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.

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.

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.

Precession and nutation in the eta Carinae binary system: evidence from the X-ray light curve

It is believed that eta Carinae is actually a massive binary system, with the wind-wind interaction responsible for the strong X-ray emission. Although the overall shape of the X-ray light curve can be explained by the high eccentricity of the binary orbit, other features like the asymmetry near periastron passage and the short quasi-periodic oscillations seen at those epochs have not yet been accounted for. In this paper we explain these features assuming that the rotation axis of eta Carinae is not perpendicular to the orbital plane of the binary system. As a consequence, the companion star will face eta Carinae on the orbital plane at different latitudes for different orbital phases and, since both the mass-loss rate and the wind velocity are latitude dependent, they would produce the observed asymmetries in the X-ray flux. We were able to reproduce the main features of the X-ray light curve assuming that the rotation axis of eta Carinae forms an angle of 29 degrees +/- 4 degrees with the axis of the binary orbit. We also explained the short quasi-periodic oscillations by assuming nutation of the rotation axis, with an amplitude of about 5 degrees and a period of about 22 days. The nutation parameters, as well as the precession of the apsis, with a period of about 274 years, are consistent with what is expected from the torques induced by the companion star.

Acquisition of Pavlovian Fear Conditioning Using beta-Adrenoceptor Activation of the Dorsal Premammillary Nucleus as an Unconditioned Stimulus to Mimic Live Predator-Threat Exposure

In the present work, we sought to mimic the internal state changes in response to a predator threat by pharmacologically stimulating the brain circuit involved in mediating predator fear responses, and explored whether this stimulation would be a valuable unconditioned stimulus (US) in an olfactory fear conditioning paradigm (OFC). The dorsal premammillary nucleus (PMd) is a key brain structure in the neural processing of anti-predatory defensive behavior and has also been shown to mediate the acquisition and expression of anti-predatory contextual conditioning fear responses. Rats were conditioned by pairing the US, which was an intra-PMd microinjection of isoproterenol (ISO; beta-adrenoceptor agonist), with amyl acetate odor-the conditioned stimulus (CS). ISO (10 and 40 nmol) induced the acquisition of the OFC and the second-order association by activation of beta-1 receptors in the PMd. Furthermore, similar to what had been found for contextual conditioning to a predator threat, atenolol (beta-1 receptor antagonist) in the PMd also impaired the acquisition and expression of OFC promoted by ISO. Considering the strong glutamatergic projections from the PMd to the dorsal periaqueductal gray (dPAG), we tested how the glutamatergic blockade of the dPAG would interfere with the OFC induced by ISO. Accordingly, microinjections of NMDA receptor antagonist (AP5, 6 nmol) into the dPAG were able to block both the acquisition, and partially, the expression of the OFC. In conclusion, we have found that PMd beta-1 adrenergic stimulation is a good model to mimic predatory threat-induced internal state changes, and works as a US able to mobilize the same systems involved in the acquisition and expression of predator-related contextual conditioning. Neuropsychopharmacology (2011) 36, 926-939; doi:10.1038/npp.2010.231; published online 5 January 2011

New Perspectives on beta-Adrenergic Mediation of Innate and Learned Fear Responses to Predator Odor

In the present study, we investigated the role of noradrenergic transmission in unconditioned and conditioned responses to predatory threats. First, we examined the effects of systemically injected beta-blockers on unconditioned and contextual conditioned response to cat odor. The centrally acting beta-blocker (propranolol) was able to impair unconditioned responses, as well as the acquisition of the contextual fear to cat odor; however, the peripherally acting (nadolol) was not effective. Next, we examined the neural substrate underlying the noradrenergic modulation of the defensive response to cat odor and focused on the dorsal premammillary nucleus (PMd), because it represents the hypothalamic site most responsive to predatory threats and, at the same time, presents a dense plexus of noradrenergic fibers. We were able to see that propranolol significantly reduced PMd-Fos expression in response to cat odor and that beta-adrenoceptor blockade in the PMd, before cat odor exposure, reduced defensive responses to the cat odor and to the cat odor-related environment. We have also shown that beta-adrenoceptor blockade in the PMd, before the exposure to cat odor-related context, impaired the contextual conditioned responses. Overall, the present results provide convincing evidence suggesting that central noradrenergic mediation is critical for the expression of unconditioned and contextual conditioned antipredatory responses. We have further shown that the PMd appears to be an important locus to mediate these beta-adrenoceptor effects.

Sensing danger through the olfactory system: The role of the hypothalamic dorsal premammillary nucleus

The dorsal premammillary nucleus (PMd) has a critical role on the expression of defensive responses to predator odor. Anatomical evidence suggests that the PMd should also modulate memory processing through a projecting branch to the anterior thalamus. By using a pharmacological blockade of the PMd with the NMDA-receptor antagonist 2-amino-5-phosphonopentanoic acid (AP5), we were able to confirm its role in the expression of unconditioned defensive responses, and further revealed that the nucleus is also involved in influencing associative mechanisms linking predatory threats to the related context. We have also tested whether olfactory fear conditioning, using coffee odor as CS, would be useful to model predator odor. Similar to cat odor, shock-paired coffee odor produced robust defensive behavior during exposure to the odor and to the associated context. Shock-paired coffee odor also up-regulated Fos expression in the PMd, and, as with cat odor, we showed that this nucleus is involved in the conditioned defensive responses to the shock-paired coffee odor and the contextual responses to the associated environment. (C) 2008 Elsevier Ltd. All rights reserved.

Dissecting the brain`s fear system reveals the hypothalamus is critical for responding in subordinate conspecific intruders

Effective defense against natural threats in the environment is essential for the survival of individual animals. Thus, instinctive behavioral responses accompanied by fear have evolved to protect individuals from predators and from opponents of the same species (dominant conspecifics). While it has been suggested that all perceived environmental threats trigger the same set of innately determined defensive responses, we tested the alternate hypothesis that different stimuli may evoke differentiable behaviors supported by distinct neural circuitry. The results of behavioral, neuronal immediate early gene activation, lesion, and neuroanatomical experiments indicate that the hypothalamus is necessary for full expression of defensive behavioral responses in a subordinate conspecific, that lesions of the dorsal premammillary nucleus drastically reduce behavioral measures of fear in these animals, and that essentially separate hypothalamic circuitry supports defensive responses to a predator or a dominant conspecific. It is now clear that differentiable neural circuitry underlies defensive responses to fear conditioning associated with painful stimuli, predators, and dominant conspecifics and that the hypothalamus is an essential component of the circuitry for the latter two stimuli.

Role of glutamate NMDA receptors and nitric oxide located within the periaqueductal gray on defensive behaviors in mice confronted by predator

The midbrain periaqueductal gray (PAG) is part of the brain system involved in active defense reactions to threatening stimuli. Glutamate N-methyl-d-aspartate (NMDA) receptor activation within the dorsal column of the PAG (dPAG) leads to autonomic and behavioral responses characterized as the fear reaction. Nitric oxide (NO) has been proposed to be a mediator of the aversive action of glutamate, since the activation of NMDA receptors in the brain increases NO synthesis. We investigated the effects of intra-dPAG infusions of NMDA on defensive behaviors in mice pretreated with a neuronal nitric oxide synthase (nNOS) inhibitor [N omega-propyl-l-arginine (NPLA)], in the same midbrain site, during a confrontation with a predator in the rat exposure test (RET). Male Swiss mice received intra-dPAG injections of NPLA (0.1 or 0.4 nmol/0.1 mu l), and 10 min later, they were infused with NMDA (0.04 nmol/0.1 mu l) into the dPAG. After 10 min, each mouse was placed in the RET. NMDA treatment enhanced avoidance behavior from the predator and markedly increased freezing behavior. These proaversive effects of NMDA were prevented by prior injection of NPLA. Furthermore, defensive behaviors (e.g., avoidance, risk assessment, freezing) were consistently reduced by the highest dose of NPLA alone, suggesting an intrinsic effect of nitric oxide on defensive behavior in mice exposed to the RET. These findings suggest a potential role of glutamate NMDA receptors and NO in the dPAG in the regulation of defensive behaviors in mice during a confrontation with a predator in the RET.

Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

Periodic window arising in the parameter space of an impact oscillator

In the bi-dimensional parameter space of an impact-pair system, shrimp-shaped periodic windows are embedded in chaotic regions. We show that a weak periodic forcing generates new periodic windows near the unperturbed one with its shape and periodicity. Thus, the new periodic windows are parameter range extensions for which the controlled periodic oscillations substitute the chaotic oscillations. We identify periodic and chaotic attractors by their largest Lyapunov exponents. (C) 2010 Elsevier B.V. All rights reserved.