Quantitative Genetics. Statistics Overview: Mean. Statistics Overview: Variance. Statistics Overview: Distributions. Chapter 22

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1 Quantitative Genetics Chapter Statistics Overview: Distributions Phenotypes on X axis, Frequencies on Y axis Statistics Overview: Mean Measure of central tendency (average) of a group of measurements X = ΣXi n Statistics Overview: Variance Indicates the variability of a group of measurements s = Σ(Xi X) (n 1) Figure. The standard deviation (s) is simply the square root of the variance 1

2 Statistics and Quantitative Traits Mean Changes in F1 Variance Changes in F Figure.9 Figure.15 Heritability How much variation in a population is due to genetics? Phenotypic Variance Calculate the variance in the population (sample) Heritability is the proportion of phenotypic variation that is caused by genetic variation. V P Components of Phenotypic Variance Variance due to Genetics: V G Genotype x Environment Interaction Phenotype of a given genotype is determined by the environment Variance due to the Environment: V GE V E

3 Variance is Additive! V P = V G + V E + V GE Figure.1 Heritability Broad Sense Heritability How much variation in a population is due to genetics? Heritability is the proportion of phenotypic variation that is caused by genetic variation. H = V G V P Broad Sense Heritability Proportion of Phenotypic Variance attributable to Genetic Variation. Ranges from to 1 Components of Genetic Variance Genetic Variance can be decomposed into: Additive Genetic Variance Dominance Genetic Variance Epistatic Genetic Variance 3

4 Additive Genetic Variance Dominance Genetic Variance V A V D Additive effects of genes on the phenotype INTRAgenic interaction (Dominance) effects on the phenotype Genic Interaction Variance Variance is Additive! V I INTERgenic interaction (Epistasis) effects on the phenotype V G = V A + V D + V I Summary Equation: V P = V A + V D + V I + V E + V GE V G CAUTION! This model deals with the VARIANCE in a POPULATION This model says nothing about the absolute value of the trait. We still don t know anything about the underlying genetics of the trait.

5 Narrow Sense Heritability Narrow Sense Heritability Proportion of Phenotypic Variance attributable to Additive Genetic Variation. Ranges from to 1 h = V A V P Additive genetic variation is primarily responsible for resemblance among relatives. Calculation of Heritability Estimation of Variance Components Parent Offspring Regression Degrees of Relatedness Estimation of Variance Components Set one Variance Component to zero: V E = All organisms grown in a common environment Very difficult in practice V G = Clonal lines or highly inbred lines (no genetic variation) Not possible with many organisms Clonal Lines V P = V G + V E + V GE 5

6 Clonal Lines Clonal Lines V P = V G + V E + V GE V G =, V GE = No genetic variation: V P = V G + V E + V GE V G =, V GE = No genetic variation: V P = V E Outbred Population: V P = V G + V E + V GE V G = V P - V E H = V G V P This estimate from Clonal lines Estimation of Variance Components Difficult to eliminate environmental variance Not possible to make genetically identical individuals in all organisms Not a commonly used method Parent Offspring Regression The slope of the regression is equal to the narrow sense heritability* Genetic variance is reflected in the fact that offspring resemble their parents Plot offspring phenotype against parental phenotype Single parent Mid Parent (Mean parent) Figure.17

7 If the offspring phenotype is regressed on only ONE PARENT, then: h = b b = h =.7 Figure.1 Degrees of Relatedness Twin Studies in Humans: Monozygotic Twins share 1% of their genes Dizygotic Twins share 5% of their genes H = (r MZ r DZ ) Degrees of Relatedness Narrow Sense Heritability estimated using full sibs (5% genes in common) and half sibs (5% genes in common). Also called sib analysis This method is quite common What Heritability Tells Us Proportion of phenotypic variance in a population that is due to (additive) genetic variation. Statistical prediction of offspring phenotype Response to selection (coming soon!) Limitations of Heritability Does NOT indicate the degree to which a trait is genetically determined. Heritability is a POPULATION measure. An individual does not have heritability! There is NO UNIVERSAL heritability for any trait. Specific to one population, in one environment 7

8 Limitations of Heritability High heritability does not preclude environmental influence on a trait. Heritability indicates nothing about the nature of population differences. Heritability is a BLACK BOX. It tells us nothing about the nature of the genetic variation it is measuring. Quantitative Trait Loci (QTL) Lots of genetic markers RFLPs, microsatellites, AFLP, mutations, Can correlate the segregation of genetic markers with Phenotype for a quantitative trait. GENETIC CROSSES Hypothetical QTL on Zebrafish Linkage Group 1 OSU (XX) OxS F 1 X SW (YY) X Irradiated outbred eggs Statistical Evidence for QTL () Most likely QTL Position Doubled haploids (DH) R1 (VI) R R7a R (II) R11 R15 (XXI) R17b R19 QTL Identified Through Composite Interval Mapping.3 ACGACA5 AGCAGG9.7 ACGATC1. ACGATC ACGATC11. AGCAGA17 1. ACGAAG7 ACGACA.7 AGCCAG 7.7. AGCAGA1. AGCAGA15. AGCAGA7 3. AGCAAG5.7 AGCAGA 1.7 AGCATC1 ACGAGA. AGCAGG1. ACGAAG5a. ACGACAa. ACGCTC. AGCCTC. ACGAAG1 R5. ACGATC1 1. ACGATC. AGCCAG7 AGCAAG17 ACGATC 1. R (XX, XIV). ACGACA3 5.9 AGCAAG11 ACGACA9 3.9 AGCCGC 7..1 AGCAGG 1.3 ACGAGA93a (XIV) AGCACG AGCCGC1 1. AGCCGT1 ACGACA17. AGCACT9 3.9 R.9 ACGAGA5 3.1 AGCATC1 ACGATC7 3. ACGAGA 1.5 AGCAGT3.7 AGCAGT11.. P53 (XX*). AGCCGC5. ACGACA7.9 ACGATC3 ACGATC9 5.. ACGACA1 AGCACT.3 ACGATC1. ACGACA1 ACGACA11 1. ACGACA13. AGCAGG. R3 7. AGCCTC1 AGCATC 9. AGCACT3.3 ACGACA5.7 ACGATC1. ACGATC5 1. ACGATC AGCAGA17 1. ACGAAG7.7 AGCCAG. AGCAGA15 3. AGCAAG5 ACGATC AGCATC1 ACGAGA AGCACA 9.9 ACGATC 5. AGCAGG 1.1 AGCCGT9 19. AGCACG 5.5 AGCACA5 R7b AGCAGG1 1. Oneu19.7. AGCCGT.3 AGCCAG11.7 ACGAGA. AGCCGC3 3. AGCCTC1 AGCAAG9.3 AGCAGA R7c..9.7 AGCCTC9 ACGAGA3 AGCACG5 AGCAGG1 R7d ACGACA3 ACGACA ACGACA19o ACGACA AGCAAG15 AGCATC ACGAAG19c AGCAGT AGCACT AGCCGC AGCCAG ACGACA39o. AGCCTC7 3.5 ACGACA19 AGCACT1 ACGAAG15.9. AGCATC3 31. AGCACT7 1. AGCAAG.1 AGCCTC 1. AGCCAG1 AGCAGA1. ACGACA1 1. R1.3 AGCCTC 35. AGCCAG5 AGCACG3 1. AGCATC5. AGCACG1 3. ACGAAG1 AGCAAG1 R9 AGCCAG9 R1 (XV) AGCCGT 13.7 ACGACA R1 (XXX) ACGAGA9 ACGACA57c AGCAAG. AGCCAG AGCACG9 AGCAAG1 3.5 ACGAAG 3..1 AGCACG AGCACT11 R17a AGCCGT AGCCGT5 AGCAGG3. 7. AGCACA13 ACGAAG3c. AGCAGG5. AGCAGA AGCAGA1. AGCAGA1 AGCACT1 AGCACA AGCAGA13 AGCAGA AGCAGA11. AGCAGT5 AGCAAG1 AGCACA1 AGCAAG3.9 AGCACA AGCCAG1 1. AGCAGG11 R1 AGCAGA. R13 (IX). AGCCAG3 ACGAAG13. AGCACA1 AGCATC11 AGCCTC AGCACT AGCAGG1 ACGACA AGCCTC11 1. AGCAGT7 1. ACGAAG1a AGCACA1 R1 (XXV).7. AGCATC AGCAGG1 AGCCAG AGCAGA.5 ACGACA1.3 AGCAGT1.7. AGCAGA3. AGCCAG. ACGAAG1 5. AGCAGT9. AGCCGT AGCAAG. ACGAAG17o 9.5 AGCATC1 ACGAAG.7 ACGAAG5 AGCAGT AGCACG 11.7 AGCACA9 AGCATC9.5 AGCATC1 9. AGCCGT7 R AGCAGG AGCCTC3 1. AGCAGT17. AGCACG1. AGCACT5. AGCACT 1. AGCACG11.9 AGCAGA1 AGCACG1 R1 AGCACA 9.9. AGCAGG AGCACG7 R AGCAAG1 1.1 AGCAAG R3 AGCCAG 1.3 AGCAGT1 R AGCATC13. AGCATC15 TTH: Length: Weight: tthr13 tthr9 tthr lenr wtr11 R13 R11 R9 R Linkage Group 1 1 lenr 1 wtr 1

9 QTL Analysis Number of QTL Additive Effect on Phenotype Epistasis, Dominance, Pleiotropy QTL x Environment Ultimately: POSITIONAL CLONING Limitations of QTL analysis Number of QTL is a MINIMUM estimate of gene number Estimate of effect can be biased unless sample sizes are large Estimate of position is very coarse Statistical Evidence for QTL () Hypothetical QTL on Zebrafish Linkage Group Mb! interval Functional Genomics Advanced QTL Analysis GENOTYPE Individual gene effects Gene x Environment Interaction Gene Expression Domains Dominance, Epistasis, Pleiotropy QTL x Environment Interaction Molecular. Basic QTL Analysis Number of Genes, Effect size, Genomic Distribution Classical Quantitative Genetics Heritability, genetic correlations, GxE, average degree of dominance PHENOTYPE Statistical Quantitative Genetics and Evolution Darwin s theory of Natural Selection: Excess capacity of individuals Lots of phenotypic variation Some of this variation is heritable The most FIT individuals will survive, and pass their (heritable) phenotypes on to their offspring Response to Selection Breeder s Equation R = h S 9

10 Response to Selection Breeder s Equation R = h S Response to Selection Breeder s Equation R = h S Narrow Sense Heritability Selection Differential Response to Selection Breeder s Equation S R = h S Offspring Mean yield of offspring Response to Selection R GREAT SCOTT! Another way to calculate Heritability! Offspring Mean yield of offspring h = R S Realized Heritability R 1

11 Limits to Selection Prelude: Modes of Selection Genetic variation exhausted Natural selection opposes further change in characteristic 11