BIO 370 Lecture Notes - Lecture 31: Epistasis, Total Variation, Heritability
Complicating factors include dominance and epistasis.
Therefore, evolutionary biologists prefer to work with a different quantity known as narrow-
sense heritability (h2), the fraction of the total variance due to additive genetic variation.
Decomposing Genotypic Effects
If all gee effets ee to oie additiely, a idiidual’s geotypi alue G could be
represented as the simple sum of gene effects.
But, we also have to consider interactions between two alleles at the same locus (dominance
effects) and interactions between alleles at different loci (epistatic effects).
(There are other complicating effects, such as
genotype * environmental interactions which we are going to ignore.)
To account for dominance and epistasis, we can further decompose P and VP.
If Genotype has Additive, Dominance and Interactive components, then
P = G + E = A + D +I + E
and
VP = VG + VE = VA + VD + VI + VE
Dominance and interaction (epistatic) components are highly context dependent –
Their effects depend strongly on the genetic background in which they occur.
Thus, exposure and response to selective forces of these non-additive components is context
dependent and, thus, response is more difficult to predict in anything but general terms (likely
to get bigger, smaller, etc.)
The additive component is independent of context.
Irrespective of genetic background, the effects of additive components of genetic variance
are the same.
To best study the response of phenotype to selection, we need to look at the fraction of the
total variation that is due to the additive genetic variation. This fraction is called the narrow-
sense heritability (h2). Mathematically, we define narrow sense-heritability as:
h2 = VA / (VA + VD + VI + VE)
Narrow sense heritability, as a measure of what fraction of the variation is accessible to natural
selection, plays an important role in predicting how phenotypes change over time as a result of
natural selection. We will see how this works shortly.
Fist, let’s osider a basic interpretation of narrow-sense heritability as a population level
measure of resemblance between parents and offspring.
find more resources at oneclass.com
find more resources at oneclass.com
Specifically, narrow-sense heritability is equal to the slope of a linear regression between the
average phenotype of two parents and the phenotype of their offspring because we will
assume that the environmental effects are the same (or at least are uncorrelated with the trait
measurements).
Remember the equation for a line?
slope of y on the x-axis :
intercept on the y axis: b
And the slope also =
We measure the co-variance of traits, where xi is the trait of the parent and yi is the
trait of the offspring.
(the sum of the deviation from the mean of variable 1, times the variation from mean of
variable 2, for each instance, divided by n-1)
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Therefore, evolutionary biologists prefer to work with a different quantity known as narrow- sense heritability (h2), the fraction of the total variance due to additive genetic variation. If all ge(cid:374)e effe(cid:272)ts (cid:449)e(cid:396)e to (cid:272)o(cid:373)(cid:271)i(cid:374)e additi(cid:448)ely, a(cid:374) i(cid:374)di(cid:448)idual"s ge(cid:374)otypi(cid:272) (cid:448)alue g could be represented as the simple sum of gene effects. To account for dominance and epistasis, we can further decompose p and vp. If genotype has additive, dominance and interactive components, then. P = g + e = a + d +i + e and. Vp = vg + ve = va + vd + vi + ve. Dominance and interaction (epistatic) components are highly context dependent . Their effects depend strongly on the genetic background in which they occur. Thus, exposure and response to selective forces of these non-additive components is context dependent and, thus, response is more difficult to predict in anything but general terms (likely to get bigger, smaller, etc. )
