use and short-distance reaction to predator chemical cues, were affected by infection status. We found that the prevalence of infection in the field was 10 times higher among gammarids collected from the stomach contents of bullheads compared with free-ranging individuals collected in the same river. In a microcosm uninfected gammarids, but not infected ones, increased the use of refuge in the presence of a bullhead. Finally, a behavioural experiment using an Y-maze olfactometer showed opposite reactions to predator odour. Whereas uninfected gammarids were significantly repulsed by the chemical cues originating from bullheads, infected ones were significantly attracted to the odour of the predator. Taken together, our results suggest that the alteration of anti-predator behaviour in infected G. pulex might enhance predation by bullheads in the field. Reversing anti-predator behaviour might thus be an efficient device by which parasites with complex life-cycles increase their trophic transmission to final hosts. Further studies should pay more attention to both the increased vulnerability of infected prey to an appropriate predator in the field and the influence of parasitic infection on the anti-predator behaviour of intermediate hosts.     

A parasite's modification of host behavior reduces predation on its host

Parasite modification of host behavior is common, and the literature is dominated by demonstrations of enhanced predation on parasitized prey resulting in transmission of parasites to their next host. We present a case in which predation on parasitized prey is reduced. Despite theoretical modeling suggesting that this phenomenon should be common, it has been reported in only a few host–parasite–predator systems. Using a system of gregarine endosymbionts in host mosquitoes, we designed experiments to compare the vulnerability of parasitized and unparasitized mosquito larvae to predation by obligate predatory mosquito larvae and then compared behavioral features known to change in the presence of predatory cues. We exposed Aedes triseriatus larvae to the parasite Ascogregarina barretti and the predator Toxohrynchites rutilus and assessed larval mortality rate under each treatment condition. Further, we assessed behavioral differences in larvae due to infection and predation stimuli by recording larvae and scoring behaviors and positions within microcosms. Infection with gregarines reduced cohort mortality in the presence of the predator, but the parasite did not affect mortality alone. Further, infection by parasites altered behavior such that infected hosts thrashed less frequently than uninfected hosts and were found more frequently on or in a refuge within the microcosm. By reducing predation on their host, gregarines may be acting as mutualists in the presence of predation on their hosts. These results illustrate a higher‐order interaction, in which a relationship between a species pair (host–endosymbiont or predator–prey) is altered by the presence of a third species.     

A study of prey-predator relations for mammals

In this paper, we present a prey-predator nonlinear model for mammals, consisting of large- and small-size prey species with group defence, in a partially protected habitat. If the prey size is small, then it is more prone to the predator at higher densities. Conversely, large prey size at higher densities tend to develop group defence. Therefore, the predator will be attracted towards that area where prey are less in number. A new physical constant has been introduced into the radiation-type condition on that part of the boundary where interaction between prey and predator takes place. This constant allows us to efficiently model group defence capabilities of the herds and its numerical values have to be determined for different pairs of prey-predator species from field observations. A way of measuring the constants involved in the model is suggested. Numerical results are provided and thoroughly discussed for a habitat of circular shape. The obtained results show that in the region away from the protected area, the density of large-size prey species is higher than that of small-size prey species, a fact that is in accordance with observations.