Autonomic tuning of a two predator,one prey system via commensalism

A single equilibrium point consisting of two predators has been said to be infinitely improbable [1]. It is shown here however that a simple modification of one parameter, to incorporate commensal foraging, can facilitate autonomic tuning of the predation rate of the commensalist and so enable the two predators to coexist. Conditions for the existence, and the stability of the equilibrium point are derived. An application of the model to the relationship between tuna and dolphin is briefly discussed.     

Scale-dependent indirect interactions between two prey species through a shared predator

We investigated the potential for indirect interactions between two prey species, pea aphids ( Acyrthosiphon pisum ) and potato leafhoppers ( Empoasca fabae ), through a shared predator (Nabis spp.), and how these interactions may change across three spatial scales. In greenhouse experiments using small clusters of plants containing pea aphids and/or potato leafhoppers, the predation rates on both pea aphids and potato leafhoppers were independent of the presence of the other species, indicating no indirect interactions. In greenhouse experiments using cages containing 48 plants, when aphids and leafhoppers were confined to separate plants among which nabids could move, pea aphids had a positive effect on the survival of potato leafhoppers from predation. The positive effect of aphids on leafhoppers occurred because nabids spent more time on plants harboring aphids, thereby drawing nabids away from plants containing leafhoppers. Finally, we measured the abundance of nabids in a large-scale experiment designed to manipulate the abundances of pea aphids and potato leafhoppers in alfalfa fields. Fields with high aphid density contained more nabids, thereby suggesting that pea aphids will have a negative indirect effect on potato leafhoppers by increasing the density of nabids within fields. Potato leafhoppers had no indirect effects on pea aphids at any scale. This study shows that indirect interactions between prey species may depend upon spatial scale, because the factors affecting a predator's diet choice on a small scale may differ from those factors affecting a predator's distribution at larger scales.     

Flip bifurcation and Neimark-Sacker bifurcation in a discrete predator prey model with harvesting

In this paper,a difference-algebraic predator prey model is proposed,and its complex dynamical behaviors are analyzed.The model is a discrete singular system,which is obtained by using Euler scheme to discretize a differential-algebraic predator-prey model with harvesting that we establish.Firstly,the local stability of the interior equilibrium point of proposed model is investigated on the basis of discrete dynamical system the­ory.Further,by applying the new normal form of difference-algebraic equations,center manifold theory and bifurcation theory,the Flip bifurcation and Neimark-Sacker bifur­cation around the interior equilibrium point are studied,where the step size is treated as the variable bifurcation parameter.Lastly,with the help of Matlab software,some numerical simulations are performed not only to validate our theoretical results,but also to show the abundant dynamical behaviors,such as period-doubling bifurcations,period 2,4,8,and 16 orbits,invariant closed curve,and chaotic sets.In particular,the corresponding maximum Lyapunov exponents are numerically calculated to corroborate the bifurcation and chaotic behaviors.     

Permanence of some ecological systems with several predator and one prey species

The stability criterion used in the following is permanence. Permanence means that all trajectories starting in the interior are ultimately bounded away from the boundary and that this bound is independent of the initial values. Hence sufficiently small fluctuations cannot lead to extinction of any species. In the following we deal with one-prey, two-predator resp. one-prey, three-predator systems and a one-prey, two-predator, one-top-predator system with three trophic levels. It turns out that the characterization of permanence for such models described by Lotka-Volterra dynamics is rather simple and elegant.     

A predator prey model with age structure

A general predator-prey model is considered in which the predator population is assumed to have an age structure which significantly affects its fecundity. The model equations are derived from the general McKendrick equations for age structured populations. The existence, stability and destabilization of equilibria are studied as they depend on the prey's natural carrying capacity and the maturation periodm of the predator. The main result of the paper is that for a broad class of maturation functions positive equilibria are either unstable for smallm or are destabilized asm decreases to zero. This is in contrast to the usual rule of thumb that increasing (not decreasing) delays in growth rate responses cause instabilities.Research supported by National Science Foundation Grant No. MCS-7901307-01Research supported by National Scholarship for Study Abroad No. EDN/S-59/80 from the government of India     

Taphonomic evidence of a Paleogene mammalian predator–prey interaction

A taphonomic study has been undertaken on an assemblage of bones and teeth of Isoptychus sp. and Thalerimys fordi (extinct rodent family Theridomyidae) from a single bed in a coastal plain setting, in the Late Eocene (Priabonian) Osborne Member, Headon Hill Formation (Hampshire Basin, UK). The vertebrate fossils show good preservation and do not bear the marks of obvious long distance transport. The two theridomyid species show similar patterns of mortality, element representation and surface modifications, which indicate similar mechanisms of accumulation. There is high mortality of juvenile and old individuals indicating accumulation of the assemblage by the action of attritional not catastrophic agents. The postcranial elements show fragmentary states and very low relative abundances. The vast majority of elongate bones (limb bones, phalanges and metapodials) are broken and exhibit a spiral irregular type of fracture with rounded fracture edges indicating that the bones were broken when they were fresh and have subsequently undergone additional modification. The enamel of most of the cheek teeth and incisors shows localized etching to various degrees and most of the bones show etching. By elimination of other modifying agents the observed etching is attributed to digestive corrosion. Collectively, these data indicate that the majority of the theridomyid individuals were eaten and digested by an animal that could cause high fragmentation during ingestion and with stomach juices of relatively high acidity. Both these features characterize mammalian carnivores. The presence of puncture marks on bones of both theridomyid species and comparisons with sizes of bite marks caused by extant mammalian carnivores suggest predation by a small mammalian carnivore about the size of an arctic fox. The extinct amphicyonid carnivoran Cynodictis cf. lacustris occurs in the same bed and the sizes of some of its teeth match well with the sizes of the puncture marks on the theridomyid bones. A predator–prey interaction is, therefore, deduced for the amphicyonid and the two theridomyid species, thereby reconstructing a small part of the continental Paleogene food chain.     

Predation on two vole species by a shared predator: antipredatory response and prey preference

In prey communities with shared predators, variation in prey vulnerability is a key factor in shaping community dynamics. Conversely, the hunting efficiency of a predator depends on the prey community structure, preferences of the predator and antipredatory behavioural traits of the prey. We studied experimentally, under seminatural field conditions, the preferences of a predator and the antipredatory responses of prey in a system consisting of two Myodes species of voles, the grey-sided vole (M. rufocanus Sund.) and the bank vole (M. glareolus Schreb.), and their specialist predator, the least weasel (Mustela nivalis nivalis L.). To quantify the preference of the weasels, we developed a new modelling framework that can be used for unbalanced data. The two vole species were hypothesised to have different habitat-dependent vulnerabilities. We created two habitats, open and forest, to provide different escape possibilities for the voles. We found a weak general preference of the weasels for the grey-sided voles over the bank voles, and a somewhat stronger preference specifically in open habitats. The weasels clearly preferred male grey-sided voles over females, whereas in bank voles, there was no difference. The activity of voles changed over time, so that voles increased their movements immediately after weasel introduction, but later adjusted their movements to times of lowered predation risk. Females that were more active had an elevated mortality risk, whereas in the case of males, the result was the opposite. We conclude that, in vulnerability to predation, the species- or habitat-specific characteristics of these prey species are playing a minor role compared to sex-specific characteristics.     

Effects of predation pressure and prey density on short-term indirect interactions between two prey species that share a common predator

1. Generalist predators are important contributors to reliable conservation biological control. Indirect interactions between prey species that share a common generalist predator can influence both community dynamics and the efficacy of biological control. 2. Laboratory cage experiments investigated the impact of the combined consumptive and non-consumptive effects of predation by adult Hippodamia convergens as a shared predator on the population growth and relative abundance of Acyrthosiphon pisum and Aphis gossypii as prey species. Predation pressure and prey density were varied. 3. At low predation pressure the indirect interaction between aphid species was asymmetrical with a proportionally greater negative impact of predation on A. gossypii than on A. pisum. At intermediate predation pressure, the indirect interaction became symmetrical. At high predation pressure and higher levels of prey density, it was asymmetrical with greater negative impact on A. pisum, often driven to local extinction while A. gossypii populations persisted. 4. A linear mixed-effects model including early population growth of both aphid species and predation pressure explained 96% and 92% of the variation in the population growth of A. pisum and A. gossypii, respectively, over an 8-day period. The overall effect of shared predation on the indirect interaction between the two aphid species is best described as apparent commensalism, where A. pisum benefited from early population growth of A. gossypii, while A. gossypii was unaffected by early population growth of A. pisum. Considering these indirect interactions is important for conservation biological control efforts to be successful.     

Life-history trade-off in two predator species sharing the same prey: a study on cassava-inhabiting mites

In cassava fields, two species of predatory mites, Typhlodromalus aripo and T. manihoti, co-occur at the plant level and feed on Mononychellus tanajoa , a herbivorous mite. The two predator species are spatially segregated within the plant: T. manihoti dwells on the middle leaves, while T. aripo occurs in the apices of the plant during the day and moves to the first leaves below the apex at night.
To monitor the prey densities experienced by the two predator species in their micro-environment, we assessed prey and predator populations in apices and on the leaves of cassava plants in the field. Prey densities peaked from November to January and reached the lowest levels in July. They were higher on leaves than in the apices. To test whether the life histories of the two predator species are tuned to the prey density they experience, we measured age-specific fecundity and survival of the two predators under three prey density regimes (1 prey female/72 h, 1 prey female/24 h and above the predators level of satiation). T. manihoti had a higher growth rate than T. aripo at high prey densities, mainly due to its higher fecundity. T. aripo had a higher growth rate at low prey density regimes, due to its late fecundity and survival. Thus, each of the two species perform better under the prey density that characterizes their micro-habitat within the plant.     

A model of prey bacteria,predator bacteria,and bacteriophage in continuous culture

Mathematical models are presented for one-, two- and three -trophic-level microbial systems in continuous culture, based on the respective interactions of Escherichia coli and limiting glucose; glucose, E. coli, and the predaceous bacterium Bdellovibrio bacteriovorus; and glucose, E. coli, B. bacteriovorus, and a virus parasitic on B. bacteriovorus. These models contain explicit time lags to represent reproductive latent periods, and the importance of these to the behavior of the models is demonstrated. The models' behavior was investigated by algebraic analysis and by computer simulation using literature values for the parameters in the equations; equilibrium conditions and stability properties for the various microbial systems are presented over a wide range of potential environmental conditions. A sensitivity analysis indicates which parameters must be most accurately known in order to validate the model experimentally. The results delineate the range of experimental conditions permitting the study of all these continuous culture systems in the laboratory and generate predictions about persistence of such multi-level microbial systems in natures     

An impulsively controlled pest management model with n predator species and a common prey

This paper investigates the dynamics of a competitive single-prey n-predators model of integrated pest management, which is subject to periodic and impulsive controls, from the viewpoint of finding sufficient conditions for the extinction of prey and for prey and predator permanence. The per capita death rates of prey due to predation are given in abstract, unspecified forms, which encompass large classes of death rates arising from usual predator functional responses, both prey-dependent and predator-dependent. The stability and permanence conditions are then expressed as balance conditions between the cumulative death rate of prey in a period, due to predation from all predator species and to the use of control, and to the cumulative birth rate of prey in the same amount of time. These results are then specialized for the case of prey-dependent functional responses, their biological significance being also discussed.     

The effects of the functional response on the bifurcation behavior of a mite predator–prey interaction model

 A predator–prey interaction model based on a system of differential equations with temperature-dependent parameters chosen appropriately for a mite interaction on apple trees is analyzed to determine how the type of functional response influences bifurcation and stability behavior. Instances of type I, II, III, and IV functional responses are considered, the last of which incorporates prey interference with predation. It is shown that the model systems with the type I, II, and III functional responses exhibit qualitatively similar bifurcation and stability behavior over the interval of definition of the temperature parameter. Similar behavior is found in the system with the type IV functional response at low levels of prey interference. Higher levels of interference are destabilizing, as illustrated by the prevalence of bistability and by the presence of three attractors for some values of the model parameters. All four systems are capable of modeling population oscillations and outbreaks. Received 12 March 1996; received in revised form 25 October 1996     

Inbreeding depression effects on extinction time in a predator—prey system

Summary Traditional methods of assessing population viability ignore both genetic—demographic interactions as well as community level dynamics. We address these deficiencies by presenting a model that investigates the effects of predation on a prey population experiencing inbreeding depression. Beginning with a simple Lotka—Volterra predator—prey system, we rewrite prey per capita mortality as a function of inbreeding. Inbreeding varies as a function of population size. Using computer simulation, we find that prey extinction times are inversely related to the level of inbreeding depression with and without predation. For all but very low levels of inbreeding depression, predation appreciably reduces persistence time. At moderate levels of inbreeding, predators go extinct before prey. When migration is introduced at low and moderate rates, persistence times only improve for those populations with low inbreeding depression measures. At a higher migration rate, persistence times are lengthened for low and moderately depressed prey populations. Increasing birth rates produce a visible, though noisy, trend towards increased times to extinction for low to moderate levels of inbreeding.     

Dynamics between a predator and a prey switching two kinds of escape motions

In nature, animals are classified into two large groups. Those that form the prey and that form the predator. A prey animal runs for its life when chased by a predatory animal. When prey animals escape from the chasing enemy, they generally use two types of evasive motion. Those are a straight-line escape motion and a zigzag-line escape motion. A fleeing prey switches between two types of evasive behavior in a manner depending on the predator's performance.I propose a mathematical model that expresses behaviors between a prey and a predator. This model brings that a straight-line escape motion is a better solution for an escape from a slow and far predator. On the other hand, an evasive motion for a near or fast enemy is a zigzag-line escape motion. This model suggests that animals have the best evasive strategy.     

Patterns of mesenchymal condensation in a multiscale, discrete stochastic model

Cells of the embryonic vertebrate limb in high-density culture undergo chondrogenic pattern formation, which results in the production of regularly spaced “islands” of cartilage similar to the cartilage primordia of the developing limb skeleton. The first step in this process, in vitro and in vivo, is the generation of “cell condensations,” in which the precartilage cells become more tightly packed at the sites at which cartilage will form. In this paper we describe a discrete, stochastic model for the behavior of limb bud precartilage mesenchymal cells in vitro. The model uses a biologically motivated reaction–diffusion process and cell-matrix adhesion (haptotaxis) as the bases of chondrogenic pattern formation, whereby the biochemically distinct condensing cells, as well as the size, number, and arrangement of the multicellular condensations, are generated in a self-organizing fashion. Improving on an earlier lattice-gas representation of the same process, it is multiscale (i.e., cell and molecular dynamics occur on distinct scales), and the cells are represented as spatially extended objects that can change their shape. The authors calibrate the model using experimental data and study sensitivity to changes in key parameters. The simulations have disclosed two distinct dynamic regimes for pattern self-organization involving transient or stationary inductive patterns of morphogens. The authors discuss these modes of pattern formation in relation to available experimental evidence for the in vitro system, as well as their implications for understanding limb skeletal patterning during embryonic development.