Complementary genes it may be defined as two or more dominant genes present on separate gene loci, which interact to produce a particular phenotypic trait, but neither of them produce a particular trait in the absence of other. Complementary genes were first studied by Bateson and Punnett in the case of flower colour of sweet pea (Lathyrus odoratus).
Complementary genes (9:7 RATIO)
Supplementary genes: They are two independent genes present on different  on different gene loci, each producing its own trait. These genes interact when present in dominant state to produce a new trait.
(Complementary genes vs Supplementary genes)
Complementary genes
Supplementary genes
They are a pair of non allelic genes, both of which independently express similar phenotypic trait.
They are a pair of nonalleic genes where only one is able to express its effect independently.
Both the genes interact to produce a completely new trait.
The interaction of the two genes modifies the expression of the independently expressing gene.
The F2 ratio is generally 9:7
The F2 ratio is generally 9:3:4

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