For example, imagine this Feynman diagram:


This is analogous to mutational homoplasy.

When comparing haplotypes, there are many possible tree topologies. Under maximum parsimony, we ignore suboptimal tree paths which certainly occur sometimes in reality. For example, imagine the following two haplotypes:

1: C A T T G

2: C A T A A

There are two mutations that make these different.

Maximum parsimony may infer this intermediate, not directly observed haplotype:


If we move from 1 to 2, the tree looks like:

C A T T G --> C A T A G --> C A T A A

However, the following is also possible:

C A T T G --> C A T A G --> C A T T G --> C A T A G


C A T T G --> C A T T C --> C A T A C --> C T T A C --> C A T A C --> C A T A C --> C A T A G

The not-directly-observed haplotype is analogous to the virtual particle. The directly observed haplotypes are the non-virtual particles. One could construct Feynman diagrams that look similar except have haplotypes instead of particles.

It is possible to imagine that some less-likely haplotypes actually are more harmonious with the observations. It seems that perturbation theory may help.

I don't have completely formalized thoughts on this. I am wondering if this has actually been used before to make a mutation process framework (e.g., an improvement to the infinite alleles model).

  • $\begingroup$ @David Thanks, fixed. I try to follow the rules but I don't know what all of them are yet $\endgroup$
    – BigMistake
    Commented Feb 11 at 17:36
  • $\begingroup$ No problem. The way SE works as a question and answer site is a bit hard to fathom initially, but I hope you persist as your expertise can clearly be of benefit. One key thing is that it is not a discussion site with a dialogue between someone with a question and someone who has an answer. The questions are supposed to be of use generally (and some of them are), discoverable by web searches. And that is why you find reference to the OP (original poster), acknowledging that a question may be edited and that it doesn't "belong" to whoever posted it, but the group in general. $\endgroup$
    – David
    Commented Feb 12 at 8:40

1 Answer 1


this is basically the argument behind maximum likelihood tree inference. Parsimony can lead to a lot of issues, as argued in the classic Felsenstein paper (linked).

Here is a brief paper discussing a particular improvement to the max likelihood method for tree inference in which substitution rates among sites are allowed to vary, which is another critical factor affecting tree topology estimation in a ML framework that can lead to the different mutational paths you show. I think it's a good entry point showing the value of ML over parsimony in incorporating multiple possible mutational paths with different interpretations (topologies).

If you are talking purely about cases in which the infinite alleles model isn't appropriate, I wrote a review on this topic a few years ago (see box 1 for some mutational paths very similar to the one that you present).

I am not sure how perturbation analysis fits into this or what the Feynman diagram means.


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