A diffusion‐based approach to stochastic individual growth and energy budget,with consequences to life‐history optimization and population dynamics

Using diffusion processes, I model stochastic individual growth, given exogenous hazards and starvation risk. By maximizing survival to final size, optimal life histories (e.g. switching size for habitat/dietary shift) are determined by two ratios: mean growth rate over growth variance (diffusion coefficient) and mortality rate over mean growth rate; all are size dependent. For example, switching size decreases with either ratio, if both are positive. I provide examples and compare with previous work on risk‐sensitive foraging and the energy–predation trade‐off. I then decompose individual size into reversibly and irreversibly growing components, e.g. reserves and structure. I provide a general expression for optimal structural growth, when reserves grow stochastically. I conclude that increased growth variance of reserves delays structural growth (raises threshold size for its commencement) but may eventually lead to larger structures. The effect depends on whether the structural trait is related to foraging or defence. Implications for population dynamics are discussed.     

On a Continuous Branching Process and Birth-Death and Immigration Models for Testing the Efficacy of Some Control Programmes for AIDS

The present communication is an attempt to describe the mode of propagation of AIDS epidemic and its control programme using a branching process as well as a birth-death and immigration model. A comparison of the project of AIDS control programme on the basis of its propagation by a continuous branching process model with that of a linear birth and death process with immigration shows a remarkable contrast. Branching process model shows that it is possible to control the propagation of the disease by suitably increasing the detection rate and lowering the infection rate. However, the propagation of AIDS models by birth and death Process with or without immigration shows that it is increasingly difficult to control the invasion of AIDS merely by controlling the birth, death and immigration parameters.     

Some remarks on the presence of organic phosphates in sediments

This article describes a new method developed to assess the size and nature of the organic phosphate pool. Using sediment suspensions from the Rhone, Garonne and Po rivers, inorganic P compounds, Fe(OOH) and CaCO₃ were removed using mild extractants at sediment pH. The residual phosphate was then fractionated into an acid soluble organic phosphate pool and a residual organic phosphate pool by acid hydrolysis (0.5 M H⁺). Both pools were quantitatively important, accounting for between 16 and 54% and 16 and 51% of total phosphate respectively. Acid hydrolysis was chosen since it yielded a distinct plateau, with high reproducibility, within 30 minutes.This fractionation permits a further study of dynamics and bioavailability of sediment org-P, without interference of Fe(OOH) and CaCO₃.In many studies in which changes in the organic pool were examined after extraction of inorganic phosphate, 0.5 M HCl was used to extract apatite bound phosphate. The results presented here show that this is likely to result in a considerable underestimation of the organic phosphate pool.     

Show Me Your Menu

This activity discusses a two-day unit on ecology implemented during the summer of 2004 using the project-based science instructional (PBSI) approach. Through collaborative fieldwork, group discussions, presentations, and reflections, students planned, implemented, and reported their own scientific investigations on the environmental health of their local park in the borough of Queens, New York City. Students' questions included a wide range of topics that dealt with plants, animals, soil and water, and the interactions and relationships between these variables. Findings from students' reports and presentations indicated that the pH of the soil and pond water system at the park, as well as the characteristics of terrestrial and aquatic organisms, differ by location. In addition, results of the unit of instruction demonstrated that it is possible to teach students science content and process in a reasonably short period using the PBSI approach.     

Statistical analysis of a dynamic model for dietary contaminant exposure

This paper is devoted to the statistical analysis of a stochastic model introduced in [P. Bertail, S. Clémençon, and J. Tressou, A storage model with random release rate for modelling exposure to food contaminants, Math. Biosci. Eng. 35 (1) (2008), pp. 35–60] for describing the phenomenon of exposure to a certain food contaminant. In this modelling, the temporal evolution of the contamination exposure is entirely determined by the accumulation phenomenon due to successive dietary intakes and the pharmacokinetics governing the elimination process inbetween intakes, in such a way that the exposure dynamic through time is described as a piecewise deterministic Markov process. Paths of the contamination exposure process are scarcely observable in practice, therefore intensive computer simulation methods are crucial for estimating the time-dependent or steady-state features of the process. Here we consider simulation estimators based on consumption and contamination data and investigate how to construct accurate bootstrap confidence intervals (CI) for certain quantities of considerable importance from the epidemiology viewpoint. Special attention is also paid to the problem of computing the probability of certain rare events related to the exposure process path arising in dietary risk analysis using multilevel splitting or importance sampling (IS) techniques. Applications of these statistical methods to a collection of data sets related to dietary methyl mercury contamination are discussed thoroughly.