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 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 Figure: 06-01C Caption: Kolreuter's cross btw dwarf & tall tobacco plants carried to the F2 generation.

Demonstrating Genetic Control of Variation Individually cross F2 at phenotypic extremes Subsequent ranges of progeny are centered on F2 phenotype Figure: 06-02C Caption: Results of East's cross btw 2 strains of Nicotiana w/different corolla lengths.

Polygenic Inheritance 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 Figure: 06-03 Caption: How the multiple-factor hypothesis accounts for the 1:4:6:4:1 phenotypic ratio of grain color when all alleles designated by uppercase letters are additive and contribute an equal amount of pigment to the phenotype.

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 1 3 1/4 2 9 5 1/16 27 7 1/64 4 81 1/256 243 11 1/1024 6 729 13 1/4096 n 3n 2n+1 (1/4)n Figure: 06-04 Caption: The results of crossing two heterozygotes when polygenic inheritance is operative with 1–5 gene pairs. Each histogram bar indicates a distinct phenotypic class from one extreme (left end) to the other extreme (right end). Each phenotype results from a different number of additive alleles.

Weight Weight Number of individuals Number of individuals Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Low environmental effect High environmental effect Number of individuals Number of individuals aa Aa AA aa Aa AA 1 2 1 1 2 1 Weight Weight Ww x Ww

Number of individuals Weight Number of individuals Weight Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Low environmental effect Number of individuals aabbcc 1 Aabbcc 6 AAbbcc 15 AaBbCc 20 AABbCc 15 AABBCc 6 AABBCC 1 Weight High environmental effect Number of individuals aabbcc 1 Aabbcc 6 AAbbcc 15 AaBbCc 20 AABbCc 15 AABBCc 6 AABBCC 1 Weight WWW www x WWW www

Statistics Numbers of individuals with that phenotype Figure: 06-05 Caption: A normal frequency distribution characterized by a bell-shaped curve. Numbers of individuals with that phenotype Range of the phenotype being measured

Mean (aka Average) and Variance Height of Population 2 Number of Individuals with Indicated Height Figure: 06-06 Caption: Two normal frequency distributions with the same mean but different amounts of variation. Height of Population 1 1ft 2.5ft 7.5ft 10ft (Height) These two populations have a mean height that is the same The range of heights in each population is quite different

Measuring the Variance Sample variance s2 Standard deviation = square root of variance Standard error s2 = (Xi - X)2 n-1 i=1 n n = # of individuals for which trait has been quantified s = s2 s  n SX =

Weight Distribution of F1 & F2 Tomato Progeny

Example Statistics Problem Weight 6 7 8 9 10 11 12 13 14 15 16 17 18 Number of Individuals F1 4 F2 1 2 3 Mean: XF1 = 12.04 Variance: s2F1 = 1.29 Stnd Dev: sF1 = 1.13 Mean: XF2 = 12.11 Variance: s2F2 = 4.27 Stnd Dev: sF2 = 2.06 12.04 ± 1.13 12.11 ± 2.06

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 – VE Variation in inbred population in same environment is due to genetic differences - VG

Environmental vs Genetic Factor Measurement If extreme phenotypes of highly inbred line are selected, do F1 show deviation from P mean? yes – variance is genetic no – variance is environmental

Broad-sense Heritability Heritability index – H2 Proportion of variance due to genetic factors VP = phenotypic variance (ie s2 for a measured trait in a population) VP = VE + VG VG = genetic variance VE = environmental variance VG VP H2 =

Narrow-sense Heritability 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 R S h2 = h2 near 1 means trait could be altered by artificial selection

Long term breeding study for corn oil content Figure 21.16A 22

Figure: 06-08 Caption: Survival rates of Drosophila carrying combinations of chromosomes from DDT-resistant and DDT-sensitive (control) strains when exposed to DDT. The results indicate that DDT resistance is polygenic, with genes on each of the major chromosomes making a major contribution. Chromosome 4 carries only a few Drosophila genes and was omitted from this analysis.

Figure: 06-08-01UN Caption: Different combos of chromosomes from control strain & resistant strain.