The rise and fall of open solar flux during the current grand solar maximum

We use geomagnetic activity data to study the rise and fall over the past century of the solar wind flow speed VSW, the interplanetary magnetic field strength B, and the open solar flux FS. Our estimates include allowance for the kinematic effect of longitudinal structure in the solar wind flow speed. As well as solar cycle variations, all three parameters show a long-term rise during the first half of the 20th century followed by peaks around 1955 and 1986 and then a recent decline. Cosmogenic isotope data reveal that this constitutes a grand maximum of solar activity which began in 1920, using the definition that such grand maxima are when 25-year averages of the heliospheric modulation potential exceeds 600 MV. Extrapolating the linear declines seen in all three parameters since 1985, yields predictions that the grand maximum will end in the years 2013, 2014, or 2027 using VSW, FS, or B, respectively. These estimates are consistent with predictions based on the probability distribution of the durations of past grand solar maxima seen in cosmogenic isotope data. The data contradict any suggestions of a floor to the open solar flux: we show that the solar minimum open solar flux, kinematically corrected to allow for the excess flux effect, has halved over the past two solar cycles.

Environmental control for layers

Light patterns have less effect on numbers of eggs laid by current stocks than on those of forty years ago, but the principles have not changed. Ovarian activity is stimulated by increasing photoperiods and suppressed by decreasing photoperiods. The light pattern used during rearing can still have large effects on age at 50% lay, even for modern stocks. Early sexual maturity maximises egg numbers but gives smaller eggs. Late maturity maximises egg size at the expense of numbers. The relationship between egg output (g/hen d) and age at first egg is curvilinear, with maximum yield occurring in flocks maturing in about the centre of their potential range. Fancy patterns of increasing daylength after maturity are probably not justified. A flock held on a constant 14h day will lay as many eggs as one given step up lighting. Intermittent lighting saves about 5% of feed consumption with no loss of output, provided that the feed has adequate amino acid content to allow for the reduced feed intake. Producers with light-proof laying houses should be taking advantage of intermittent lighting. The recommended light intensity for laying houses is still 10 lx, although the physiological threshold for response to changes in photoperiod is closer to 2 lx. Very dim (0.05 lx) light filtering into blacked out houses will not stimulate the hypothalamic receptors responsible for photo-sexual responses, but may affect the bird's biological clock, which can alter its response to a constant short photoperiod. Feed intake shows a curvilinear dependence on environmental temperature. At temperatures below the panting threshold, performance can be maintained by adjusting the feed so as to maintain an adequate intake of critical amino acids. Above the panting threshold, the hen is unable to take in enough energy to maintain normal output. There is no dietary modification which can effectively offset this problem. Diurnally cycling temperatures result in feed intake and egg production equivalent to that observed under a constant temperature equal to the mean of the cycle. When the poultry house is cooler at night than by day, it helps to provide light so that the birds can feed during the cooler part of the cycle.

Estimating numbers of infectious units from serial dilution assays

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.

Asymptotic normality in mixtures of power series distributions

The problem of estimating the individual probabilities of a discrete distribution is considered. The true distribution of the independent observations is a mixture of a family of power series distributions. First, we ensure identifiability of the mixing distribution assuming mild conditions. Next, the mixing distribution is estimated by non-parametric maximum likelihood and an estimator for individual probabilities is obtained from the corresponding marginal mixture density. We establish asymptotic normality for the estimator of individual probabilities by showing that, under certain conditions, the difference between this estimator and the empirical proportions is asymptotically negligible. Our framework includes Poisson, negative binomial and logarithmic series as well as binomial mixture models. Simulations highlight the benefit in achieving normality when using the proposed marginal mixture density approach instead of the empirical one, especially for small sample sizes and/or when interest is in the tail areas. A real data example is given to illustrate the use of the methodology.

CAMCR: Computer assisted mixture model analysis for capture-recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.