Random and fixed effects in plant genetics

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Abstract
A general model for any type of genetic entry is developed which takes into account both the factorial model of gene effects and the ancestral sources, whether inbred lines or outbred varieties, of the genes. Utilizing the model, various genetic designs of fixed entries are explored for the estimation of genetic effects and the testing of genetic hypotheses. These designs consisted of generation means — parents, crosses, various types of backcrosses, and so on — stemming from one or more pairs of parents, and of hybrid combinations from factorial mating designs. Limitations, from the standpoint of genetic effects that can be estimated and genetic hypotheses that can be tested, are developed in considerable detail. When entries from the factorial mating designs are considered to be random, attention is focused on the estimation of genetic variances, rather than effects, and on the concomitant changes in the tests of genetic hypotheses. While there is considerable improvement over fixed entries in the number of types of genetic variances that can be estimated, and of genetic hypotheses that can be tested, they are still very limited in contrast to what would be most desirable.