Limit cycles of a predator-prey model with intratrophic predation

Hill, Joe M., Lloyd, Noel G., Pearson, Jane M., 'Limit cycles of a predator-prey model with intratrophic predation', Journal of Mathematical Analysis and Applications Volume 349, Issue 2, 15 January 2009, Pages 544-555

Competitive processes in controlled cationic ring-opening polymerization of oxetane:a Lotka-Volterra predator-prey model of two growing species competing for the same resources

The activation-deactivation pseudo-equilibrium coefficient Qt and constant K0 (=Qt x PaT1,t = ([A1]x[Ox])/([T1]x[T])) as well as the factor of activation (PaT1,t) and rate constants of elementary steps reactions that govern the increase of Mn with conversion in controlled cationic ring-opening polymerization of oxetane (Ox) in 1,4-dioxane (1,4-D) and in tetrahydropyran (THP) (i.e. cyclic ethers which have no homopolymerizability (T)) were determined using terminal-model kinetics. We show analytically that the dynamic behavior of the two growing species (A1 and T1) competing for the same resources (Ox and T) follows a Lotka-Volterra model of predator-prey interactions. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Predator-prey models: an application for the plankton dynamics of lake Geneva

In this paper we present a hierarchical Bayesian analysis for a predator-prey model applied to ecology considering the use of Markov Chain Monte Carlo methods. We consider the introduction of a random effect in the model and the presence of a covariate vector. An application to ecology is considered using a data set related to the plankton dynamics of lake Geneva for the year 1990. We also discuss some aspects of discrimination of the proposed models.

Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting using Variational Iteration Method

Due to wide range of interest in use of bio-economic models to gain insight into the scientific management of renewable resources like fisheries and forestry,variational iteration method (VIM) is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting.The results are compared with the results obtained by Adomian decomposition method and reveal that VIM is very effective and convenient for solving nonlinear differential equations.

Voyage au coeur de la prédation entre vendeurs et acheteurs : une nouvelle théorie en vente et marketing

Résumé : II existe une tension inhérente au sein de la relation en cours de développement entre un vendeur et un acheteur. Le vendeur craint que l'acheteur lui fasse perdre son temps et l'acheteur, lui, doute de l'honnêteté du vendeur. Tous deux s'interrogent sur le niveau de confiance et de coopération à accorder à l'autre. Il est possible, après tout, que le vendeur soit à l'affût de la moindre faiblesse de l'acheteur pour profiter de la situation et s'enrichir à ses dépens, ou, vice-versa, que l'acheteur cherche à profiter du vendeur. La présente thèse examine les tensions entre vendeurs et acheteurs en ayant recours à la théorie enracinée élargie, qui comprend une série de boucles investigatrices formées de revues des écrits scientifiques et de cueillettes de données qualitatives et quantitatives. Elle cherche à démontrer que la prédation perçue (l'impression que l'autre abuse de nous de manière coordonnée) affecte négativement la bonne entente entre les parties prenantes de la transaction. La thèse suggère aussi que le phénomène de prédation existe dans toutes les sphères d'activités humaines, y compris dans le domaine juridique. Le modèle PARDU (prédateur-proie) initialement développé pour discuter du phénomène de prédation débouche, au fil de la recherche, sur le modèle OPERA et la grille MESLY®, qui offrent des applications pratiques pour mieux gérer la prédation informationnelle.||Abstract : There is an inherent tension between a seller and a buyer as their relationship progresses towards closing the deal. The salesperson fears that the buyer wastes his time, which he could otherwise spend towards real potential buyers. The buyer questions the sincerity of the salesperson. Both evaluate the amount of trust and coopération they should invest in the relationship. It is possible, after ail, that the salesperson wants to take advantage of every weakness he detects in the buyer in order to guarantee the sale, and it is equally possible that the buyer tries to fool the salesperson, with false credit information for example. This thesis examines tensions that exist between salespeople and buyers by using an extended version of grounded theory, by which date is collected and analysed both qualitatively and quantitatively. It demonstrates that perceived prédation reduces considerably the quality of the relationship. The thesis suggests that the phenomenon of prédation exists in every sphere of human activity, including in the légal system. The PARDU Model (predator-prey) initially developed to discuss the phenomenon of predation evolves, as the research progresses, towards the OPERA Model and the MESLY® grid, which offer pratical tools to better manage informational predation.

CRITICAL BEHAVIOR AND THRESHOLD OF COEXISTENCE OF A PREDATOR-PREY STOCHASTIC MODEL IN A 2D LATTICE

We investigate the critical behavior of a stochastic lattice model describing a predator-prey system. By means of Monte Carlo procedure we simulate the model defined on a regular square lattice and determine the threshold of species coexistence, that is, the critical phase boundaries related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. A finite size scaling analysis is employed to determine the order parameter, order parameter fluctuations, correlation length and the critical exponents. Our numerical results for the critical exponents agree with those of the directed percolation universality class. We also check the validity of the hyperscaling relation and present the data collapse curves.

The stochastic nature of predator-prey cycles

We study by numerical simulations the time correlation function of a stochastic lattice model describing the dynamics of coexistence of two interacting biological species that present time cycles in the number of species individuals. Its asymptotic behavior is shown to decrease in time as a sinusoidal exponential function from which we extract the dominant eigenvalue of the evolution operator related to the stochastic dynamics showing that it is complex with the imaginary part being the frequency of the population cycles. The transition from the oscillatory to the nonoscillatory behavior occurs when the asymptotic behavior of the time correlation function becomes a pure exponential, that is, when the real part of the complex eigenvalue equals a real eigenvalue. We also show that the amplitude of the undamped oscillations increases with the square root of the area of the habitat as ordinary random fluctuations. (C) 2009 Elsevier B.V. All rights reserved.

On certain new exact solutions of a diffusive predator-prey system

We construct exact solutions for a system of two coupled nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the G'/G expansion method, we derive exact solutions to this model for two different wave speeds. For each wave velocity we report three different forms of solutions. We also discuss the biological relevance of the solutions obtained. © 2012 Elsevier B.V.

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

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The role of productivity in the ecological and evolutionary dynamics of predator-prey interaction

Productivity is predicted to drive the ecological and evolutionary dynamics of predator-prey interaction through changes in resource allocation between different traits. However, resources are seldom constantly available and thus temporal variation in productivity could have considerable effect on the species' potential to evolve. To study this, three long-term microbial laboratory experiments were established where Serratia marcescens prey bacteria was exposed to predation of protist Tetrahymena thermophila in different prey resource environments. The consequences of prey resource availability for the ecological properties of the predator-prey system, such as trophic dynamics, stability, and virulence, were determined. The evolutionary changes in species traits and prey genetic diversity were measured. The prey defence evolved stronger in high productivity environment. Increased allocation to defence incurred cost in terms of reduced prey resource use ability, which probably constrained prey evolution by increasing the effect of resource competition. However, the magnitude of this trade-off diminished when measured in high resource concentrations. Predation selected for white, non-pigmented, highly defensive prey clones that produced predation resistant biofilm. The biofilm defence was also potentially accompanied with cytotoxicity for predators and could have been traded off with high motility. Evidence for the evolution of predators was also found in one experiment suggesting that co-evolutionary dynamics could affect the evolution and ecology of predator-prey interaction. Temporal variation in resource availability increased variation in predator densities leading to temporally fluctuating selection for prey defences and resource use ability. Temporal variation in resource availability was also able to constrain prey evolution when the allocation to defence incurred high cost. However, when the magnitude of prey trade-off was small and the resource turnover was periodically high, temporal variation facilitated the formation of predator resistant biofilm. The evolution of prey defence constrained the transfer of energy from basal to higher trophic levels, decreasing the strength of top-down regulation on prey community. Predation and temporal variation in productivity decreased the stability of populations and prey traits in general. However, predation-induced destabilization was less pronounced in the high productivity environment where the evolution of prey defence was stronger. In addition, evolution of prey defence weakened the environmental variation induced destabilization of predator population dynamics. Moreover, protozoan predation decreased the S. marcescens virulence in the insect host moth (Parasemia plantaginis) suggesting that species interactions outside the context of host-pathogen relationship could be important indirect drivers for the evolution of pathogenesis. This thesis demonstrates that rapid evolution can affect various ecological properties of predator-prey interaction. The effect of evolution on the ecological dynamics depended on the productivity of the environment, being most evident in the constant environments with high productivity.

Integrability and singularity structure of predator‐prey system

The ‘‘extended’’ ARS (Ablowitz, Ramani, and Segur) algorithm is introduced to characterize a dynamical system as Painlevé or otherwise; to that end, it is required that the formal series—the Laurent series, logarithmic, algebraic psi series about a movable singularity—are shown to converge in the deleted neighborhood of the singularity. The determinations thus obtained are compared with those following from the α method of Painlevé. An attempt is made to relate the structure of solutions about a movable singularity with that of first integrals (when they exist). All these ideas are illustrated by a comprehensive analysis of the general two‐dimensional predator‐prey system.

Anti-grazing properties of the toxic dinoflagellate Karlodinium veneficum during predator-prey interactions with the copepod Acartia tonsa

Karlodinium veneficum (syn. Karlodinium micrum, Bergholtz et al. 2006; J Phycol 42:170–193) is a small athecate dinoflagellate commonly present in low levels in temperate, coastal waters. Occasionally, K. veneficum forms ichthyotoxic blooms due to the presence of cytotoxic, hemolytic compounds, putatively named karlotoxins. To evaluate the anti-grazing properties of these karlotoxins, we conducted food removal experiments using the cosmopolitan copepod grazer Acartia tonsa. Wild-caught, adult female A. tonsa were exposed to 6 monoalgal or mixed algal diets made using bloom concentrations of toxic (CCMP 2064) and non-toxic (CSIC1) strains of K. veneficum. Ingestion and clearance rates were calculated using the equations of Frost (1972). Exposure to the toxic strain of K. veneficum did not contribute to an increased mortality of the copepods and no significant differences in copepod mortality were found among the experimental diets. However, A. tonsa had significantly greater clearance and ingestion rates when exposed to a monoalgal diet of the non-toxic strain CSIC1 than when exposed to the monoalgal diet of toxic strain CCMP 2064 and mixed diets dominated by this toxic strain. These results support the hypothesis that karlotoxins in certain strains of K. veneficum deter grazing by potential predators and contribute to the formation and continuation of blooms.