A Threshold-Based Weather Model for Predicting Stripe Rust Infection in Winter Wheat.

Wheat stripe rust (caused by Puccinia striiformis f. sp. tritici) is a major threat in most wheat growing regions worldwide, which potentially causes substantial yield losses when environmental conditions are favorable. Data from 1999 to 2015 for three representative wheat-growing sites in Luxembourg were used to develop a threshold-based weather model for predicting wheat stripe rust. First, the range of favorable weather conditions using a Monte Carlo simulation method based on the Dennis model were characterized. Then, the optimum combined favorable weather variables (air temperature, relative humidity, and rainfall) during the most critical infection period (May-June) was identified and was used to develop the model. Uninterrupted hours with such favorable weather conditions over each dekad (i.e., 10-day period) during May-June were also considered when building the model. Results showed that a combination of relative humidity >92% and 4°C < temperature < 16°C for a minimum of 4 continuous hours, associated with rainfall ≤0.1 mm (with the dekad having these conditions for 5 to 20% of the time), were optimum to the development of a wheat stripe rust epidemic. The model accurately predicted infection events: probabilities of detection were ≥0.90 and false alarm ratios were ≤0.38 on average, and critical success indexes ranged from 0.63 to 1. The method is potentially applicable to studies of other economically important fungal diseases of other crops or in different geographical locations. If weather forecasts are available, the threshold-based weather model can be integrated into an operational warning system to guide fungicide applications.

Asymptotic analysis of the Poisson-Boltzmann equation in biological membrane channels.

The Poisson-Boltzmann equation has been increasingly used for the description of biomolecular systems in order to derive their electrostatic properties. We here consider a domain consisting of two living cells which communicate through a system of proteins which assemble at specific membrane areas building microchannels called gap junctions. We describe the asymptotic behavior of the solution of the Poisson-Boltzmann equation posed in this domain. Using Γ-convergence tools, we derive some electrostatic properties of the biological membrane with respect to a vanishing parameter which is simultaneously associated to the membrane thinness, to the diameter of the gap junction microchannels and to the Debye length parameter which characterizes the spatial scale electrostatic interactions between particles within the gap junctions.