Biological Conservation of a Prey–Predator System Incorporating Constant Prey Refuge Through Provision of Alternative Food to Predators: A Theoretical Study

We describe a prey–predator system incorporating constant prey refuge through provision of alternative food to predators. The proposed model deals with a problem of non-selective harvesting of a prey–predator system in which both the prey and the predator species obey logistic law of growth. The long-run sustainability of an exploited system is discussed through provision of alternative food to predators. We have analyzed the variability of the system in presence of constant prey refuge and examined the stabilizing effect on predator–prey system. The steady states of the system are derived and dynamical behavior of the system is extensively analyzed around steady states. The optimal harvesting policy is formulated and solved with the help of Pontryagin’s maximal principle. Our objective is to maximize the monetary social benefit through protecting the predator species from extinction, keeping the ecological balance. Results finally illustrated with the help of numerical examples.     

Impact of Fear in a Delayed Predator–Prey System with Prey Refuge in Presence of Additional Food

Biophysics - It is observed from field experiments on terrestrial vertebrates that direct predation on predator–prey interaction can not only affect the population dynamics but the indirect...     

Modelling Disease Introduction as Biological Control of Invasive Predators to Preserve Endangered Prey

Invasive species are a significant cause of bio-diversity loss particularly in island ecosystems. It has been suggested to release pathogenic parasites as an efficient control measure of these mostly immune-naïve populations. In order to explore the potential impacts of such bio-control approach, we construct and investigate mathematical models describing disease dynamics in a host population that acts as a predator embedded in a simple food chain. The consequences of Feline Immunodeficiency Virus (FIV) introduction into a closed ecosystem are addressed using a bi-trophic system, comprising an indigenous prey (birds) and an introduced predator (cats). Our results show that FIV is unlikely to fully eradicate cats on sub-Antarctic islands, but it can be efficient in depressing their population size, allowing for the recovery of the endangered prey. Depending on the ecological setting and disease transmission mode (we consider proportionate mixing as well as mass action), successful pathogen invasion can induce population oscillations that are not possible in the disease-free predator–prey system. These fluctuations can be seen as a mixed blessing from a management point of view. On the one hand, they may increase the extinction risk of the birds. On the other hand, they provide an opportunity to eradicate cats more easily in combination with other methods such as trapping or culling.     

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.     

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.     

Community Response of Mammalian Predators and Their Prey to Motorways: Implications for Predator–Prey Dynamics

Understanding the interactions between predators and prey is essential for predicting the effects of disturbances to ecosystems. Motorways produce changes in the surrounding biotic and abiotic environment and hence have multiple impacts on wildlife. Some species are known to change their activity patterns in the proximity of motorways but the implications for the structure of food webs are unknown. This study analyzes the activity patterns of both mammalian predators and their prey species near nine motorways in attempt to clarify how motorways affect the mammalian community. Habitat structural variables were also sampled to control the effects of microhabitat on relative prey abundance. Our results revealed different activity patterns of both predators and prey near motorways that are independent of structural differences in microhabitat. Both the red fox and small mammals were found to use the zone close to the motorways more frequently, whereas lagomorphs and mustelids were less active there. These differences suggest that motorways favor the population of the predator that is most tolerant of human activity, the red fox, whose activity could have both direct and indirect effects on that of other members of the predator and prey community. On the one hand, the red fox seems to act as “top predator” and mustelids to follow a “safety match” strategy avoiding the area close to the motorway where fox is more active. On the other hand, abundances of prey species are negatively associated with the activity of their most frequent predators. This study is the first to assess how the proximity to motorways affects the activity of mammals in two levels of the food web and opens the field for research to understand the processes driving the detected patterns. Moreover, such effects at the community scale should be taken into account when evaluating the impacts of motorways on the surrounding ecosystems.     

Dynamics of a Prey–Predator System with Herd Behaviour in Both and Strong Allee Effect in Prey

Biophysics - This paper mainly deals with the prey?predator dynamics where both the prey and predator exhibit herd behavior. Positivity, boundedness, some extinction criteria, stability of...     

Optimal Culling and Biocontrol in a Predator–Prey Model

Invasive species cause enormous problems in ecosystems around the world. Motivated by introduced feral cats that prey on bird populations and threaten to drive them extinct on remote oceanic islands, we formulate and analyze optimal control problems. Their novelty is that they involve both scalar and time-dependent controls. They represent different forms of control, namely the initial release of infected predators on the one hand and culling as well as trapping, infecting, and returning predators on the other hand. Combinations of different control methods have been proposed to complement their respective strengths in reducing predator numbers and thus protecting endangered prey. Here, we formulate and analyze an eco-epidemiological model, provide analytical results on the optimal control problem, and use a forward–backward sweep method for numerical simulations. By taking into account different ecological scenarios, initial conditions, and control durations, our model allows to gain insight how the different methods interact and in which cases they could be effective.     

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...     

The Role of Viral Infection in Pest Control: A Mathematical Study

In this paper, we propose a mathematical model of viral infection in pest control. As the viral infection induces host lysis which releases more virus into the environment, on the average ‘κ’ viruses per host, κ∈(1,∞), so the ‘virus replication parameter’ is chosen as the main parameter on which the dynamics of the infection depends. There exists a threshold value κ ₀ beyond which the infection persists in the system. Still for increasing the value of κ, the endemic equilibrium bifurcates towards a periodic solution, which essentially indicates that the viral pesticide has a density-dependent ‘numerical response’ component to its action. Investigation also includes the dependence of the process on predation of natural enemy into the system. A concluding discussion with numerical simulation of the model is also presented.     

Permanence and Extinction of a Diffusive Predator–Prey Model with Robin Boundary Conditions

The main concern of this paper is to study the dynamic of a predator–prey system with diffusion. It incorporates the Holling-type-II and a modified Leslie–Gower functional responses under Robin boundary conditions. More concretely, we study the dissipativeness of the system by using the comparison principle, and we derive a criteria for permanence and for predator extinction.     

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...     

Does Intraspecific Size Variation in a Predator Affect Its Diet Diversity and Top-Down Control of Prey?

It has long been known that intraspecific variation impacts evolutionary processes, but only recently have its potential ecological effects received much attention. Theoretical models predict that genetic or phenotypic variance within species can alter interspecific interactions, and experiments have shown that genotypic diversity in clonal species can impact a wide range of ecological processes. To extend these studies to quantitative trait variation within populations, we experimentally manipulated the variance in body size of threespine stickleback in enclosures in a natural lake environment. We found that body size of stickleback in the lake is correlated with prey size and (to a lesser extent) composition, and that stickleback can exert top-down control on their benthic prey in enclosures. However, a six-fold contrast in body size variance had no effect on the degree of diet variation among individuals, or on the abundance or composition of benthic or pelagic prey. Interestingly, post-hoc analyses revealed suggestive correlations between the degree of diet variation and the strength of top-down control by stickleback. Our negative results indicate that, unless the correlation between morphology and diet is very strong, ecological variation among individuals may be largely decoupled from morphological variance. Consequently we should be cautious in our interpretation both of theoretical models that assume perfect correlations between morphology and diet, and of empirical studies that use morphological variation as a proxy for resource use diversity.     

Modeling the Effect of Prey Refuge on a Ratio-Dependent Predator–Prey System with the Allee Effect

The extinction of species is a major threat to the biodiversity. The species exhibiting a strong Allee effect are vulnerable to extinction due to predation. The refuge used by species having a strong Allee effect may affect their predation and hence extinction risk. A mathematical study of such behavioral phenomenon may aid in management of many endangered species. However, a little attention has been paid in this direction. In this paper, we have studied the impact of a constant prey refuge on the dynamics of a ratio-dependent predator–prey system with strong Allee effect in prey growth. The stability analysis of the model has been carried out, and a comprehensive bifurcation analysis is presented. It is found that if prey refuge is less than the Allee threshold, the incorporation of prey refuge increases the threshold values of the predation rate and conversion efficiency at which unconditional extinction occurs. Moreover, if the prey refuge is greater than the Allee threshold, situation of unconditional extinction may not occur. It is found that at a critical value of prey refuge, which is greater than the Allee threshold but less than the carrying capacity of prey population, system undergoes cusp bifurcation and the rich spectrum of dynamics exhibited by the system disappears if the prey refuge is increased further.     

A New Stochastic Individual-Based Model for Pattern Formation and its Application to Predator–Prey Systems

Reaction–diffusion theory has played a very important role in the study of pattern formation in biology. However, a group of individuals is described by a single state variable representing population density in reaction–diffusion models, and interaction between individuals can be included only phenomenologically. In this paper, we propose a new scheme that seamlessly combines individual-based models with elements of reaction–diffusion theory and apply it to predator–prey systems as a test of our scheme. In the model, starvation periods and the time to reproductive maturity are modeled for individual predators. Similarly, the life cycle and time to reproductive maturity of an individual prey are modeled. Furthermore, both predators and prey migrate through a two-dimensional space. To include animal migration in the model, we use a relationship between the diffusion and the random numbers generated according to a two-dimensional bivariate normal distribution. Despite the simplicity of this model, our scheme successfully produces logistic patterns and oscillations in the population size of both predator and prey. The peak for the predator population oscillation lags slightly behind the prey peak. The simplicity of this scheme will aid additional study of spatially distributed negative-feedback systems.     

Pattern Formation,Long-Term Transients,and the Turing–Hopf Bifurcation in a Space- and Time-Discrete Predator–Prey System

Understanding of population dynamics in a fragmented habitat is an issue of considerable importance. A natural modelling framework for these systems is spatially discrete. In this paper, we consider a predator–prey system that is discrete both in space and time, and is described by a Coupled Map Lattice (CML). The prey growth is assumed to be affected by a weak Allee effect and the predator dynamics includes intra-specific competition. We first reveal the bifurcation structure of the corresponding non-spatial system. We then obtain the conditions of diffusive instability on the lattice. In order to reveal the properties of the emerging patterns, we perform extensive numerical simulations. We pay a special attention to the system properties in a vicinity of the Turing–Hopf bifurcation, which is widely regarded as a mechanism of pattern formation and spatiotemporal chaos in space-continuous systems. Counter-intuitively, we obtain that the spatial patterns arising in the CML are more typically stationary, even when the local dynamics is oscillatory. We also obtain that, for some parameter values, the system’s dynamics is dominated by long-term transients, so that the asymptotical stationary pattern arises as a sudden transition between two different patterns. Finally, we argue that our findings may have important ecological implications.     

Linear and Weakly Nonlinear Stability Analyses of Turing Patterns for Diffusive Predator–Prey Systems in Freshwater Marsh Landscapes

We study a diffusive predator–prey model describing the interactions of small fishes and their resource base (small invertebrates) in the fluctuating freshwater marsh landscapes of the Florida Everglades. The spatial model is described by a reaction–diffusion system with Beddington–DeAngelis functional response. Uniform bound, local and global asymptotic stability of the steady state of the PDE model under the no-flux boundary conditions are discussed in details. Sufficient conditions on the Turing (diffusion-driven) instability which induces spatial patterns in the model are derived via linear analysis. Existence of one-dimensional and two-dimensional spatial Turing patterns, including rhombic and hexagonal patterns, are established by weakly nonlinear analyses. These results provide theoretical explanations and numerical simulations of spatial dynamical behaviors of the wetland ecosystems of the Florida Everglades.     

Do Behavioral Foraging Responses of Prey to Predators Function Similarly in Restored and Pristine Foodwebs?

Efforts to restore top predators in human-altered systems raise the question of whether rebounds in predator populations are sufficient to restore pristine foodweb dynamics. Ocean ecosystems provide an ideal system to test this question. Removal of fishing in marine reserves often reverses declines in predator densities and size. However, whether this leads to restoration of key functional characteristics of foodwebs, especially prey foraging behavior, is unclear. The question of whether restored and pristine foodwebs function similarly is nonetheless critically important for management and restoration efforts. We explored this question in light of one important determinant of ecosystem function and structure--herbivorous prey foraging behavior. We compared these responses for two functionally distinct herbivorous prey fishes (the damselfish Plectroglyphidodon dickii and the parrotfish Chlorurus sordidus) within pairs of coral reefs in pristine and restored ecosystems in two regions of these species' biogeographic ranges, allowing us to quantify the magnitude and temporal scale of this key ecosystem variable's recovery. We demonstrate that restoration of top predator abundances also restored prey foraging excursion behaviors to a condition closely resembling those of a pristine ecosystem. Increased understanding of behavioral aspects of ecosystem change will greatly improve our ability to predict the cascading consequences of conservation tools aimed at ecological restoration, such as marine reserves.     

Effects of Temperature and Turbulence on the Predator–Prey Interactions between a Heterotrophic Flagellate and a Marine Bacterium

Biotic and abiotic factors can influence interactions between microbial grazers and their prey, thus impacting both the cycling of biogenic carbon within the surface layer of the ocean and the export of carbon to the deep ocean and higher trophic levels. In this study, microcosm experiments were used to evaluate the combined effect of temperature and turbulence on the growth rate of a marine bacterium (Vibrio splendidus), a protistan predator (Paraphysomonas sp.), and the community grazing impact of Paraphysomonas sp. on V. splendidus. It was found that the artificial turbulence generated (1.35 × 10⁻¹ cm² s⁻³) significantly increased the rates of growth of Paraphysomonas sp. at high (>10°C), but not low (<5°C) temperatures, and that turbulence had no effect on the growth of V. splendidus. Both flagellate and bacterial growth were temperature dependent and decreased 4- to 6-fold as temperatures decreased from 15 to 0°C. Bacterial grazing mortality by Paraphysomonas sp. was 1.3- to 2.5-fold greater in the turbulent than static treatments among all four temperatures, and the rates of cell-specific ingestion of bacteria by Paraphysomonas sp. was 2-fold greater at 15 and 10°C in the turbulent than in the static treatment. Hence, this study shows that turbulence can influence nanoflagellate grazing at temperatures >5°C and suggests that at low temperatures, increased viscosity may limit the size of organisms that can be affected by small-scale turbulence.Present address (M.P. Delaney): Goddard Earth Sciences & Technology Center, NASA Goddard Space Flight Center, Mail Code 900.1, Greenbelt, MD 20771     

Soybean Aphid Predators in Québec and the Suitability of Aphis glycines as Prey for Three Coccinellidae

Since its invasion of North America in 2000, the soybean aphid, Aphis glycines Matsumura (Homoptera: Aphididae) has notably changed the arthropod community of the soybean agroecosystem. The objectives of this study were to characterize the foliar predatory fauna associated with A. glycines in commercial soybean fields in Québec, Canada, and to evaluate the suitability of A. glycines as prey for three coccinellid species: Harmonia axyridis Pallas, Propylea quatuordecimpunctata L. and Coleomegilla maculata lengi Timberlake (Coleoptera: Coccinellidae). Field surveys showed that several predators responded rapidly to expanding and increasing populations of the soybean aphid. Coccinellidae were the most important aphidophagous predators observed in 2002 (58.6%) and 2003 (44.8%), with mainly four native and naturalized species co-occurring with the soybean aphid throughout the growing season. Measurement of fitness parameters under laboratory conditions (survival, development time, longevity, fecundity) indicated that A. glycines is an excellent prey for the development and reproduction of all three of the coccinellid species studied. The intrinsic rate of natural increase (r_m) was highest for H. axyridis (0.238 d⁻¹), intermediate for P. quatuordecimpunctata (0.215 d⁻¹) and lowest for C. maculata (0.134 d⁻¹).