Effect of pea bacterial blight (Pseudomonas syringae pv. pisi) on the yield of spring sown combining peas (Pisum sativum)

Field trials to examine the effect of pea bacterial blight (Pseudomonas syringae pv. pisi) (Psp) on the yield of combining peas were carried out at five sites (HRI Wellesbourne, ADAS Rosemaund, ADAS Terrington, PGRO, SASA East Craigs) in the UK in 1990, 1991 and 1992. Healthy seed, cv. Solara, and seed naturally infected with Psp Race 2 was sown in large plots (c. 200 m²) in the open or under nets to prevent bird damage by pigeons. Despite relatively low disease severity levels (< 15% leaf area) and separation by at least 12 m of cv. Consort (resistant to Race 2) between plots there was considerable spread of disease into plots sown with healthy seed. Regression analysis demonstrated a significant relationship between yield and disease. Of the disease measurements examined, disease severity on the leaves (stipules) at growth stage 208 was found to be the best predictor of yield. A model containing environmental and bird damage terms, in addition to disease, suggested that a yield loss of 0.98 t/ha would be expected for a disease severity score of 1, equivalent to 5% leaf area affected, at growth stage 208.     

The Estimation of a Multivariate Fitness Function from Several Samples Taken from a Population

The situation is considered where the multivariate distribution of certain variables X₁, X₂, …, X_p is changing with time in a population because natural selection related to the X's is taking place. It is assumed that random samples taken from the population at times t₁, t₂, …, t_s are available and it is desirable to estimate the fitness function w_t(x₁, x₂,…,x_p) which shows how the number of individuals with X_i = x_i, i = 1, 2, …, p at time t is related to the number of individuals with the same X values at time zero. Tests for population changes are discussed and indices of the selection on the population dispersion and the population mean are proposed. The situation with a multivariate normal distribution is considered as a special case. A maximum likelihood method that can be applied with any form of population distribution is proposed for estimating w_t. The methods discussed in the paper are illustrated with data on four dimensions of male Egyptian skulls covering a time span from about 4500 B.C. to about 300 A.D. In this case there seems to have been very little selection on the population dispersion but considerable selection on means.     

Estimation of Linear Regression Model with Random Coefficients Ensuring Almost Non-Negativity of Variance Estimators

For a linear regression model with random coefficients, this paper considers the estimation of the mean of coefficient vector which, in turn, involves the estimation of variances of random coefficients. The conventional estimation methods for it sometimes provides negative estimates. In order to circumvent this kind of difficulty, a proposal is forwarded and is examined in the light of existing ones.