Genetics of Quantitative Traits

Quantitative Trait Any trait that demonstrates a range of phenotypes that can be quantified Height Weight Coloration Size

Continuous Variation vs Discrete Phenotypic Classes Continuous variation –Offspring show a range of phenotypes of intermediate range relative to the parental phenotype extremes Discrete classes –Offspring show phenotype exactly like either parent (dominance/recessiveness) –or in a single intermediate class (incomplete dominance) –or have a combinatorial phenotype (co-dominance)

Example of Continuous Variation

Demonstrating Genetic Control of Variation Individually cross F 2 at phenotypic extremes Subsequent ranges of progeny are centered on F 2 phenotype

Polygenic Inheritance A trait controlled by multiple genes with additive and non-additive allele types Additive allele (Uppercase) –an allele which contributes to the observe phenotype causes more color, height, weight, etc.. Non-additive allele (lowercase) –an allele which does not contribute to observed phenotype causes less color, height, weight, etc…

Polygenic Control of Wheat Color P F1F1

Wheat Color Defined by Two Genes A and B are additive alleles of two genes a and b are non-additive alleles of the same two genes The number of additive and non-additive alleles in each genotype defines a distinct phenotype –4 additive alleles  AABB –3 additive alleles  AaBB, AABb, –2 additive alleles  aaBB, AAbb, AaBb –1 additive allele  Aabb, aaBb –0 additive alleles  aabb Give 5 phenotype classes

How Many Genes Control a Trait? & How Many Phenotypes are Possible? Genes (n) Genotypic Classes Phenotypic Classes Fraction like either parent 1331/4 2951/ / / / /4096 n3n3n 2n+1(1/4) n

Statistics Range of the phenotype being measured Numbers of individuals with that phenotype

Mean (aka Average) and Variance These two populations have a mean height that is the same The range of heights in each population is quite different Height of Population 1 Height of Population 2 1ft 10ft 2.5ft 7.5ft (Height) Number of Individuals with Indicated Height

Measuring the Variance Sample variance s 2 Standard deviation = square root of variance Standard error s =  s 2 s  n SXSX = n = # of individuals for which trait has been quantified s 2 =  (X i - X) 2 n-1 i=1 n

Weight Distribution of F 1 & F 2 Tomato Progeny

Example Statistics Problem Weight Number of Individuals F1F F2F Mean: X F1 = Variance: s 2 F1 = 1.29 Stnd Dev: s F1 = 1.13 Mean: X F2 = Variance: s 2 F2 = 4.27 Stnd Dev: s F2 = ± ± 2.06 See table 6.4 (4 th ed) or table 5.4 (3 rd ed)

Nature or Nurture Phenotypic variation due to genetic factors Phenotypic variation due to environmental factors Heritability –Broad-sense Measure of variance due to genetics vs environment –Narrow-sense Measure of selectability

Identifying Environmental vs Genetic Factors Influencing Variability Inbred strains –an inbred population is highly homozygous –lethal recessives are lost –allele frequencies are stabilized Variation in inbred populations in differing environments is due to environmental factors – V E Variation in inbred population in same environment is due to genetic differences - V G

If extreme phenotypes of highly inbred line are selected, do F 1 show deviation from P mean? –yes – variance is genetic –no – variance is environmental Environmental vs Genetic Factor Measurement

Broad-sense Heritability Heritability index – H 2 Proportion of variance due to genetic factors V P = phenotypic variance (ie s 2 for a measured trait in a population) V P = V E + V G V G = genetic variance V E = environmental variance VGVG VPVP H 2 =

Narrow-sense Heritability R S h 2 = S = deviation of selected population mean from whole population mean R = deviation of offspring mean from whole parental population mean ratio of R to S describes narrow-sense heritability – ie how selectable is the trait h 2 near 1 means trait could be altered by artificial selection