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 F2 at phenotypic extremes

• Subsequent ranges of progeny are centered on F2 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

F1

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 3 1/4

2 9 5 1/16

3 27 7 1/64

4 81 9 1/256

5 243 11 1/1024

6 729 13 1/4096

n 3n 2n+1 (1/4)n

Statistics

Range of the phenotype being measured

Num

bers

of

indi

vidu

als

wit

h th

at p

heno

type

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 10ft2.5ft 7.5ft

(Height)

Num

ber

of I

ndiv

idua

ls w

ith

Indi

cate

d H

eigh

t

Measuring the Variance

• Sample variance s2

• Standard deviation = square root of variance

• Standard error

s = s2

s

nSX =

n = # of individuals for which trait has been quantified

s2 = (Xi - X)2

n-1

i=1

n

Weight Distribution of F1 & F2 Tomato Progeny

Example Statistics Problem

Weight6 7 8 9 10 11 12 13 14 15 16 17 18

Number of Individuals

F1 4 14 16 12 6

F2 1 1 2 0 9 13 17 14 7 4 3 0 1

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

See table 6.4 (4th ed) or table 5.4 (3rd 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 – VE

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

• If extreme phenotypes of highly inbred line are selected, do F1 show deviation from P mean?– yes – variance is genetic

– no – variance is environmental

Environmental vs Genetic Factor Measurement

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

R

Sh2 =

• 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

h2 near 1 means trait could be altered by artificial selection