Transcript What Causes Phenotypic Variation Among Individuals

Evolution by Natural Selection
as a Syllogism
1. If individuals in a population vary with respect to a
particular trait that has some genetic basis
AND
2. If the variants differ with respect to their abilities to
survive and reproduce in the present environment
THEN
3. There will be an increase in the frequency of
individuals having those traits that increased fitness
in the next generation
The Syllogism Parallels the
Breeder’s Equation
R = h2S
The breeder’s equation
Parallel between the Syllogism and
the Breeder’s Equation
1. If individuals in a population vary with respect to a
particular trait that has some genetic basis
AND
2. If the variants differ with respect to their abilities to
survive and reproduce in the present environment
THEN
3. There will be an increase in the frequency of
individuals having those traits that increased fitness
in the next generation
h2
S
R
Selection on a Quantitative Trait
Consider a situation where there is a clear “selective event” within
a generation
Mean phenotypic trait in
Response (R)
= mean Zoffspring – mean Zparents next generation
Mean phenotypic trait
value BEFORE selection
Mean phenotypic trait
value AFTER selection
frequency
Selection differential (S)
= mean Zafter – mean
Zbefore
phenotype
The Breeder’s Equation predicts the mean phenotype of the next generation
Evolutionary Response to Selection
on a Quantitative Trait
Offspring
trait value
Mean of
offspring of
selected
parents
Slope = 1.0
h2 = 1.0
R
Population
mean
When h2 = 1,
R=S
S
Mean
before
Mean
after
Parent trait value
Evolutionary Response to Selection
on a Quantitative Trait
Offspring
trait value
Mean of
offspring of
selected
parents
Slope = 1.0
h2 = 1.0
R
Population
mean
When h2 = 1,
R=S
S
Mean
before
Mean
after
Parent trait value
Evolutionary Response to Selection
on a Quantitative Trait
Offspring
trait value
Slope = 0.5
h2 = 0.5
Mean of
offspring of
selected
parents
Population
mean
R
When h2 < 1,
R<S
S
Mean
before
Mean
after
Parent trait value
Evolutionary Response to Selection
on a Quantitative Trait
Across Multiple Generations
R1
_
z0
R2
z1
R3
z2
• The displacement of the
mean of the character each
generation is the response to
selection
• Given the same strength of
selection, a larger heritability
means a larger response.
z3
• If heritability doesn’t change,
constant selection yields
constant response
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
Characterizing a Quantitative Trait
Mean (average)
z
# of individuals
Variance
(mean squared deviation from mean)
  zi  z 

N
Z
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
classic experiments of Clausen, Keck and Hiesey (1948) on Achillea:
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
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
Plasticity 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
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!
Measuring Heritability
Offspring phenotypic trait value
Heritability is the slope of the regression between offspring and
mid-parent phenotype
slope =
h2= 0.89
Slope = 0.89
covariance between parent & offspring
variance of parents
1
 x  x  y  y 

n
1
2
x  x

n
Can look at other relatives too!
Mid-parent phenotypic trait value
Slope(mom,daughter) = ½ h2
Slope(half-sibs) = ¼ h2