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Is it possible that there are traits that might not be possible objects of the selection because of highly sensitive dependence on genotypes? The context of my thought came when I was having a discussion, more philosophical/political, with someone who was asserting individual characters (e.g. being good or bad) are innate in some sense. My impression is that, to whatever extent genetic determination of observable personality is the case, it'd be a highly complex phenomenon that could depend on many genes, and such matters are very much up in the air. This led me to thinking more abstractly about whether there could be such a thing as a trait that depended on so many genes-- to make it simple, let's say the entire genome-- and depended on in in a way that made it essentially a random trait.

For example, let's say there's a trait T, and we are looking at a creature that has a genome of only three base pairs, and to make it simple let's suppose the genetic code was binary, 1s and 0s (so eight possible genomes). So 100 represented an entire genome for whatever this is. And suppose that T was completely determined by genome (or else, that probability of T was determined by genome), and that the trait T was distributed over genomes such that T={000,110,101,011} and not T={100,010,001,111}. Visually, one could picture the genomes as corners on the unit cube in three dimensions, and T has been distributed so that any two corners separated by a single edge are opposite with respect to T, or, equivalently, that any two corners that can be connected by a minimum of two edges are of the same class with respect to T.

If there is no copying error in genomes then we can have selection for T; for instance, we can have pressure that favors one of the four genomes that cause T. But suppose there is always some random genetic error when a new individual is made. Say, for instance, the third spot is always randomly 1 or 0 with probability .5, and that there's no reducing the genetic randomness below this threshold. Then it seems impossible for there to be selective pressure for or against T, for any non-random distribution on the first two digits still just moves probability around genomes that give a net 50% probability of T being instantiated or not, because in the way I've assigned T, it is statistically independent of the value of any particular (or even any two) genes.

In essence, the trait is so very sensitive to changes in genome-- changing any single gene completely changes the trait-- that whether or not it is instantiated is swings back and forth with any random genetic changes. This is reminiscent of chaos in classical mechanics; some systems are simply so sensitive to underlying conditions that they are no subject to control and prediction in the fullest sense (though that doesn't mean they have to be fully random like the thing I've made here). Just on this basis a phenomenon like this seems formally possible, but my question, as someone who doesn't actually know the field, is whether it's in fact a known or theorized phenomenon, and if so what it would be called. Do there exist, or is it possible there exist, traits that are so sensitive to changes in genome that they can't be objects of selection because they fall under some barrier of genetic "noise," or perhaps things that at least start to look like that on a spectrum? Or are genomes always more "continuous" than this, so that, for pretty much everything, a small change in genotype leads to a small change in phenotype? If that were the case for some reason, then I think what I'm describing couldn't happen.

My apologies if my question is amateurish and my use of the language isn't quite right; I've never posted here before, and I'm a mathematician who's only just beginning to go back and self-educate on chemical and biological sciences, and this was a random thought I had while brushing my teeth, and didn't have the vocabulary to successfully search for and recognize answers.

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Don't want to get too down into the weeds here, I think you are making things rather complicated (thus someone else's downvote), but here are a few notes:

  • I would recommend looking up epistasis, which is a fundamental concept in genetics. (https://en.wikipedia.org/wiki/Epistasis). There are many ways in which a trait can be non-responsive to selection, one way is complex epistasis, which can have an effect on selection similar to what you say, in the case of (for example) sign epistasis.

  • Another way a trait can be not affected by selection is just not being important - if the selection coefficient (https://en.wikipedia.org/wiki/Selection_coefficient) is smaller than the inverse of the population size, selection will not work.

  • When I was first learning to code I made a toy model of a genotype:phenotype map here that can simulate both cases I think: https://github.com/maximilianpress/teaching_code/blob/master/EvoSim.r. It won't win any prizes but it illustrates the issue rather clearly IMO.

I would suggest reading a bit and maybe playing with the toy model to think about this more.

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