If a gene has for instance three alleles, p, q, and r, then could p be dominant to q, q be dominant to r, but r be dominant to p? Can a gene that is recessive to one allele not be dominant to another allele that is dominant to the second? If it can, what are some examples of traits that do this?
To some extent, it depends on what you mean by "dominance". If you take a phenotypic definition of dominance, then the answer is (technically) yes, you could imagine such a gene system.
That is, imagining alleles p, q, and r, and three phenotypes P, Q, and R, with the following homozygous behavior:
- pp ➞ P
- qq ➞ Q
- rr ➞ R
Then you could theoretically imagine the following heterozygous behavior:
- pq ➞ P
- qr ➞ Q
- pr ➞ R
In that sense, p is dominant to q, q is dominant to r, and r is dominant to p.
The problem arises in trying to figure out the underlying biochemical rationale for such a system.
In the typical cases where we talk about dominant and recessive alleles, we're talking about a single axis of functionality, particularly an all-or-nothing case: The dominant gene has activity, and the recessive gene doesn't. If you have one or two dominant alleles, you have activity and thus the dominant phenotype, and if you have no dominant alleles you have no activity and thus the recessive phenotype.
It doesn't have to be all or nothing. That's where incomplete dominance comes in. If you have two dominant alleles you have a lot of activity. If you have one dominant allele you have less activity If you have no dominant alleles, you have no activity.
In some cases, dominance is not gain of activity, but rather loss. This is termed a "dominant negative". The normal, recessive allele has a certain activity, and the dominant negative allele can come in and shut off that activity. A frequent mechanism of action for a dominant negative is to non-productively out-compete the recessive allele for binding sites.
Such a single-axis explanation of dominance can't contain your proposed system. However, there are systems where there are multiple axes of activity. The ABO blood group system is a good example. Here you have three alleles, a, b and o. a codes for A activity. b codes for B activity, and o is inactive for both. Thus you have both a and b being dominant to o, but neither is dominant to each other, resulting in an AB blood group when both are present.
However, as long as we're just adding activity, we still can't realize your cyclical dominance system - we'll be stuck with co-dominance.
Totally hypothetical system:
To support your cyclical dominance system, we can possibly combine multiple activity a dominant negative. Here's one possible system that I came up with.
The allele p induces activity A, but is a dominant negative (that is, actively suppresses) toward activity B. The allele q induces B, but is inactive toward A. The allele r is inactive toward B, but is a dominant negative toward activity A So we have the following:
- pp ➞ A ➞ P
- qq ➞ B ➞ Q
- rr ➞ O ➞ R
- pq ➞ A ➞ P (q tries to have activity B, but is suppressed by p)
- qr ➞ B ➞ Q
- pr ➞ O ➞ R (p tries to have activity A, but is suppressed by r)
Is there a set of genes which has such a system? I'm not aware of any. Notice that to get such a cyclical dominance, you need to not only have multiple activities but also dominant negatives - and in the correct correspondences. If such a system exists, it would be very unlikely.
Dominance by silencing the other allele
The mechanisms by which dominance work are still very much unknown. One type of mechanism that will be of particular interest to this question is the modifier of dominance where the protein product of an allele silence the expression of the other allele in order to cause dominance relationship.
Is the pattern you describe possible?
In such system, I can imagine a case where allele
A1 would silence
A2 which would silence
A3 which would silence
A1. I can't think of any reason such a pattern should not exist. However, I am not aware of evidence of such pattern.
The interesting case of SI in Arabidopsis thaliana
This type of dominance (dominance through silencing the other allele) has been reported in the self-incomtability locus of Arabidospsis theliana (Durand et al. 2014). At this specific locus there are 6 alleles but they have a very hierchical relationship where
A1 silences all other alleles,
A2 silences all alleles but
A3 silences all other alleles but