Regulation mechanisms in spatial stochastic development models

The aim of this paper is to analyze different regulation mechanisms in spatial continuous stochastic development models. We describe the density behavior for models with global mortality and local establishment rates. We prove that the local self-regulation via a competition mechanism (density dependent mortality) may suppress a unbounded growth of the averaged density if the competition kernel is superstable.Comment: 19 page

A randomised double-blind placebo-controlled trial investigating the behavioural effects of vitamin, mineral and n-3 fatty acid supplementation in typically developing adolescent schoolchildren

This material is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © 2015 The Authors. Published by Cambridge University Press.Nutrient deficiencies have been implicated in anti-social behaviour in schoolchildren; hence, correcting them may improve sociability. We therefore tested the effects of vitamin, mineral and n-3 supplementation on behaviour in a 12-week double-blind randomised placebo-controlled trial in typically developing UK adolescents aged 13–16 years (n 196). Changes in erythrocyte n-3 and 6 fatty acids and some mineral and vitamin levels were measured and compared with behavioural changes, using Conners’ teacher ratings and school disciplinary records. At baseline, the children’s PUFA (n-3 and n-6), vitamin and mineral levels were low, but they improved significantly in the group treated with n-3, vitamins and minerals (P=0·0005). On the Conners disruptive behaviour scale, the group given the active supplements improved, whereas the placebo group worsened (F=5·555, d=0·35; P=0·02). The general level of disciplinary infringements was low, thus making it difficult to obtain improvements. However, throughout the school term school disciplinary infringements increased significantly (by 25 %; Bayes factor=115) in both the treated and untreated groups. However, when the subjects were split into high and low baseline infringements, the low subset increased their offences, whereas the high-misbehaviour subset appeared to improve after treatment. But it was not possible to determine whether this was merely a statistical artifact. Thus, when assessed using the validated and standardised Conners teacher tests (but less clearly when using school discipline records in a school where misbehaviour was infrequent), supplementary nutrition might have a protective effect against worsening behaviour.Peer reviewe

COMPETITIVE OR WEAK COOPERATIVE STOCHASTIC LOTKA-VOLTERRA SYSTEMS CONDITIONED TO NON-EXTINCTION

International audienceWe are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a stochastic Lotka-Volterra system, obtained as limit of renormalized interacting birth and death processes. The weak cooperation assumption allows the system not to blow up. We study the existence and uniqueness of a quasi-stationary distribution, that is convergence to equilibrium conditioned to non extinction. To this aim we generalize in two-dimensions spectral tools developed for one-dimensional generalized Feller diffusion processes. The existence proof of a quasi-stationary distribution is reduced to the one for a $d$-dimensional Kolmogorov diffusion process under a symmetry assumption. The symmetry we need is satisfied under a local balance condition relying the ecological rates. A novelty is the outlined relation between the uniqueness of the quasi-stationary distribution and the ultracontractivity of the killed semi-group. By a comparison between the killing rates for the populations of each type and the one of the global population, we show that the quasi-stationary distribution can be either supported by individuals of one (the strongest one) type or supported by individuals of the two types. We thus highlight two different long time behaviors depending on the parameters of the model: either the model exhibits an intermediary time scale for which only one type (the dominant trait) is surviving, or there is a positive probability to have coexistence of the two species

Quasi-stationary regime of a branching random walk in presence of an absorbing wall

A branching random walk in presence of an absorbing wall moving at a constant velocity $v$ undergoes a phase transition as the velocity $v$ of the wall varies. Below the critical velocity $v_c$, the population has a non-zero survival probability and when the population survives its size grows exponentially. We investigate the histories of the population conditioned on having a single survivor at some final time $T$. We study the quasi-stationary regime for $v<v_c$ when $T$ is large. To do so, one can construct a modified stochastic process which is equivalent to the original process conditioned on having a single survivor at final time $T$. We then use this construction to show that the properties of the quasi-stationary regime are universal when $v\to v_c$. We also solve exactly a simple version of the problem, the exponential model, for which the study of the quasi-stationary regime can be reduced to the analysis of a single one-dimensional map.Comment: 2 figures, minor corrections, one reference adde

Vital Rates from the Action of Mutation Accumulation

New models for evolutionary processes of mutation accumulation allow hypotheses about the age-specificity of mutational effects to be translated into predictions of heterogeneous population hazard functions. We apply these models to questions in the biodemography of longevity, including proposed explanations of Gompertz hazards and mortality plateaus

Rule-Based Cell Systems Model of Aging using Feedback Loop Motifs Mediated by Stress Responses

Investigating the complex systems dynamics of the aging process requires integration of a broad range of cellular processes describing damage and functional decline co-existing with adaptive and protective regulatory mechanisms. We evolve an integrated generic cell network to represent the connectivity of key cellular mechanisms structured into positive and negative feedback loop motifs centrally important for aging. The conceptual network is casted into a fuzzy-logic, hybrid-intelligent framework based on interaction rules assembled from a priori knowledge. Based upon a classical homeostatic representation of cellular energy metabolism, we first demonstrate how positive-feedback loops accelerate damage and decline consistent with a vicious cycle. This model is iteratively extended towards an adaptive response model by incorporating protective negative-feedback loop circuits. Time-lapse simulations of the adaptive response model uncover how transcriptional and translational changes, mediated by stress sensors NF-κB and mTOR, counteract accumulating damage and dysfunction by modulating mitochondrial respiration, metabolic fluxes, biosynthesis, and autophagy, crucial for cellular survival. The model allows consideration of lifespan optimization scenarios with respect to fitness criteria using a sensitivity analysis. Our work establishes a novel extendable and scalable computational approach capable to connect tractable molecular mechanisms with cellular network dynamics underlying the emerging aging phenotype

Re-evaluating a test of the heterogeneity explanation for mortality plateaus.

[Drapeau, M.D., Gass, E.K., Simison, M.D., Mueller, L.D., Rose, M.R., 2000. Testing the heterogeneity theory of late-life mortality plateaus by using cohorts of Drosophila melanogaster, Experimental Gerontology, 35 71-84.] tested, in populations of Drosophila melanogaster, a prediction of the heterogeneity explanation for mortality plateaus. They concluded that heterogeneity could not explain their results. We contend here that the statistical analysis was flawed. It was declared that there was no difference between the mortality plateaus of three different strains, on the basis of averaged outcomes. In fact, the results for the different strains were quite different. Most trials showed the expected lowering of the mortality plateaus for the flies selected for robustness, but these effects were washed out by a small number of very large opposing deviations. There is ample reason to believe that the opposing deviations are artifacts of fitting an overly restrictive hazard-rate model. When we fit more appropriate models, the evidence points toward a rejection of the null hypothesis (of identical plateaus), hence toward modest support for the heterogeneity explanation

Chasing balls through martingale fields

We consider the way sets are dispersed by the action of stochastic flows derived from martingale fields. Under fairly general continuity and ellipticity conditions, the following dichotomy result is shown: any nontrivial connected set χ either contracts to a point under the action of the flow, or its diameter grows linearly in time, with speed at least a positive deterministic constant A. The linear growth may further be identified (again, almost surely), with a much stronger behavior, which we call "ball-chasing": if ψ is any path with Lipschitz constant smaller than A, the ball of radius e around ψ (t) contains points of the image of χ for an asymptotically positive fraction of times t. If the ball grows as the logarithm of time, there are individual points in χ whose images eventually remain in the ball