Introduction. Field plot technique. Data management and validation. Design of plant breeding trials. Spatial analysis. Unreplicated trials. Interference between plots. Multi-environment testing and genotype x environment interaction. Analysis of series of variety trials. Resource allocation for selection systems.

Statistical Methods for Plant Variety Evaluation

The problem of measuring surface parameters of tribological importance such as peak curvature has been considerably simplified. Using discrete random process analysis tribological parameters of a wide range of surfaces can now be expressed and measured in terms of just two points on the measured autocorrelation function and the r.m.s. value of the surface. In addition, the contribution each 9 scale of size ’ of asperity makes to an overall parameter can be assessed quantitatively. Many new expressions relating tribological parameters to the autocorrelation function have been derived using a limiting procedure which produces results entirely consistent with equivalent continuous theory. Using this theory it is now possible to predict ‘gap’ parameters between two surfaces in contact in terms of simple additive parameters of each surface. Finally a new statistical model of the surface has been developed which encompasses many types of engineering surface.

Discrete properties of random surfaces

Two new approximations for multivariate normal probabilities for rectangular regions, based on conditional expectations and regression with binary variables, are proposed. One is a second-order approximation that is much more accurate but also more numerically time-consuming than the first-order approximation. A third approximation, based on the moment-generating function of a truncated multivariate normal distribution, is proposed for orthant probabilities only. Its accuracy is between the first- and second-order approximations when the dimension is less than seven and the correlations are not large. All of the approximations get worse as correlations get larger. These new approximations offer substantial improvements on previous approximations. They also compare favorably with the methods of Genz for numerical evaluation of the multivariate normal integral. The approximation methods should be especially useful within a quasi-Newton routine for parameter estimation in discrete models that involv...

Approximations to Multivariate Normal Rectangle Probabilities Based on Conditional Expectations

Recent Work on the Design of Experiments: A Bibliography and a Review

Optimum allocation of resources is of fundamental importance for the efficiency of breeding programs. The objectives of our study were to (1) determine the optimum allocation for the number of lines and test locations in hybrid maize breeding with doubled haploids (DHs) regarding two optimization criteria, the selection gain ΔGk and the probability Pk of identifying superior genotypes, (2) compare both optimization criteria including their standard deviations (SDs), and (3) investigate the influence of production costs of DHs on the optimum allocation. For different budgets, number of finally selected lines, ratios of variance components, and production costs of DHs, the optimum allocation of test resources under one- and two-stage selection for testcross performance with a given tester was determined by using Monte Carlo simulations. In one-stage selection, lines are tested in field trials in a single year. In two-stage selection, optimum allocation of resources involves evaluation of (1) a large number of lines in a small number of test locations in the first year and (2) a small number of the selected superior lines in a large number of test locations in the second year, thereby maximizing both optimization criteria. Furthermore, to have a realistic chance of identifying a superior genotype, the probability Pk of identifying superior genotypes should be greater than 75%. For budgets between 200 and 5,000 field plot equivalents, Pk > 75% was reached only for genotypes belonging to the best 5% of the population. As the optimum allocation for Pk(5%) was similar to that for ΔGk, the choice of the optimization criterion was not crucial. The production costs of DHs had only a minor effect on the optimum number of locations and on values of the optimization criteria.

D. J. Finney

Papers

An Experimental Study of Certain Screening Processes

Cumulants of Truncated Multinomial Distributions