On the determination of relative fitness from frequencies of genotypes in subsequent generations : Part I. Algebra of reproduction and selection in populations with discrete generations.

An algebraic treatment of reproduction and selection processes in populations of diploids with discrete generation cycles is presented. The main objective was a determination of the conditions under which the selection coefficients for the various genotypes can be determined solely on the basis of known frequencies of genotypes in two subsequent generations. In part two, to be published later, the statistical properties of a special fitness estimator, proposed by Hayman, are considered. Confidence intervals and tests of significance concerning hypotheses about fitness are established and checked by computer simulation studies.