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.

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.

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.

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.

Stochastic lattice gas model describing the dynamics of the SIRS epidemic process

We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed of individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local rules and involves the following cyclic process: S -> I -> R -> S (SIRS). The open process S -> I -> R (SIR) is studied as a particular case of the SIRS process. The epidemic process is analyzed at different levels of description: by a stochastic lattice gas model and by a birth and death process. By means of Monte Carlo simulations and dynamical mean-field approximations we show that the SIRS stochastic lattice gas model exhibit a line of critical points separating the two phases: an absorbing phase where the lattice is completely full of S individuals and an active phase where S, I and R individuals coexist, which may or may not present population cycles. The critical line, that corresponds to the onset of epidemic spreading, is shown to belong in the directed percolation universality class. By considering the birth and death process we analyze the role of noise in stabilizing the oscillations. (C) 2009 Elsevier B.V. All rights reserved.

Merging Resource Availability with Isotope Mixing Models: The Role of Neutral Interaction Assumptions

Background: Bayesian mixing models have allowed for the inclusion of uncertainty and prior information in the analysis of trophic interactions using stable isotopes. Formulating prior distributions is relatively straightforward when incorporating dietary data. However, the use of data that are related, but not directly proportional, to diet (such as prey availability data) is often problematic because such information is not necessarily predictive of diet, and the information required to build a reliable prior distribution for all prey species is often unavailable. Omitting prey availability data impacts the estimation of a predator's diet and introduces the strong assumption of consumer ultrageneralism (where all prey are consumed in equal proportions), particularly when multiple prey have similar isotope values. Methodology: We develop a procedure to incorporate prey availability data into Bayesian mixing models conditional on the similarity of isotope values between two prey. If a pair of prey have similar isotope values (resulting in highly uncertain mixing model results), our model increases the weight of availability data in estimating the contribution of prey to a predator's diet. We test the utility of this method in an intertidal community against independently measured feeding rates. Conclusions: Our results indicate that our weighting procedure increases the accuracy by which consumer diets can be inferred in situations where multiple prey have similar isotope values. This suggests that the exchange of formalism for predictive power is merited, particularly when the relationship between prey availability and a predator's diet cannot be assumed for all species in a system.

SMALL MAMMAL PREY SELECTION BY TWO OWL SPECIES IN SOUTHEASTERN BRAZIL

A variety of factors influence prey selection by predators. Because Barn Owls (Tyto alba) and Burrowing Owls (Athene cunicularia) differ in size and foraging tactics, we expected differential predation on small mammal prey. We hypothesized that the Barn Owl, all active predator, would prey on smaller and younger individuals than the Burrowing Owl, a sit-and-wait predator. We used pellet analyses to evaluate selection of small mammals by the two owls in relation to prey), species, age, and size at the Ecological Station of Itirapina, state of Sao Paulo, in southeastern Brazil. Small mammals constituted most of the prey individuals and biomass in the diet of Barn Owls. Although Burrowing Owls consumed a wider range of taxa, small mammals represented one-third of all biomass consumed. With respect. to small mammals, Barn Owls foraged selectively relative to prey species, size, and age. Burrowing Owls foraged opportunistically relative to prey species, but selectively relative to prey size and age. Barn Owls selected smaller and younger (juvenile and subadult) individuals of the delicate vesper mouse (Calomys tener) and Burrowing Owls preyed more oil larger and older (subadult only) individuals. morphology and behavior of both prey and predators may explain this differential predation. Our data suggest that the active predator feeds oil smaller and younger prey, and the sit-and-wait predator took relatively larger and older prey.

Critical behavior of the susceptible-infected-recovered model on a square lattice

By means of numerical simulations and epidemic analysis, the transition point of the stochastic asynchronous susceptible-infected-recovered model on a square lattice is found to be c(0)=0.176 500 5(10), where c is the probability a chosen infected site spontaneously recovers rather than tries to infect one neighbor. This point corresponds to an infection/recovery rate of lambda(c)=(1-c(0))/c(0)=4.665 71(3) and a net transmissibility of (1-c(0))/(1+3c(0))=0.538 410(2), which falls between the rigorous bounds of the site and bond thresholds. The critical behavior of the model is consistent with the two-dimensional percolation universality class, but local growth probabilities differ from those of dynamic percolation cluster growth, as is demonstrated explicitly.

Cellular prion protein modulates defensive attention and innate fear-induced behaviour evoked in transgenic mice submitted to an agonistic encounter with the tropical coral snake Oxyrhopus guibei

The cellular prion protein (PrPC) is a neuronal anchored glycoprotein that has been associated with distinct functions in the CNS, such as cellular adhesion and differentiation, synaptic plasticity and cognition. Here we investigated the putative involvement of the PrPC in the innate fear-induced behavioural reactions in wild-type (WT), PrPC knockout (Prnp(0/0)) and the PrPC overexpressing Tg-20 mice evoked in a prey versus predator paradigm. The behavioural performance of these mouse strains in olfactory discrimination tasks was also investigated. When confronted with coral snakes, mice from both Prnp(0/0) and Tg-20 strains presented a significant decrease in frequency and duration of defensive attention and risk assessment, compared to WT mice. Tg-20 mice presented decreased frequency of escape responses, increased exploratory behaviour, and enhancement of interaction with the snake, suggesting a robust fearlessness caused by PrPC overexpression. Interestingly, there was also a discrete decrease in the attentional defensive response (decreased frequency of defensive alertness) in Prnp(0/0) mice in the presence of coral snakes. Moreover, Tg-20 mice presented an increased exploration of novel environment and odors. The present findings indicate that the PrPC overexpression causes hyperactivity, fearlessness, and increased preference for visual, tactile and olfactory stimuli-associated novelty, and that the PrPC deficiency might lead to attention deficits. These results suggest that PrPC exerts an important role in the modulation of innate fear and novelty-induced exploration. (C) 2008 Published by Elsevier B.V.

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