Trying to understand, in plain English, Patrick Moran's famous example of fitness continually decreasing

I wish again to express a heartfelt thanks to Joe Felsenstein who has graciously provided his graduate level textbook on Evolutionary Genetics free-of-charge. I have a copy of his Magnum Opus on Phylogeny which I purchased for $110, and would gladly buy another one of his books if he chooses to write one.

I purchased pop gen text books by Gillespie, Hartle and Clarke, but I felt Joe’s free-of-charge book is the best and easiest to read and understand.

Some weeks ago, I was alerted to something I was totally unaware of in population genetics, namely the problem of continuous fitness decrease in certain cases of two-loci or multi-loci diploid populations.

I haven’t slugged through the math in detail yet, but it’s sometimes helpful to get an intuitive picture of what the symbols are trying to describe. To the best of my understanding the problem is that there is incomplete Mendelian segregation – that is to say some alleles don’t shuffle randomly during meiosis, but rather are linked because of physical proximity on the same chromosome.

This leads to the possibility that an allele at one loci that would other wise be unfavored is linked to another loci where there is an allele that is favored. This situation can of course change over time, but Moran was able to show that the complication of linkage creates a situation where the multi-loci version of mean relative fitness can go down continuously, and even down to minimum level that will be the final equilibrium. Is that right or am I totally misunderstanding the root of the problem? Or can the problem only be understood in purely mathematical terms laid out in that section of the book?

One writer has likened the multi-loci situation to a function with saddle points in 3D space where one can’t make a general statement of whether a given path on the surface will inevitably go up or down:

From Joe’s book page 378 that discusses Moran’s famous counter example to the idea that fitness is always maximized:

it is easy to show that not only can recombination lead to a continual decrease of mean fitness during the course of evolution, but it leads to an equilibrium state which has lowered mean fitness. This is quite frequently found in multi-locus models.

This seemingly dysfunctional property of recombination raises the question of why recombination is present at all. It may be a by product of other cellular phenomena…

Consider sickle-cell anemia, where a single copy of the gene confers resistance to malaria, but two copies bring on a painful disease. That’s not the same as linked loci, but the effects are similar.

Hi Dan,

Thanks for the response. You’re the only biostatistician that I know of.

Dumb question: Do biostatisticians get involved in population genetics too? You’re the only biostatistician I know.

Not dumb! Yes they do, but I have no experience with that.
There is an emerging area of Statistical Genetics, and one of our faculty specializes in that.

Not so dumb, and yes they do. Statistical Genetics is an emerging specialty area, and one of our faculty does work on this. I have no experience with this myself.

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