Three different models, a two-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. It is clarified that there are five components that can be reckoned with in the analysis of reciprocal crosses, including distinct maternal and paternal variances. Estimation of the components and tests of hypotheses concerning them are outlined for two types of mating designs with reciprocals. One design involves a factorial mating design between two 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.
Biometrics is a scientific journal emphasizing the role of statistics and mathematics in the biological sciences. Its object is to promote and extend the use of mathematical and statistical methods in pure and applied biological sciences by describing developments in these methods and their applications in a form readily assimilable by experimental scientists. JSTOR provides a digital archive of the print version of Biometrics. The electronic version of Biometrics is available at http://www.blackwell-synergy.com/servlet/useragent?func=showIssues&code;=biom. Authorized users may be able to access the full text articles at this site.
The International Biometric Society is an international society for the advancement of biological science through the development of quantitative theories and the application, development and dissemination of effective mathematical and statistical techniques. The Society welcomes as members biologists, mathematicians, statisticians, and others interested in applying similar techniques.
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Biometrics
© 1977 International Biometric Society
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