IV. Variation in Quantitative Traits A. Quantitative
Effects
Slide 2
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.
Slide 3
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.
Slide 4
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.
Slide 5
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.
Slide 6
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)
Slide 7
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 F1s (b). Mating F1s creates F2s, 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
Slide 8
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
Slide 9
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 QTLs for color near markers 1 and 5. M.
Lewisii F1 M. cardinalis
Slide 10
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 genes effect. M. Lewisii F1 M.
cardinalis
Slide 11
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.
Slide 12
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.
Slide 13
IV. Variation in Quantitative Traits A. Quantitative Effects B.
Partitioning Variance 1. Partitioning Phenotypic Variance
Slide 14
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)
Slide 15
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)
Slide 16
- 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) AND THESE CAN
BE VERY IMPORTANT: ENV 1ENV 2 PHENOTYPE GENOTYPE 1 GENOTYPE 2
Slide 17
ENV 1ENV 2 PHENOTYPE GENOTYPE 1 GENOTYPE 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.
Slide 18
ENV 1ENV 2 PHENOTYPE GENOTYPE 1 GENOTYPE 2 The "direct effect"
of 'genotype' would compare mean phenotype of Genotype 1 vs. mean
phenotype of Genotype 2. There is no difference.
Slide 19
ENV 1ENV 2 PHENOTYPE GENOTYPE 1 GENOTYPE 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.
Slide 20
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
Slide 21
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
Slide 22
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)
Slide 23
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 As (AA) adds more
Slide 24
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
Slide 25
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 (h 2 ) =
V(a)/V(p)
Slide 26
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 (h 2 ) = V(a)/V(p)
easier to measure
Slide 27
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.
Slide 28
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.
Slide 29
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.
Slide 30
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
Slide 31
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)
Slide 32
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
Slide 33
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 = h s 2
Slide 34
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.
Slide 35
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?
Slide 36
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.
Slide 37
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.
Slide 38
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.
Slide 39
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?
Slide 40
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
Slide 41
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).
Slide 42
Can we use these data to predict how these genotypes would
grow, relative to one another, in another environment?
Slide 43
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? No. Although there is high heritability in BOTH
populations for plant height.
Slide 44
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.
Slide 45
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 doesnt mean that genetic differnces
explain the differrence between ethic groups in this trait.
Especially because environments vary.
Slide 46
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.
Slide 47
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).
Slide 48
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 H 2 for clothes wearing = Vg/Vp =
9.9/10.0 = 0.99. WOW! WHAT A HUGE GENETIC CONTRIBUTION!!!
Slide 49
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 Ve is the same for both groups The Jim
Twins
Slide 50
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.
Slide 51
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.