Fact: Different genetics texts do not use the same definitions for codominant. Some use a phenotype-based definitions and others a biochemical definition. And different genetics texts do not use the same definitions for incomplete dominant. Again either a phenotype-based definition or a biochemical definition. And there is not a one to one correlation between definitions based on phenotype and definitions based on biochemistry. Two genes that are biochemically codominant can produce a heterozygote with a phenotype that is intermediate between the two homozygotes.
Fact: A and B blood types are codominant because we use a sensitive chemical test. To the naked human eye, both are just red. In other words, sensitivity of the test can affect conclusions.
Fact: Distinguishing between codominant and incomplete dominant requires adding another term -- overdominance. Overdominance = the heterozygous form is not intermediate between the two homozygotes. The heterozygote is superior in performance or has a survival advantage compared to either homozygote.
Fact: Matings of codominant and incomplete dominant and overdominant genes produce the same results. In all three, the two homozygotes and the heterozygote can be distinguished. And the genotype results are the same as the phenotype results for a given mating.
Fact: "Codominant" has fewer characters than either "incomplete dominant" or "overdominant". Therefore, "codominant" is easiest to write.
Fact: Three definitions are easier to teach than five definitions.
Conclusion: Splitting mutant genes into three categories (dominant, codominant, recessive) is simpler for a breeder to use and teach than splitting mutant genes into five categories (dominant, codominant, incomplete dominant, overdominant, recessive).
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