Estimating numbers of infectious units from serial dilution assays

Summary.  The paper concerns the design and analysis of serial dilution assays to estimate the infectivity of a sample of tissue when it is assumed that the sample contains a finite number of indivisible infectious units such that a subsample will be infectious if it contains one or more of these units. The aim of the study is to estimate the number of infectious units in the original sample. The standard approach to the analysis of data from such a study is based on the assumption of independence of aliquots both at the same dilution level and at different dilution levels, so that the numbers of infectious units in the aliquots follow independent Poisson distributions. An alternative approach is based on calculation of the expected value of the total number of samples tested that are not infectious. We derive the likelihood for the data on the basis of the discrete number of infectious units, enabling calculation of the maximum likelihood estimate and likelihood-based confidence intervals. We use the exact probabilities that are obtained to compare the maximum likelihood estimate with those given by the other methods in terms of bias and standard error and to compare the coverage of the confidence intervals. We show that the methods have very similar properties and conclude that for practical use the method that is based on the Poisson assumption is to be recommended, since it can be implemented by using standard statistical software. Finally we consider the design of serial dilution assays, concluding that it is important that neither the dilution factor nor the number of samples that remain untested should be too large.     

Influence of grass suppression and sowing rate on the establishment and persistence of forb dominated urban meadows

In practice in the UK, grasses and ruderal forbs recruited from the urban soil seed bank often have a detrimental impact on establishment and development of sown meadows. This study investigated the effect of graminicide, and sowing rate on establishment, survival and longer term development of sown meadow forbs. A seed mix containing 19 forb species was sown at two sowing rates in a randomized block experiment in Sheffield, UK. The two most abundant grasses recruited, Arrhenatherum elatius, and Holcus lanatus, were highly damaging to survival and development of sown forbs. Cutting the meadow to 50 mm during the first year did not alleviate grass competition. Weedy ruderal forbs had a lesser effect on sown forbs than the perennial grasses. Where a graminicide was used, sown forb density and biomass were significantly higher in the second and third year of the study, and forb richness significantly greater in all 3 years. Sown forb density was higher at the high sowing rate in all three years, and forb richness in years 1 and 2. Sowing rate did not significantly increase forb biomass in any year. In general, suppressing grass growth had a more beneficial effect on sown forb establishment and development than increasing sowing rate.