Transcript What Causes Phenotypic Variation Among Individuals

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
Quantitative Variation
or Continuous variation
• continuous and quantitative refer to variation, polygenic
refers to the mode of inheritance, ("many genes")
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
Mean (average)
z
# of individuals
Variance in Phenotype (VP)
(mean squared deviation from mean)
  zi  z 

N
Z
(Phenotype)
2
What Causes Phenotypic Variation
Among Individuals
# of individuals
Genetics?
Environment?
Both?
Z
VP  VG  VE  VG x E
Partitioning Variance
VP  VG  VE  VG x E
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
Genetic Variance can be subdivided:
VADD
VDOM
VEPI
VEPI = phenotypic variation due to
epistatic effects (when the effect of
the allele depends on the identity
of alleles at different loci)
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)
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
Additive effects
only
10
8
6
W/ dominance
10
10
6
a
d
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:
VENV VCOM VMAT
VEN V= phenotypic variation due to
random environmental influences
VCOM = phenotypic variation due to
common family influences
VMAT = phenotypic variation due to
maternal influences
Maternal Environment Effect in
Guppy Offspring Size
Food stressed mothers produce larger offspring
Offspring Size (mg)
1.4
1.3
1.2
1.1
1
0.9
Low
High
Maternal Food Level
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
VADD
VDOM
VEPI
VE
VG x E
VENV 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]
VADD
Total Phenotypic Variance (VP)
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
ADD only 10
8
6
2
w/ DOM 10
10
6
2
d
0
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
Offspring = .25(6)+.5(8)+.25(10) = 8
Parents = 10
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
Offspring phenotypic trait value
Heritability is the slope of the regression between offspring and
mid-parent phenotype
slope =
covariance between parent & offspring
variance of parents
h2= 0.89
Slope = 0.89
Can look at other relatives too!
Mid-parent phenotypic trait value
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.
VADD
VADD
Total Phenotypic Variance (VP)
Total Phenotypic Variance (VP)