The Mathematical Basis of Phenotype Ratios

Certain classical experiments in genetics provide interesting ratios amongst the offspring population which relate to the pattern of the inheritance of the parents’ features. In this paper these ratios are analysed.

The occurrence of each class in each ratio is found to be 3 ^n‐x and the sum of the classes of a ratio to be 4ⁿ where nis the number of genes in the system and xthe number of features which are recessive. The classes when grouped show group coefficients to be in accordance with Pascal's Triangle, and the ratios themselves are shown to be a particular case of the binomial expansion (p+q)ⁿ where pis 3 and qis 1.

Some aspects of the value of this analysis to a biologist are considered.