The effect of potato variety mixtures on epidemics of late blight, in relation to plot size and level of resistance

Potatoes of a number of varieties of contrasting levels of resistance were planted in pure or mixed stands in four experiments over 3 years. Three experiments compared the late blight severity and progress in mixtures with that in pure stands. Disease on susceptible or moderately resistant varieties typical of those in commercial use was similar in mixtures and pure stands. In 2 of 3 years, there were slight reductions on cv. Sante, which is moderately susceptible, in mixture with cv. Cara, which is moderately resistant. Cara was unaffected by this mixture. Mixtures of an immune or near-immune partner with Cara or Sante substantially reduced disease on the latter. The effect of the size of plots of individual varieties or mixtures on blight severity was compared in two experiments. Larger plots had a greater area under the disease progress curve, but the average rate of disease progress was greater in smaller plots; this may be because most disease progress took place later, under more favourable conditions, in the smaller plots. In one experiment, two planting densities were used. Density had no effect on disease and did not interact with mixture effects. The overall conclusion is that, while mixtures of potato varieties may be desirable for other reasons, they do not offer any improvement on the average of the disease resistance of the components.

Use of the ratio plot in capture-recapture estimation

Statistical graphics are a fundamental, yet often overlooked, set of components in the repertoire of data analytic tools. Graphs are quick and efficient, yet simple instruments of preliminary exploration of a dataset to understand its structure and to provide insight into influential aspects of inference such as departures from assumptions and latent patterns. In this paper, we present and assess a graphical device for choosing a method for estimating population size in capture-recapture studies of closed populations. The basic concept is derived from a homogeneous Poisson distribution where the ratios of neighboring Poisson probabilities multiplied by the value of the larger neighbor count are constant. This property extends to the zero-truncated Poisson distribution which is of fundamental importance in capture–recapture studies. In practice however, this distributional property is often violated. The graphical device developed here, the ratio plot, can be used for assessing specific departures from a Poisson distribution. For example, simple contaminations of an otherwise homogeneous Poisson model can be easily detected and a robust estimator for the population size can be suggested. Several robust estimators are developed and a simulation study is provided to give some guidance on which should be used in practice. More systematic departures can also easily be detected using the ratio plot. In this paper, the focus is on Gamma mixtures of the Poisson distribution which leads to a linear pattern (called structured heterogeneity) in the ratio plot. More generally, the paper shows that the ratio plot is monotone for arbitrary mixtures of power series densities.