SummarySaunders & Eccleston (1992) presented an approach to the design of 2‐level factorial experiments for continuous processes. It determined sets of contrasts between the observations that could be well estimated, and then selected a design so that those contrasts estimated the parameters of interest. This paper shows that a well‐estimated contrast must have a large number of changes of sign or level, and also be ‘paired’ in a particular sense. It develops an algorithm which constructs designs that must have a large number of changes of sign, evenly spread among the contrasts and optimal or near optimal. When such designs exist they are often preferable to those produced by the reverse foldover algorithm of Cheng & Steinberg (1991).

A method of sampling is described which is a compromise between systematic sampling and stratified random sampling. It has less potential for bias than systematic sampling and also avoids the practical problems associated with stratified random sampling.

The underlying theory for determining the estimation error variance of the mean of samples taken from a moving stream is reviewed. Situations where standard formulae will give incorrect results are identified and appropriate corrections given for those situations. On the basis of this theory, a simplified method, using only results for a linear variogram, is proposed. The proposed method is shown to work correctly for multistage sampling and also when the variogram itself is varying. Examples are given of the application of the method to determination of the estimation error variance and to the design of sampling schemes.

The numerical schemes used to calculate the stationary distributions of Markov chains arising from a genetical problem on inbreeding plant populations with selection are described. Careful treatment is necessary because the distributions are surprisingly ill-behaved analytically. Examples are given, and the moments of the distributions are also derived.

For the haploid genetic model of Moran, the joint distribution of the numbers of distinct ancestors of a collection of nested subsamples is derived. These results are shown to apply to the diffusion approximations of a wide variety of other genetic models, including the Wright–Fisher process. The results allow us to relate the ancestries of populations sampled at different times. Analogous results for a line-of-descent process that incorporates the effect of mutation are given. Some results about the ages of alleles in an infinite-alleles model are described.

SUMMARY Previous results on competition of epidemics are extended to the case of the general epidemic. Coupling techniques are used for the stochastic model. A result of Kurtz is used to carry the result over to the deterministic case.

An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

When two or more epidemic agents are simultaneously present in a population, they may interact to increase or decrease each other's effectiveness. One form of interaction is "competition" where each agent confers immunity to the others. Such competition occurs, for example, between different strains of myxomatosis in rabbit populations. We consider some consequences of introducing competition into mathematical epidemic models. Both deterministic and stochastic simple epidemic models are examined. In either case the conclusions are similar: the faster spreading epidemic has a considerable advantage.

SummaryUsing the Poisson approximation to the Binomial distribution, we construct an approximate maximum likelihood estimator (MLE) for a class of chain binomial models. Our estimator proves to have properties which may make it preferable to the exact WLE.

Myxomatosis is a viral disease used in the control of rabbit populations. On the basis of previously published data we construct a model for the transmission of myxomatosis and attempt to fit it to observations on an epidemic of the disease. The model is of the chain-binomial type in discrete time and includes fixed latent and infectious periods. Using a modification of homogeneous mixing, we obtain a reasonable fit to the data.

An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.

We show, in the context of a neurobiological problem, that ζ a(α)−ζ a(β) increases with a, while ζ a (α)/ζ a (β) decreases with a, where 0 < β < α < 1 and ζ a (α) is the α th quantile of either the gamma distribution with shape parameter a, or a scaled F distribution with parameters 2a and 2m for any m.

When yeast cells reproduce, scars are left on the parent cell where the offspring has budded. Using a branching process model, it is possible to obtain the expectations of numbers of cells with 0, 1, 2, ... offspring. In this paper, theoretical results are tested against empirical data for three types of yeast cells. We examine the hypothesis that birth and death rates of cells with no previus offspring may differ from those of cells with one or more offspring. It is suggested that the oscillatory empricial results for the proportions of cells with 0, 1, 2, 3 and 4 offspring may be due to different mean budding times for these cells.

The parity of an individual in a population process is the number of offspring that individual has produced. If Nk(t) is the number of individuals of parity k at time t in a birth-and-death process and we show that, conditional on N(t)→ ∞,