In:Introduction to Quantitative Genetics Falconer …

1 1 NORMAL DISTRIBUTIONS OF PHENOTYPESMiceFruit FliesIn: introduction to Quantitative Genetics Falconer & mackay 1996 CHARACTERIZING A NORMAL DISTRIBUTIONM eanand varianceare two quantities that describe a normal PARAMETERS FOR Quantitative Genetics Mean:The sum of all measurements divided by the number of measurements Variance:The average squared deviation of the observations from the mean 2222211 xxNNxxxxxxVariancein 2 CORRELATIONS AMONG CHARACTERS OR RELATIVES0+ Covariance: yyxxNyxCovji 1,COMPONENTS OF PHENOTYPIC VARIATION The total phenotypicvariance for a character (VP) is a function of: genetic variance(VG) the variance among the mean phenotypes of different genotypes Environmental variance(VE) the variance among phenotypes expressed by replicate members of the same genotypeVP= VG+ VE Differences between monozygotic twins are due to environmental : Lynch & Walsh.

2 1998. Genetics and Analysis of Quantitative Traits. Sinauer VARIATION WITHIN PURE LINES3 COMPONENTS OF genetic VARIATIONVG= VA+ VD + VI The total geneticvariance for a character (VG) is a function of: Additive genetic variance(VA) variation due to the additive effects of alleles Dominance genetic variation(VD) variation due to dominance relationships among alleles Epistatic genetic variation(VI) variation due to interactions among lociDOMINANCE VERSUS ADDITIVE genetic VARIANCE Dominance variance is due to dominance deviations, which describe the extent to which heterozygotes are not exactly intermediate between the homozygotes. The additive genetic variance is responsible for the resemblance between parents and offspring. The additive genetic variance is the basis for the response to BETWEEN RELATIVES When there is genetic variation for a character there will be a resemblance between relatives.

3 Relatives will have more similar trait values to each other than to unrelated BETWEEN RELATIVES DEPENDS ON THE DEGREE OF RELATIONSHIPM onozygotic twinsFull sibsParent-offspringHalf sibsSlope of a plot of two variables (x,y) = Cov (x,y) / Var (x)xyDEGREE OF RELATEDNESS AND THE COMPONENTS OF PHENOTYPIC COVARIANCEVA= additive genetic varianceVD= dominance genetic varianceVEs= variance due to shared environmentRelationshipPhenotypic covarianceMonozygotic twins:VA+ VD+ VEsParent-offspring VAFull sibs( VA) +( VD) +VEsHalf sibs, or Grandparent grandchild VAHERITABILITY The heritability(h2) of a trait is a measure of the degree of resemblance between additive genetic variance (VA)/ phenotypic variance (VP)Heritability ranges from 0 to 1(Traits with no genetic variation have a heritability of 0)5 HERITABILITYh2= VA/ VP = VA/ (VG+ VE) Since heritability is a function of the environment (VE),it is a context is influenced by both, The environment that organisms are raised in, and The environment that they are measured HERITABILITY FROM REGRESSION slope = b = Cov (x,y)/Var (x)Method of estimationCOV(x,y)h2 Slope (b)

4 Offspring-Single parent VA2bb= h2 Half-sib VA4bb= h2 Offspring-Grandparent VA4bb= h2 Offspring-Midparent-bb= h2 HERITABILITY OF BEAK DEPTH IN DARWINS FINCHES6IN: Falconer & mackay . introduction to Quantitative FOR SOME TRAITS IN ANIMAL SPECIESh2(%)HERITABILITIES FOR DIFFERENT TYPES OF TRAITSFROM:Mousseau & Roff. historyBehaviorPhysiologyMorphologyTHE UNIVARIATE BREEDERS EQUATION:R = h2 SResponse to SelectionSelection differentialHeritabilityWhere:PA2 VVh (Additive genetic Variance)(Phenotypic Variance)7 ARTIFICIAL SELECTION IN DOMESTIC ANIMALS Grey Jungle fowlSRESPONSE TO SELECTION WHEN h2= 1/3 The selection differential (S) = mean of selected individuals mean of the base population The response to selection:R = h2 SSVISUALIZING THE SELECTION DIFFERENTIAL8 RESPONSE TO SELECTION For a given intensity of selection, the response to selection is determined by the heritabilityLow heritabilitySee Box Z&ER = h2 SESTIMATING h2 USING THE BREEDER S EQUATION PPOOSRhSlope **29 MODES OF SELECTIONFig.

5 Z&ESELECTION ON Quantitative TRAITS Stabilizing and Directional selectionFitnessFrequencyPhenotypic valuePhenotypic meanDirectionalStabilizingTHEADAPTIVELAN DSCAPER esponse to Directional Selection:10 Response to Directional Selection:Fig. Z&EResponse to Directional Selection: In:Introduction to Quantitative Genetics Falconer & mackay 1996