Parametric Analysis of a Predator–prey System Stabilized by a Top Predator

We present a complete parametric analysis of a predator–prey system influenced by a top predator. We study ecosystems with abundant nutrient supply for the prey where the prey multiplication can be considered as proportional to its density. The main questions we examine are the following: (1) Can the top predator stabilize such a system at low densities of prey? (2) What possible dynamic behaviors can occur? (3) Under which conditions can the top predation result in the system stabilization? We use a system of two nonlinear ordinary differential equations with the density of the top predator as a parameter. The model is investigated with methods of qualitative theory of ODEs and the theory of bifurcations. The existence of 12 qualitatively different types of dynamics and complex structure of the parametric space are demonstrated. Our studies of phase portraits and parametric diagrams show that a top predator can be an important factor leading to stabilization of the predator-prey system with abundant nutrient supply. Although the model here is applied to the plankton communities with fish (or carnivorous zooplankton) as the top trophic level, the general form of the equations allows applications of our results to other ecological systems.     

How Predator Food Preference can Change the Destiny of Native Prey in Predator–Prey Systems

The aim of this work is to develop and analyse a mathematical model for a predator-2 preys system arising in insular environments. We are interested in the evolution of a native prey population without behavioural traits to cope with predation or competition, after the introduction of alien species. Here, we consider a long living bird population with low fertility rate. We point out the effects of the preference of the predator for either juvenile or adult stages. In addition, we study the impact of alien prey introduction in such a model. We use a reaction-diffusion system with a singular logistic right hand side. The aim of this work is to bring interesting dynamics to the fore. As a first example, oscillatory behaviour takes place in the model without alien preys and when predators have an average preference coefficient. Introduction of alien preys can lead to species extinction.     

Predator–prey system with strong Allee effect in prey

Global bifurcation analysis of a class of general predator–prey models with a strong Allee effect in prey population is given in details. We show the existence of a point-to-point heteroclinic orbit loop, consider the Hopf bifurcation, and prove the existence/uniqueness and the nonexistence of limit cycle for appropriate range of parameters. For a unique parameter value, a threshold curve separates the overexploitation and coexistence (successful invasion of predator) regions of initial conditions. Our rigorous results justify some recent ecological observations, and practical ecological examples are used to demonstrate our theoretical work.     

Modeling of Multifactor Taxis in a Predator–Prey System

Biophysics - A model of predator–prey dynamics in a spatially heterogeneous range is considered using a system of two nonlinear equations of the diffusion–advection reaction. The...     

Impacts of Biotic Resource Enrichment on a Predator–Prey Population

The environmental carrying capacity is usually assumed to be fixed quantity in the classical predator–prey population growth models. However, this assumption is not realistic as the environment generally varies with time. In a bid for greater realism, functional forms of carrying capacities have been widely applied to describe varying environments. Modelling carrying capacity as a state variable serves as another approach to capture the dynamical behavior between population and its environment. The proposed modified predator–prey model is based on the ratio-dependent models that have been utilized in the study of food chains. Using a simple non-linear system, the proposed model can be linked to an intra-guild predation model in which predator and prey share the same resource. Distinct from other models, we formulate the carrying capacity proportional to a biotic resource and both predator and prey species can directly alter the amount of resource available by interacting with it. Bifurcation and numerical analyses are presented to illustrate the system’s dynamical behavior. Taking the enrichment parameter of the resource as the bifurcation parameter, a Hopf bifurcation is found for some parameter ranges, which generate solutions that posses limit cycle behavior.     

Predator–prey interactions and changing environments: who benefits?

While aquatic environments have long been thought to be more moderate environments than their terrestrial cousins, environmental data demonstrate that for some systems this is not so. Numerous important environmental parameters can fluctuate dramatically, notably dissolved oxygen, turbidity and temperature. The roles of dissolved oxygen and turbidity on predator-prey interactions have been discussed in detail elsewhere within this issue and will be considered only briefly here. Here, we will focus primarily on the role of temperature and its potential impact upon predator-prey interactions. Two key properties are of particular note. For temperate aquatic ecosystems, all piscine and invertebrate piscivores and their prey are ectothermic. They will therefore be subject to energetic demands that are significantly affected by environmental temperature. Furthermore, the physical properties of water, particularly its high thermal conductivity, mean that thermal microenvironments will not exist so that fine-scale habitat movements will not be an option for dealing with changing water temperature in lentic environments. Unfortunately, there has been little experimental analysis of the role of temperature on such predator-prey interactions, so we will instead focus on theoretical work, indicating that potential implications associated with thermal change are unlikely to be straightforward and may present a greater threat to predators than to their prey. Specifically, we demonstrate that changes in the thermal environment can result in a net benefit to cold-adapted species through the mechanism of predator-prey interactions.     

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.     

Adaptive Control Based Harvesting Strategy for a Predator–Prey Dynamical System

This paper deals with designing a harvesting control strategy for a predator–prey dynamical system, with parametric uncertainties and exogenous disturbances. A feedback control law for the harvesting rate of the predator is formulated such that the population dynamics is asymptotically stabilized at a positive operating point, while maintaining a positive, steady state harvesting rate. The hierarchical block strict feedback structure of the dynamics is exploited in designing a backstepping control law, based on Lyapunov theory. In order to account for unknown parameters, an adaptive control strategy has been proposed in which the control law depends on an adaptive variable which tracks the unknown parameter. Further, a switching component has been incorporated to robustify the control performance against bounded disturbances. Proofs have been provided to show that the proposed adaptive control strategy ensures asymptotic stability of the dynamics at a desired operating point, as well as exact parameter learning in the disturbance-free case and learning with bounded error in the disturbance prone case. The dynamics, with uncertainty in the death rate of the predator, subjected to a bounded disturbance has been simulated with the proposed control strategy.     

Bayesian Inference for Functional Response in a Stochastic Predator–Prey System

We present a Bayesian method for functional response parameter estimation starting from time series of field data on predator–prey dynamics. Population dynamics is described by a system of stochastic differential equations in which behavioral stochasticities are represented by noise terms affecting each population as well as their interaction. We focus on the estimation of a behavioral parameter appearing in the functional response of predator to prey abundance when a small number of observations is available. To deal with small sample sizes, latent data are introduced between each pair of field observations and are considered as missing data. The method is applied to both simulated and observational data. The results obtained using different numbers of latent data are compared with those achieved following a frequentist approach. As a case study, we consider an acarine predator–prey system relevant to biological control problems.     

Can Camera Traps Monitor Komodo Dragons a Large Ectothermic Predator?

Camera trapping has greatly enhanced population monitoring of often cryptic and low abundance apex carnivores. Effectiveness of passive infrared camera trapping, and ultimately population monitoring, relies on temperature mediated differences between the animal and its ambient environment to ensure good camera detection. In ectothermic predators such as large varanid lizards, this criterion is presumed less certain. Here we evaluated the effectiveness of camera trapping to potentially monitor the population status of the Komodo dragon (Varanus komodoensis), an apex predator, using site occupancy approaches. We compared site-specific estimates of site occupancy and detection derived using camera traps and cage traps at 181 trapping locations established across six sites on four islands within Komodo National Park, Eastern Indonesia. Detection and site occupancy at each site were estimated using eight competing models that considered site-specific variation in occupancy (ψ)and varied detection probabilities (p) according to detection method, site and survey number using a single season site occupancy modelling approach. The most parsimonious model [ψ (site), p (site*survey); ω = 0.74] suggested that site occupancy estimates differed among sites. Detection probability varied as an interaction between site and survey number. Our results indicate that overall camera traps produced similar estimates of detection and site occupancy to cage traps, irrespective of being paired, or unpaired, with cage traps. Whilst one site showed some evidence detection was affected by trapping method detection was too low to produce an accurate occupancy estimate. Overall, as camera trapping is logistically more feasible it may provide, with further validation, an alternative method for evaluating long-term site occupancy patterns in Komodo dragons, and potentially other large reptiles, aiding conservation of this species.     

Predator–prey ratios on cocoa along a land-use gradient in Indonesia

Tropical landscapes are dominated by agroecosystems, but the potential value of agroecosystems for the survival of species is often overlooked. In agroecosystems, species conservation is especially important when functional groups such as predators are affected. In Central Sulawesi, we sampled arthropods on cocoa in a gradient of land-use intensity from extensively used forest gardens to intensively used agroforestry systems. The abundance and diversity of all arthropods did not correlate with land-use intensity, so human impact was not followed by high species losses. However, the number of species and abundance of the phytophagous arthropods increased and that of the entomophagous arthropods decreased with land-use intensity. The reduced predator–prey ratio in intensified systems can be related to their reduced species richness of shade trees and the changed microclimate (increased temperature, decreased humidity and canopy cover). In conclusion, transformation of traditional into intensified agroforestry systems had a great impact on arthropod community structure on cocoa. Since predator–prey ratios decreased with increasing land-use intensity, local farmers should have least pest problems in the traditionally diversified agroforestry systems.     

Predator migration in response to prey density: What are the consequences?

A predator-prey metapopulation model with two identical patches and only migration of the predator is investigated. Local predator-prey interaction is described by the so-called Rosenzweig-MacArthur model, while the migration term of the predator is put in a nonlinear form, which is derived by extending the Holling time budget argument to migration. In particular, a dimensionless parameter theta is introduced to quantify the migration tendency of predators while they are handling their prey, which gives rise to a family of models connecting two extremes: predators have no inclination to migrate while handling prey (theta = 0) and standard diffusion (theta = 1). Various aspects of the model, including changes in the number and the stability of equilibria and limit cycles, are investigated. We then focus on the key question: "Does spatial structure lead to a substantial damping of the violent oscillations exhibited by many predator-prey models?". It is known that the answer is "yes" if one adopts standard diffusion (theta = 1). However, we present substantial evidence that the answer is "no" if one takes theta = 0. We conclude that the migration submodel is an important constituent of a spatial predator-prey model and that the issue deserves scrutiny, both experimentally and theoretically.     

Along Came a Spider: Using Live Arthropods in a Predator–Prey Activity

We developed a predator–prey activity with eighth-grade students in which they used wolf spiders (Lycosa carolinensis), house crickets (Acheta domestica), and abiotic factors to address how (1) adaptations in predators and prey shape their interaction and (2) abiotic factors modify the interaction between predators and prey. We tested student understanding with pre- and postquizzes, written observations, and interpretations of graphical results.     

The Ideal Free Distribution in a Predator–Prey Model with Multifactor Taxis

Biophysics - The concept of an ideal free distribution (IFD) is analyzed for the predator–prey system in an inhomogeneous ring-shaped habitat. Diffusion–reaction–advection...     

Shedding Light on Microbial Predator–Prey Population Dynamics Using a Quantitative Bioluminescence Assay

This study assessed the dynamics of predation by Bdellovibrio bacteriovorus HD 100. Predation tests with two different bioluminescent strains of Escherichia coli, one expressing a heat-labile bacterial luciferase and the other a heat-stable form, showed near identical losses from both, indicating that protein expression and stability are not responsible for the “shutting-off” of the prey bioluminescence (BL). Furthermore, it was found that the loss in the prey BL was not proportional with the predator-to-prey ratio (PPR), with significantly greater losses seen as this value was increased. This suggests that other factors also play a role in lowering the prey BL. The loss in BL, however, was very consistent within nine independent experiments to the point that we were able to reliably estimate the predator numbers within only 1 h when present at a PPR of 6 or higher, Using a fluorescent prey, we found that premature lysis of the prey occurs at a significant level and was more prominent as the PPR ratio increased. Based upon the supernatant fluorescent signal, even a relatively low PPR of 10–20 led to approximately 5 % of the prey population being prematurely lysed within 1 h, while a PPR of 90 led to nearly 15 % lysis. Consequently, we developed a modified Lotka–Volterra predator–prey model that accounted for this lysis and is able to reliably estimate the prey and bdelloplast populations for a wide range of PPRs.     

Evidence for the Predator Attraction Hypothesis in an amphibian predator–prey system

Many species possess damage-released chemical alarm cues that function in alerting nearby individuals to a predator attack. One hypothesis for the evolution and/or maintenance of such cues is the Predator Attraction Hypothesis, where predators, rather than prey, are the “intended” recipients of these cues. If a predator attack attracts additional predators, these secondary predators might interfere with the predation event, providing the prey with a better chance to escape. In this study, we conducted two experiments to explore this hypothesis in an amphibian predator/prey system. In Experiment 1, we found that tiger salamanders (Ambystoma mavortium) showed a foraging attraction to chemical cues from wood frog (Lithobates sylvaticus) tadpoles. Salamanders that were experienced with tadpole prey, in particular, were strongly attracted to tadpole alarm cues. In Experiment 2, we observed experimental encounters between a tadpole and either one or two salamanders. The presence of the second predator caused salamanders to increase attack speed at the cost of decreased attack accuracy (i.e., increasing the probability that the tadpole would escape attacks). We also found that the mere presence of visual and chemical cues from a second predator did not affect this speed/accuracy trade-off but did cause enough of a distraction to increase tadpole survival. Thus, our findings are consistent with the Predator Attraction Hypothesis for the evolution and/or maintenance of alarm cues.     

Alternative Prey and Abundance Covariance Switches an Intraguild Predator’s Functional Response

Positive or negative prey abundance covariances play an important role in determining prey preference of predators. The goal here was to understand how variations in abundance of two blowfly prey species, a native and a non-native species, influence the switching behavior and functional response of Chrysomya albiceps, an intraguild predatory blowfly, under laboratory conditions. The results suggest C. albiceps prefers to consume a native prey species rather than a non-native prey species. However, when prey densities covariate negatively, both species were consumed at the same rate, changing predator’s functional response from type II to type III. The conditions that trigger the switching behavior in blowfly communities are discussed in detail in this study.     

Modeling the Fear Effect in Predator–Prey Interactions with Adaptive Avoidance of Predators

Recent field experiments on vertebrates showed that the mere presence of a predator would cause a dramatic change of prey demography. Fear of predators increases the survival probability of prey, but leads to a cost of prey reproduction. Based on the experimental findings, we propose a predator–prey model with the cost of fear and adaptive avoidance of predators. Mathematical analyses show that the fear effect can interplay with maturation delay between juvenile prey and adult prey in determining the long-term population dynamics. A positive equilibrium may lose stability with an intermediate value of delay and regain stability if the delay is large. Numerical simulations show that both strong adaptation of adult prey and the large cost of fear have destabilizing effect while large population of predators has a stabilizing effect on the predator–prey interactions. Numerical simulations also imply that adult prey demonstrates stronger anti-predator behaviors if the population of predators is larger and shows weaker anti-predator behaviors if the cost of fear is larger.     

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.