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IV. Variation in Quantitative Traits
A. Quantitative Effects
IV. Variation in Quantitative Traits
A. Quantitative Effects
- the more factors that influence a trait (genetic and environmental) , the more
'continuously variable' the variation in that trait will be.
IV. Variation in Quantitative Traits
A. Quantitative Effects
- For instance, a single
gene trait, with two
alleles and incomplete
dominance, can only
have three phenotypes
(variants). A two gene
trait with additive effects
(height ‘dose’) can make
5 phenotypes (‘dose’ =
0, 1, 2, 3, 4), and so
forth.
IV. Variation in Quantitative Traits
A. Quantitative Effects
- the more genes that influence a trait, the more 'continuously variable' the
variation in that trait will be.
- For instance, a single gene trait, with two alleles and incomplete dominance,
can only have three phenotypes (variants). AA, Aa, aa (Tall, medium, short)
However, a two-gene trait with incomplete dominance at both loci can have
nine variants: AA, Aa, aa X BB, Bb, bb
- So, as the number of genes affecting a trait increase, the variation possible
can increase multiplicatively.
IV. Variation in Quantitative Traits
A. Quantitative Effects
- the more genes that influence a trait, the more 'continuously variable' the
variation in that trait will be.
- For instance, a single gene trait, with two alleles and incomplete dominance,
can only have three phenotypes (variants). AA, Aa, aa (Tall, medium, short)
However, a two-gene trait with incomplete dominance at both loci can have
nine variants: AA, Aa, aa X BB, Bb, bb
-So, as the number of genes affecting a trait increase, the variation possible
can increase multiplicatively.
-If there are environmental effects, then the distribution of phenotypes can be
continuous.
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
- The phenotypic variation that we see in continuous traits is due to a number
of factors that can be "lumped" as environmental or genetic.
V(phen) = V(env) + V(gen)
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
- The phenotypic variation that we see in continuous traits is due to a number
of factors that can be "lumped" as environmental or genetic.
V(phen) = V(env) + V(gen)
- Actually, even this is a gross simplification, because it does not recognize
the contribution that Genotype-by-Environment interactions can have.
V(phen) = V(e) + V(g) + V(e*g)
- Actually, even this is a gross simplification, because it does not recognize
the contribution that Genotype-by-Environment interactions can have.
V(phen) = V(e) + V(g) + V(e*g)
GENOTYPE 1
AND THESE CAN BE VERY IMPORTANT:
PHENOTYPE
GENOTYPE 2
ENV 1
ENV 2
The "direct effect" of environment would compare mean phenotype of organisms
in Env 1 vs. mean phenotype in Env 2. There is no difference.
GENOTYPE 1
PHENOTYPE
GENOTYPE 2
ENV 1
ENV 2
The "direct effect" of 'genotype' would compare mean phenotype of Genotype 1
vs. mean phenotype of Genotype 2. There is no difference.
GENOTYPE 1
PHENOTYPE
GENOTYPE 2
ENV 1
ENV 2
But there is a SIGNIFICANT "genotype x environment" interaction. The effect of
environment on the phenotype depends on the genotype. This important
component of variation is often obscured in simplistic direct models.
GENOTYPE 1
PHENOTYPE
GENOTYPE 2
ENV 1
ENV 2
For example:
=E
Height
=B
Mather
Stanford
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
- The phenotypic variation that we see in continuous traits is due to a number
of factors that can be "lumped" as environmental or genetic.
V(phen) = V(env) + V(gen)
- Actually, even this is a gross simplification, because it does not recognize
the contribution that Genotype-by-Environment interactions can have.
V(phen) = V(e) + V(g) + V(e*g)
- Ultimately, the goal of evolutionary studies is to determine the contribution
of genetic variation, because this is the only variation that is heritable and can
evolve. “Broad-sense” heritability = H2 = Vg/Vp
Heritable variation: the genetic variation that makes offspring look like a parent.
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
- The phenotypic variation that we see in continuous traits is due to a number
of factors that can be "lumped" as environmental or genetic.
V(phen) = V(env) + V(gen)
- Actually, even this is a gross simplification, because it does not recognize
the contribution that Genotype-by-Environment interactions can have.
V(phen) = V(e) + V(g) + V(e*g)
- Ultimately, the goal of evolutionary studies is to determine the contribution
of genetic variation, because this is the only variation that is heritable and can
evolve. “Broad-sense” heritability = H2 = Vg/Vp
PROBLEMS:
1 – not all ‘genetic variation’ is heritable
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
In sexually reproducing species, parents do not pass ALL their genes to each
offspring. Therefore, similarity of phenotype in a common environment
CAN’T be due to the PARENT’S genotype, alone.
Suppose a parent contributes an ‘a’ allele to an offspring. What could make
it’s phenotypic effect DIFFERENT in the offspring from effect in parent?
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
In sexually reproducing species, parents do not pass ALL their genes to each
offspring. Therefore, similarity of phenotype in a common environment
CAN’T be due to the PARENT’S genotype, alone.
Suppose a parent contributes an ‘a’ allele to an offspring. What could make
it’s phenotypic effect DIFFERENT in the offspring from effect in parent?
- other alleles at that locus that dominate it. (‘dominance’ effects)
- other genes at different loci that affect it epistatically. (‘epistatic effects)
There is variation due to 'additive' genetic variance, 'dominance' genetic
variance, 'epistasis', and a variety of other contributors (sex linkage) that can
be modeled.
V(g) = V(a) + V(d) + V(ep)
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
- Even the genetic variation is more complex than one might think. There is
variation due to 'additive' genetic variance, 'dominance' genetic variance,
'epistasis', and a variety of other contributors that can be modeled.
- We will concern ourselves with 'additive variation'
Consider the “a” locus. If the 'A' allele is adaptive, then AA individuals will
have higher fitness than the mean fitness of the population. Their offspring,
as a consequence of inheriting this adaptive gene, will also have a higher
fitness than the population, as a whole. This allele 'adds' fitness. 2 A’s (AA)
adds more if the gene exhibits incomplete dominance.
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
- Broad-sense (H2) = V(g)/V(p)
PROBLEMS:
1 – not all ‘genetic variation’ is heritable
2. – usually measured by:
- A ‘common garden’ experiment:
- Assume V(e) = 0
- attribute all differences to genetics
(combines additive, dominance, and env).
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
- Broad-sense (H2) = V(g)/V(p)
PROBLEMS:
1 – not all ‘genetic variation’ is heritable
2. – usually measured by:
- A ‘common garden’ experiment:
- Raise ‘clones’ in different environments
- Assume V(g) = 0
- attribute all differences to the environment
- denies possibility fo G X E effect
MORE in a BIT…
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
- Broad-sense (H2) = V(g)/V(p)
- Narrow-sense (h2) = V(a)/V(p)
An easier way to correctly measure the genetic contribution to similarities between
offspring and parents.
Calculate the average
phenotype of two
parents, and calculate
the average phenotype
of their offspring.
Graph these points
across sets of parents
and their offspring.
The slope of the best-fit
line (least-squares
linear regression)
describes the strength
of the “heritability” of
the trait.
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Calculating Heritability from Selection Experiments
- Consider a variable population, with mean phenotype = x.
x
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Calculating Heritability from Selection Experiments
- Consider a variable population, with mean phenotype = x.
- Select organisms with a more extreme phenotype (x + 5) to breed.
x
Breeders, mean= x+5
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Calculating Heritability from Selection Experiments
- Consider a variable population, with mean phenotype = x.
- Select organisms with a more extreme phenotype (x + 5) to breed.
x
Breeders, mean= x+5
- - The selection differential, S = (mean of breeders) - (mean of pop)
S = (x + 5) - (x) = 5
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Calculating Heritability from Selection Experiments
- Consider a variable population, with mean phenotype = x.
- Select organisms with a more extreme phenotype (x + 5) to breed.
Breeders, mean= x+5
S= 5
x
Measure Offspring
calculate mean = x + 4
x1
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Calculating Heritability from Selection Experiments
- Consider a variable population, with mean phenotype = x.
- Select organisms with a more extreme phenotype (x + 5) to breed.
Breeders, mean= x+5
S= 5
x
Measure Offspring
calculate mean = x + 4
x1
R = ‘response to selection = (mean of offspring) – (mean of original
population) = (x + 4) – x = 4.
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Calculating Heritability from Selection Experiments
- Consider a variable population, with mean phenotype = x.
- Select organisms with a more extreme phenotype (x + 5) to breed.
Breeders, mean= x+5
S= 5
x
- Selection Diff. = 5
- Response = 4
x1
Narrow-sense heritability = h2 = R/S = 0.8
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Calculating Heritability from Selection Experiments
- Consider a variable population, with mean phenotype = x.
- Select organisms with a more extreme phenotype (x + 5) to breed.
Breeders, mean= x+5
S= 5
x
- Selection Diff. = 5
- Response = 4
x1
Narrow-sense heritability = h2 = R/S = 0.8
The more the offspring ‘look-like” their parents, the greater the h2
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Calculating Heritability from Selection Experiments
As selection proceeds, most variation is environmental or dominance and
response to selection slows.
1.0
x
F(Additive
genes)
xt
- So, counterintuitively, adaptive traits may show low heritability...they have
already been selected for, and most of the phenotypic variation NOW is
probably environmental.
EXAMPLE: Polar bears all have genetically determined white fur - it has been
adaptive and has become fixed in their population. But they still vary in coat color
(phenotype) as a result of dirt, etc. But the offspring of dirty bears will be just as
white as the offspring of clean bears... no response to selection for 'dirty bears'
because all the variation is environmental at this point.
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Calculating Heritability from Selection Experiments
4. Misuses of Heritability:
Heritability is a property of a trait, in a given population, in a given environment.
It provides no insight for comparisons across populations in different
environments…. Why?
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Calculating Heritability from Selection Experiments
4. Misuses of Heritability:
Heritability is a property of a trait, in a given population, in a given environment.
It provides no insight for comparisons across populations in different
environments…. Why?
GENOTYPE X ENVIRONMENT
INTERACTIONS
Consider the growth of these
individual (and genetically
different) plants in a common
garden in Stanford, CA. These
differences are GENOTYPIC
DIFFERENCES, because the
environmental variation is “0”
(same environment).
Can we use these data to
predict how these genotypes
would grow, relative to one
another, in another
environment?
Consider the growth of these
individual (and genetically
different) plants in a common
garden in Stanford, CA. These
differences are GENOTYPIC
DIFFERENCES, because the
environmental variation is “0”
(same environment).
No. Although there is high
heritability in BOTH populations
for plant height.
Can we use these data to
predict how these genotypes
would grow, relative to one
another, in another
environment?
Consider the growth of these
individual (and genetically
different) plants in a common
garden in Stanford, CA. These
differences are GENOTYPIC
DIFFERENCES, because the
environmental variation is “0”
(same environment).
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
4. Misuses of Heritability:
Heritability DOES NOT equal “genetically based”
Many traits that are determined genetically are fixed, with no genetic
variation, and so have very low heritability.
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
4. Misuses of Heritability:
Heritability DOES NOT equal “genetically based”
1) Many traits that are determined genetically are fixed, with
no genetic variation, and so have very low heritability.
2) IF heritability is measured on one population in one
environment, you cannot ascribe phenotypic variation BETWEEN groups –
especially if they are in different environments, to ‘heritability’ and genetic
factors. Ethnic groups differ in mean I.Q. And when measured in one
population, I.Q. is heritable. But that doesn’t mean that “genetic differences”
explain the difference between ethic groups in this trait…. Especially because
environments vary.
MZ-DZ twin studies: Vp = Vg + Ve
- MZ twins: Vg = 0, so Vp for a trait = only Ve.
twin studies:
Some social
psychologists believe that
we can determine
“heritability” or “genetic
contribution” (!) to a trait
by examining the degree
of similarity between
‘monozygotic’ (identical)
and ‘dizygotic’ (fraternal)
twins.
MZ-DZ twin studies: Vp = Vg + Ve
- MZ twins: Vg = 0, so Vp for a trait = only Ve.
- DZ twins: Us DZ twins to measure Vg = Vp – Ve (mz)
- problem: MZ twins are often treated more alike than DZ
twins. So, many of their similarities may be environmental, too. Thus, Ve is
underestimated.
- when this artificially LOW Ve is subtracted from Vp for DZ
twins, it OVERESTIMATES the genetic contribution to that trait.
For MZ twins, clothes choice shows very little variation. (Ve = 0.1).
MZ-DZ twin studies: Vp = Vg + Ve
- MZ twins: Vg = 0, so Vp for a trait = only Ve.
- DZ twins: Us DZ twins to measure Vg = Vp – Ve (mz)
- problem: MZ twins are often treated more alike than DZ
twins. So, many of their similarities may be environmental, too. Thus, Ve is
underestimated.
- when this artificially LOW Ve is subtracted from Vp for DZ
twins, it OVERESTIMATES the genetic contribution to that trait.
For MZ twins, clothes choice shows very little variation. (Ve = 0.1).
DZ twins dress different (Vp = 10.0).
Vg = Vp – Ve = 10.0 – 0.1 = 9.9
H2 for ‘clothes wearing’ = Vg/Vp = 9.9/10.0 = 0.99.
WOW! WHAT A HUGE GENETIC CONTRIBUTION!!!
MZ-DZ twin studies: Vp = Vg + Ve
Hmmmm… MZ twins are treated more similarly than DZ twins
in their homes, so Ve differs between the groups. Hmmmm…. Suppose we
compare MZ and DZ twins reared apart, through adoption? Then Ve will be the
same across groups, and greater similarity among MZ twins must be a function
of greater genetic similarity.
MZ
DZ
“The Jim Twins”
Ve is the same for
both groups
• As youngsters, each Jim had a dog named "Toy."
• Each Jim had been married two times -- the first wives were both
called "Linda" and the second wives were both called "Betty."
• One Jim had named his son "James Allan" and the other Jim had
named his son "James Alan."
• Each twin had driven his light-blue Chevrolet to Pas Grille beach in
Florida for family vacations.
• Both Jims smoked Salem cigarettes and drank Miller Lite beer.
• Both Jims had at one time held part-time posts as sheriffs.
• Both were fingernail biters and suffered from migraine headaches.
• Each Jim enjoyed leaving love notes to his wife throughout the
house.
I.Q.: Statistically significant differences in mean performances of ethnic
groups in U.S. Also, I.Q. (as measured in single populations) is heritable.
“Most scholars accept that I.Q. in the human species as a whole is
substantially heritable, somewhere between 40 percent and 80 percent,
meaning that much of the observed variation in I. Q. is genetic.” – Murray and
Herrnstein (1994). No. And even if so, so what? Much of the variation is
environmental.
IV. Variation in Quantitative Traits
C. Identifying Loci Contributing to Quantitative Traits
1. Quantitative Trait Loci (QTL) mapping
Monkeyflowers – genus Mimulus
(Bradshaw et al. 1998)
Occur in the Sierras, with overlapping
elevational distributions. They readily
hybridize, but no hybrids are found in
nature – possibly because they
attract different pollinators.
The species vary in flower shape and
structure. Since they each “breed
true” for their particular phenotypes,
we assume they are homozygous at
loci influencing these traits.
Since they hybridize, we can form
heterozygous F1’s (b).
Mating F1’s creates F2’s, which show
quantitative variation in color, shape,
and nectar volume (12 measured
traits, like corolla width, stamen
length, anthocyanins in petal, etc.)
M. Lewisii
F1
M. cardinalis
M. lewisii
M. cardinalis
AABBCCDD
aabbccdd
F1
AaBbCcDd
X
AaBbCcDd
Number of genotypes possible in F2?
M. lewisii
M. cardinalis
AABBCCDD
aabbccdd
F1
AaBbCcDd
X
AaBbCcDd
Number of genotypes possible in F2?
A
B
C
D
AA
Aa
Aa
BB
Bb
bb
CC
Cc
cc
DD
Dd
dd
3
x
3
x
3
x
3
= 81 genotypic combinations
Identify ‘marker’ loci across the
genome – loci that are:
1 - unique in the genome
2 – homozygous in each species
3 – distributed over all chromosomes
These are often “single nucleotide
polymorphisms” (SNP’s), repeats,
transposons, restrictions sites
SNP: Single bases that differ
between the species at a given point
in the genome.
M. lewisii:
CCCTTGCA
All homozygous for C in this position
M. cardinalis: C C A T T G C A
All homozygous for A in this position
M. Lewisii
F1
M. cardinalis
Identify ‘marker’ loci across the
genome – loci that are:
1 - unique in the genome
2 – homozygous in each species
3 – distributed over all chromosomes
The Goal:
Find associations between F2 ‘marker’
genotypes and either color or shape.
Many genes with small effects or a few
genes with large effects?
So, maybe (j) and (g) are homozygous
with the M. lewisii allele at markers
1and 5, while (l) is homozygous for the
M. cardinalis marker allele at markers
1 and 5. This association between
marker genotype and parental
phenotype suggests that there are
QTL’s for color and/or shape near
markers 1 and 5.
M. Lewisii
F1
M. cardinalis
Identify ‘marker’ loci across the
genome – loci that are:
1 - unique in the genome
2 – homozygous in each species
3 – distributed over all chromosomes
The Goal:
Find associations between F2 ‘marker’
genotypes and either color or shape.
Many genes with small effects or a few
genes with large effects?
WHY would the association occur?
WHY might the “C” SNP from M.
lewisii show up at a higher frequency
than expected with the PINK color of
F2 individuals, while the “A” SNP from
M. cardinalis shows up in greater
frequency of F2 with red flowers?
M. Lewisii
F1
M. cardinalis
Identify ‘marker’ loci across the
genome – loci that are:
1 - unique in the genome
2 – homozygous in each species
3 – distributed over all chromosomes
The Goal:
Find associations between F2 ‘marker’
genotypes and either color or shape.
Many genes with small effects or a few
genes with large effects?
WHY would the association occur?
WHY might the “C” SNP from M.
lewisii show up at a higher frequency
than expected with the PINK color of
F2 individuals, while the “A” SNP from
M. cardinalis shows up in greater
frequency of F2 with red flowers?
LINKAGE
M. Lewisii
F1
M. cardinalis
Identify ‘marker’ loci across the
genome – loci that are:
1 - unique in the genome
2 – homozygous in each species
3 – distributed over all chromosomes
The Goal:
So, we have used the concept of
linkage (and “linkage disequilibrium”,
really) between a marker locus and
phenotypic trait to isolate a region
that influences the trait.
Markers that are associated with a
phenotypic trait are:
Quantitative Trait Loci (QTL’s)
M. Lewisii
F1
M. cardinalis
Most relationships between markers and phenotypic traits were weak (explaining <
20% of the phenotypic variance). But a few, 9 of 12 floral traits, %’s were much
higher.
One marker explained over 80% of the
variation in color. Genotypes varying ONLY at
this locus and are visited by bees and
hummingbirds, respectively.
Single genes can exert strong effects that can
be driven quickly to fixation by selection.
Determining the actual gene in the region, and the
protein and action of the protein influencing the trait,
requires additional “genetic dissection” of
‘Candidate Loci’ in the region.
We only know that genetic variation in
this region near the maker is associated
with phenotypic variation in the trait. We
don’t know the number, specific location,
or gene action that creates the
phenotype.
Coat color in Peromyscus polionotus
Lighter color due to
mutation in Agouti
locus, which
interferes with the
receptor (and
decreases the
deposition of
melanin).
Lighter color due to a
mutation in
melanocortin-1
receptor, which
decreased the activity
of the receptor.
GWA – Genome-wide association mapping
Do not do a pedigree analysis; screen a large population (1000’s of individuals).
Divide population by a phenotype: presence or absence of a disease.
Do a complete analyses of their genotypes at 1000’s of markers (SNP’s).
Look for non-random associations (linkage) between particular makers and a
disease.
But there is a SIGNIFICANT "genotype x environment" interaction. The effect of
environment on the phenotype depends on the genotype. This important
component of variation is often obscured in simplistic direct models.
GENOTYPE 1
PHENOTYPE
GENOTYPE 2
ENV 1
ENV 2
For example:
=E
Height
=B
Mather
Stanford