Week 10: Quantitative Genetics

Joe Felsenstein

Genome 562

Week 10: Quantitative Genetics – p.1/11

The Biometricians

Francis Galton (1822-1911) Karl Pearson (1857-1936)

Week 10: Quantitative Genetics – p.2/11

Francis Galton sees a law of heredity

... or what he thinks is one. These days we’d just say he saw a bivariatenormal distribution.

Week 10: Quantitative Genetics – p.3/11

Ronald Aylmer Fisher (1890-1962)

about 1930 in 1952

Fisher, R. A. 1918. The correlation between relatives on the supposition ofmendelian inheritance. Philosophical Transactions of the Royal Society ofEdinburgh, 52: 399 – 433.

Week 10: Quantitative Genetics – p.4/11

A one-locus quantitative character

Week 10: Quantitative Genetics – p.5/11

A two-locus quantitative character

Week 10: Quantitative Genetics – p.6/11

Distributions with different numbers of locin = 1 n = 2

n = 10n = 5

Each has a number of completely dominant loci (all of equal effect), withsize of effects scaled so that overall genetic variance is equal, and with an

environmental effect that contributes 20% of the variation.Week 10: Quantitative Genetics – p.7/11

Regression of offspring on a parent

6 8 10 12 14

6

8

10

12

14

Off

sp

rin

g

Parent

Week 10: Quantitative Genetics – p.8/11

Regression of offspring on a parent

−4 −2 0 2 4

−4

−2

0

2

4

Parent − Mean

Off

sp

rin

g −

Mean

Week 10: Quantitative Genetics – p.9/11

Regression of effects at one locus on gene dose

a12

a11

a22

0 1 2

11

12

22

x (dosage of A )1

a

δ

δ

δ

+1 1

α α

+α αα α+

1 22 2

ij

Week 10: Quantitative Genetics – p.10/11

Jay L. Lush (1896-1982)

about 1960 Animal Breeding Plans

Week 10: Quantitative Genetics – p.11/11