Can recessive alleles produce codominance?

Can recessive alleles produce codominance?

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Maybe I'm confused by the term "codominance", but I wondering if codominance only occurs with two dominant alleles.

Can two recessive alleles produce codominance in an individual?

Likewise, can two recessive alleles produce incomplete dominance?

An allele is not dominant or recessive by itself. It is dominant or recessive compared to another allele. Therefore, if you consider one locus (position on a sequence) that has two alleles (bi-allelic locus), you cannot have two dominant or two recessive alleles. It is like saying that two things are darker. In reality you can either say that one is darker than the other one or that the color is as dark as the other one. So either one allele is dominant (or partially dominant) and the other is necessarily recessive (or partially recessive) or the two alleles are codominant.

Think of a gene that influence a phenotypic trait such as tail length for example. This locus is bi-allelic (two different alleles (=variant of a gene) exist (=segregate) at this locus). We'll call the two alleles $A$ and $B$. An individual that homozygous $AA$ has trait value $M_{AA}$. The homozygotes $AB$ have trait value $M_{AB}$ and individuals $BB$ have trait values $M_{BB}$. Viewing this in a table it gives:

$$ egin{array}{c|lcr} ext{Genotype} & ext{Tail length} hline ext{AA} & M_{AA} ext{AB} & M_{AB} ext{BB} & M_{BB} end{array} $$

The following table gives the tail length of the different genotypes under the different types of interactions (dominance, partial dominance and co-dominance).

$$ egin{array}{c|lcr} ext{Interaction} & ext{AA} & ext{AB} & ext{BB} hline ext{A is dominant and B is recessive} & M_{AA} & M_{AA} = M_{AB} & M_{BB} & & M_{AA} > M_{AB} > M_{BB} ext{Partial Dominance} & M_{AA} & ext{or} & M_{BB} & & M_{AA} < M_{AB} < M_{BB} ext{Codominance} & M_{AA} & M_{AB} = frac{M_{AA} + M_{BB}}{2} & M_{BB} end{array} $$

Because, in the codominance case $M_{AB}$ is necessarily between the values of $M_{AA}$ and $M_{BB}$ ($M_{AA} > M_{AB} > M_{BB}$ or $M_{AA} < M_{AB} < M_{BB}$), one can consider codominance as being a special case of partial dominance where neither $A$ or $B$ dominates because they both contribute as much to the determination of the tail length.

Various definitions may exist for such concepts as well as for overdominance (also sometimes called heterozygous advantage) or stabilizing selection for examples. Those definitions differ in the sense that they sometimes apply to the value of the quantitative trait, to the fitness value (which is another quantitative trait) or to genetic polymorphism.

When two alleles show codiminance, they are not described as dominant or recessive relative to each other. They are simply codiminant to each other. The same applies to incomplete dominance.

Note that all these terms are relative to the alleles you're talking about. An allele that is dominant over one allele may be recessive to another and codiminant with yet another.

Shorter answer:

The dominant/recessive paradigm that is taught in middle school and high school is not universally applicable. It accurately describes only a small number of phenotypes, compared to all the genotype/phenotype interactions which an organism exhibits. It was a useful place to start when it came to unraveling the relationship between genes and phenotypes, but it is very limited.

So trying to shoehorn all phenotypes into that paradigm is a serious mistake. Just because all of your homework problems are solved using it doesn't mean that it's applicable to all real-life situations.