Re: Heritability of fitness


"Perplexed in Peoria" <jimmenegay@xxxxxxxxxxxxx> wrote in message news:dp7s9c$27ln$1@xxxxxxxxxxxxxxxxxxxxxx
> To analyze this, it is useful to start with the textbook definition of
> heritability. Of course, since these definitions were produced by
> statisticians, they are interested not in heritibility of a trait,
> but rather the heritability of variation in a character.
> Here are some definitions, as I recall them:
>
> V is the total variance in a character.
> It is broken into four components V = V_a + V_d + V_i + V_e
> V_a is the 'additive genetic variance'
> V_d is the 'dominance variance' due to interactions between the two gene
> copies on different chromosomes at a single locus
> V_i is the 'interaction variance' due to epistatic interactions between
> genes at different loci
> V_e is the 'environmental variance' due to the fact that no two organisms
> experience exactly the same environment. For example, one individual
> may be hit by lightening, while his twin brother is not.
> For convenience, V_g is the 'total genetic variance': V_g = V_a + V_d + V_i
>
> H^2 is the 'broad-sense heritability' and is defined as V_g / V
> That is, it is the fraction of the total variance (in fitness, say)
> which can be attributed to the organisms genes.
> h^2 is the 'narrow sense heritability' and is defined as V_a / V
> It is important because (whether you like it or not) V_a is the only
> component of the variance which responds to selection in a sexually
> reproducing population. By contrast, if the population were to
> reproduce by cloning, then H^2 would be the appropriate notion of
> heritability since reproduction would not break up the non-additive
> 'dominance' and 'epistasis' features of the parent's genome.
>
> I hope I have these definitions right.

I got these definitions from the textbook "An Introduction to
Genetic Analysis (4th ed.) by Suzuki, Griffiths, Miller, and
Lewontin. It is a bit on the elementary side, but it was the
best my local library could supply.

Since *** Lewontin is one of the authors, and since this edition
was published in the late 1980s, the book is careful to explain
that the relative partition of variance into the components V_g
and V_e is not cast in stone. It is not a property of a particular
trait (human IQ, say) that its heritability H^2 is a particular
number. Instead, the heritability will vary as variability is
added or removed from the environment, as the scope of the sample
is changed, or simply as a result of gene frequency changes.
This was explained again and again.

Well, long about the fifth time that Lewontin began beating this
already moribund horse, I got to thinking. It is not just
the partition of V into V_g and V_e that is shiftable. Many
of the same arguments apply to the partition of V_g into V_a,
V_d, and V_i. Changes in gene frequencies change the distribution
among these categories. For example, a rare recessive allele
produces some V_d but very little V_a. But when the allele becomes
common, the variance is mostly V_a with a little V_d.

It occured to me that in a structured population, different groups
may have different allele frequencies and that what is strictly
heritable V_a variation in one group may be V_i variation in
another group and may not respond to selection. It also occurred
to me that we can partition variance into within-group and
between-group components. And finally, it occurred to me that
something like the Price equations might be the right analytical
framework for investigating this kind of question.

Then I remembered that I don't really understand the Price
equations, so I went back to reading Lewontin's preaching.
But perhaps someone more mathematically adept than myself
can make something of this. ;-)


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