Predation and the evolution of gregariousness. I. Models for concealment and evasion

The contribution of predation to the evolution of gregariousness is examined, and it is suggested that the needs of both predator and prey to conceal themselves and to detect the other may have been a major factor directing the development of social behaviour. This implies that it is important to consider the sensory capacities and the strategies open to both sides. Some relevant features of sensory detection are discussed and illustrated by an experiment on visual summation. These features are taken into account in devising two models for the interaction between predator and prey which allow the relative advantages of different dispersion patterns to be assessed. The first model assumes that the prey's main resource is concealment: it then appears that when detection will result in only one kill group formation is usually of advantage, but when the predator may destroy all or a proportion of a discovered group, it may be better to be solitary. A second model assumes that the prey have resources for evasion and defence. The occurrence of a kill will then be determined by priority of detection and under this constraint kill rate is lowered by group formation and falls with increasing group size.     

An eco-epidemiological system with infected prey and predator subject to the weak Allee effect

In this article, we propose a general prey–predator model with disease in prey and predator subject to the weak Allee effects. We make the following assumptions: (i) infected prey competes for resources but does not contribute to reproduction; and (ii) in comparison to the consumption of the susceptible prey, consumption of infected prey would contribute less or negatively to the growth of predator. Based on these assumptions, we provide basic dynamic properties for the full model and corresponding submodels with and without the Allee effects. By comparing the disease free submodels (susceptible prey–predator model) with and without the Allee effects, we conclude that the Allee effects can create or destroy the interior attractors. This enables us to obtain the complete dynamics of the full model and conclude that the model has only one attractor (only susceptible prey survives or susceptible-infected coexist), or two attractors (bi-stability with only susceptible prey and susceptible prey–predator coexist or susceptible prey-infected prey coexists and susceptible prey–predator coexist). This model does not support the coexistence of susceptible-infected-predator, which is caused by the assumption that infected population contributes less or are harmful to the growth of predator in comparison to the consumption of susceptible prey.     

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.     

Community structure and stability analysis for intraguild interactions among host, parasitoid, and predator

Intraguild predation (IGP) occurs when one species preys on a competitor species that shares a common resource. Modifying a prey–predator model with prey infection, we propose a model of IG interactions among host, parasitoid, and predator, in which the predator eats parasitized and unparasitized hosts, and the adult parasitoid density is explicitly expressed. Parameter dependences of community structure, including stability of the system, were analytically obtained. Depending on interaction strength (parasitization and predation on unparasitized and parasitized hosts), the model provides six types of community structure: (1) only the host exists, (2) the host and predator coexist stably, (3) the host and parasitoid coexist stably, (4) the host–parasitoid population dynamics are unstable, (5) the three species coexist stably, and (6) the population dynamics of the three species are unstable. In contrast to a traditional prey–predator model with prey infection, which predicts that population dynamics are always locally stable, our model predicts that they are unstable when the parasitization rate is high.     

Effect of the cyclopoid copepod Mesocyclops thermocyclopoides on the interactions between the predatory rotifer Asplanchna intermedia and its prey Brachionus calyciflorus and B. angularis

In many shallow, eutrophic subtropical ponds, brachionid rotifers are common prey of the predatory copepod Mesocyclops thermocyclopoides. The predatory rotifer Asplanchna intermedia, which is itself a potential prey of the copepod, also feeds preferentially on brachionids. We studied in the laboratory the population dynamics of two mutually competing prey species, Brachionus angularis and B. calyciflorus, in the presence of the two predators A. intermedia and M. thermocyclopoides. The experimental design included separate population dynamics studies with one prey–one predator, two prey–one predator, one prey–two predator, and two prey–two predator systems. These combinations were compared with controls, in which both the prey species (B. angularis and B. calyciflorus) were grown separately and in combination with each other. In the absence of any predator, B. angularis generally eliminated the larger B. calyciflorus. Selective predation by the copepod allowed B. calyciflorus to persist longer in competition with B. angularis. Feeding by M. thermocyclopoides on A. intermedia reduced the predation pressure on B. calyciflorus. However, given enough time, the cyclopoid copepod was able to eliminate both the brachionids as well as the predatory Asplanchna.     

Effects of predator-specific defence on community complexity

Summary Some properties of community structure are explored using co-evolutionary theory. We consider mathematical models of food webs in which all species in a community adopt foraging behaviours and antipredator behaviours that maximize individual fitness. If the antipredator behaviour of a prey is effective against all its enemies, the number of prey—predator links in a food web must be less than the sum of the numbers of prey and predator species. However, if an increase in a prey's attention to one type of predator decreases its attention to another type of predator, there may be no limit on the number of predator species using a common set of prey species. Predator-specific defence allows a much more complex community structure than non-specific defence. Predator-specific defence more frequently allows a large niche overlap between predators than does non-specific defence. The high connectivity of some fish communities in Lake Tanganyika may be an example of this phenomenon.     

Estimating the prevalence and strength of non-independent predator effects

Understanding whether multiple predator species have independent effects on shared prey is critical for understanding community dynamics. We describe the prevalence and strength of non-independence between predators by quantifying the prey’s risk of predation and the degree to which it deviates from the risk predicted from a null model of independent predator effects. Specifically, we document how frequently non-independent effects occur among ten different multiple predator combinations with mayfly larvae as prey. These predator combinations vary both predator density and predator species richness. Overall, the predator effects were non-independent and translated to an average of 27% fewer prey being consumed compared to independent predator effects. Non-independence of this magnitude is likely to have population level consequences for the prey and influence the distribution or prey preference of predators. Closer inspection shows that much of the risk reduction in this system is weak, to the point of being indistinguishable from independent predator effects, while few effects are strong. This pattern of many weak interactions and few strong ones parallels the pattern of interaction strengths documented previously in intertidal communities. Consequently, understanding strong interactors in multiple predator systems may help us understand the importance of a species.     

Empirical studies of escape behavior find mixed support for the race for life model

Escape theory has been exceptionally successful in conceptualizing and accurately predicting effects of numerous factors that affect predation risk and explaining variation in flight initiation distance (FID; predator–prey distance when escape begins). Less explored is the relative orientation of an approaching predator, prey, and its eventual refuge. The relationship between an approaching threat and its refuge can be expressed as an angle we call the “interpath angle” or “Φ,” which describes the angle between the paths of predator and prey to the prey’s refuge and thus expresses the degree to which prey must run toward an approaching predator. In general, we might expect that prey would escape at greater distances if they must flee toward a predator to reach its burrow. The “race for life” model makes formal predictions about how Φ should affect FID. We evaluated the model by studying escape decisions in yellow-bellied marmots Marmota flaviventer, a species which flees to burrows. We found support for some of the model’s predictions, yet the relationship between Φ and FID was less clear. Marmots may not assess Φ in a continuous fashion; but we found that binning angle into 4 45° bins explained a similar amount of variation as models that analyzed angle continuously. Future studies of Φ, especially those that focus on how different species perceive relative orientation, will likely enhance our understanding of its importance in flight decisions.     

Complex dynamic behaviour of autonomous microbial food chains

 The dynamic behaviour of food chains under chemostat conditions is studied. The microbial food chain consists of substrate (non-growing resources), bacteria (prey), ciliates (predator) and carnivore (top predator). The governing equations are formulated at the population level. Yet these equations are derived from a dynamic energy budget model formulated at the individual level. The resulting model is an autonomous system of four first-order ordinary differential equations. These food chains resemble those occuring in ecosystems. Then the prey is generally assumed to grow logistically. Therefore the model of these systems is formed by three first-order ordinary differential equations. As with these ecosystems, there is chaotic behaviour of the autonomous microbial food chain under chemostat conditions with biologically relevant parameter values. It appears that the trajectories on the attractors consists of two superimposed oscillatory behaviours, a slow one for predator–top predator and a fast one for the prey–predator on one branch at which the top predator increases slowly. In some regions of the parameter space there are multiple attractors. Received 8 November 1995; received in revised form 7 January 1997     

Evolution towards oscillation or stability in a predator–prey system

We studied a prey–predator system in which both species evolve. We discuss here the conditions that result in coevolution towards a stable equilibrium or towards oscillations. First, we show that a stable equilibrium or population oscillations with small amplitude is likely to occur if the prey''s (host''s) defence is effective when compared with the predator''s (parasite''s) attacking ability at equilibrium, whereas large-amplitude oscillations are likely if the predator''s (parasite''s) attacking ability exceeds the prey''s (host''s) defensive ability. Second, a stable equilibrium is more likely if the prey''s defensive trait evolves faster than the predator''s attack trait, whereas population oscillations are likely if the predator''s trait evolves faster than that of the prey. Third, when the adaptation rates of both species are similar, the amplitude of the fluctuations in their abundances is small when the adaptation rate is either very slow or very fast, but at an intermediate rate of adaptation the fluctuations have a large amplitude. We also show the case in which the prey''s abundance and trait fluctuate greatly, while those of the predator remain almost unchanged. Our results predict that populations and traits in host–parasite systems are more likely than those in prey–predator systems to show large-amplitude oscillations.     

Does Mutual Interference Affect the Feeding Rate of Aphidophagous Coccinellids? A Modeling Perspective

Mutual interference involves direct interactions between individuals of the same species that may alter their foraging success. Larvae of aphidophagous coccinellids typically stay within a patch during their lifetime, displaying remarkable aggregation to their prey. Thus, as larvae are exposed to each other, frequent encounters may affect their foraging success. A study was initiated in order to determine the effect of mutual interference in the coccinellids’ feeding rate. One to four 4^th larval instars of the fourteen-spotted ladybird beetle Propylea quatuordecimpunctata were exposed for 6 hours into plastic containers with different densities of the black bean aphid, Aphis fabae, on potted Vicia faba plants. The data were used to fit a purely prey-dependent Holling type II model and its alternatives which account for interference competition and have thus far been underutilized, i.e. the Beddington-DeAngelis, the Crowley-Martin and a modified Hassell-Varley model. The Crowley-Martin mechanistic model appeared to be slightly better among the competing models. The results showed that although the feeding rate became approximately independent of predator density at high prey density, some predator dependence in the coccinellid’s functional response was observed at the low prey—high predator density combination. It appears that at low prey densities, digestion breaks are negligible so that the predators do waste time interfering with each other, whereas at high prey densities time loss during digestion breaks may fully accommodate the cost of interference, so that the time cost may be negligible.     

Multiple predator effects result in risk reduction for prey across multiple prey densities

Investigating how prey density influences a prey’s combined predation risk from multiple predator species is critical for understanding the widespread importance of multiple predator effects. We conducted experiments that crossed six treatments consisting of zero, one, or two predator species (hellgrammites, greenside darters, and creek chubs) with three treatments in which we varied the density of mayfly prey. None of the multiple predator effects in our system were independent, and instead, the presence of multiple predator species resulted in risk reduction for the prey across both multiple predator combinations and all three levels of prey density. Risk reduction is likely to have population-level consequences for the prey, resulting in larger prey populations than would be predicted if the effects of multiple predator species were independent. For one of the two multiple predator combinations, the magnitude of risk reduction marginally increased with prey density. As a result, models predicting the combined risk from multiple predator species in this system will sometimes need to account for prey density as a factor influencing per-capita prey death rates.     

Influence of consumer mutual interference on the stabilization of a three-level trophic system

In this paper, we present a three-level (food–prey–predator) trophic food chain which includes consumer mutual interference (MIF). In contrast with other analyses, we consider the effect of both prey and predator MIF on the dynamics of a three-level trophic system. MIF is generally considered to exert a stabilizing effect on population dynamics based on the predator–prey model. However, results from analytical and numerical simulations utilizing a simple three-species food chain model suggest that while the addition of prey MIF to the model provides a stabilizing influence, as the chaotic dynamics collapse to a stable steady state, adding only predator MIF to the model can only stabilize the system at intermediate MIF values. The three-species trophic food chain is also stabilized when combination of both prey and predator MIF is added to the model. Our work serves to provide insight into the effects of MIF in the real world.     

Bayesian birds: A simple example of Oaten's stochastic model of optimal foraging

Allan Oaten (1977, Theor. Pop. Biol.12, 263–285) has argued that stochastic models of optimal foraging may produce results qualitatively different from those of the analogous deterministic models. Oaten's model is very general and difficult to understand intuitively. In this paper a simple, tractable model is considered in which the predator searches each patch systematically (without going over the same area twice) until he exhausts the patch or decides the patch is not very good. It is assumed that each patch contains a fixed number of bits, each of which may contain a prey. The number of prey per patch is assumed to have a binomial distribution with n equal to the number of bits and p being a random variable having a beta distribution. After searching each bit the predator decides whether to leave the patch or not according to how many prey it has found. In this paper the best strategy is determined and the long-term rate of feeding is compared with that of the naive animal that searches each patch completely. The advantage of being a Bayesian is determined for a variety of environmental conditions.     

Deimatic Display in the European Swallowtail Butterfly as a Secondary Defence against Attacks from Great Tits

Background

Many animals reduce the risk of being attacked by a predator through crypsis, masquerade or, alternatively, by advertising unprofitability by means of aposematic signalling. Behavioural attributes in prey employed after discovery, however, signify the importance of also having an effective secondary defence if a predator uncovers, or is immune to, the prey’s primary defence. In butterflies, as in most animals, secondary defence generally consists of escape flights. However, some butterfly species have evolved other means of secondary defence such as deimatic displays/startle displays. The European swallowtail, Papilio machaon, employs what appears to be a startle display by exposing its brightly coloured dorsal wing surface upon disturbance and, if the disturbance continues, by intermittently protracting and relaxing its wing muscles generating a jerky motion of the wings. This display appears directed towards predators but whether it is effective in intimidating predators so that they refrain from attacks has never been tested experimentally.

Methodology/Principal Findings

In this study we staged encounters between a passerine predator, the great tit, Parus major, and live and dead swallowtail butterflies in a two-choice experiment. Results showed that the dead butterfly was virtually always attacked before the live butterfly, and that it took four times longer before a bird attacked the live butterfly. When the live butterfly was approached by a bird this generally elicited the butterfly’s startle display, which usually caused the approaching bird to flee. We also performed a palatability test of the butterflies and results show that the great tits seemed to find them palatable.

Conclusions/Significance

We conclude that the swallowtail’s startle display of conspicuous coloration and jerky movements is an efficient secondary defence against small passerines. We also discuss under what conditions predator-prey systems are likely to aid the evolution of deimatic behaviours in harmless and palatable prey.     

Irreversible prey diapause as an optimal strategy of a physiologically extended Lotka–Volterra model

We propose an optimal control framework to describe intra-seasonal predator–prey interactions, which are characterized by a continuous-time dynamical model comprising predator and prey density, as well as the energy budget of the prey over the length of a season. The model includes a time-dependent decision variable for the prey, representing the portion of the prey population in time that is active, as opposed to diapausing (a state of physiological rest). The predator follows autonomous dynamics and accordingly it remains active during the season. The proposed model is a generalization of the classical Lotka–Volterra predator–prey model towards non-autonomous dynamics that furthermore includes the effect of an energy variable. The model has been inspired by a specific biological system of predatory mites (Acari: Phytoseiidae) and prey mites (so-called fruit-tree red spider mites) (Acari: Tetranychidae) that feed on leaves of apple trees—its parameters have been instantiated based on laboratory and field studies. The goal of the work is to understand the decisions of the prey mites to enter diapause (a state of physiological rest) given the dynamics of the predatory mites: this is achieved by solving an optimization problem hinging on the maximization of the prey population contribution to the next season. The main features of the optimal strategy for the prey are shown to be that (1) once in diapause, the prey does not become active again within the same season and hence diapause is an irreversible process; (2) for the vast majority of parameter space, the portion of prey individuals entering diapause within the season does not decrease in time; (3) with an increased number of predators, the optimal population strategy for the prey is to start diapause earlier and to enter diapause more gradually. This optimal population strategy will be studied for its ESS properties in a sequel to the work presented in this article.     

On optimal predator search

Search tactics are explored for animals hunting randomly distributed prey in two-dimensional habitats. The predator chooses between two modes of search: continuous travel and alternating pause-travel. A model based on renewal processes is derived for the predator's net rate of energy intake. The model is used to explore the optimal mode of search, search height, pause duration (“giving-up time”) and move length. Energy expenditure for search is assumed to increase from perchtravel over continuous travel to hover-travel. Prey detectability is assumed to be higher for the pausing than for the travelling predator. The following predictions emerge: The relative merits of the different search modes are mainly determined by the relative magnitudes of energy consumption rates and prey detection efficiencies at pausing and travelling. The energetically cheaper among two search modes reaches its highest relative merit at low prey density and detectability. As either increases, a more expensive search tactic may become superior. If the rate of energy expenditure increases considerably at locomotion, pause-travel tactics may be superior to continuous travel. This requires that the search can be performed from sufficient height, because net energy gain decreases rapidly below the optimum search height. It is greater for pause-travel than for continuous travel, and it increases slightly with decreasing prey density, and markedly with increasing prey detectability. With perch-travel or hover-travel tactics, the optimal giving-up time decreases with increasing prey density and detectability. The optimal move length increases with detectability. Empirical evidence coincides qualitatively with several predictions. Possibilities for further tests of the model are discussed, as are observed behavioural and morphological features on which the search model may shed light.     

Predator-Prey Interactions Shape Thermal Patch Use in a Newt Larvae-Dragonfly Nymph Model

Thermal quality and predation risk are considered important factors influencing habitat patch use in ectothermic prey. However, how the predator’s food requirement and the prey’s necessity to avoid predation interact with their respective thermoregulatory strategies remains poorly understood. The recently developed ‘thermal game model’ predicts that in the face of imminent predation, prey should divide their time equally among a range of thermal patches. In contrast, predators should concentrate their hunting activities towards warmer patches. In this study, we test these predictions in a laboratory setup and an artificial environment that mimics more natural conditions. In both cases, we scored thermal patch use of newt larvae (prey) and free-ranging dragonfly nymphs (predators). Similar effects were seen in both settings. The newt larvae spent less time in the warm patch if dragonfly nymphs were present. The patch use of the dragonfly nymphs did not change as a function of prey availability, even when the nymphs were starved prior to the experiment. Our behavioral observations partially corroborate predictions of the thermal game model. In line with asymmetric fitness pay-offs in predator-prey interactions (the ‘life-dinner’ principle), the prey’s thermal strategy is more sensitive to the presence of predators than vice versa.