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Recently, I learned about polygenic traits and it got me wondering, are there any truly Mendelian traits where the trait displayed exists in a total binary?

I have looked at some questions on the forum and this one is close enough, though I suspect that the degree to which ear wax is dry or wet would vary from individual to individual.

I understand that most of our groups for anything are imperfect and so a perfect binary trait (such as yellow-green peas, which, I believe, also do have a gradient in their coloration, they can't all have the exact same pigmentation) isn't very likely, but could it exist?

Sorry if the post isn't really detailed, I'm not experienced in biology so I don't know which sources to look for.

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George Box is credited with the aphorism "All models are wrong, but some are useful" in the context of statistics, but the same concept applies to concepts like Mendelianism which are also really a type of model applied to data.

Perhaps the simplest mechanism behind a Mendelian trait is a functional versus non-functional enzyme; let's imagine it's an enzyme that catalyzes a step in pigment formation. With the enzyme, a red-colored molecule is produced. Without it, there is no red. In many cases the enzyme concentration won't be particularly important, and you'll have a simple recessive Mendelian trait: as long as you have at least one functional copy, you get red pigment. If you have zero functional copies, no red.

If that's all the variation you have in the population you're looking at, then the Mendelian model works great. But it's also extremely unlikely that this is truly the only possible source of variation in color, even if it's the only variation you observe.

For example, there is going to be some pathway that produces the reactant for the red-making enzyme to work with, and any changes in any of the biology associated with that pathway can potentially change pigmentation, too.

There is going to be regulation of the expression of the red pigmenting enzyme, too; that regulation might start to make the copy number important if expression becomes very low. It might make the coloration more sporadic or patterned if expression becomes variable among cell populations.

Finally, there's no reason for there to be only two alleles of some gene; in a real population many different alleles will exist, and while some are going to be interchangeable with respect to phenotype (for example, it doesn't matter for phenotype what the specific mutation is that makes a gene product non-functional), others will not be.

So, the Mendelian model for phenotype is almost certainly wrong or at least not comprehensive; the question is about when it is and isn't useful, despite being wrong, and there are lots of cases when it's useful. When someone says a trait is Mendelian, you should translate that as "A Mendelian model is useful for describing the variation in this trait in the population we're talking about"; they are not necessarily (and should not be) making a claim that the trait is somehow intrinsically Mendelian, there is no such thing.

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  • $\begingroup$ Doesn't this come down to your definition of "trait", really? In your example, if you define "trait" as the visible phenotype, the cell's color, then sure, there can be other mechanisms that would change the color. If, however, you define the trait as whether we have a functional enzyme or not, then wouldn't you say it is indeed perfectly mendelian? $\endgroup$
    – terdon
    May 16 at 9:54
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    $\begingroup$ @terdon In the real world it's unlikely that the only variations that exist in an enzyme are "functional" and "not". There is certainly no enzyme where alleles must sort into those two categories. I'd say at the point you've decided to sort s trait into a binary functional/non-functional you've already chosen to apply a Mendelian model to the data. $\endgroup$
    – Bryan Krause
    May 16 at 11:44
  • $\begingroup$ Ha! Fair point, yes. $\endgroup$
    – terdon
    May 16 at 11:49
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    $\begingroup$ @terdon I guess I'd also encourage people not to focus too much on Box's "wrong" and remember the "useful" part is there, too! F = ma is also a wrong model, but for many contexts you'll have only data that do not conflict with it out to many decimal places and for which it would be a waste of time to use any other model! $\endgroup$
    – Bryan Krause
    May 16 at 11:58

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