Quantitative Genetics

• Up until now, we have dealt with characters (actually genotypes) controlled by a single locus, with only two alleles:

Discrete Variation

Many Traits are Polygenic

• continuous and quantitative refer to variation, polygenic refers to the mode of inheritance, ("many genes")

Quantitative Variationor Continuous variation

Studying Quantitative Traits

• It would be impossibly difficult to use the same approach as population genetics to consider inheritance at many many loci, especially if the number of loci is unknown

• We need to look at DISTRIBUTIONS of characters rather than frequencies of alleles

Characterizing a Quantitative Trait#

of i

nd

ivid

ua

ls

Z

Mean (average)

( )2

iz z

N

Σ −=

z=

Variance in Phenotype (VP) (mean squared deviation from mean)

(Phenotype)

What Causes Phenotypic Variation Among Individuals

Z

# o

f in

div

idu

als Genetics?

Environment?

Both?

P G E G x EV V V V= + +

Partitioning Variance

P G E G x EV V V V= + +

Total Phenotypic Variance (VP)

VG VE VG x E

Fig 8.26

Unspecified source population

Partitioning Variance

Total Phenotypic Variance (VP)

VG VE VG x E

VADDVEPI

Genetic Variance can be subdivided:

VADD= phenotypic variation due to the additive effects of alleles

VDOM = phenotypic variation due to dominance effects (when the effect of the allele depends on the identity of the other allele at that locus)

VEPI = phenotypic variation due to epistatic effects (when the effect of the allele depends on the identity of alleles at different loci)

VDOM

Dominance and Epistasis

BbEE

bbEE

BBee

bbee

BBEE

BBEe

BbEe

Bbee

bbEe

Additive Genetic Variation

VADD= phenotypic variation due to the additive effects of alleles

Consider a gene with 2 alleles, A1 and A2:

A1 A1 A1 A2 A2 A2 a d

Additive effects only

10 8 6

W/ dominance 10 10 6

How much does each additional copy of A1 add to phenotype?

Which of these can be passed on to offspring?

Partitioning Variance

Total Phenotypic Variance (VP)

VG VE VG x E

Environmental Variance can be subdivided:

VEN V= phenotypic variation due to random environmental influences

VCOM = phenotypic variation due to common family influences

VMAT = phenotypic variation due to maternal influences

VENV VCOM VMAT

Maternal Environment Effect in Guppy Offspring Size

Food stressed mothers produce larger offspring

0.9

1

1.1

1.2

1.3

1.4

Low High

Maternal Food Level

Offspring Size (mg)

Reznick and Yang 1993

Breaking the Stick of Variation

• By breaking the stick of variation, we can determine how much of the phenotypic variation is due to each component.

• Selection acts on phenotypic variation, but can only cause evolution if the variation is heritable

• Broad-sense heritability: H2 = VG/VP

• Narrow-sense heritability: h2 = VA/VP

Partitioning Variance

Total Phenotypic Variance (VP)

VG VE VG x E

VDOM VEPIVADDVENV VCOM VMAT VG x E

heritability (h2) = the proportion of phenotypic variation that is due to the additive effects of alleles [how much of VP is made up by VADD]

Total Phenotypic Variance (VP)VADD

Why only Additive Genetic Variance?The additive effects of alleles are responsible for the

degree of similarity between parents and offspring

Additive effects

a = the effect of substituting an A1 or A2 allele

Why is there spread around the phenotypic values of 6, 8, and 10 for each genotype?

VE

Dominant A2

  A2A2 A1A2 A1A1 a dADD only 10 8 6 2 0w/ DOM 10 10 6 2 2

Why only Additive Genetic Variance?The additive effects of alleles are responsible for the

degree of similarity between parents and offspring

Additive effects Dominant A2

A1A2 x A1A2

Parents = 8 Parents = 10

Offspring = .25(6)+.5(8)+.25(10) = 8 Offspring = .25(6)+.5(10)+.25(10) = 9

Dominance causes offspring phenotype to deviate from parental phenotype!

So, What is Heritability?Heritability describes the proportion of variation in trait

that can respond to selection

Broad-sense Heritability (H2 = h2B = VG/VP)

– could include dominance and epistatic variation

Narrow-sense Heritability (h2= VA/VP)– proportion of phenotypic variance that is due to

additive genetic causes

Measuring Heritability

Heritability is the slope of the regression between offspring and mid-parent phenotype

Mid-parent phenotypic trait value

Off

sprin

g ph

enot

ypic

tra

it va

lue

Slope = 0.89

h2= 0.89

covariance between parent & offspringvariance of parentsslope =

Can look at other relatives too!

Slope(mom,daughter) = ½ h2

Slope(half-sibs) = ¼ h2

Meaning of Heritability

• Evolution by natural selection can only occur in pops A & B• h2=0 in pop C--> none of the variation is due to VA

• h2 is undefined, there is no variation

Notes about h2

1) Heritability is NOT THE PROBABILITY A TRAIT IS INHERITED OR THE PROBABILITY A TRAIT HAS A GENETIC BASIS

2) Estimates of heritability are specific to the population in which they are measured.

3) heritabilities are statements about variance, not means (e.g., the number of eyes in humans has a 0 heritability, but this doesn't mean that eye number is not under genetic control)

4) high heritability doesn't mean environment doesn't matter or, vice versa, low heritability doesn't mean genes aren't important.

Total Phenotypic Variance (VP)VADD

Total Phenotypic Variance (VP)VADD