1Genetics of Complex Traits:Quantitative GeneticsGenetic VariationContinuous Variation (height)Discrete Variation(presence/absence of tail)PolygenicEnvironmental influencesHave continuous (not discrete) distributionsCan be measured on a quantitative scaleHeightWeightAthletic abilityRisk of heart diseaseRisk of diabetesRisk of cancerQuantitative Genetics121012GenotypeFrequencyRR Rr rrDiscrete distributionPartial dominanceIntermediate dominance= “additive” gene action2abaBAbABF2:aabbaaBbAabbAaBbabaBAbABaaBbaaBBAaBbAaBBAabbAaBbAAbbAABbAaBbAaBBAABbAABBRedLt RedPinkLt PinkLt RedPinkLt RedPinkPinkLt PinkLt RedPinkPinkLt PinkLt PinkwhiteAll PinkAaBbxAaBbF1:aabb whitexAABB redP:1 Red: 4 Lt Red: 6 Pink: 4 Lt Pink: 1 white Two additive genes: discretephenotypic distribution146410123456Red Lt Red Pink Light Pink WhiteColor of wheat kernels: threeadditive genesaabbcc AABBCCAaBbCCFrequency Distribution of Height ofthe Bandmean=68 inches3Mean = = 68 inches! x =xii=1n"n Variance = = 9.5 in2! "2= Var =xi# x( )2i=1n$n #1( ) Properties ofdistributionsn =160Types of VariancePhenotypic variance: total variance ofthe population, includes variation fromgenes and from the environmentGenetic variance: the variance that isdue to variation among individuals inthe alleles that they have, excludesenvironmentally-caused variationPhenotypicVarianceVar = 9.5 in2Phenotypic variance = Genetic variance + Environ. variance VP = VG + VEMean = 68 in4Genetic variance = Additive variance + Dominance Variance VG = VA + VDVP = VA + VD + VEPhenotypic variance = Genetic variance + Environ. variance VP = VG + VEDominance effectsAdditive effectsAAAaaaBBBbbb+2+2+0+2+1+0P:AABBxaabb20cm16 cmF1:AaBb 19cmF2 Genotypes:AABBAABbAAbbAaBBAaBbAabbaaBBaaBbaabbGenotypicEffects+4+3+2+4+3+2+2+1+0Phenotype(cm)201918201918181716F2 proportions:1/162/161/162/164/162/161/162/161/16Additive and Dominance Effects(No Environmental Effects)Dominance effectsAdditive effectsAAAaaaBBBbbb+2+2+0+2+1+0F1:Aa BbxAa Bb19 cm19 cmF2 Genotypes:AABBAABbAAbbAaBBAaBbAabbaaBBaaBbaabbGenotypicEffects+4+3+2+4+3+2+2+1+0Phenotype(cm)201918201918181716F2 proportions:1/162/161/162/164/162/161/162/161/16VP = VA + VD + VEVar = 1.333 cm21.333 = 1.0 +0.333 + 0Mean = 18.5 cm00.10.20.30.416 17 18 19 20Length in inchesFrequency in populationVP = 1.333 cm2VA = 1.0VD = 0.333VE = 05HeritabilityBroad-sense heritability H2 = VG/VPNarrow-sense heritability h2 = VA/VPVP = VA + VD + VE1.333 = 1.0 +0.333 + 0 = 1.0 = 0.75Uses of heritability• The degree to which offspring resembletheir parents is determined by thenarrow-sense heritability h2• The efficacy of natural and artificialselection is also determined by h2h2 = 1h2 = 0VA/VP = 1VA/VP = 06Efficacy of artificial selection:size of LabradorsBreeder’s QuestionQ: A horse breeder wants towin the Kentucky Derby. Ifshe breeds her mare to areally fast stallion, howlikely is it that the colt willbe faster than all the otherthree-year-olds when it runsin the Derby?A: It depends on the heritability of runningspeedBreeder’s Equation• R = h2 S• S = Selection differential difference between selected parents and thepopulation as a whole (within a generation)• R = response to selection difference between selected offspring and theunselected population (across generations)Breeder’s EquationR = h2 SA dog breeder chooses his largest dogs tobreed together. The average height of thebreed is 60 cm (at the shoulder), and thedogs he chooses to breed average 70 cmtall.He knows from previous work that theheritability of height is 0.5.How big can he expect the offspring to be?R = h2 S =0.5 * 10cm = 5cm7Breeder’s EquationR = h2 S = 0.5 * 10 cm = 5 cmIf the response to selection is 5 cm, hecan expect his puppies to grow to be60 cm + 5 cm = 65 cm tallExactly the same equationcan be used to understandnatural selection!Efficacy of natural selection:Darwin’s finchesIf large billsare favored indrought years,what effect willan El Ninoyear have onthepopulation?h2 = 0.88R = h2 SBirds that survive the drought have billsthat are 2 mm deeper (on average)than the population mean.Q: What will happen to the average billdepth in the next
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