Genetics of Complex Traits: Quantitative Genetics

1. Genetics of Complex Traits:Quantitative Genetics

2. Continuous Variation (height) Genetic Variation Discrete Variation (presence/absence of tail)

3. Quantitative Genetics Height Weight Athletic ability Risk of heart disease Risk of diabetes Risk of cancer Polygenic Environmental influences Have continuous (not discrete) distributions Can be measured on a quantitative scale

4. Intermediate dominance = “additive” gene action Partial dominance Discrete distribution

5. Red Lt Red Pink Lt Red Lt Red Pink Pink Lt Pink Pink Lt Pink Pink Lt Red Lt Pink white Lt Pink Pink 1 Red: 4 Lt Red: 6 Pink: 4 Lt Pink: 1 white

6. Two additive genes: discrete phenotypic distribution

7. Color of wheat kernels: three additive genes aabbcc AABBCC AaBbCC

8. Frequency Distribution of Height of the Band mean=68 inches

9. n =160 Properties of distributions Mean = = 68 inches Variance = = 9.5 in2

11. Types of Variance Phenotypic variance: total variance of the population, includes variation from genes and from the environment Genetic variance: the variance that is due to variation among individuals in the alleles that they have, excludes environmentally-caused variation

12. Mean = 68 in Phenotypic Variance Var = 9.5 in2 Phenotypic variance = Genetic variance + Environ. variance VP = VG + VE

13. Phenotypic variance = Genetic variance + Environ. variance VP = VG + VE Genetic variance = Additive variance + Dominance Variance VG = VA + VD VP = VA + VD + VE

14. AdditiveandDominanceEffects (No Environmental Effects)

15. Mean = 18.5 cm Var = 1.333 cm2 VP = VA + VD + VE 1.0 + 1.333 = 0.333 + 0

16. VP = 1.333 cm2 VA = 1.0 VD = 0.333 VE = 0

17. 1.0 + 1.333 = 0.333 + 0 Heritability VP = VA + VD + VE = 1.0 Broad-sense heritability H2 = VG/VP = 0.75 Narrow-sense heritability h2 = VA/VP

18. Uses of heritability • The degree to which offspring resemble their parents is determined by the narrow-sense heritability h2 • The efficacy of natural and artificial selection is also determined by h2

20. h2 = 1 VA/VP = 1 h2 = 0 VA/VP = 0

21. Efficacy of artificial selection: size of Labradors

22. Breeder’s Question Q: A horse breeder wants to win the Kentucky Derby. If she breeds her mare to a really fast stallion, how likely is it that the colt will be faster than all the other three-year-olds when it runs in the Derby? A: It depends on the heritability of running speed

23. Breeder’s Equation • R = h2 S • S = Selection differential difference between selected parents and the population as a whole (within a generation) • R = response to selection difference between selected offspring and the unselected population (across generations)

24. Breeder’s Equation R = h2 S A dog breeder chooses his largest dogs to breed together. The average height of the breed is 60 cm (at the shoulder), and the dogs he chooses to breed average 70 cm tall. He knows from previous work that the heritability of height is 0.5. How big can he expect the offspring to be? 0.5 * 10cm = 5cm R = h2 S =

25. Breeder’s Equation R = h2 S = 0.5 * 10 cm = 5 cm If the response to selection is 5 cm, he can expect his puppies to grow to be 60 cm + 5 cm = 65 cm tall

26. Exactly the same equation can be used to understand natural selection!

27. Efficacy of natural selection:Darwin’s finches

28. If large bills are favored in drought years, what effect will an El Nino year have on the population? h2 = 0.8

29. R = h2 S Birds that survive the drought have bills that are 2 mm deeper (on average) than the population mean. Q: What will happen to the average bill depth in the next generation?