Explicit model for searching behavior of predator

The authors present an approach for explicit modeling of spatio-temporal dynamics of predator-prey community. This approach is based on a reaction-diffusion-adjection PD (prey dependent) system. Local kinetics of population is determined by logistic reproduction function of prey, constant natural mortality of predator and Holling type 2 trophic function. Searching behavior of predator is described by the advective term in predator balance equation assuming the predator acceleration to be proportional to the prey density gradient. The model was studied with zero-flux boundary conditions. The influence of predator searching activity on the community dynamics, in particular, on the emergence of spatial heterogeneity, has been investigated by linear analysis and numerical simulations. It has been shown how searching activity may effect the persistence of species, stabilizing predator-prey interactions at very low level of pest density. It has been demonstrated that obtaining of such dynamic regimes does not require the use of complex trophic functions.     

Predator overcomes the Allee effect due to indirect prey–taxis

A mathematical model for spatiotemporal dynamics of prey–predator system was studied by means of linear analysis and numerical simulations. The model is a system of PDEs of taxis–diffusion–reaction type, accounting for the ability of predators to detect the locations of higher prey density, which is formalized as indirect prey–taxis, according to hypothesis that the taxis stimulus is a substance being continuously emitted by the prey, diffusing in space and decaying with constant rate in time (e.g. odour, pheromone, exometabolit). The local interactions of the prey and predators are described by the classical Rosenzweig – MacArthur system, which is modified in order to take into account the Allee effect in the predator population. The boundary conditions determine the absence of fluxes of population densities and stimulus concentration through the habitat boundaries. The obtained results suggest that the prey–taxis activity of the predator can destabilize both the stationary and periodic spatially-homogeneous regimes of the species coexistence, causing emergence of various heterogeneous patterns. In particular, it is demonstrated that formation of local dense aggregations induced by prey–taxis allows the predators to overcome the Allee effect in its population growth, avoiding the extinction that occurs in the model in the absence of spatial effects.     

Mathematical model of active migrations as feeding strategy in trophic communities

Models of spatial and temporal dynamics of trophic communities are considered and numerically investigated. Stability of equilibriums of two trophic levels models is analytically studied. Active migrations are described on the bases of idea that acceleration of directed migration of predators is pro-rate the density gradient of prey populations. High migration activity of predators ensures the stability of complex non-uniform spatial regimes even when the abundance of predators is constant. In this case both summarized consumption of preys by predators and total number of preys considerably exceed equilibrium meanings of homogeneous regime, that takes place when predators are not able to migrate directionally. In three levels trophic system plant resource-pest-predator the increase in migration activity of predator leads to the increase of its abundance and the abundance of pest while the biomass of the resource decreases. This result is interpreted as an example of non-effective biological control when predators with high searching ability are used.     

Predator interference emerging from trophotaxis in predator–prey systems: An individual-based approach

An individual-based model describing predator–prey interactions within a closed rectangular habitat was developed to study how different assumptions about the individual movements lead to the emergence at the population level of various kinds of prey- and predator-dependence in the spatially aggregated trophic function.In addition to random walk, both species are capable of directional movement, i.e., the model accounts for the predator prey-taxis and evasion of predators by prey individuals. The taxis stimulus of each species is the odour of the other species, which is distributed continuously in space. Spatial behaviour of individuals is determined by the specific response to the odour gradient and the tendency to maintain the taxis velocity.In order to facilitate the assessment of the trophic function, the model allows removing the effect of demographic density variations on the predator ration, keeping population sizes constant.Analyzing the dependence of the trophic function with the average predator density, we found that, depending on the intensity of taxis, the predator population exhibits various degrees of interference, from very low to very high values. In particular, a moderate taxis generates distinct levels of interference including the ratio-dependent case. The letter maximizes the average consumption rate.A new generalized function containing ratio-dependence and prey-dependence as special cases, at high and low population abundances, is suggested. This trophic function fits the simulated data better than the Hassell–Varley–Holling expression does.     

Microscale patchiness of the distribution of copepods (Harpacticoida) as a result of trophotaxis

A minimal conceptual model has been built that is capable of explaining the microscale heterogeneity observed in the benthic trophic system of harpacticoid copepods grazing on diatom microalgae. Alternative models of trophotaxis in predator-prey systems are considered in which the stimulus for predator movement is prey density, attractant secreted by the prey, or predator satiation. The model in which taxis is determined by predator satiety proves the most suitable for describing the harpacticoid-diatom dynamics.     

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.     

A ratio-dependent food chain model and its applications to biological control

While biological controls have been successfully and frequently implemented by nature and human, plausible mathematical models are yet to be found to explain the often observed deterministic extinctions of both pest and control agent in such processes. In this paper we study a three trophic level food chain model with ratio-dependent Michaelis-Menten type functional responses. We shall show that this model is rich in boundary dynamics and is capable of generating such extinction dynamics. Two trophic level Michaelis-Menten type ratio-dependent predator-prey system was globally and systematically analyzed in details recently. A distinct and realistic feature of ratio-dependence is its capability of producing the extinction of prey species, and hence the collapse of the system. Another distinctive feature of this model is that its dynamical outcomes may depend on initial populations levels. Theses features, if preserved in a three trophic food chain model, make it appealing for modelling certain biological control processes (where prey is a plant species, middle predator as a pest, and top predator as a biological control agent) where the simultaneous extinctions of pest and control agent is the hallmark of their successes and are usually dependent on the amount of control agent. Our results indicate that this extinction dynamics and sensitivity to initial population levels are not only preserved, but also enriched in the three trophic level food chain model. Specifically, we provide partial answers to questions such as: under what scenarios a potential biological control may be successful, and when it may fail. We also study the questions such as what conditions ensure the coexistence of all the three species in the forms of a stable steady state and limit cycle, respectively. A multiple attractor scenario is found.     

Differential Effects of Plant Species on a Mite Pest (Tetranychus Urticae) and its Predator (Phytoseiulus Persimilis): Implications for Biological Control

The influence of plant species on the population dynamics of the spider mite pest, Tetranychus urticae, and its predator, Phytoseiulus persimilis, was examined as a prerequisite to effective biological control on ornamental nursery stock. Experiments have been done to investigate how the development, fecundity and movement of T. urticae, and the movement of P. persimilis were affected by plant species. A novel experimental method, which incorporates plant structure, was used to investigate the functional response of P. persimilis. Development times for T. urticae were consistent with published data and did not differ with plant species in a biologically meaningful way. Plant species was shown to have a major influence on fecundity (P < 0.001) and movement of the pest mite (P < 0.01), but no influence on the movement of the predator. The movement of both pest and predator was shown to be related to the density of the adult pest mites on the plant (P < 0.001). Plant structure affected the functional response, particularly in relation to the ability of the predator to locate prey at low densities. The impact of these findings on the effective use of biological control on ornamental nursery stock is discussed.     

Prey temporarily escape from predation in the presence of a second prey species

1. Indirect interactions between populations of different prey species mediated by a shared predator population are known to affect prey dynamics. 2. Depending on the temporal and spatial scale, these indirect interactions may result in positive (apparent mutualism), neutral or negative effects (apparent competition) of the prey on each other's densities. Although there is ample evidence for the latter, evidence for apparent mutualism is scarce. 3. The effectiveness of using one species of predator for biological control of more than one pest species depends on the occurrence of such positive or negative effects. 4. We used an experimental system consisting of the two prey species Western flower thrips (Franklineilla occidentalis Pergande) and greenhouse whitefly (Trialeurodes vaporariorum Westwood) and a shared predator, the phytoseiid mite Amblyseius swirskii Athias‐Henriot. We released all three species on the same plant and studied their dynamics and distribution along rows of plants. 5. We expected that the more mobile prey species (thrips) would escape temporarily in the presence of the other prey species (whitefly) by dispersing from plants with the predator. The predator was expected to disperse slower in the presence of two prey species because of the higher availability of food. 6. Evidence was found for slower dispersal of predators and short‐term escape of thrips from predation when whiteflies were present, thus confirming the occurrence of short‐term apparent mutualism. 7. The apparent mutualism resulted in a cascade to the first trophic level: a higher proportion of fruits was damaged by thrips in the presence of whiteflies. 8. We conclude that apparent mutualism can be an important phenomenon in population dynamics, and can significantly affect biological control of pest species that share a natural enemy.     

Host-parasitoid spatial ecology: a plea for a landscape-level synthesis

A growing body of literature points to a large-scale research approach as essential for understanding population and community ecology. Many of our advances regarding the spatial ecology of predators and prey can be attributed to research with insect parasitoids and their hosts. In this review, we focus on the progress that has been made in the study of the movement and population dynamics of hosts and their parasitoids in heterogeneous landscapes, and how this research approach may be beneficial to pest management programs. To date, few studies have quantified prey and predator rates and ranges of dispersal and population dynamics at the patch level--the minimum of information needed to characterize population structure. From host-parasitoid studies with sufficient data, it is clear that the spatial scale of dispersal can differ significantly between a prey and its predators, local prey extinctions can be attributed to predators and predator extinction risk at the patch level often exceeds that of the prey. It is also evident that populations can be organized as a single, highly connected (patchy) population or as semi-independent extinction-prone local populations that collectively form a persistent metapopulation. A prey and its predators can also differ in population structure. At the landscape level, agricultural studies indicate that predator effects on its prey often spill over between the crop and surrounding area (matrix) and can depend strongly on landscape structure (e.g. the proportion of suitable habitat) at scales extending well beyond the crop margins. In light of existing empirical data, predator-prey models are typically spatially unrealistic, lacking important details on boundary responses and movement behaviour within and among patches. The tools exist for conducting empirical and theoretical research at the landscape level and we hope that this review calls attention to fertile areas for future exploration.     

Climate change effects on behavioral and physiological ecology of predator–prey interactions: Implications for conservation biological control

Habitat management under the auspices of conservation biological control is a widely used approach to foster conditions that ensure a diversity of predator species can persist spatially and temporally within agricultural landscapes in order to control their prey (pest) species. However, an emerging new factor, global climate change, has the potential to disrupt existing conservation biological control programs. Climate change may alter abiotic conditions such as temperature, precipitation, humidity and wind that in turn could alter the life-cycle timing of predator and prey species and the behavioral nature and strength of their interactions. Anticipating how climate change will affect predator and prey communities represents an important research challenge. We present a conceptual framework—the habitat domain concept—that is useful for understanding contingencies in the nature of predator diversity effects on prey based on predator and prey spatial movement in their habitat. We illustrate how this framework can be used to forecast whether biological control by predators will become more effective or become disrupted due to changing climate. We discuss how changes in predator–prey interactions are contingent on the tolerances of predators and prey species to changing abiotic conditions as determined by the degree of local adaptation and phenotypic plasticity exhibited by species populations. We conclude by discussing research approaches that are needed to help adjust conservation biological control management to deal with a climate future.     

The influence of generalist predators in spatially extended predator–prey systems

The presence of generalist predators is known to have important ecological impacts in several fields. They have wide applicability in the field of biological control. However, their role in the spatial distribution of predator and prey populations is still not clear. In this paper, the spatial dynamics of a predator–prey system is investigated by considering two different types of generalist predators. In one case, it is considered that the predator population has an additional food source and can survive in the absence of the prey population. In the other case, the predator population is involved in intraguild predation, i.e., the source of the additional food of the predator coincides with the food source of the prey population and thus both prey and predator populations compete for the same resource. The conditions for linear stability and Turing instability are analyzed for both the cases. In the presence of generalist predators, the system shows different pattern formations and spatiotemporal chaos which has important implications for ecosystem functioning not only in terms of their predictability, but also in influencing species persistence and ecosystem stability in response to abrupt environmental changes. This study establishes the importance of the consideration of spatial dynamics while determining optimal strategies for biological control through generalist predators.     

A mechanistic model for interference and Allee effect in the predator population

We present the results of simulations in an individual-based model describing spatial movement and predator-prey interaction within a closed rectangular habitat. Movement of each individual animal is determined by local conditions only, so any collective behavior emerges owing to self-organization. It is shown that the pursuit of prey by predators entails predator interference, manifesting itself at the population level as the dependency of the trophic function (individual ration) on predator abundance. The stabilizing effect of predator interference on the dynamics of a predator-prey system is discussed. Inclusion of prey evasion induces apparent cooperation of predators and further alters the functional response, giving rise to a strong Allee effect, with extinction of the predator population upon dropping below critical numbers. Thus, we propose a simple mechanistic interpretation of important but still poorly understood behavioral phenomena that underlie the functioning of natural trophic systems.     

Invasion theory and biological control

Recent advances in the mathematical theory of invasion dynamics have much to offer to biological control. Here we synthesize several results concerning the spatiotemporal dynamics that occur when a biocontrol agent spreads into a population of an invading pest species. We outline conditions under which specialist and generalist predators can influence the density and rate of spatial spread of the pest, including the rather stringent conditions under which a specialist predator can successfully reverse a pest invasion. We next discuss the connections between long distance dispersal and invasive spread, emphasizing the different consequences of fast spreading pests and predators. Recent theory has considered the effects of population stage-structure on invasion dynamics, and we discuss how population demography affects the biological control of invading pests. Because low population densities generally characterize early stages of an invasion, we discuss the lessons invasion theory teaches concerning the detectability of invasions. Stochasticity and density-dependent dynamics are common features of many real invasions, influencing both the spatial character (e.g. patchiness) of pest invasions and the success of biocontrol agents. We conclude by outlining theoretical results delineating how stochastic effects and complex dynamics generated by density dependence can facilitate or impede biological pest control.     

Regional persistence of locally unstable predator/prey populations

Phytoseiid mites are efficient predators capable of completely destroying colonies of spider mites. Thus, coexistence of phytoseiids and their tetranychid prey at a local scale (typically an individual plant) is not likely for more than a single predator/prey cycle. However, the species may coexist at a regional scale, i.e. in a complex environment consisting of many plants, provided local colonisations, extinctions and recolonisations occur asynchronously. This review investigates some of the factors responsible for establishing and maintaining spatial asynchrony between local populations of prey and predators, such as dispersal, environmental heterogeneity and demographic stochasticity. Existing predator/prey models are considered in order to find agreement between theory and empirical data. Based on our current knowledge of spatial processes and their importance for the overall dynamics and persistence of predator/prey interactions, some consequences and aspects for biological control of crop pests by means of natural enemies are outlined.     

Population abundance and movement of Frankliniella species and Orius insidiosus in field pepper

1 A recent study revealed the capacity of the Orius insidiosus to suppress populations of Frankliniella spp. in field pepper during the spring when thrips are rapidly colonizing and reproducing. In this study, population abundance in pepper during spring, summer, and autumn was determined to understand better predator/prey dynamics under local conditions. Local movement between pepper flowers also was quantified to examine how population attributes of the predator allow suppression of rapidly moving populations of prey. 2 Randomized complete block experiments established in the autumn of 1998 and the spring of 1999 included treatments of biological and synthetic insecticides, which altered the population densities of predator and prey. Numbers of O. insidiosus in relation to prey were sufficient in 1998 to prevent build‐up of thrips populations. In 1999, populations of thrips were unable to recover from near extinction owing to persistence of the predator. The predator rapidly recolonized plots treated with insecticide. 3 Greenhouse plants of the same age as field plants were used to monitor movement by predators and prey. Movement by F. occidentalis was limited, whereas F. tritici and F. bispinosa moved rapidly to the greenhouse plants. The males of each thrips species moved more rapidly than the females. There was evidence that rapid movement assisted F. tritici and F. bispinosa in avoiding predation, but O. insidiosus also moved very rapidly to the greenhouse plants. This attribute explains the predator's ability to suppress thrips rapidly even when populations are rapidly colonizing and reproducing in the flowers.     

How population loss through habitat boundaries determines the dynamics of a predator–prey system

The increased persistence of predator–prey systems when interactions are distributed through the space has been acknowledged by both empirical and theoretical studies. One salient feature of predator–prey interactions in heterogeneous space, for example, is the existence of cycles with reduced amplitude when compared with a homogeneous landscape. Although the role of spatial interactions in shaping the dynamics of predator–prey systems has been extensively studied, still very few works have focused on the effects of habitat loss and fragmentation on these systems. In this work, we study the population dynamics of a predator–prey system in a single finite habitat with flux at the boundaries. Species movement and growth are described through a reaction–diffusion model with Rosenzweig–MacArthur type local interactions. Conforming with the existing literature, we find that the reduction of habitat size, or increasing of species movement rates equivalently, has the potential to decrease the amplitude of oscillations and even bring the system to a steady coexistence equilibrium above a threshold. We observe, however, situations in which this trend is reversed. This occurs when species movement rates and response at patch boundaries interact to induce non-trivial patterns of species distributions. These distributions are characterized by anti-correlation between predator and prey, creating then spatial refugia for prey. Our results highlight the role of population loss through habitat boundaries in determining the dynamics of predator–prey interactions.     

The dynamics of two diffusively coupled predator-prey populations

I analyze the dynamics of predator and prey populations living in two patches. Within a patch the prey grow logistically and the predators have a Holling type II functional response. The two patches are coupled through predator migration. The system can be interpreted as a simple predator-prey metapopulation or as a spatially explicit predator-prey system. Asynchronous local dynamics are presumed by metapopulation theory. The main question I address is when synchronous and when asynchronous dynamics arise. Contrary to biological intuition, for very small migration rates the oscillations always synchronize. For intermediate migration rates the synchronous oscillations are unstable and I found periodic, quasi-periodic, and intermittently chaotic attractors with asynchronous dynamics. For large predator migration rates, attractors in the form of equilibria or limit cycles exist in which one of the patches contains no prey. The dynamical behavior of the system is described using bifurcation diagrams. The model shows that spatial predator-prey populations can be regulated through the interplay of local dynamics and migration.     

Bottom‐up processes drive reproductive success in an apex predator

One of the central goals of the field of population ecology is to identify the drivers of population dynamics, particularly in the context of predator–prey relationships. Understanding the relative role of top‐down versus bottom‐up drivers is of particular interest in understanding ecosystem dynamics. Our goal was to explore predator–prey relationships in a boreal ecosystem in interior Alaska through the use of multispecies long‐term monitoring data. We used 29 years of field data and a dynamic multistate site occupancy modeling approach to explore the trophic relationships between an apex predator, the golden eagle, and cyclic populations of the two primary prey species available to eagles early in the breeding season, snowshoe hare and willow ptarmigan. We found that golden eagle reproductive success was reliant on prey numbers, but also responded prior to changes in the phase of the snowshoe hare population cycle and failed to respond to variation in hare cycle amplitude. There was no lagged response to ptarmigan populations, and ptarmigan populations recovered quickly from the low phase. Together, these results suggested that eagle reproduction is largely driven by bottom‐up processes, with little evidence of top‐down control of either ptarmigan or hare populations. Although the relationship between golden eagle reproductive success and prey abundance had been previously established, here we established prey populations are likely driving eagle dynamics through bottom‐up processes. The key to this insight was our focus on golden eagle reproductive parameters rather than overall abundance. Although our inference is limited to the golden eagle–hare–ptarmigan relationships we studied, our results suggest caution in interpreting predator–prey abundance patterns among other species as strong evidence for top‐down control.     

Predation across spatial scales in heterogeneous environments

A hierarchy of scales is introduced to the spatially heterogeneous Lotka-Volterra predator-prey diffusion model, and its effects on the model's spatial and temporal behavior are studied. When predators move on a large scale relative to prey, local coupling of the predator-prey interaction is replaced by global coupling. Prey with low dispersal ability become narrowly confined to the most productive habitats, strongly amplifying the underlying spatial pattern of the environment. As prey diffusion rate increases, the prey distribution spreads out and predator abundance declines. The model retains neutrally stable Lotka-Volterra temporal dynamics: different scales of predator and prey dispersal do not stabilize the interaction. The model predicts that, for prey populations that are limited by widely ranging predators, species with low dispersal ability should be restricted to discrete high density patches, and those with greater mobility should be more uniformly distributed at lower density.