Quadratic Analyses of Reciprocal Crosses

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Abstract
Three different models, a 2-way factorial model for familiarity, an orthogonalizing transform of this model to a diallel model and a bio model more representative of the biological situation, are interrelated in terms of their components of variance and covariance. There are 5 components that can be dealt with in analysis of reciprocal crosses, including distinct maternal and paternal variances. Estimation of the components and tests of hypotheses concerning them are outlined for 2 types of mating designs with reciprocals. One design involves a factorial mating design between 2 distinct sets of parents or parental lines and the other a diallel of all crosses from a single set of parents or parental lines. Both designs provide the same types of information and similar tests of hypotheses. At least some parts of the analyses corresponding to the factorial model are required to separate the maternal and paternal variances. A least squares partitioning of the sums of squares according to the diallel model, but with expectations expressed in terms of the bio model, provides most of the tests of hypotheses of interest. Worked examples are given.

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