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.

A comparison of the seasonal movements of tiger sharks and green turtles provides insight into their predator-prey relationship

During the reproductive season, sea turtles use a restricted area in the vicinity of their nesting beaches, making them vulnerable to predation. At Raine Island (Australia), the highest density green turtle Chelonia mydas rookery in the world, tiger sharks Galeocerdo cuvier have been observed to feed on green turtles, and it has been suggested that they may specialise on such air-breathing prey. However there is little information with which to examine this hypothesis. We compared the spatial and temporal components of movement behaviour of these two potentially interacting species in order to provide insight into the predator-prey relationship. Specifically, we tested the hypothesis that tiger shark movements are more concentrated at Raine Island during the green turtle nesting season than outside the turtle nesting season when turtles are not concentrated at Raine Island. Turtles showed area-restricted search behaviour around Raine Island for ~3–4 months during the nesting period (November–February). This was followed by direct movement (transit) to putative foraging grounds mostly in the Torres Straight where they switched to area-restricted search mode again, and remained resident for the remainder of the deployment (53–304 days). In contrast, tiger sharks displayed high spatial and temporal variation in movement behaviour which was not closely linked to the movement behaviour of green turtles or recognised turtle foraging grounds. On average, tiger sharks were concentrated around Raine Island throughout the year. While information on diet is required to determine whether tiger sharks are turtle specialists our results support the hypothesis that they target this predictable and plentiful prey during turtle nesting season, but they might not focus on this less predictable food source outside the nesting season.

Incorporating anthropogenic effects into trophic ecology: predator-prey interactions in a human-dominated landscape

Apex predators perform important functions that regulate ecosystems worldwide. However, little is known about how ecosystem regulation by predators is influenced by human activities. In particular, how important are top-down effects of predators relative to direct and indirect human-mediated bottom-up and top-down processes? Combining data on species' occurrence from camera traps and hunting records, we aimed to quantify the relative effects of top-down and bottom-up processes in shaping predator and prey distributions in a human-dominated landscape in Transylvania, Romania. By global standards this system is diverse, including apex predators (brown bear and wolf), mesopredators (red fox) and large herbivores (roe and red deer). Humans and free-ranging dogs represent additional predators in the system. Using structural equation modelling, we found that apex predators suppress lower trophic levels, especially herbivores. However, direct and indirect top-down effects of humans affected the ecosystem more strongly, influencing species at all trophic levels. Our study highlights the need to explicitly embed humans and their influences within trophic cascade theory. This will greatly expand our understanding of species interactions in human-modified landscapes, which compose the majority of the Earth's terrestrial surface.

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)

Multiobjective Biogeography-Based Optimization Based on Predator-Prey Approach

Biogeography is the science that studies the geographical distribution and the migration of species in an ecosystem. Biogeography-based optimization (BBO) is a recently developed global optimization algorithm as a generalization of biogeography to evolutionary algorithm and has shown its ability to solve complex optimization problems. BBO employs a migration operator to share information between the problem solutions. The problem solutions are identified as habitat, and the sharing of features is called migration. In this paper, a multiobjective BBO, combined with a predator-prey (PPBBO) approach, is proposed and validated in the constrained design of a brushless dc wheel motor. The results demonstrated that the proposed PPBBO approach converged to promising solutions in terms of quality and dominance when compared with the classical BBO in a multiobjective version.

Predator-prey interactions: jaguar predation on caiman in a floodplain forest

Advances in the understanding of ecological factors determining predatorprey interactions have provided a strong theoretical background on diet preferences of predators. We examined patterns of jaguar predation on caiman in southern Pantanal, Brazil. We investigated factors affecting predation rates and vulnerability of caiman to predation by jaguars. We recorded 114 caiman mortality incidents. Predation accounted for 62.3% (n = 71) of all caiman found dead, while other causes of mortality (nonpredation) accounted for 37.7% (n = 43). We found that jaguars prey on a broad size range of caiman body and caiman predation was influenced by distance to forests. During dry seasons, 70% (n = 49) of deaths were due to predation, while 30% (n = 21) were due to nonpredation causes. However, we found no significant relationship between annual and monthly killings of caiman and rainfall totals by year and month (r = 0.130, r = -0.316). The annual flooding regime may be a more important factor influencing prey selection by jaguars. Although neotropical crocodilians are relatively well studied, their interactions with jaguars have been mostly ignored and should be prioritized in future studies.

Predator-prey: interactions between the spiny waterflea (Bythotrephes longimanus) and pumpkinseed sunfish (Lepomis gibbosus)

Small pumpkinseed sunfish ( Lepomis gibbosus), were found to be capable of removing the spine of Bythotrephes longimanus, an invasive cladoceran. Because fish consumption may be important in the dispersal or control of Bythotrephes, aquarium feeding experiments were conducted to 1) establish if the spine removal behavior of the pumpkinseeds was locally unique; 2) quantify how frequently pumpkinseeds exhibit the behavior; 3) determine if pumpkinseed handle Bythotrephes more quickly than other species of fish; and 4) verify if Bythotrephes' resting eggs pass through the digestive systems of pumpkinseeds in viable condition. The experiments revealed that pumpkinseeds (45-70 mm TL) from two geographic regions were more successful (100%) at removing Bythotrephes' spine, and handled Bythotrephes more quickly than yellow perch (Perca flavescens) (49-57 mm TL) and smallmouth bass (Micropterus dolomieu) (50-57mm TL) used in the study. Of 244 live Bythotrephes' resting eggs fed to the pumpkinseeds, 104 (42.6%) passed through their digestive systems. From those eggs, only 10 successfully hatched. Preliminary enclosure experiments were carried out and indicated that pumpkinseeds will consume Bythotrephes in natural settings. These findings provide new evidence that certain fish, with specialized morphology for prey manipulation, have the ability to influence the distribution and establishment of Bythotrephes.

Putting prey and predator into the CO2 equation-qualitative and quantitative effects of ocean acidification on predator-prey interactions

Little is known about the impact of ocean acidification on predator-prey dynamics. Herein, we examined the effect of carbon dioxide (CO(2)) on both prey and predator by letting one predatory reef fish interact for 24 h with eight small or large juvenile damselfishes from four congeneric species. Both prey and predator were exposed to control or elevated levels of CO(2). Mortality rate and predator selectivity were compared across CO(2) treatments, prey size and species. Small juveniles of all species sustained greater mortality at high CO(2) levels, while large recruits were not affected. For large prey, the pattern of prey selectivity by predators was reversed under elevated CO(2). Our results demonstrate both quantitative and qualitative consumptive effects of CO(2) on small and larger damselfish recruits respectively, resulting from CO(2)-induced behavioural changes likely mediated by impaired neurological function. This study highlights the complexity of predicting the effects of climate change on coral reef ecosystems.

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.

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.