An Estimation Procedure for the Joint Distribution of Spatial Direction and Thickness of Flat Bodies Using Vertical Sections. Part II: An application in soil micromorphology

In soil micromorphology fissures are considered in vertical sections. To get information about the properties of the soil the joint distribution of spatial direction and width of these fissures is of interest. The fissures are mathematically generalized to flat bodies which are defined as stationary weighted surface processes with the weight “thickness”. In a typical point of the surface process suitable, joint parametric distributions of direction and thickness are assumed. The parameters have to be estimated from measurements on vertical sections which are taken from the soil. On these sections only a visible thickness and a visible angle can be observed. The joint distribution of these variables can be expressed by the joint distribution of spatial direction and thickness with the same parameters and in this indirect way the parameters can be estimated. The paper describes how to randomize the vertical section and how to measure the visible variables on the sections. The Chi-Square method is proposed for the parameter estimation. Further it is discussed how to derive good starting values for the numerical procedure. All this is demonstrated in a simulation study using the Bingham-Mardia distribution for the direction and the lognormal distribution for the thickness including a way to correlate the mean thickness and the direction. Finally an application in soil micromorphology is demonstrated for one soil horizon.     

Estimation of Individual Growth Curves by Empirically Weighted Least Squares

The simultaneous estimation of individual growth curves and a mean growth curve is accomplished by weighted least squares. A polynomial curve is fitted for each individual and the polynomial parameters are linear functions of parameters corresponding to covariates. A simple, computationally efficient variance-covariance estimator is derived. The resultant estimate is used in the weighted least squares estimation. The results are compared to empirical Bayes estimation.     

Resistance of wild wheat to stripe rust: Predictive method by ecology and allozyme genotypes

From 114 accessions of wild emmer wheat from 11 sites in Israel, known for their allozymic variation (Nevo & al. 1982), individual genotypes were tested for resistance to one isolate of stripe rust both in the seedling stage in a growth chamber and in the adult plant stage in the field. The results indicate that resistance to stripe rust in seedlings and adults are significantly correlated (r_s = 0.40, p < 0.001). Genetic polymorphisms of resistance to stripe rust vary geographically and are predictable by climatic, as well as allozymic markers. Three variable combinations of rainfall, evaporation, and temperature explain significantly 0.40–0.53 of the spatial variance in disease resistance to stripe rust, suggesting the operation of natural selection. Several allozyme genotypes are significantly associated with disease resistance. We conclude that natural populations of wild emmer wheat in Israel contain large amounts of disease resistance genes. These populations could be effectively screened and then utilized by the phytopathologist for identifying resistant genotypes and producing new resistant cultivars.Patterns of Resistance of Wild Wheat to Pathogens in Israel II.