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.

Reaction-diffusion stochastic lattice model for a predator-prey system

We have the purpose of analyzing the effect of explicit diffusion processes in a predator-prey stochastic lattice model. More precisely we wish to investigate the possible effects due to diffusion upon the thresholds of coexistence of species, i. e., the possible changes in the transition between the active state and the absorbing state devoid of predators. To accomplish this task we have performed time dependent simulations and dynamic mean-field approximations. Our results indicate that the diffusive process can enhance the species coexistence.

The role of predator overlap in the robustness and extinction of a four species predator-prey network

Predators and preys often form species networks with asymmetric patterns of interaction. We study the dynamics of a four species network consisting of two weakly connected predator-prey pairs. We focus our analysis on the effects of the cross interaction between the predator of the first pair and the prey of the second pair. This is an example where the predator overlap, which is the proportion of predators that a given prey shares with other preys, is not uniform across the network due to asymmetries in patterns of interaction. We explore the behavior of the system under different interaction strengths and study the dynamics of survival and extinction. In particular, we consider situations in which the four species have initial populations lower than their long-term equilibrium, simulating catastrophic situations in which their abundances are reduced due to human action or environmental change. We show that, under these reduced initial conditions, and depending on the strength of the cross interaction, the populations tend to oscillate before re-equilibrating, disturbing the community equilibrium and sometimes reaching values that are only a small fraction of the equilibrium population, potentially leading to their extinction. We predict that, contrary to one`s intuition, the most likely scenario is the extinction of the less predated preys. (C) 2010 Elsevier B.V. All rights reserved.

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.

Role of noise in population dynamics cycles

Noise is an intrinsic feature of population dynamics and plays a crucial role in oscillations called phase-forgetting quasicycles by converting damped into sustained oscillations. This function of noise becomes evident when considering Langevin equations whose deterministic part yields only damped oscillations. We formulate here a consistent and systematic approach to population dynamics, leading to a Fokker-Planck equation and the associate Langevin equations in accordance with this conceptual framework, founded on stochastic lattice-gas models that describe spatially structured predator-prey systems. Langevin equations in the population densities and predator-prey pair density are derived in two stages. First, a birth-and-death stochastic process in the space of prey and predator numbers and predator-prey pair number is obtained by a contraction method that reduces the degrees of freedom. Second, a van Kampen expansion in the inverse of system size is then performed to get the Fokker-Planck equation. We also study the time correlation function, the asymptotic behavior of which is used to characterize the transition from the cyclic coexistence of species to the ordinary coexistence.

Time correlation function in systems with two coexisting biological species

We study a stochastic lattice model describing the dynamics of coexistence of two interacting biological species. The model comprehends the local processes of birth, death, and diffusion of individuals of each species and is grounded on interaction of the predator-prey type. The species coexistence can be of two types: With self-sustained coupled time oscillations of population densities and without oscillations. We perform numerical simulations of the model on a square lattice and analyze the temporal behavior of each species by computing the time correlation functions as well as the spectral densities. This analysis provides an appropriate characterization of the different types of coexistence. It is also used to examine linked population cycles in nature and in experiment.

Effect of crab size and habitat type on the locomotory activity of juvenile shore crabs, Carcinus maenas

Post-settlement processes are a major focus in the study of the dynamics of marine populations and communities. Post-settlement movement of juveniles is an important, but often ignored, process which affects local predator-prey and competitive interactions. We used benthic suction sampling and pitfall traps to examine density and locomotory activity of Carcinus maenas juveniles in different intertidal habitat types in the Rio Mira Estuary, Portugal, to better understand intra-specific interactions in a system where density-dependent processes are known to regulate population dynamics. As expected, significantly higher densities of juvenile shore crabs were found from bare mud compared to densely vegetated habitats. At the time of sampling, small and intermediate stages together outnumbered by far the larger juveniles. Conversely, larger crabs were much more frequent than smaller ones in traps. A locomotory index (LI), i.e. the ratio between crab catch in pitfall traps and their density within their moving range, is proposed as a measure of movement. LI analyses indicated that: (1) movement is an order of magnitude higher in large than small juveniles and much higher in sparse than dense vegetation cover; (2) activity of small juveniles is mostly crepuscular, regardless of vegetation cover; and (3) movement of large juveniles is very limited in dense Zostera patches, but very high in sparsely vegetated areas, during the day and night. These results suggest that small juveniles are relatively protected under dense vegetation cover due to lower mobility of larger crabs, and provide evidence of temporal segregation of activity windows between juvenile crabs of different sizes, which may be a key mechanism to reduce cannibalism and therefore increase the carrying capacity of nursery habitats. (C) 2008 Elsevier Ltd. All rights reserved.

Olfactory eavesdropping between two competing stingless bee species

Foragers can improve search efficiency, and ultimately fitness, by using social information: cues and signals produced by other animals that indicate food location or quality. Social information use has been well studied in predator-prey systems, but its functioning within a trophic level remains poorly understood. Eavesdropping, use of signals by unintended recipients, is of particular interest because eavesdroppers may exert selective pressure on signaling systems. We provide the most complete study to date of eavesdropping between two competing social insect species by determining the glandular source and composition of a recruitment pheromone, and by examining reciprocal heterospecific responses to this signal. We tested eavesdropping between Trigona hyalinata and Trigona spinipes, two stingless bee species that compete for floral resources, exhibit a clear dominance hierarchy and recruit nestmates to high-quality food sources via pheromone trails. Gas chromatography-mass spectrometry of T. hyalinata recruitment pheromone revealed six carboxylic esters, the most common of which is octyl octanoate, the major component of T. spinipes recruitment pheromone. We demonstrate heterospecific detection of recruitment pheromones, which can influence heterospecific and conspecific scout orientation. Unexpectedly, the dominant T. hyalinata avoided T. spinipes pheromone in preference tests, while the subordinate T. spinipes showed neither attraction to nor avoidance of T. hyalinata pheromone. We suggest that stingless bees may seek to avoid conflict through their eavesdropping behavior, incorporating expected costs associated with a choice into the decision-making process.

Periodic-orbit analysis and scaling laws of intermingled basins of attraction in an ecological dynamical system

Chaotic dynamical systems with two or more attractors lying on invariant subspaces may, provided certain mathematical conditions are fulfilled, exhibit intermingled basins of attraction: Each basin is riddled with holes belonging to basins of the other attractors. In order to investigate the occurrence of such phenomenon in dynamical systems of ecological interest (two-species competition with extinction) we have characterized quantitatively the intermingled basins using periodic-orbit theory and scaling laws. The latter results agree with a theoretical prediction from a stochastic model, and also with an exact result for the scaling exponent we derived for the specific class of models investigated. We discuss the consequences of the scaling laws in terms of the predictability of a final state (extinction of either species) in an ecological experiment.

GLOBAL WELL-POSEDNESS AND NON-LINEAR STABILITY OF PERIODIC TRAVELING WAVES FOR A SCHRODINGER-BENJAMIN-ONO SYSTEM

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrodinger-Benjamin-Ono system) for low-regularity initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schrodinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called dnoidal, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.

Investigation of the hypothalamic defensive system in the mouse

The hypothalamus plays especially important roles in various endocrine, autonomic, and behavioral responses that guarantee the survival of both the individual and the species. In the rat, a distinct hypothalamic defensive circuit has been defined as critical for integrating predatory threats, raising an important question as to whether this concept could be applied to other prey species. To start addressing this matter, in the present study, we investigated, in another prey species (the mouse), the pattern of hypothalamic Fos immunoreactivity in response to exposure to a predator (a rat, using the Rat Exposure Test). During rat exposure, mice remained concealed in the home chamber for a longer period of time and increased freezing and risk assessment activity. We were able to show that the mouse and the rat present a similar pattern of hypothalamic activation in response to a predator. Of particular note, similar to what has been described for the rat, we observed in the mouse that predator exposure induces a striking activation in the elements of the medial hypothalamic defensive system, namely, the anterior hypothalamic nucleus, the dorsomedial part of the ventromedial hypothalamic nucleus and the dorsal premammillary nucleus. Moreover, as described for the rat, predator-exposed mice also presented increased Fos levels in the autonomic and parvicellular parts of the paraventricular hypothalamic nucleus, lateral preoptic area and subfornical region of the lateral hypothalamic area. In conclusion, the present data give further support to the concept that a specific hypothalamic defensive circuit should be preserved across different prey species. (C) 2008 Elsevier B.V. All rights reserved.

Evidence for the thalamic targets of the medial hypothalamic defensive system mediating emotional memory to predatory threats

Previous studies from our laboratory have documented that the medial hypothalamic defensive system is critically involved in processing actual and contextual predatory threats, and that the dorsal premammillary nucleus (PMd) represents the hypothalamic site most responsive to predatory threats. Anatomical findings suggest that the PMd is in a position to modulate memory processing through a projecting branch to specific thalamic nuclei, i.e., the nucleus reuniens (RE) and the ventral part of the anteromedial nucleus (AMv). In the present study, we investigated the role of these thalamic targets in both unconditioned (i.e., fear responses to predatory threat) and conditioned (i.e., contextual responses to predator-related cues) defensive behaviors. During cat exposure, all experimental groups exhibited intense defensive responses with the animals spending most of the time in the home cage displaying freezing behavior. However, during exposure to the environment previously associated with a cat, the animals with combined RE + AMv lesions, and to a lesser degree, animals with single AMv unilateral lesions, but not animals with single RE lesions, presented a reduction of contextual conditioned defensive responses. Overall, the present results provide clear evidence suggesting that the PMd`s main thalamic targets (i.e., the nucleus reuniens and the AMv) seem to be critically involved in the emotional memory processing related to predator cues. (C) 2010 Elsevier Inc. All rights reserved.

Stability of periodic optical solitons for a nonlinear Schrodinger system

This paper is concerned with the existence and nonlinear stability of periodic travelling-wave solutions for a nonlinear Schrodinger-type system arising in nonlinear optics. We show the existence of smooth curves of periodic solutions depending on the dnoidal-type functions. We prove stability results by perturbations having the same minimal wavelength, and instability behaviour by perturbations of two or more times the minima period. We also establish global well posedness for our system by using Bourgain`s approach.

The CoRoT-7 planetary system: two orbiting super-Earths

We report on an intensive observational campaign carried out with HARPS at the 3.6 m telescope at La Silla on the star CoRoT-7. Additional simultaneous photometric measurements carried out with the Euler Swiss telescope have demonstrated that the observed radial velocity variations are dominated by rotational modulation from cool spots on the stellar surface. Several approaches were used to extract the radial velocity signal of the planet(s) from the stellar activity signal. First, a simple pre-whitening procedure was employed to find and subsequently remove periodic signals from the complex frequency structure of the radial velocity data. The dominant frequency in the power spectrum was found at 23 days, which corresponds to the rotation period of CoRoT-7. The 0.8535 day period of CoRoT-7b planetary candidate was detected with an amplitude of 3.3 m s(-1). Most other frequencies, some with amplitudes larger than the CoRoT-7b signal, are most likely associated with activity. A second approach used harmonic decomposition of the rotational period and up to the first three harmonics to filter out the activity signal from radial velocity variations caused by orbiting planets. After correcting the radial velocity data for activity, two periodic signals are detected: the CoRoT-7b transit period and a second one with a period of 3.69 days and an amplitude of 4 m s(-1). This second signal was also found in the pre-whitening analysis. We attribute the second signal to a second, more remote planet CoRoT-7c. The orbital solution of both planets is compatible with circular orbits. The mass of CoRoT-7b is 4.8 +/- 0.8 (M(circle plus)) and that of CoRoT-7c is 8.4 +/- 0.9 (M(circle plus)), assuming both planets are on coplanar orbits. We also investigated the false positive scenario of a blend by a faint stellar binary, and this may be rejected by the stability of the bisector on a nightly scale. According to their masses both planets belong to the super-Earth planet category. The average density of CoRoT-7b is rho = 5.6 +/- 1.3 g cm(-3), similar to the Earth. The CoRoT-7 planetary system provides us with the first insight into the physical nature of short period super-Earth planets recently detected by radial velocity surveys. These planets may be denser than Neptune and therefore likely made of rocks like the Earth, or a mix of water ice and rocks.