Theoretical and Experimental Study of Self Fertilized Populations

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Abstract
This paper is concerned with the derivation of the expected values of sample covariances and variance components in terms of genotypic variances and covariances for populations produced from crossing two homo-zygous lines and subsequent self-fertilization. Such genotypic variances and covariances have been defined by authors including Fisher, Mather, Homer and Kempthorne. Use is made of random variables such as oit, where o it = 1 if the genotype of the plant labeled i in an experiment corresponds to the tth genotype in a list of possible genotypes and zero otherwise. Application was made to maturity data of a soybean experiment. In this experiment 21 covariances and 9 variance components, unconfounded with environmental effects, were estimated. A completely additive model fitted this set of data as well as did two more complex models, explaining 96% of the variation among the sample covariances and variance components.