Genetics of Complex Traits Quantitative Genetics Genetic Variation Discrete Variation presence absence of tail Continuous Variation height Quantitative Genetics Polygenic Environmental influences Have continuous not discrete distributions Can be measured on a quantitative scale 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 1 1 1 Frequency 0 RR Rr Genotype rr P AABB red AaBb F1 F2 AB x aabb white x AaBb All Pink AB AABB Red AABb Ab AABb Lt Red AAbb aB AaBB Lt Red AaBb ab AaBb Pink Aabb Lt Red aB AaBB Pink AaBb Pink Aabb Lt Pink Pink aaBB Pink Lt Pink aaBb Lt Pink aaBb Lt Pink aabb white Ab ab Lt Red AaBb Pink 1 Red 4 Lt Red 6 Pink 4 Lt Pink 1 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 Color of wheat kernels three additive genes aabbcc AABBCC AaBbCC Frequency Distribution of Height of the Band mean 68 inches n 160 Properties of distributions n Mean x x i 1 n i 68 inches n Variance 2 Var x i 1 i x n 1 2 9 5 in 2 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 Mean 68 in Phenotypic Variance Var 9 5 in2 Phenotypic variance Genetic variance Environ variance VP VG VE Phenotypic variance Genetic variance Environ variance VP VG VE Genetic variance Additive variance Dominance Variance VG VP VA VA VD VD VE Additive and Dominance Effects No Environmental Effects P Dominance effects AA Aa aa 2 2 0 AABB 20cm F1 F2 Genotypes Genotypic Effects Additive effects BB Bb bb 2 1 0 aabb 16 cm x Aa Bb 19 cm AABB AABb AAbb AaBB AaBb Aabb aaBB aaBb aabb 4 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 Dominance effects AA Aa aa 2 2 0 F1 F2 Genotypes Genotypic Effects Additive effects BB Bb bb 2 1 0 Aa Bb 19 cm x AABB AABb AAbb AaBB AaBb Aa Bb 19 cm Aabb aaBB aaBb aabb 4 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 VD 1 0 0 333 VE 0 VP VA VD VE 1 333 cm2 1 0 0 333 0 0 4 0 3 0 2 0 1 0 population 16in Frequency 17 18 19 Length in inches 20 Heritability VP 1 333 VA VD 1 0 0 333 Broad sense heritability VE 0 H2 VG VP 1 0 Narrow sense heritability h2 VA VP 0 75 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 h 2 h2 1 h2 0 VA VP 1 VA VP 0 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 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 Exactly the same equation can be used to understand natural selection Efficacy of natural selection Darwin s finches h 0 8 2 If large bills are favored in drought years what effect will an El Nino year have on the population 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
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