The simplest possible model of the sex determination process adding autosomal influence to a minimal number of sex chromosomes was developed to explain matings of Tilapia (Sarotherodon) species. Eighteen different genotypes, each having two autosomes (AA, Aa, or aa) and two sex chromosomes (WX, WY, WW, XY, XX or YY) involved in sex determination, are predicted by the theory. Their sex (10 males and 8 females) were determined using a series of directed graphs, showing the relative strength of the chromosome pairs, developed on the basis of Chen's sex ratio results (Chen 1969). This theoretical model predicts eight different sex ratios (0βΆ1, 1βΆ3, 3βΆ5, 1βΆ1, 9βΆ7, 5βΆ3, 3βΆ1, 1βΆ0 ββΆβ); three of them are not predicted by the WXYZ theory. The greatest part of these sex ratios have been obtained experimentally in extensive series of crosses between related species of Tilapia and their hybrids, carried out by several authors. The theory succeeds in explaining all of Chen's results, including those ratios 5βΆ3 and 0βΆ1 seen in certain crosses but not predicted by the WXYZ theory. The importance of the autosomes is seen in comparisons of the genotype pairs (AaWY, aaWY), (AaXY, aaXY) and (AAWW, AaWW) in which the first genotype in each case is male while the second is female as proven by the sex ratio results. The members of the pair differ only in the substitution of one autosome for the other. To test the theory, experiments consisting of hormonal sex reversion and a series of crosses are proposed. Finally, theoretical and practical implications of the theory are discussed.