The distribution of the effects of mutations

Pursuant to this very helpful discussion with @glipsnort ,

I have attempted to draw together the pieces of what he’s said into a graphical format. For reference, here is the DFE given to us originally by Motoo Kimura:

Which, I must say rather shamefully, is one-sided. But a one-sided distribution is not what I’m after.

I invite @glipsnort and @Joe_Felsenstein to comment on the below DFE, which seems to be what Dr. Schaffner is implying with his explanation:

Now we see Kimura’s distribution, with the alleged beneficials included on the positive side of the chart. The shaded regions represent effectively neutral mutations and the threshold of selection. Since Dr Schaffner has suggested that there is no overall direction to the effectively neutral mutations, the only conclusion is that the right side (beneficials) must exactly counterbalance the left side (deleterious). All parties apparently agree that selectable beneficials are extremely rare compared to deleterious mutations.

Discuss. Is this an accurate DFE? Is this what you meant to imply, Dr. Schaffner?

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More or less, yes. Keep in mind that we know far more about the genome than Kimura did.


Thanks. Here’s a follow-up question.

There’s something odd about the above distribution. Note that the curve rapidly and suddenly changes direction at the threshold of selection on the beneficial side, but not on the corresponding deleterious side.

What accounts for this?

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I note that this graph has neither a horizontal nor a vertical scale, and it’s truncated at the top. Further, we can have no empirical confirmation of anything within the red region of the graph.


The way you chose to draw it, and nothing more that I can see.


It seems to me the shape of the curve must depend on how well-adapted some organism is to it’s environment. Just to highlight this, imagine how the curve would have to look for the two extremes: The genetically perfect organism where no further beneficial mutations are possible(here all possible mutations must either belong to the set of deleterious or strictly neutral), and the totally nonfunctional genome(where further mutations must either be strictly neutral, or beneficial).

As you “bring up” an organism from the floor of the totally nonfunctional genome, the better adapted it becomes the smaller will the proportion of beneficial mutations become. To the worst possible but still living organism, there must be a much larger proportion of beneficial mutations available, than there are to the second-best-possible organism.

The worst possible but still living organism can’t have any slightly deleterious mutation available to it, all deleterious mutations must result in lethality(if it could get less fit, then that would be the worst possible but still living organism). That means all mutations of small effect available to the worst possible but still living organism must be beneficial.

It follows that it does not make physical or biological sense to insist that the ratio of beneficials to deleterious mutations, whether in totality or those of small effect, would have to remain constant.


The beneficial side changes because a different process operates above the threshold than below it. The deleterious side doesn’t change because, as @john_harshman already said, you drew it that way.


What is this different process? All these mutations are spontaneous and unguided. This is the way it looks before selection or any other “processes” in biology have a chance to act upon it.

I drew it that way because Kimura drew it that way. He apparently didn’t feel there would be any difference in process related to that threshold.

I think there are many good reasons to believe that the ratio remains at least largely similar, if not constant. I think all the experts would agree that it’s only an approximation of the general trend. If the ratio is wildly different in different environments, then drawing this chart makes no sense to begin with, since it would be meaningless.

Selection, of course. As has been explained to you repeatedly – within the last hour, in fact – real genomes are the result of a lengthy history of selection, which means that most selectable variants are already optimized, which means that above the threshold there are very few favorable options left. Below the threshold, selection hasn’t acted, so there are lots of favorable mutations possible.

Now, do you understand this or not? Because having you ask the same question over and over, just to receive the same answer over and over, is pretty annoying.


And he knew exactly as much as you do about what the actual distribution is in that regime.


Yes I believe I understand your meaning. I have also understood you to say that the threshold of selection lines up (for all intents and purposes) exactly with the threshold between junk and non-junk. Such that essentially all of the mutations in the shaded region are junk mutations, and all the mutations in the non-shaded region are functional mutations. Is this right?

No. Most mutations to junk DNA are way, way below the threshold. For humans, the threshold is historically between 1e-4 and 1e-5, while the kind of selective effect I was talking about for junk DNA is about 8 orders of magnitude smaller.


Do we really want to use this term? I don’t think so…


Let’s pretend that we have a second color for shading (let’s say, yellow). Now let’s shade the portion of the maroon area yellow that corresponds to the fraction of effectively neutral mutations in functional (non-junk) DNA.

Will we have the same amount of yellow on both sides of the Y axis? In other words, is there an equal percentage of effectively neutral mutations affecting functional DNA in both directions (beneficial and deleterious)?

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Why not? It seems appropriate to me.
ETA: I’d settle for ‘otiose DNA’, though.

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Or “DNA more tolerant to mutation”. “Junk” carries a lot of baggage you may not intend, and is outside the scope of this topic.

Considering that he’s compared it previously to the results of a monkey banging on a typewriter, I’m not entirely sure he wouldn’t intend that baggage.

Notably, this is an off topic digression (with some relevance) that may be split, so carry on without feeling need to engage it.


The nonfunctionality of junk DNA, which is conveyed quite well by ‘junk DNA’ and not at all by ‘DNA more tolerant of mutation’, is entirely within the scope of this topic.