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Lecture 6:Chapter 3.3 Quantitative genetics
Many traits take quantitative instead of qualitative values, and are determined by many genes
Genetics and inheritance of quantitative traits is described in statistical terms.
Resemblance between relatives:
- Related individuals share alleles relatives have similar phenotypes
How to measure similarity?
- Covariance measures how much two variables vary together
o Difficult to interpret (scale dependent)
- The standardized version of the covariance, the correlation coefficient
- -1 < corr < +1
- The sign + or – tells you the direction, the closer the relation to +1 or -1 the more precise it is.
Resemblance between relatives:
- Related individuals partly carry the same alleles
o They have similar phenotypes
- Measure of similarity
o Covariance and correlation of their phenotypes
- Degrees of similarity (covariance, table 3.4)
o Identical twins: COV(Zi,Zj) = VG
o Parent-offspring: COV(Zi,Zj) = ½ VA
o Full brothers/ sisters: COV(Zi,Zj) = ½ VA + ¼ VD
o Half-brothers/ sisters: COV(Zi,Zj) = ¼ VA
- Beware: similarity due to shared environment
, - Degrees of similarity (correlation)
o Identical twins: Corr(Zi,Zj) = VG / VZ
o Parent-offspring: Corr(Zi,Zj) = ½ h2
o Full brothers/ sisters: Corr(Zi,Zj) = ½ h2 + ( ¼ VD / VZ)
o Half-brothers/ sisters: Corr(Zi,Zj) = ¼ h2
- VA refers to the alleles. (Check this is recording!!!)
- This may be less than you think!
o E.g. correlation between length of two full brothers
H2 ≈ 0.9 correlation = 0.5 * 0.9 = 0.45
Often: relatives are similar also due to other reasons: shared environment
(e.g. family diet)
How can we know VA without knowing the genes?
- If individuals carrying the same alleles are similar, then those alleles must affect the trait
VA > 0
- VA can be estimated from resemblance between relatives.
- Half-brothers/ sisters: COV(Zi, Zj) = ¼ VA
- estimated VA = 4 Cov(half sibs)
- Estimated h2 = 4 Corr(half sibs)
Evolutionary genetic models of response to selection
- Heritable traits positively related to fitness tent to increase over time
There is a continuous relation between traits and fitness. In natural selection you usually don’t know
how strong the selection is. And how strong the response to selection is.
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