BIO 305 1st Edition Lecture 11 Outline of Last Lecture I. Chromosomal TranslocationsII. Inheritance of Fragile X SyndromeIII. More DiseasesIV. Vocabulary and Sample QuestionsOutline of Current Lecture I. Quantitative Genetics and Additive EffectsII. Normal Distribution and 6 ParametersIII. HeritabilityA. Broad-sense HeritabilityB. Narrow-sense HeritabilityIV. Vocabulary and Sample QuestionsCurrent LectureI. Intro to Quantitative GeneticsWhat are traits that can be quantified?Plant height, days to maturity, seed yield, IQ, bristle number, human weight: all of these are phenotypes with two things in common – they can are discontinuous and have continuous variationWe can use statistics to measure variation in phenotype:Ex: In a cross between tall and dwarf tobacco plants:F1 generation: while frequency stays the same, see that all offspring have a height in-between tall and dwarf F2 generation: you can see both a variation in height whose frequencies match the pattern of a standard bell curve – more individuals will look like the F1 but you will see deviations in height with the most different from the F1 in the smallest frequenciesEdward East’s ExperimentsFound that when he crossed corolla’s (long and short type), F1 showed a bell-shaped variation and F2 had wider range of variation with a smaller peak.When F2 was separated into 3 different ranges of length and these three groups were selfed: they each produced variation in height with bell-shapes curvesWhy are do the phenotypes in length vary this way?Polygenic inheritance - The quantitative phenotypes are controlled by a large number of Mendelian genes in what is called the multiple-factor hypothesisWhat is responsible for continuous variation?Additive Alleles: 3 Rules1) Several pairs of genes “add up” to account for variation in phenotype2) Each gene locus is occupied by either an additive allele or non-additive allele3) Effect of each additive allele = other additive alleles at other gene lociHow does additivity affect Mendelian genetics, as we know it? Ex: Grain color, 2 genes, 2 phenotypesP: Cross true breeding red grain and true breeding white grainF1: All heterozygous: all intermediate in colorF2: Now you’re looking at allele frequency in order to observe additive effects, so you can conduct a forked-line diagram using a 1:2:1 ratio and then again for the other geneto get the proportions of each genotype, Assign appropriate phenotypes (any AA or BB will contribute to color while aa or bb will result in lighter color, add each up)Will see a bell curve in frequency of alleles: 1:4:6:4:1What if there are three genes controlling grain color?With three genes, there will be seven phenotypes.Nielsson-Ehle’s experiment with kernel color in wheat confirmed that three pairs of independentlyassorting alleles and incomplete dominance accounted for kernel color variationFor additive genes:If n = number of genes involved, thennumber of different phenotypes that can result = 2n+1Thus, the higher the gene number, the more variation there will be AND the lower the intermediate phenotype frequency will beHow do we estimate the number of polygenes, aka how many genes underlie a particular trait?Must look at both extremes:The proportion of F2 individuals expressing either extreme phenotype = 1/(4^n)If there is only one gene, we expect to see ¼ progenies that are at the end of this distributionWe expect to see 2/16, if there are two genesWe expect to see 1/1024 of progenies if there are four genes and so on…Note: Even if the traits are discontinuous, the underlying mechanism may be continuousII. Normal Distribution and 6 Parameters What are the six parameters of distribution that we have to look at? (Memorize these!)1st: The MeanThe arithmetic average of a set of data Sometimes, Xi = Frequency * number of individuals2nd: Variance Amount of variationVariance is represented by the width of the distribution curve3rd: Standard deviationSquare root of varianceNormal distribution: 1sd - 68.3%, 2sd - 95.5%, and 3sd - 99.7%4th: Standard ErrorA measure of the precision of the estimate of the mean As the sample size increases, error decreases5th: CovarianceA measure of how much variation is common to both variables6th: Correlation Coefficient, Where r2 measures the fraction of the variation in Y that is explainable by the variation in XFurther Analysis of Correlation coefficient:0.0 = strongly uncorrelated1.0 = perfectly correlatedIf slope = 0 OR pattern is a weird shape while correlation = 0, x does not predict yAnalysis of Quantitative Characters Example:X = categories, F = # individuals in each categoryFOR F1: n = 4+14+16+12+6 = 52sum of F(x) = (10*4) + (11*14) + (12*16) + (13*12) + (14*6) = 626sum of F(x)^2 = (40*10) + (154*11) + (192*12) + (156*13) + (84*14) = 7,602Thus, the F1 Mean = 626/52 = 12.04And variance (s^2) = n(sum of F(x)^2) – (sum of F(x))^2n(n-1)= (52 x 7602 – 626^2) / (52*(52 - 1)) = 1.29Repeat process for F2 to get:n = 1+1+2+9+13+17+14+7+4+3+1 = 72F(x) = 6+7+16+90+143+204+182+98+60+48+18 = 872F(x)^2= 36+49+128+900+1573+2448+2366+1372+900+768+324 = 10,864F2 Mean = 10.75F2 variance = (72*10,864)-(872^2) / 72(72-1) = (782208 – 760,384) / 5112 = 4.27III. HeritabilityHeritability is defined as the study of the contribution of genetic factors to phenotypic variation for a given trait in a certain population under a certain environmentGenes and environment control populationFor a given trait, need to know which population and the conditions of the environmentThus, there are specific factors:V = variance by genes + V by environment + V genetic interactive with environmentParallel lines = there is no interaction between genes and environmentNon-parallel = while it is true that both genes grow better with increase in soil fertility,difference in slope shows that there is interaction between gene and environmentA. Broad-sense Heritability: Example:Total variance vs. Genetic Variance?We cannot calculate unless we first make an assumption that there is no interaction: Vgxe = 0 This graph is homogenous, genotypically. soIn humans, we cannot do crosses. So how do we estimate heritability?1) Use exclusively monozygotic twins reared apart (aka same genes, different environment)Broad-sense heritability = correlation coefficient between these monozygotic twinsEx: Five pairs of twins, looking at IQ. We expect that we shouldn’t see a correlation because they are from different environments. But