Paweł Jankowski

An improved method to estimate the uncertainty of models describing the seasonal maturation of Venturia inaequalis ascospores

Abstract A simple method for reducing the uncertainty intervals of models describing the maturation of Venturia inaequalis (Cooke) Wint ascospores is described. The number of trapped ascospores related to the current accumulated degree days of the season, and the confidence interval predicted with the historical ascospore release datasets, were used to re-calculate the confidence interval for the ascospore proportion for the rest of the season. The historical uncertainty in ascospore proportion was described with logistic functions fitted to upper and lower confidence limits of the mean of fitted values for several years of ascospore release data. The re-calculated confidence interval was derived by the determination of the total number of ascospores that would be trapped during the season, if the current day cumulative release were at either the upper or lower confidence limit of the historical data. The method was examined by applying three models of ascospore maturation and using ascospore trap and weather data collected in Skierniewice, Poland during the period from 2005 to 2009. The historical uncertainties were established by the calibration of models to the data from 2005–2007. The effectiveness of the method was simulated using data of 2008 and 2009. In these years, the re-calculated confidence interval was never greater than the historical confidence interval and was often 3–4 times smaller than it, even though ascospore release observations in 2009 strongly differed from those of the years 2005–2007. In conclusion, the proposed method may be an effective approach to a more precise description of V. inaequalis ascospores maturation.

Allocation Constraints in Stratification

When a finite population is to be stratified, one of constraints in stratification is that sample sizes from strata may not be greater than the corresponding stratum sizes and may not be smaller than two. There are several ways of treating this allocation constraint, each providing an alternative approach to stratification. In this article, it is shown that a choice of the approach has a bearing on stratification efficiency. Unfortunately, no particular approach out of the four compared is shown to be the most efficient for each population studied. In addition, the approaches are applied to stratify a real population.