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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. 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
Identify ‘marker’ loci across the
genome – loci that are:
1 - unique in the genome
2 – homozygous in each species
3 – distributed over all chromosomes
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 correlations 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 correlation between marker
genotype and parental phenotype
suggests that there are QTL’s for
color 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:
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.
In addition, the strength of the
relationship (the amount of
phenotypic variance explained by
differences in genotypes), describes
the strength of the gene’s effect.
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.
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
1. Partitioning Phenotypic Variance
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Identifying Loci Contributing to Quantitative Traits
C. 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. Identifying Loci Contributing to Quantitative Traits
C. 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
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Identifying Loci Contributing to Quantitative Traits
C. 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 = Vg/Vp
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Identifying Loci Contributing to Quantitative Traits
C. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Identifying Loci Contributing to Quantitative Traits
C. 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 (sex linkage) that can be
modeled.
V(g) = V(a) + V(d) + V(ep)
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Identifying Loci Contributing to Quantitative Traits
C. 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'
Think of an individual that is AA. If the 'A' allele is adaptive, then their fitness
will be higher 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…
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Identifying Loci Contributing to Quantitative Traits
C. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
- Broad-sense (H) = V(g)/V(p) - difficult to measure
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Identifying Loci Contributing to Quantitative Traits
C. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
- Broad-sense (H) = V(g)/V(p) - difficult to measure
- Narrow-sense (h2) = V(a)/V(p)
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Identifying Loci Contributing to Quantitative Traits
C. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
- Broad-sense (H) = V(g)/V(p) - difficult to measure
- Narrow-sense (h2) = V(a)/V(p) – easier to measure
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. Identifying Loci Contributing to Quantitative Traits
C. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Calculating Heritability from Selection Experiments
- Consider a variable population, with mean phenotype = x.
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Identifying Loci Contributing to Quantitative Traits
C. 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.
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Identifying Loci Contributing to Quantitative Traits
C. 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.
- The selection differential, S = (mean of breeding pop) - (mean of entire pop)
S = (x + 5) - (x) = 5
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Identifying Loci Contributing to Quantitative Traits
C. 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.
- The selection differential, S = (mean of breeding pop) - (mean of entire pop)
S = (x + 5) - (x) = 5
- Suppose the offspring mean phenotype = (x + 4)
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Identifying Loci Contributing to Quantitative Traits
C. 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.
- The selection differential, S = (mean of breeding pop) - (mean of entire pop)
S = (x + 5) - (x) = 5
- Suppose the offspring mean phenotype = (x + 4)
- The Response to Selection = R = difference between the whole original
population and the offspring: R = (X + 4) - (x) = 4
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Identifying Loci Contributing to Quantitative Traits
C. 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.
- The selection differential, S = (mean of breeding pop) - (mean of entire pop)
S = (x + 5) - (x) = 5
- Suppose the offspring mean phenotype = (x + 4)
- The Response to Selection = R = difference between the whole original
population and the offspring: R = (X + 4) - (x) = 4
- The heritability (narrow sense) = R/S = 4/5 = 0.8. because R = h2 s
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Identifying Loci Contributing to Quantitative Traits
C. 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.
- The selection differential, S = (mean of breeding pop) - (mean of entire pop)
S = (x + 5) - (x) = 5
- Suppose the offspring mean phenotype = (x + 4)
- The Response to Selection = R = difference between the whole original
population and the offspring: R = (X + 4) - (x) = 4
- The heritability (narrow sense) = R/S = 4/5 = 0.8.
- The closer the offspring are to their particular parents (in amount of
deviation from the whole population), the greater the heritability and the more
rapid the response to selection.
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Identifying Loci Contributing to Quantitative Traits
C. 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.
- The selection differential, S = (mean of breeding pop) - (mean of entire pop)
S = (x + 5) - (x) = 5
- Suppose the offspring mean phenotype = (x + 4)
- The Response to Selection = R = difference between the whole original
population and the offspring: R = (X + 4) - (x) = 4
- The heritability (narrow sense) = R/S = 4/5 = 0.8.
- The closer the offspring get to their particular parents (in amount of
deviation from the whole population), the greater the heritability and the more
rapid the response to selection.
- This quantifies the evolutionarily important genetic variance (heritability is
also V(add)/V(phen), remember?
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Identifying Loci Contributing to Quantitative Traits
C. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Calculating Heritability from Selection Experiments
- This quantifies the evolutionarily important genetic variance (heritability is
also V(add)/V(phen), remember)?
- So, through a series of selection experiments, we can determine how
responsive a trait is to selective pressure.
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Identifying Loci Contributing to Quantitative Traits
C. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Calculating Heritability from Selection Experiments
- This quantifies the evolutionarily important genetic variance (heritability is
also V(add)/V(phen), remember)?
- So, through a series of selection experiments, we can determine how
responsive a trait is to selective pressure. As selection proceeds, most
variation is environmental or dominance and response to selection slows.
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Identifying Loci Contributing to Quantitative Traits
C. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Calculating Heritability from Selection Experiments
- This quantifies the evolutionarily important genetic variance (heritability is
also V(add)/V(phen), remember)?
- So, through a series of selection experiments, we can determine how
responsive a trait is to selective pressure. As selection proceeds, most
variation is environmental or dominance and response to selection slows.
- 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. Identifying Loci Contributing to Quantitative Traits
C. 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. Identifying Loci Contributing to Quantitative Traits
C. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
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. Identifying Loci Contributing to Quantitative Traits
C. 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. Identifying Loci Contributing to Quantitative Traits
C. 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) 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 differnces”
explain the differrence 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.