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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 effetcs, then the ditributioin 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 a 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 a 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. 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. 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
- 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. 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. 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. 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. 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. 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. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
- 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. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
- 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. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
- 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. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
- 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. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
- 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. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
- 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. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
- 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. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
- 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. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
- 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. Partitioning Variance
1. Partitioning Phenotypic Variance
2. Partitioning Genetic Variation
3. Heritability
- 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 phneotypic 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. 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?
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 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”
Many traits that are determined genetically are fixed, with no genetic
variation, and so have very low heritability.
Finally, a take on twin studies:
Some social psychologists beileve that we can determine “heritability” or
“genetic contribution” to a triat by examining the degree of similarity between
‘monozygotic’ (identical) and ‘dizygotic’ (fraternal) twins.
Finally, a take on twin studies:
Some social psychologists beileve that we can determine “heritability” or
“genetic contribution” to a triat by examining the degree of similarity between
‘monozygotic’ (identical) and ‘dizygotic’ (fraternal) twins.
If twins are reared apart (so that the environments are presumed to be
randomized and ‘equal’ across the populations), then traits that show greater
correlations between mz twins suggest a greater degree of genetic
involvement.
Finally, a take on twin studies:
Some social psychologists beileve that we can determine “heritability” or
“genetic contribution” to a triat by examining the degree of similarity between
‘monozygotic’ (identical) and ‘dizygotic’ (fraternal) twins.
If twins are reared apart (so that the environments are presumed to be
randomized and ‘equal’ across the populations), then traits that show greater
correlations between mz twins suggest a greater degree of genetic
involvement.
Problem: You don’t know that the environments are similar or different.
The Jim twins: http://science.howstuffworks.com/genetic-science/twin1.htm
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
C. Selection on Quantitative Traits
- Traits affected by many genes have a higher
probability of including a pleiotrophic gene – a gene that
affects more than one trait. So, we might expect complex,
quantitative traits to be CORRELATED to other traits.
If selection is acting on both traits in different ways,
neither will be “optimized”. Adaptations will be a
compromise, depending on the relative strengths of the
selective pressures, the relative values of the adaptive
traits, and their heritabilities (ease with which they can
respond to selection).
Consider the Grant’s work on medium ground finches during the drought of ‘76-’77.
Birds with deep and narrow beaks had the greatest fitness.
Consider the Grant’s work on medium ground finches during the drought of ‘76-’77.
Birds with deep and narrow beaks had the greatest fitness. But beak depth and
beak width are POSITIVELY CORRELATED (probably developmentally).
Consider the Grant’s work on medium ground finches during the drought of ‘76-’77.
Birds with deep and narrow beaks had the greatest fitness. But beak depth and
beak width are POSITIVELY CORRELATED (probably developmentally).
So, although
selection should
have pushed the
pop along the
blue line, it went
along the green
line.
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
C. Selection on Quantitative Traits
D. Selection and Genetic Variation
IV. Variation in Quantitative Traits
A. Quantitative Effects
B. Partitioning Variance
C. Selection on Quantitative Traits
D. Selection and Genetic Variation
- modes of selection and phenotypic variation:
-modes of selection:
- directional: changes the mean phenotype and
tends to reduce variation.
-modes of selection:
- stabilizing: does not change the mean but
reduces variation.
-modes of selection:
- disruptive: does not change the mean but
increases variation.
Directional
Stabilizing:
Disruptive:
African
seedcrackers;
disruptive
selection due
to efficiencies
on large or
small seeds.
D. Selection and Genetic Variation
- modes of selection and phenotypic variation:
if most selection is directional and stabilizing, then
variation is reduced; including genetic variation (these are
quantitative traits, not single genes maintained by
heterozygote advantage at one locus).
D. Selection and Genetic Variation
- modes of selection and phenotypic variation:
if most selection is directional and stabilizing, then
variation is reduced; including genetic variation (these are
quantitative traits, not single genes maintained by
heterozygote advantage at one locus).
But, even for very adaptive traits, there is usually still
phenotypic and genetic variation. Why?
D. Selection and Genetic Variation
- modes of selection and phenotypic variation:
- sources of variation
- new adaptive mutations are constantly produced
and are increasing in frequency in the population.
D. Selection and Genetic Variation
- modes of selection and phenotypic variation:
- sources of variation:
- new adaptive mutations are constantly produced
and are increasing in frequency in the population.
- deleterious mutations are maintained at low
frequency; especially for genes contributing to quantitative
traits where the selective pressure on any one locus may be
weak.
D. Selection and Genetic Variation
- modes of selection and phenotypic variation:
- sources of variation:
- new adaptive mutations are constantly produced
and are increasing in frequency in the population.
- deleterious mutations are maintained at low
frequency; especially for genes contributing to quantitative
traits where the selective pressure on any one locus may be
weak, or recessive alleles.
- disruptive, frequency dependent, multiple niche
polymorphisms, etc., in which the adaptive value of existing
alleles changes through time or across space within the
population.