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Transcript
Genetic Variation Genetics of Complex Traits: Quantitative Genetics Discrete Variation (presence/absence of tail) Continuous Variation (height) Quantitative Genetics Height Weight Athletic ability Risk of heart disease Risk of diabetes Risk of cancer Intermediate dominance = “additive” gene action Partial dominance 2 2 Discrete distribution Frequency Polygenic Environmental influences Have continuous (not discrete) distributions Can be measured on a quantitative scale 1 1 1 0 RR Rr rr Genotype 1 P: F1: F2: AB Ab AABB red AaBb AB AABB Red AABb Lt Red aB AaBB Lt Red ab AaBb Pink x x aabb white AaBb All Pink Ab AABb Lt Red aB AaBB Lt Red ab AaBb Pink AAbb Pink AaBb Pink AaBb Pink aaBB Pink Aabb Lt Pink aaBb Lt Pink Aabb Lt Pink aaBb Lt Pink aabb white Two additive genes: discrete phenotypic distribution 6 6 5 4 4 4 3 2 1 1 1 0 Red Lt Red Pink Light Pink White 1 Red: 4 Lt Red: 6 Pink: 4 Lt Pink: 1 white Color of wheat kernels: three additive genes Frequency Distribution of Height of the Band mean=68 inches aabbcc AABBCC AaBbCC 2 n =160 Properties of distributions n "x Mean = x = i=1 n i = 68 inches n ! 2 Variance = " = Var = $( x i #x i=1 (n #1) ) 2 = 9.5 in2 ! Mean = 68 in 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 Phenotypic Variance Var = 9.5 in2 Phenotypic variance = Genetic variance + Environ. variance VP = VG + VE 3 Additive and Dominance Effects (No Environmental Effects) Phenotypic variance = Genetic variance + Environ. variance VP = VG + Dominance effects AA Aa aa +2 +2 +0 AABB 20cm VE P: Genetic variance = Additive variance + Dominance Variance VP = VA = VA + + VD VD Dominance effects AA Aa aa +2 +2 +0 F1: F2 Genotypes: Genotypic Effects + VE x AABB AABb AAbb AaBB AaBb Aabb aaBB aaBb aabb +3 +2 +4 +3 +2 +2 +1 +0 Phenotype (cm) 20 19 18 20 19 18 18 17 16 F2 proportions: 1/16 2/16 1/16 2/16 4/16 2/16 1/16 2/16 1/16 Mean = 18.5 cm Var = 1.333 cm2 VP = 1.333 = VA AABB +4 +3 Phenotype (cm) 20 19 F2 proportions: 1/16 2/16 + VD + 1.0 + 0.333 + VE 0 AABb AAbb VP VA VD VE Aa Bb 19 cm +4 Aa Bb 19 cm F2 Genotypes: Genotypic Effects Additive effects BB Bb bb +2 +1 +0 Aa Bb 19 cm x F1: Frequency in population VG Additive effects BB Bb bb +2 +1 +0 aabb 16 cm = = = = AaBB AaBb Aabb aaBB aaBb aabb +2 +4 +3 +2 +2 +1 +0 18 20 19 18 18 17 16 1/16 2/16 4/16 2/16 1/16 2/16 1/16 1.333 cm2 1.0 0.333 0 0.4 0.3 0.2 0.1 0 16 17 18 19 20 Length in inches 4 Heritability VP = 1.333 = VA + VD Uses of heritability + 1.0 + 0.333 + Broad-sense heritability VE 0 H2 = VG/VP = 1.0 Narrow-sense heritability h2 = VA/VP = 0.75 • 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 h2 = 1 h2 = 0 VA/VP = 1 VA/VP = 0 5 Efficacy of artificial selection: size of Labradors 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 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) 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? R = h2 S = 0.5 * 10cm = 5cm 6 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 Exactly the same equation can be used to understand natural selection! 60 cm + 5 cm = 65 cm tall Efficacy of natural selection: Darwin’s finches h2 = 0.8 If large bills are favored in drought years, what effect will an El Nino year have on the population? 7 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? 8