Dynamics analysis of a predator–prey system with harvesting prey and disease in prey species

In this paper, a predator–prey system with harvesting prey and disease in prey species is given. In the absence of time delay, the existence and stability of all equilibria are investigated. In the presence of time delay, some sufficient conditions of the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analysing the corresponding characteristic equation, and the properties of Hopf bifurcation are given by using the normal form theory and centre manifold theorem. Furthermore, an optimal harvesting policy is investigated by applying the Pontryagin's Maximum Principle. Numerical simulations are performed to support our analytic results.     

Effects of prey dispersal on predator–prey interactions in streams

1. We studied the effect of mesh size (6 and 3 mm) on interactions between brown trout ( Salmo trutta ) and benthic invertebrates in enclosures placed in a stream in southern Sweden. We also compared how different prey exchange rates affected interactions between trout and invertebrates.
2. Trout had strong impacts on some benthic taxa, and different mesh sizes produced different patterns. Trout affected the abundance of 10 of the 21 taxa examined, six in enclosures with 3 mm mesh and six in enclosures with 6 mm mesh. The abundance of nine of the prey taxa was lower in the presence of trout, only leptocerids were more numerous in the presence of trout.
3. Our measurements of prey immigration/emigration, together with trout diet data, suggest that direct consumption by trout, rather than avoidance behaviour by prey, explains most decreases in prey abundance. There was avoidance behaviour by only two of the twenty-one prey taxa, with trout inducing emigration of the mayflies Baetis rhodani and Paraleptophlebia sp.
4. Trout indirectly increased periphyton biomass in both 3 and 6 mm enclosures. The effect of trout on periphyton was probably due to strong effects of trout on the grazer, Baetis rhodani , Heptagenia sp. and Paralepthoplebia sp.
5. Our results suggest that mesh size, through its effects on exchange rates of prey, may affect interactions between predators and prey in running waters, but that the effects of dispersal and predation on invertebrates are taxon specific.     

The influence of prey hardness on Daphnia's selectivity for large prey

Two comparable methods were used to study the feeding of four species of Daphnia on large spherical particles which differed in size and hardness. The first method used gut analysis to estimate the selectivities of daphnids feeding in a broad size range of a single particle type, including polystyrene beads (4–60 µm diameter) in the laboratory and Eudorina colonies (10–90 µm) in the field. In the second method, Daphnia of different sizes fed in a mixture of 6.5 µm Chlamydomonas and one of eight test particles. Smaller daphnids were less effective in feeding on large test particles. Nonlinear regression was therefore used to estimate the Daphnia body size at which the clearance rate on a test particle was reduced to 50% of that for Chlamydomonas. The results of both methods show that prey size and hardness are both very important in determining daphnid feeding selectivity. For a given particle size, soft algae (naked and gelatinous flagellates) are more readily ingested than hard algae (diatoms and dinoflagellates), and hard algae are more readily ingested than polystyrene beads. Daphnia can feed effectively on algae that are 2–5 times larger than the largest ingestible bead.     

Size-dependent predator–prey relationships between perch and their fish prey

Size-dependent interactions between piscivorous perch Perca fluviatilis (age ≥1 year) and their fish prey age 0 year perch, pikeperch Sander lucioperca and roach Rutilus rutilus in the biomanipulated Bautzen Reservoir indicated that the highest ratio of prey total length ( L _T) to predator L _T was 59%. Perch L _T and prey fish L _T were positively and linearly related. Perch L _T was strongly related with both gape width and gape height. Within the range 80–110 mm L _T, the gape height of perch exceeded gape width, while beginning at 120 mm L _T the gape width exceeded gape height. The minimum, maximum and mean prey L _T and prey body depths of all three prey species increased with increasing predator size, but the increases in mean sizes of perch and pikeperch as prey were less than that of roach. The low limit of the 'predation window' observed in this study coupled with results of previous studies on perch in the Bautzen Reservoir indicated that perch had a major impact on the population dynamics of both perch and pikeperch.     

Spatial variability in prey phenology determines predator movement patterns and prey survival

Species have phenological variation among local habitats that are located at relatively small spatial scales. However, less studies have tested how this spatial variability in phenology can mediate intra-/inter-specific interactions. When predators track phenological variation of prey among local habitats, survival of prey within a local habitat strongly influenced by phenological synchrony with their conspecifics in adjacent habitats. Theory predicts that phenological synchrony among local habitats increases prey survival in local habitat within spatially structured environments because the predators have to make a habitat choice for foraging. Consequently, total survival of prey at regional scale should be higher. By using a spatially explicit field experiment, we tested above hypothesis using a prey–predator interaction between tadpole (Rhacophorus arboreus) and newt (Cynops pyrrhogaster). We established enclosures (≈regional scale) consisting of two tanks (≈local habitat scale) with different degree of prey phenological synchrony. We found that phenological synchrony of prey between tanks within each enclosure decreased the mean residence time of the predator in each tank, which resulted in higher survival of prey at a local habitat scale, supporting the theoretical prediction. Furthermore, individual-level variation in predator residence time explained the between-tank variation in prey survival in enclosures with phenological synchrony, implying that movement patterns of the predator can mediate variation in local population dynamics of their prey. However, total survival at each enclosure was not higher under phenological synchrony. These results suggest the importance of relative timing of prey phenology, not absolute timing, among local habitats in determining prey–predator interactions.     

Predator experience on cryptic prey affects the survival of conspicuous aposematic prey

Initially, aposematism, which is an unprofitable trait, e.g. noxiousness conspicuously advertised to predators, appears to be a paradox since conspicuousness should increase predation by naive predators. However, reluctance of predators for eating novel prey (e.g. neophobia) might balance the initial predation caused by inexperienced predators. We tested the novelty effects on initial predation and avoidance learning in two separate conspicuousness levels of aposematic prey by using a 'novel world' method. Half of the wild great tits (Parus major) were trained to eat cryptic prey prior to the introduction of an aposematic prey, which potentially creates a bias against the aposematic morph. Both prey types were equally novel for control birds and they should not have shown any biased reluctance for eating an aposematic prey. Knowledge of cryptic prey reduced the expected initial mortality of the conspicuous morph to a random level whereas control birds initially ate the conspicuous morph according to the visibility risk. Birds learned to avoid conspicuous prey in both treatments but knowledge of cryptic prey did not increase the rate of avoidance learning. Predators' knowledge of cryptic prey did not reduce the predation of the less conspicuous aposematic prey and additionally predators did not learn to avoid the less conspicuous prey. These results indicate that predator psychology, which was shown as reluctance for attacking novel conspicuous prey, might have been important in the evolution of aposematism.     

Dynamic changes in prey choice by stickleback during simultaneous encounter with large prey

When a three-spined stickleback Gasterosteus aculeatus encountered prey simultaneously the probability of hanging and the median pursuit time were greater than when prey were encountered sequentially. During simultaneous prey encounter fish did not choose to attack the more profitable prey but instead the nearer prey was handled first except when the difference between the two prey sizes was large. No difference was found in the level of total energetic intake by the fish regardless of prey size pairing. Fish that handled and ate the first prey of a pair in <5 s attacked the second prey with a high probability of success, demonstrating an opportunistic feeding strategy. Importantly however, the fish did not choose to maximize long term energy intake rate by eating both prey, but rather short-term considerations over the course of feeding took precedence. With an empty stomach, the probability of a fish eating ( P _eat) the first prey handled was high regardless of prey size. As stomach fullness increased, the P _eat the first prey handled decreased if it was the larger prey. Hence, the fish were unselective when the stomach was empty but thereafter there was a shift in preference towards the smaller prey. The decision of which prey to attack and eat appeared to be based on short-term energy considerations and the level of stomach fullness. This study demonstrates that feeding on a short-term scale is a crucial factor to take account of when analysing fish feeding during simultaneous prey encounter.     

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.     

Effects of prey quality on social wasps when given a choice of prey

The effect of prey quality on foraging behavior and colony demographics of the social wasp Polistes fuscatus was examined by providing a choice between non‐toxic prey (Manduca sexta caterpillars) and sublethally toxic prey (Junonia coenia caterpillars), and then comparing the performance of these colonies to others given only the non‐toxic prey. In the choice, one of two types of Manduca were used: those fed an artificial diet or those fed plantain (Plantago lanceolata), which contains iridoid glycosides (IGs) that Junonia coenia store but which Manduca does not. Despite the negative correlation between the number of Junonia prey used and number of adult offspring produced, when a surplus of non‐toxic prey was available, the wasps did not completely avoid the toxic prey. However, they were more discriminating when the choice was between Manduca fed an artificial diet and Junonia fed plantain vs. when both prey species had eaten the plantain. Because the wasps had a choice of prey types and had a surplus of prey on about one‐third of the days, the wasps were able to take enough non‐toxic prey to avoid some of the negative consequences of IGs. For example, the total number of wasp offspring per nest was not affected, but mean weight of female offspring per colony was less for colonies given both prey types eating plantain, compared to that for colonies fed only non‐toxic prey, or those given a choice of non‐toxic prey vs. toxic prey. In addition, compared to the control (only non‐toxic prey), the proportion of males produced was less in the treatment that provided a clear contrast between non‐toxic and toxic prey. Why these wasps did not avoid the toxic prey is discussed.     

Spatial processes can determine the relationship between prey encounter rate and prey density

Theoretical models frequently assume that the rate at which a searching predator encounters prey increases linearly with prey density. In a recent experiment using great tits searching for winter moth caterpillars, the time to find the first prey item did not decline as quickly with density as the standard theory assumes. Using a spatial simulation model, we show that prey aggregation and/or spatially correlated searching behaviour by the predator can generate a range of relationships, including results that are qualitatively similar to those found in the great tit experiment. We suggest that further experiments are required to determine whether the explanation proposed here is correct, and that theoretical work is needed to determine how this behaviour is likely to influence the ecological and evolutionary dynamics of predator-prey communities.     

Rapid prey evolution can alter the structure of predator–prey communities

Although microevolution has been shown to play an important role in pairwise antagonistic species interactions, its importance in more complex communities has received little attention. Here, we used two Pseudomonas fluorescens prey bacterial strains (SBW25 and F113) and Tetrahymena thermophila protist predator to study how rapid evolution affects the structuring of predator–prey communities. Both bacterial strains coexisted in the absence of predation, and F113 was competitively excluded in the presence of both SBW25 and predator during the 24‐day experiment, an initially surprising result given that F113 was originally poorer at growing, but more resistant to predation. However, this can be explained by SBW25 evolving greater antipredatory defence with a lower growth cost than F113. These results show that rapid prey evolution can alter the structure of predator–prey communities, having different effects depending on the initial composition of the evolving community. From a more applied perspective, our results suggest that the effectiveness of biocontrol bacteria, such as F113, could be weaker in communities characterized by intense bacterial competition and protist predation.     

Variable prey development time suppresses predator–prey cycles and enhances stability

Although theoretical models have demonstrated that predator–prey population dynamics can depend critically on age (stage) structure and the duration and variability in development times of different life stages, experimental support for this theory is non‐existent. We conducted an experiment with a host–parasitoid system to test the prediction that increased variability in the development time of the vulnerable host stage can promote interaction stability. Host–parasitoid microcosms were subjected to two treatments: Normal and High variance in the duration of the vulnerable host stage. In control and Normal‐variance microcosms, hosts and parasitoids exhibited distinct population cycles. In contrast, insect abundances were 18–24% less variable in High‐ than Normal‐variance microcosms. More significantly, periodicity in host–parasitoid population dynamics disappeared in the High‐variance microcosms. Simulation models confirmed that stability in High‐variance microcosms was sufficient to prevent extinction. We conclude that developmental variability is critical to predator–prey population dynamics and could be exploited in pest‐management programs.     

Kleptoparasitic prey competition in shoaling fish: effects of familiarity and prey distribution

Familiarity is thought to stabilize dominance hierarchies andreduce aggressive interactions within groups of socially livinganimals. Though familiarity has been widely studied in shoalingfish, few studies have investigated changes in prey competitionas a function of time spent together within groups of initiallyunfamiliar individuals. In this study, we created shoals ofthree-spined stickleback (Gasterosteus aculeatus) and monitoredchanges in foraging rates and related competitive behaviorswithin shoals over a 4-week period in experimental series whereprey was spatially and temporally concentrated or dispersed.Prey share was unequal under both prey distribution modes, anddisparity in prey share was not seen to change as trials progressed.Interestingly, the contest rate for prey items fell over timewhen individuals were competing for dispersed prey but not whenprey were concentrated. We found no evidence that fish showedassociation preferences for either group members that had consumeda greater or lesser proportion of prey during trials. Thoughthe intensity of competition may be reduced by increased groupstability in nature, this is likely to be strongly dependenton the way prey resources are distributed through space andtime.     

Unidirectional prey-predator facilitation: apparent prey enhance predators' foraging success on cryptic prey

Food availability can strongly affect predator-prey dynamics. When change in habitat condition reduces the availability of one prey type, predators often search for other prey, perhaps in a different habitat. Interactions between behavioural and morphological traits of different prey may influence foraging success of visual predators through trait-mediated indirect interactions (TMIIs), such as prey activity and body coloration. We tested the hypothesis that foraging success of stream-dwelling cutthroat trout (Onchorhyncus clarki) on cryptically coloured, less-active benthic prey (larval mayfly; Paraleptophebia sp.) can be enhanced by the presence of distinctly coloured, active prey (larval stonefly shredder; Despaxia augusta). Cutthroat trout preyed on benthic insects when drifting invertebrates were unavailable. When stonefly larvae were present, the trout ate most of the stoneflies and also consumed a higher proportion of mayflies than under mayfly only treatment. The putative mechanism is that active stonefly larvae supplied visual cues to the predator that alerted trout to the mayfly larvae. Foraging success of visual predators on cryptic prey can be enhanced by distinctly coloured, active benthic taxa through unidirectional facilitation to the predators, which is a functional change of interspecific interaction caused by a third species. This study suggests that prey-predator facilitation through TMIIs can modify species interactions, affecting community dynamics.     

Dazzle coloration and prey movement

Many traits in animals reduce the rate of attack from visually hunting predators, including camouflage, warning signals and mimicry. In addition, some animal markings may reduce the likelihood that an attack ends in successful capture. These might include dazzle markings, high-contrast patterns that make the estimation of speed and trajectory difficult. However, until now, no study has experimentally tested whether some markings may achieve such an effect. We developed a computer 'game' where human 'predators' have to capture computer-generated prey moving across a background. In two experiments, we find that although uniform camouflaged targets were among the hardest to capture, so were a range of high-contrast conspicuous patterns, such as bands and zigzags. Prey were also more difficult to capture against more heterogeneous than uniform backgrounds, and at faster speeds of movement. As such, we find the first experimental evidence that conspicuous patterns, similar to those found in a wide range of real animals, make the capture of moving prey more challenging. Various anti-predator markings may work prey during motion, and some animals may combine such dazzle patterns with other functions, such as camouflage, thermoregulation, sexual and warning signals.     

Positive effect of predators on prey growth rate through induced modifications of prey behaviour

Many prey modify behaviour in response to predation risk and this modification frequently leads to a foraging rate reduction. Although this reduction can have a clear direct negative effect on prey growth rate, theory predicts that a net positive effect can occur when the combined reduction in foraging by the entire population leads to a large increase in resource level. Here, I present experimental results that corroborate this counterintuitive prediction: the predation threat of 'nonlethal' caged larval dragonflies ( Anax longipes ) caused a net increase in small bullfrog ( Rana catesbeiana ) growth. A behavioural response (i.e. a reduction in activity level and microhabitat usage) was likely to have negatively affected growth, but was offset by a positive effect on growth from a large increase in resource levels (measured using a bioassay). Further, the positive Anax effect was dependent on nutrient level, illustrating the role of the resource response magnitude. Results of this study are discussed in the context of studies in which Anax had the opposite (i.e. negative) effect on tadpole growth. Predator-induced modifications in prey behaviour can have large negative or positive effects on prey growth, the sign and magnitude of which are dependent on relative species density and resource dynamics.     

Reversed predator–prey cycles are driven by the amplitude of prey oscillations

Ecoevolutionary feedbacks in predator–prey systems have been shown to qualitatively alter predator–prey dynamics. As a striking example, defense–offense coevolution can reverse predator–prey cycles, so predator peaks precede prey peaks rather than vice versa. However, this has only rarely been shown in either model studies or empirical systems. Here, we investigate whether this rarity is a fundamental feature of reversed cycles by exploring under which conditions they should be found. For this, we first identify potential conditions and parameter ranges most likely to result in reversed cycles by developing a new measure, the effective prey biomass, which combines prey biomass with prey and predator traits, and represents the prey biomass as perceived by the predator. We show that predator dynamics always follow the dynamics of the effective prey biomass with a classic ¼‐phase lag. From this key insight, it follows that in reversed cycles (i.e., ¾‐lag), the dynamics of the actual and the effective prey biomass must be in antiphase with each other, that is, the effective prey biomass must be highest when actual prey biomass is lowest, and vice versa. Based on this, we predict that reversed cycles should be found mainly when oscillations in actual prey biomass are small and thus have limited impact on the dynamics of the effective prey biomass, which are mainly driven by trait changes. We then confirm this prediction using numerical simulations of a coevolutionary predator–prey system, varying the amplitude of the oscillations in prey biomass: Reversed cycles are consistently associated with regions of parameter space leading to small‐amplitude prey oscillations, offering a specific and highly testable prediction for conditions under which reversed cycles should occur in natural systems.     

Feeding, prey selection and prey encounter mechanisms in the heterotrophic dinoflagellate Noctiluca scintillans

The heterotrophic dinoflagellate Noctiluca scintillans has anegligible swimming ability and feeds predominantly on immobileprey. How, then, does it encounter prey? Noctiluca scintillansis positively buoyant and, therefore, we hypothesized that itintercepts prey particles during ascent and/or that microscaleshear brings it into contact with prey. Noctiluca scintillanshas a specific carbon content 1–2 orders of magnitudeless than that typical for protists and, thus, an inflated volume.It also has a density slightly less than that of the ambientwater and therefore ascends at high velocities (-1 m h^–1).In stagnant water, clearance rates of latex spheres (5–80µm) increased approximately with prey particle size squared.This scaling is consistent with N.scintillans being an interceptionfeeder. However, absolute clearance rates were substantiallylower than those predicted by modeling N.scintillans both asa spherical and as a cylindrical collector. The latter modelassumes that prey particles are collected on the string of mucusthat may form at the tip of the tentacle. Feeding, growth andprey selection experiments all demonstrated that diatoms arecleared at substantially higher rates than latex beads and otherphytoplankters, particularly dinoflagellates. We propose thatdiatoms stick more efficiently than latex beads to the mucusof N.scintillans and that dinoflagellates reduce fatal contactbehaviorally. We conclude that N.scintillans is an interceptionfeeder and that the high ascent velocity accounts for encounterswith prey. However, the flow field around the cell-mucus complexis too complicated to be described accurately by simple geometricmodels. Fluid shear (0.7–1.8 s^–1 had a negativeimpact on feeding rates, which were much less than predictedby models. Noctiluca scintillans can survive starvation forlong periods (>3 weeks), it can grow at low concentrationsof prey (-15 µg C l^–1), but growth saturates onlyat very high prey concentrations of 500–1000 µgC l^–1 or more. We demonstrate how the functional biologyof N.scintillans is consistent with its spatial and seasonaldistribution, which is characterized by persistence in the plankton,blooms in association with high concentrations of diatoms, andsurface accumulation during quiescent periods or exponentialdecline in abundance with depth during periods of turbulentmixing.