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.     

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.     

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     

The Effects of Predator Evolution and Genetic Variation on Predator–Prey Population-Level Dynamics

This paper explores how predator evolution and the magnitude of predator genetic variation alter the population-level dynamics of predator–prey systems. We do this by analyzing a general eco-evolutionary predator–prey model using four methods: Method 1 identifies how eco-evolutionary feedbacks alter system stability in the fast and slow evolution limits; Method 2 identifies how the amount of standing predator genetic variation alters system stability; Method 3 identifies how the phase lags in predator–prey cycles depend on the amount of genetic variation; and Method 4 determines conditions for different cycle shapes in the fast and slow evolution limits using geometric singular perturbation theory. With these four methods, we identify the conditions under which predator evolution alters system stability and shapes of predator–prey cycles, and how those effect depend on the amount of genetic variation in the predator population. We discuss the advantages and disadvantages of each method and the relations between the four methods. This work shows how the four methods can be used in tandem to make general predictions about eco-evolutionary dynamics and feedbacks.     

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.     

One New Species and One New Record ofJumping Spiders （Araneae： Salticidae） from India

This paper presents the first result of the study on the jumping spiders collected during the India 2002 Expedition held by P. Sipek and M. Fikacek from the Charles University, Prague. Hitherto only 3 species of the genus Curubis were known from Sri Lanka, no females were found (SIMON 1902, ZABKA 1988, PROSZYNSKI 2003). A new species from India, Curubis sipeki sp. nov. (also only in male sex), is described. Bristowia heterospinosa REIMOSER, 1934 is reported for the first time from India.     

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...     

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.     

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.     

A Jump-Growth Model for Predator–Prey Dynamics: Derivation and Application to Marine Ecosystems

This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master equation, we derive a deterministic equation for the macroscopic dynamics, which we call the deterministic jump-growth equation, and a linear Fokker–Planck equation for the stochastic fluctuations. The McKendrick–von Foerster equation, used in previous studies, is shown to be a first-order approximation, appropriate in equilibrium systems where predators are much larger than their prey. The model has a power-law steady state consistent with the approximate constancy of mass density in logarithmic intervals of body mass often observed in marine ecosystems. The behaviours of the stochastic process, the deterministic jump-growth equation, and the McKendrick–von Foerster equation are compared using numerical methods. The numerical analysis shows two classes of attractors: steady states and travelling waves.     

Epithelial Polarity: Interactions Between Junctions and Apical–Basal Machinery

Epithelial polarity is established and maintained by competition between determinants that define the apical and basolateral domains. Cell–cell adhesion complexes, or adherens junctions, form at the interface of these regions. Mutations in adhesion components as well as apical determinants normally lead to an expansion of the basolateral domain. Here we investigate the genetic relationship between the polarity determinants and adhesion and show that the levels of the adhesion protein Armadillo affect competition. We find that in arm mutants, even a modest reduction in the basolateral component lgl leads to a full apical domain expansion or lgl phenotype. By using an allelic series of Armadillo mutations, we show that there is a threshold at which basolateral expansion can be reversed. Further, in embryos lacking the Wingless signaling component zw3, the same full apical expansion occurs again with only a reduction in lgl. We propose a model where zw3 regulates protein levels of apical and adhesion components and suggest that a reciprocal interaction between junctions and polarity modules functions to maintain stable apical and basolateral domains.A major reason that epithelial cells require apical–basal polarity is to differentiate between the interior of the organism and the external environment. To accomplish this, epithelial cells generate molecularly distinct domains along their plasma membranes: an apical domain that is exposed to the outside, a basolateral domain that contacts the interior, and, in between, an adhesion complex that holds the cell sheet together. In Drosophila embryos, at least three polarity complexes are used to establish and maintain this subcellular organization commonly known as apical–basal cell polarity. On the apical side, the Crumbs (Crb) and Stardust (Std, Pals) proteins form one complex (Jurgens et al. 1984; Tepass et al. 1990; Tepass and Knust 1993; Wodarz et al. 1995; Muller and Wieschaus 1996). The second one is composed of Bazooka (Baz, Par-3), Par-6, and atypical protein kinase C (aPKC) (Wieschaus et al. 1984; Muller and Wieschaus 1996; Wodarz et al. 2000; Hutterer et al. 2004). On the opposite or basolateral side of the cell, Lethal giant larvae (Lgl), Discs large (Dlg), and Scribble (Scrib) determine the basolateral domain of the plasma membrane (Gateff and Schneiderman 1974; Mechler et al. 1985; Woods and Bryant 1989; Bilder and Perrimon 2000). In between the complexes lie the adherens junctions (AJ) composed of E-cadherin, Armadillo (Arm, β-catenin), and α-catenin (Oda et al. 1993, 1994; Peifer et al. 1993; Tepass et al. 1996).In Drosophila embryos, mutations that affect apical components often lead to the crumbs phenotype, where ectodermal cells lose integrity and many die through apoptosis. The surviving cells secrete cuticle in a discontinuous fashion, leaving pieces apparently floating within the eggshell (Tepass et al. 1990; Tanentzapf and Tepass 2003). This phenotype is also seen in embryos deficient for AJ proteins (Oda et al. 1993; Cox et al. 1996; Magie et al. 2002). On the other hand, mutations that affect the basolateral genes display a very different phenotype. Zygotic only (Z) mutants for scrib, lgl, and dlg have a significant maternal mRNA contribution that allows normal embryonic development to proceed. Phenotypes are observed only in larvae, which die with significantly overgrown imaginal discs (Gateff 1978; Bilder and Perrimon 2000). Removal of the maternal mRNA complement, as well as the zygotic contribution (M/Z) through the induction of germline clones, leads to a poorly differentiated and convoluted cuticle with a bubbly appearance (Figure 1) (Bilder et al. 2003; Tanentzapf and Tepass 2003).Open in a separate windowFigure 1.—Schema and cuticles representing wild-type vs. the opposing phenotypes of apical and basolateral expansion. (A) A wild-type cuticle shows rows of denticles separated by naked regions in a highly organized or patterned fashion. The apical determinants localize to the apical surface of cells, establishing the apical domain (green), the basolateral determinants localize to the basolateral surface of cells, establishing the basolateral domain (blue), and the adherens junctions (red) form at the interface between these two opposing regions. (B) The crumbs phenotype is observed when an apical determinant is mutated, causing an expansion of the basolateral domain. (C) The lgl phenotype, or bubble phenotype, is observed when a basolateral determinant is mutated, causing an expansion of the apical domain.These studies led to a comprehensive competition model where apical and basal components opposed each other (Figure 1, schema); however, a strangely neglected topic was the interaction of junctions and the apical and basal determinants. Therefore, we used a genetic approach to investigate the interaction of apical–basal polarity proteins and adherens junctions.     

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.     

Multiple Limit Cycles in a Gause Type Predator–Prey Model with Holling Type III Functional Response and Allee Effect on Prey

This work aims to examine the global behavior of a Gause type predator–prey model considering two aspects: (i) the functional response is Holling type III and, (ii) the prey growth is affected by the Allee effect. We prove the origin of the system is an attractor equilibrium point for all parameter values. It has also been shown that it is the ω-limit of a wide set of trajectories of the system, due to the existence of a separatrix curve determined by the stable manifold of the equilibrium point (m,0), which is associated to the Allee effect on prey. When a weak Allee effect on the prey is assumed, an important result is obtained, involving the existence of two limit cycles surrounding a unique positive equilibrium point: the innermost cycle is unstable and the outermost stable. This property, not yet reported in models considering a sigmoid functional response, is an important aspect for ecologists to acknowledge as regards the kind of tristability shown here: (1) the origin; (2) an interior equilibrium; and (3) a limit cycle of large amplitude. These models have undoubtedly been rather sensitive to disturbances and require careful management in applied conservation and renewable resource contexts.     

Predator–prey interactions and the cannibalism of larvae of Armigeres subalbatus (Diptera: Culicidae)

Predation and cannibalism can affect the co-existence of mosquito species or the assemblage of mosquito species (i.e., community structure). In this study, predatory feeding patterns and cannibalism of larvae of Armigeres subalbatus mosquitoes were quantified under laboratory conditions using Aedes albopictus and Culex uniformis larvae as prey organisms. Rate of consumption of prey larvae and the rate of cannibalism of 1st to 4th instar larvae of Armigeres subalbatus were reported at 24 h intervals with and without alternative food supplement. Both the 3rd and 4th instar larvae of Ar. subalbatus showed a substantial predation on the larvae of Ae. albopictus (33.6 ± 4.4) and Cx uniformis (47.3 ± 7.6). The cannibalism of the predatory larvae was strongly correlated to the larval density (r = 0.9). The predator and the prey density and the given food type were significant factors that determined the rate of pupation, death and the emergence as adults. A significant relationship was shown for the co-occurrence of predatory larvae and the prey larvae at the 85 natural breeding habitats observed at the field (χ² = 74.4, p < 0.001). Nine breeding sites (10.6%) were positive for both prey and predatory larvae. Our study showed robust information about the predatory and cannibalistic behavior of Ar. subalbatus larvae emphasizing their role in managing the population structure of mosquito communities.     

Finite-Difference Schemes for Reaction–Diffusion Equations Modeling Predator–Prey Interactions in M<Emphasis Type="SmallCaps">ATLAB</Emphasis>

We present two finite-difference algorithms for studying the dynamics of spatially extended predator–prey interactions with the Holling type II functional response and logistic growth of the prey. The algorithms are stable and convergent provided the time step is below a (non-restrictive) critical value. This is advantageous as it is well-known that the dynamics of approximations of differential equations (DEs) can differ significantly from that of the underlying DEs themselves. This is particularly important for the spatially extended systems that are studied in this paper as they display a wide spectrum of ecologically relevant behavior, including chaos. Furthermore, there are implementational advantages of the methods. For example, due to the structure of the resulting linear systems, standard direct, and iterative solvers are guaranteed to converge. We also present the results of numerical experiments in one and two space dimensions and illustrate the simplicity of the numerical methods with short programs MATLAB. Users can download, edit, and run the codes from http://www.uoguelph.ca/~mgarvie/, to investigate the key dynamical properties of spatially extended predator–prey interactions.     

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.