Pattern formation in prey-taxis systems

In this paper, we consider spatial predator–prey models with diffusion and prey-taxis. We investigate necessary conditions for pattern formation using a variety of non-linear functional responses, linear and non-linear predator death terms, linear and non-linear prey-taxis sensitivities, and logistic growth or growth with an Allee effect for the prey. We identify combinations of the above non-linearities that lead to spatial pattern formation and we give numerical examples. It turns out that prey-taxis stabilizes the system and for large prey-taxis sensitivity we do not observe pattern formation. We also study and find necessary conditions for global stability for a type I functional response, logistic growth for the prey, non-linear predator death terms, and non-linear prey-taxis sensitivity.     

Your worst enemy could be your best friend: predator contributions to invasion resistance and persistence of natives

Native predators are postulated to have an important role in biotic resistance of communities to invasion and community resilience. Effects of predators can be complex, and mechanisms by which predators affect invasion success and impact are understood for only a few well-studied communities. We tested experimentally whether a native predator limits an invasive species’ success and impact on a native competitor for a community of aquatic insect larvae in water-filled containers. The native mosquito Aedes triseriatus alone had no significant effect on abundance of the invasive mosquito Aedes albopictus. The native predatory midge Corethrella appendiculata, at low or high density, significantly reduced A. albopictus abundance. This effect was not caused by trait-mediated oviposition avoidance of containers with predators, but instead was a density-mediated effect caused by predator-induced mortality. The presence of this predator significantly reduced survivorship of the native species, but high predator density also significantly increased development rate of the native species when the invader was present, consistent with predator-mediated release from interspecific competition with the invader. Thus, a native predator can indirectly benefit its native prey when a superior competitor invades. This shows the importance of native predators as a component of biodiversity for both biotic resistance to invasion and resilience of a community perturbed by successful invasion.     

Pattern formation in prey-taxis systems

In this paper, we consider spatial predator-prey models with diffusion and prey-taxis. We investigate necessary conditions for pattern formation using a variety of non-linear functional responses, linear and non-linear predator death terms, linear and non-linear prey-taxis sensitivities, and logistic growth or growth with an Allee effect for the prey. We identify combinations of the above non-linearities that lead to spatial pattern formation and we give numerical examples. It turns out that prey-taxis stabilizes the system and for large prey-taxis sensitivity we do not observe pattern formation. We also study and find necessary conditions for global stability for a type I functional response, logistic growth for the prey, non-linear predator death terms, and non-linear prey-taxis sensitivity.     

Amphipod (Gammarus minus) responses to predators and predator impact on amphipod density

Recent theoretical work suggests that predator impact on local prey density will be the result of interactions between prey emigration responses to predators and predator consumption of prey. Whether prey increase or decrease their movement rates in response to predators will greatly influence the impact that predators have on prey density. In stream systems the type of predator, benthic versus water-column, is expected to influence whether prey increase or decrease their movement rates. Experiments were conducted to examine the response of amphipods (Gammarus minus) to benthic and water-column predators and to examine the interplay between amphipod response to predators and predator consumption of prey in determining prey density. Amphipods did not respond to nor were they consumed by the benthic predator. Thus, this predator had no impact on amphipod density. In contrast, amphipods did respond to two species of water-column predators (the predatory fish bluegills, Lepomis macrochirus, and striped shiners, Luxilus chrysocephalus) by decreasing their activity rates. This response led to similar positive effects on amphipod density at night by both species of predatory fish. However, striped shiners did not consume many amphipods, suggesting their impact on the whole amphipod “population” was zero. In contrast, bluegills consumed a significant number of amphipods, and thus had a negative impact on the amphipod “population”. These results lend support to theoretical work which suggests that prey behavioral responses to predators can mask the true impact that predators have on prey populations when experiments are conducted at small scales. Received: 21 March 1997 / Accepted: 15 December 1997     

Ecological effects of invasive alien species on native communities,with particular emphasis on the interactions between aphids and ladybirds

The ecological effects of introduced species on native organisms can sometimes, but not always be significant. The risks associated with invasive alien pests are difficult to quantify. This paper concentrates on the ecological effects of invasive insect predators that feed on pest insects, because the former may potentially affect the biological control of the latter. The literature indicates that invasive predatory insects generally are resistant to changes in environmental conditions, long-lived and voracious with a high reproductive rate, high dispersal ability, able to spread very rapidly across landscapes and exhibit phenotypic plasticity. Their colonization of patches of prey may induce native predators to leave, but the evidence that invaders negatively affect the abundance of the native species is scarce and not persuasive. Insect predators do not substantially affect the abundance of their prey, if the ratio of generation time of the predator to that of the prey is large (the generation time ratio hypothesis), therefore the effect of an invasion by long-lived alien predators on systems consisting of long-lived native predators and short-lived prey on the abundance of the prey is hard to detect.     

Prey-taxis destabilizes homogeneous stationary state in spatial Gause–Kolmogorov-type model for predator–prey system

We consider a continuous taxis-diffusion-reaction system of partial-differential equations describing spatiotemporal dynamics of a predator–prey system. The local kinetics of the system is defined by general Gause–Kolmogorov-type model. The predator ability to pursue the prey is modelled by the Patlak–Keller–Segel taxis model, assuming that movement velocities of predators are proportional to the gradients of specific cues emitted by prey (e.g., odour, pheromones, exometabolites). The linear stability analysis of the model showed that the non-trivial homogeneous stationary regime of the model becomes unstable with respect to small heterogeneous perturbations with increase of prey-taxis activity; an Andronov–Hopf bifurcation occurs in the system when the taxis coefficient of predator exceeds its critical bifurcation value that exists for all admissible values of model parameters. These findings generalize earlier results obtained for particular cases of the Gause–Kolmogorov-type model assuming logistic reproduction of the prey population and the Holling types I and II functional responses of the predator population. Numerical simulations with theta-logistic growth of the prey population and the Ivlev functional response of predators illustrate and support results of the analytical study.     

The advantage of alternative tactics of prey and predators depends on the spatial pattern of prey and social interactions among predators

Individual variation in behavioral strategies is ubiquitous in nature. Yet, explaining how this variation is being maintained remains a challenging task. We use a spatially-explicit individual-based simulation model to evaluate the extent to which the efficiency of an alternative spacing tactic of prey and an alternative search tactic of predators are influenced by the spatial pattern of prey, social interactions among predators (i.e., interference and information sharing) and predator density. In response to predation risk, prey individuals can either spread out or aggregate. We demonstrate that if prey is extremely clumped, spreading out may help when predators share information regarding prey locations and when predators shift to area-restricted search following an encounter with prey. However, dispersion is counter-selected when predators interact by interference, especially under high predator density. When predators search for more randomly distributed prey, interference and information sharing similarly affect the relative advantage of spreading out. Under a clumped prey spatial pattern, predators benefit from shifting their search tactic to an area-restricted search following an encounter with prey. This advantage is moderated as predator density increases and when predators interact either by interference or information sharing. Under a more random prey pattern, information sharing may deteriorate the inferior search tactic even more, compared to interference or no interaction among predators. Our simulation clarifies how interactions among searching predators may affect aggregation behavior of prey, the relative success of alternative search tactics and their potential to invade established populations using some other search or spacing tactics.     

Resource-Dependent Giving-Up Time of the Predatory Mite, Phytoseiulus persimilis

We examined the effect of prey (Tetranychus urticae) egg density on leaving rate of the predatory mite, Phytoseiulus persimilis, from leaf disks using predators with different feeding experiences and levels of external volatile cues related to their prey. Predators stayed longer on disks with prey eggs than on those without prey eggs. However, at each prey egg density predators stayed longer in the absence of prey-related volatiles from an external source. Starved predators stayed longer in a prey patch than those that had not experienced starvation. At each prey density, starved P. persimilis consumed a greater proportion of prey eggs than satiated predators. The total prey consumption of starved predators appears to be related to their longer residence time on source disks compared to satiated predators and also the per capita consumption rate was greater for starved predators compared to satiated predators.     

Predator–prey naïveté, antipredator behavior,and the ecology of predator invasions

We present a framework for explaining variation in predator invasion success and predator impacts on native prey that integrates information about predator–prey naïveté, predator and prey behavioral responses to each other, consumptive and non‐consumptive effects of predators on prey, and interacting effects of multiple species interactions. We begin with the ‘naïve prey’ hypothesis that posits that naïve, native prey that lack evolutionary history with non‐native predators suffer heavy predation because they exhibit ineffective antipredator responses to novel predators. Not all naïve prey, however, show ineffective antipredator responses to novel predators. To explain variation in prey response to novel predators, we focus on the interaction between prey use of general versus specific cues and responses, and the functional similarity of non‐native and native predators. Effective antipredator responses reduce predation rates (reduce consumptive effects of predators, CEs), but often also carry costs that result in non‐consumptive effects (NCEs) of predators. We contrast expected CEs versus NCEs for non‐native versus native predators, and discuss how differences in the relative magnitudes of CEs and NCEs might influence invasion dynamics. Going beyond the effects of naïve prey, we discuss how the ‘naïve prey’, ‘enemy release’ and ‘evolution of increased competitive ability’ (EICA) hypotheses are inter‐related, and how the importance of all three might be mediated by prey and predator naïveté. These ideas hinge on the notion that non‐native predators enjoy a ‘novelty advantage’ associated with the naïveté of native prey and top predators. However, non‐native predators could instead suffer from a novelty disadvantage because they are also naïve to their new prey and potential predators. We hypothesize that patterns of community similarity and evolution might explain the variation in novelty advantage that can underlie variation in invasion outcomes. Finally, we discuss management implications of our framework, including suggestions for managing invasive predators, predator reintroductions and biological control.     

Predator impacts on stream benthic prey

The impact that predators have on benthic, macroinvertebrate prey density in streams is unclear. While some studies show a strong effect of predators on prey density, others show little or no effect. Two factors appear to influence the detection of predator impact on prey density in streams. First, many field studies have small sample sizes and thus might be unable to detect treatment effects. Second, streams contain two broad classes of predators, invertebrates and vertebrates, which might have different impacts on prey density for a variety of reasons, including availability of refuge for prey and prey emigration responses to the two types of predators. In addition, predatory vertebrates have more complex prey communities than predatory invertebrates; this complexity might reduce the impact that predatory vertebrates have on prey because of indirect effects. I conducted a meta-analysis on the results of field studies that manipulate predator density in enclosures to determine (1) if predators have a significant impact on benthic prey density in streams, (2) if the impacts that predatory invertebrates and vertebrates have differ, and (3) if predatory vertebrates have different impacts on predatory prey versus herbivorous prey. The results of the meta-analysis suggest that on average predators have a significant negative effect on prey density, predatory invertebrates have a significantly stronger impact than predatory vertebrates, and predatory vertebrates do not differ in their impact on predatory versus herbivorous invertebrate prey. Three methodological variables (mesh size of enclosures, size of enclosures, and experimental duration) were examined to determine if cross correlations exist that may explain the differences in impact between predatory invertebrates and vertebrates. No correlation exists between mesh size and predator impact. Over all predators, no correlation exists between experimental duration and predator impact; however, within predatory invertebrates a correlation does exist between these variables. Also, a correlation was found between enclosure size and predator impact. This correlation potentially explains the difference in impact between predatory invertebrates and predatory vertebrates. Results of the meta-analysis suggest two important areas for future research: (1) manipulate both types of predators within the same system, and (2) examine their impacts on the same spatial scale.     

Emergent Allee effects in top predators feeding on structured prey populations

Top predators that forage in a purely exploitative manner on smaller stages of a size-structured prey population have been shown to exhibit an Allee effect. This Allee effect emerges from the changes that predators induce in the prey-population size distribution and represents a feedback of predator density on its own performance, in which the feedback operates through and is modified by the life history of the prey. We demonstrate that these emergent Allee effects will occur only if the prey, in the absence of predators, is regulated by density dependence in development through one of its juvenile stages, as opposed to regulation through adult fecundity. In particular, for an emergent Allee effect to occur, over-compensation is required in the maturation rate out of the regulating juvenile stage, such that a decrease in juvenile density will increase the total maturation rate to larger/older stages. If this condition is satisfied, predators with negative size selection, which forage on small prey, exhibit an emergent Allee effect, as do predators with positive size selection, which forage on large adult prey. By contrast, predators that forage on juveniles in the regulating stage never exhibit emergent Allee effects. We conclude that the basic life-history characteristics of many species make them prone to exhibiting emergent Allee effects, resulting in an increased likelihood that communities possess alternative stable states or exhibit catastrophic shifts in structure and dynamics.     

A functional response model of a predator population foraging in a patchy habitat

1. Functional response models (e.g. Holling's disc equation) that do not take the spatial distributions of prey and predators into account are likely to produce biased estimates of predation rates. 2. To investigate the consequences of ignoring prey distribution and predator aggregation, a general analytical model of a predator population occupying a patchy environment with a single species of prey is developed. 3. The model includes the density and the spatial distribution of the prey population, the aggregative response of the predators and their mutual interference. 4. The model provides explicit solutions to a number of scenarios that can be independently combined: the prey has an even, random or clumped distribution, and the predators show a convex, sigmoid, linear or no aggregative response. 5. The model is parameterized with data from an acarine predator-prey system consisting of Phytoseiulus persimis and Tetranychus urticae inhabiting greenhouse cucumbers. 6. The model fits empirical data quite well and much better than if prey and predators were assumed to be evenly distributed among patches, or if the predators were distributed independently of the prey. 7. The analyses show that if the predators do not show an aggregative response it will always be an advantage to the prey to adopt a patchy distribution. On the other hand, if the predators are capable of responding to the distribution of prey, then it will be an advantage to the prey to be evenly distributed when its density is low and switch to a more patchy distribution when its density increases. The effect of mutual interference is negligible unless predator density is very high. 8. The model shows that prey patchiness and predator aggregation in combination can change the functional response at the population level from type II to type III, indicating that these factors may contribute to stabilization of predator-prey dynamics.     

Effects of successive predator attacks on prey aggregations

We study the cumulative effect of successive predator attacks on the disturbance of a prey aggregation using a modelling approach. Our model intends to represent fish schools attacked by both aerial and underwater predators. This individual-based model uses long-distance attraction and short-distance repulsion between prey, which leads to prey aggregation and swarming in the absence of predators. When intermediate-distance alignment is added to the model, the prey aggregation displays a cohesive displacement, i.e., schooling, instead of swarming. Including predators, i.e. with repulsion behaviour for prey to predators in the model, leads to flash expansion of the prey aggregation after a predator attack. When several predators attack successively, the prey aggregation dynamics is a succession of expanding-grouping-swarming/schooling phases. We quantify this dynamics by recording the changes in the simulated prey aggregation radius over time. This radius is computed as the longest distance of individual prey to the aggregation centroid, and it is assumed to increase along with prey disturbance. The prey aggregation radius generally increases during flash expansion, then decreases during grouping until reaching a constant lowest level during swarming/schooling. This general dynamics is modulated by several parameters: the frequency, direction (vertical vs. horizontal) and target (centroid of the prey aggregation vs. random prey) of predator attacks; the distance at which prey detect predators; the number of prey and predators. Our results suggest that both aerial and underwater predators are more efficient at disturbing fish schools by increasing their attack frequency at such level that the fish cannot return to swarming/schooling. We find that a mix between aerial and underwater predators is more efficient at disturbing a fish school than a single type of attack, suggesting that aerial and underwater foragers may gain mutual benefits in forming foraging groups.     

Monoclonal antibodies reveal changes in predator efficiency with prey spatial pattern

Spatially explicit predator–prey interactions can alter the predatory potential of natural enemies augmented through conservation biological control. To test hypotheses regarding such interactions and predatory efficiency, we used a combination of molecular techniques and mark–release–recapture to study the foraging behaviour of a generalist carabid predator, Poecilus cupreus , in response to spatial patterns of its cereal aphid prey ( Metapolophium dirhodum and Sitobion avenae ). Beetle and aphid numbers were measured across two grids of sampling locations, within which aphid spatial pattern had been manipulated to generate patchy and more homogenous distributions. Aphid consumption was measured by enzyme-linked immunosorbent assays (ELISA) of beetle gut contents, using an aphid-specific monoclonal antibody. Movement and distribution patterns suggest that P. cupreus does not aggregate at, nor instigate prey-taxis within, aphid patches. However, more than two-thirds of the 2169 P. cupreus tested by ELISA had consumed aphids and the proportion of beetles containing aphid proteins was positively related to aphid density. Against expectation, the proportion of predators feeding on aphids was greatest where prey were homogenously distributed, and this was attributed to the loss of partial refuges for prey in aphid patches. The functional value of this type of uniform foraging strategy is ideally suited to early colonization of the crop habitat, when aphid numbers are low, before populations build up and form strong spatial patterns.     

Non-lethal effects of predators on prey growth rates depend on prey density and nutrient additions

A number of studies show that predators can depress prey growth rates by inducing reductions in foraging activity, but the size of this non-lethal effect is quite variable. Here I investigate how prey density and resource productivity may alter the extent to which predators depress the growth rates of their prey. Theory predicts that when resources are overgrazed, an increase in predation risk will have little net effect on individual food intake because the decline in foraging effort will be offset by an increase in resource level. Thus, the non-lethal effects of predators on prey growth rates should depend upon prey density and resource productivity in a predictable manner, with the growth penalty imposed by predators being strongest when resources are undergrazed and weakest when resources are overgrazed. I tested this hypothesis by manipulating predation risk, prey density, and nutrient additions in a mesocosm experiment with the pulmonate snail Helisoma trivolvis . Refuge use by snails was 45% higher in the presence of caged crayfish than in their absence. Snail growth rates were reduced, on average, by 24% in the presence of caged crayfish. However, the magnitude of the growth penalty exacted by crayfish depended on snail density and nutrient additions. When snails were stocked at high density and nutrient additions were low, growth suppression was just 2.6%. At the other extreme, when snails were at low density and nutrient additions were high, growth suppression was 44.6%. Thus, the non-lethal effects of predators on prey growth depend on environmental context, illustrating an important link between individual traits and system-level properties.     

Habitat destruction in a simple predator-prey patch model: how predators enhance prey persistence and abundance

We model a metapopulation of predator-prey patches using both spatially implicit or mean-field (MF) and spatially explicit (SE) approaches. We show that in the MF model there are parameter regimes for which prey cannot persist in the absence of predators, but can in their presence. In addition, there are parameter regimes for which prey may persist in isolation, but the presence of predators will increase prey patch density. Predators may thus enhance prey persistence and overall abundance. The key mechanism responsible for this effect is the occurrence of prey dispersal from patches that are occupied by both prey and predators. In addition, these patches should be either long-lived, such as that occurs when predators keep prey from overexploiting its local resource, or the presence of a predator on a patch should significantly enhance the prey dispersal out of that patch. In the SE approach these positive effects of predators on prey persistence and abundance occur for even larger parameter ranges than in the MF model. Prey dispersal from predator-prey patches may thus be important for persistence of both species as a community, independent of the modeling framework studied. Comparison of the MF and SE approaches shows that local dispersal constraints can have the edge over global dispersal for the persistence of the metapopulation in regimes where the two species have a beneficial effect on each other. In general, our model provides an example of feedback in multiple-species metapopulations that can make the implementation of conservation schemes based on single-species arguments very risky.     

Omnivorous food web,prey preference and allochthonous nutrient input

This work purports to analyze the influence of allochthonous nutrient input into consumer level in the ultimate dynamics of an omnivory food web, where consumption is dictated by non-switching and switching predators. Within this behavioral context, prey consumption structure is shown to have a markedly effect on food web dynamics under a gradient of allochthonous input and primary productivity. A striking feature is that in the non-switching model invasion of consumer and predator occurs sequentially in this order as density of carrying capacity increases, while in the switching model both predators and consumers are able to invade and persist irrespective of the considered carrying capacity levels.     

Multi-predator effects across life-history stages: non-additivity of egg- and larval-stage predation in an African treefrog

The effects of multiple predators on their prey are frequently non‐additive because of interactions among predators. When prey shift habitats through ontogeny, many of their predators cannot interact directly. However, predators that occur in different habitats or feed on different prey stages may still interact through indirect effects mediated by prey traits and density. We conducted an experiment to evaluate the combined effects of arboreal egg‐stage and aquatic larval‐stage predators of the African treefrog, Hyperolius spinigularis. Egg and larval predator effects were non‐additive – more Hyperolius survived both predators than predicted from their independent effects. Egg‐stage predator effects on aquatic larval density and size and age at hatching reduced the effectiveness of larval‐stage predators by 70%. Our results indicate that density‐ and trait‐mediated indirect interactions can act across life‐stages and habitats, resulting in non‐additive multi‐predator effects.     

Generalist and specialist predators that mediate permanence in ecological communities

 General dynamic models of systems with two prey and one or two predators are considered. After rescaling the equations so that both prey have the same intrinsic rate of growth, it is shown that there exists a generalist predator that can mediate permanence if and only if there is a population density of a prey at which its per-capita growth rate is positive yet less than its competitor’s invasion rate. In particular, this result implies that if the outcome of competition between the prey is independent of initial conditions, then there exists a generalist predator that mediates permanence. On the other hand, if the outcome of competition is contingent upon initial conditions (i.e., the prey are bistable), then there may not exist a suitable generalist predator. For example, bistable prey modeled by the Ayala–Gilpin (θ-Logistic) equations can be stabilized if and only if θ<1 for one of the prey. It is also shown that two specialist predators always can mediate permanence between bistable prey by creating a repelling heteroclinic cycle consisting of fixed points and limit cycles. Received 10 August 1996; received in revised form 21 March 1997     

Do native predators benefit from non‐native prey?

Despite knowledge on invasive species’ predatory effects, we know little of their influence as prey. Non‐native prey should have a neutral to positive effect on native predators by supplementing the prey base. However, if non‐native prey displace native prey, then an invader's net influence should depend on both its abundance and value relative to native prey. We conducted a meta‐analysis to quantify the effect of non‐native prey on native predator populations. Relative to native prey, non‐native prey similarly or negatively affect native predators, but only when studies employed a substitutive design that examined the effects of each prey species in isolation from other prey. When native predators had access to non‐native and native prey simultaneously, predator abundance increased significantly relative to pre‐invasion abundance. Although non‐native prey may have a lower per capita value than native prey, they seem to benefit native predators by serving as a supplemental prey resource.