Transcript Quantitative Inheritance - NAU jan.ucc.nau.edu web server

Quantitative Inheritance - Pt.1
Chapter 8
1
Quantitative phenotypes
• Continuously variable, expressed as a quantity:
– height, weight, running speed, morphology (beak depth, beak
width), number of offspring (fitness), IQ score, behavior (novelty
seeking), serum cholesterol, etc., etc.
•
•
•
•
Generally show a bell-shaped (normal) distribution
Are controlled by several to many genes
Are influenced, often strongly, by environment
A main goal of many quantitative genetic studies is to
determine the heritability of a trait – the degree to which
phenotypic variation among individuals is due to genetic
differences among individuals, or the degree to which
offspring resemble their parents
2
Quantitative vs. discrete (Mendelian) phenotypes
• A “classic” Mendelian phenotype is a trait that is
controlled by a single gene and which comes in two
discrete “flavors” – dominant and recessive – or three
“flavors” if there is co-dominance or incomplete
dominance
• Classic Mendelian traits show clear-cut phenotypic ratios
in controlled crosses, such as the 3:1 F2 ratio in a
monohybrid cross with dominance
• Because they show continuous, rather than discrete,
variation, quantitative phenotypes do not yield clear-cut
phenotypic ratios in controlled crosses
3
Some quantitative traits in humans (Fig. 8.1)
4
A short history of quantitative genetics – 1
• Francis Galton (a cousin of Charles Darwin) is the father
of quantitative genetics, often referred to in early years as
biometrics
– Hereditary Genius, 1869
• Note that quantitative genetics developed initially in the
absence of any knowledge of Mendelian genetics – based
on statistical descriptions of phenotypic correlations
between relatives
• After the re-discovery of Mendel in 1900, there ensued a
long controversy about whether the mechanism of
inheritance of quantitative traits was fundamentally
different from that of Mendelian traits, and even whether
natural selection could act effectively on quantitative traits
5
A short history of quantitative genetics – 2
• Work by Edward East (1916) on inheritance of corolla
height in longflower tobacco, and theoretical work by R.A.
Fisher reconciled the Mendelians and the biometricians by
showing that quantitative inheritance could be explained
on the assumption of Mendelian genetics, and with the
additional assumptions that several to many genes
controlled the variation in the quantitative phenotype and
that the phenotype was also affected by environment.
– Fisher, R.A. 1918. The correlation between relatives on the
supposition of Mendelian inheritance.
– This is the paper in which Fisher coined the term “variance”
– This is not the only instance that we will see of the close
association between quantitative genetics and statistics
6
Inheritance
of corolla
height in
longflower
tobacco
under the
assumption
of a single
controlling
gene and
incomplete
dominance
(Fig. 8.2a)
7
Inheritance of
corolla height in
longflower
tobacco under the
assumption of two
controlling,
independently
assorting,
incompletely
dominant genes,
with equal and
additive effects on
the phenotype
(Fig. 8.2b)
8
Inheritance of
corolla height in
longflower
tobacco under the
assumption of six
controlling,
independently
assorting,
incompletely
dominant genes,
with equal and
additive effects on
the phenotype
(Fig. 8.2c)
9
Analysis of the 6-locus model
• In the 6-locus model on the previous slide, we are
not likely to recover the parental phenotypes
unless we look at a very large number of F2
individuals
• P(homozygous for all lower-case alleles) = (1/4)6
= 1/4096
• This looks like blending inheritance in which the
extreme parental phenotypes are not recovered in
the F2
• But, according to Mendelian genetics, the parental
alleles are still intact
10
Analysis of the 6-locus model (continued)
• East realized that, consistent with Mendelian
inheritance, most F2 individuals would be
heterozygous at most loci and would have
intermediate phenotypes
• But, he also reasoned that if the parental alleles
were still intact, as predicted by Mendelian
genetics, he could recover the parental phenotypes
by selecting for increased and decreased corolla
height starting with the F2
11
Selection on
corolla
length in
longflower
tobacco is
consistent
with
Mendelian
inheritance
(Fig. 8.3)
12
Analysis of selection on corolla height
• East was able, with only 3 generations of artificial
selection, to recover phenotypes that resembled the parents
— the parental alleles were still there — short and tall
corollas had not been lost by blending inheritance
• In modern terminology, we would say that selection
increased the frequencies of alleles that produced the
selected phenotype, and more individuals became
homozygous for those alleles at more loci
• Note that the individuals in each parental strain don’t all
have exactly the same phenotype: their variation reflects
environmental effects on the phenotype (assuming that
they are highly inbred and homozygous)
13
Identifying genes that control variation in
quantitative traits — quantitative trait loci (QTLs)
• QTL mapping
• Candidate loci
– Both approaches depend upon the development
of molecular genetic technology, particularly
DNA sequencing, during the last 10 - 15 years
14
QTL Mapping
• Life span in Drosophila melanogaster
15
A hypothetical map of 2 QTLs and 7 markers
on a chromosome
M
M2
M3
M4
M5
M6
M7
1
QTL
QTL
The Mi are the marker loci. Microsatellite loci are often used as
markers. Marker genotype is determined by electrophoresis.
Two QTLs are represented by red triangles.
Note: we do not know in advance if any QTL are on the
chromosome, or, if there are, where they are located
16
Interval Mapping – QTL in interval (1)
Short-lived inbred line, S
M1
QS
c1
P:
M1
Long-lived inbred line, L
M2
m1
c2
QS
QL
c1
M2
m1
M1
QS
c1
F1:
m1
m2
c2
QL
m2
M2
c2
QL
m2
17
Interval Mapping – QTL in interval (2)
• In the F2, differences in life span among marker
genotypes indicate a life span QTL in the marker
interval
• In the F2, the life span phenotypes of individuals
that carry chromosomes with crossovers between
the markers give information about where in the
interval the QTL is located
18
Interval Mapping – QTL in interval (3)
F2 marker genotype
“Non-crossovers”
M1M2/M1M2
M1M2/m1m2
m1m2/m1m2
Crossovers
M1m2/M1M2
M1m2/m1m2
m1M2/M1M2
m1M2/m1m2
Likely F2 QTL
genotype
Likely F2
phenotype
QS / QS
QS / QL
QL / QL
short life
?
long life
QTL close to M1
QTL close to M2
QS/ QS
QS /QL
QL / QS
QL / QL
QL / QS
QL / QL
QS / QS
QS / QL
19
Interval Mapping – no QTL in interval (1)
Short-lived inbred line, S
Long-lived inbred line, L
M3
M4
m3
m4
M3
M4
m3
m4
P:
M3
M4
m3
m4
F1:
20
Interval Mapping – no QTL in interval (2)
• In the F2, we expect no differences in life span
among marker genotypes because there is no QTL
in the marker interval
21
Interval Mapping – no QTL in interval (3)
F2 marker genotype
Likely F2 QTL
genotype
Likely F2
phenotype
“Non-crossovers”
M3M4/M3M4
M3M4/m3m4
m3m4/m3m4
null
null
null
average
average
average
Crossovers
M3m4/M3M4
M3m4/m3m4
m3M4/M3M4
m3M4/m3m4
null
null
null
null
average
average
average
average
22
QTL Mapping – the Likelihood map
• The statistical test of whether or not a QTL is located at a
given position on a chromosome is based on a comparison
of the likelihood (= probability) of the observed data on the
assumption of no QTL at the position versus the likelihood
of the data on the assumption that there is a QTL at the
position
• This allows us to calculate a likelihood ratio (LR) for a
QTL at each position along a chromosome, which results
in a likelihood map
• Peaks in the likelihood map that are above an established
threshold for statistical significance indicate the presence
and location of a QTL
23
80
Females
70
60
LR
50
40
30
20
10
0
0
15
30
45
60
75
90
105
Map position
D. melanogaster chromosome 3 likelihood map for life span QTL
Each line represents a cross between a different pair of parental lines (horizontal
line is the experiment-wise significance threshold, a = 0.05, and the diamonds
show marker locations). Red arrows indicate QTL that are present in more than
one cross. There is evidence here for at least 4 life span QTL.
Forbes, S. N., R. K. Valenzuela, P. Keim, and P. M. Service. 2004. Quantitative trait loci
affecting life span in replicated populations of Drosophila melanogaster. I. Composite
interval mapping. Genetics 168:301-311.
24
70
Females
60
LR
50
40
30
20
10
0
0
15
30
45
60
75
90
105
Map position
D. melanogaster chromosome 2 likelihood map for life span QTL
Each line represents a cross between a different pair of parental lines (horizontal
line is the experiment-wise significance threshold, a = 0.05, and the diamonds
show marker locations). Red arrows indicate QTL that are present in more than
one cross. There is evidence here for at least 1 life span QTL.
Forbes, S. N., R. K. Valenzuela, P. Keim, and P. M. Service. 2004. Quantitative trait loci
affecting life span in replicated populations of Drosophila melanogaster. I. Composite
interval mapping. Genetics 168:301-311.
25
The shortcomings of QTL mapping
• Interval mapping is not very precise.
Typically it locates QTLs to fairly broad
regions of chromosomes. These regions
may contain hundreds of genes.
• More precision is possible, but with a lot
more work, and we are still not likely to
identify the actual genes
26
Candidate Loci
• Another approach to identifying QTLs is to
look directly at genes that are suspected,
usually on the basis of known function of
the gene product, to play a role in
determining a quantitative phenotype
• These genes are referred to as candidate
genes
27
Analysis of a candidate locus – 1
• Benjamin et al. (1996) looked for a
relationship between allelic variation in the
gene D4 dopamine receptor (D4DR) and
novelty seeking behavior in humans, a
quantitative trait as measured by a score on
a questionnaire
• Dopamine is a neurotransmitter involved in
communication between brain cells
28
Analysis of a candidate locus – 2
• Alleles of the D4DR gene vary in the
number of copies of a 48 bp tandem repeat
(2 - 8 repeats)
• Alleles were classified as “short” or “long”
• “Novelty seeking” expresses a continuum
between “excitable, impulsive, exploratory”
personality and “reflective, stoic, rigid”
personality
29
Association
between
genotypes at
the D4
dopamine
receptor
(D4DR) gene
and “noveltyseeking score”
(Fig 8.10)
30
Analysis of a candidate locus – 3
• Individuals with at least one “long” allele scored,
on average, 3 points higher on the questionnaire
than did “short” homozygotes
• The D4DR gene explains about 3-4% of the
variation in novelty seeking scores
• That’s not very much. If novelty seeking has
reasonably high heritability, we expect that there
are other genes that affect it.
31
Measuring heritable variation
• How much of the phenotypic variation in a
trait is due to genetic differences among
individuals?
• How much of it is due to environmental
effects on individuals?
• What is the heritability of a trait?
32
Components of variance
• The total variation in a trait is called the
phenotypic variance, VP
• The variation among individuals that is due to
genetic differences among individuals is the
genetic variance, VG
• The variation among individuals that is due to
environmental effects is environmental variance,
VE
• With some simplifying instructions, VP = VG + VE
33
Broad-sense heritability, H2
• H2 = VG / VP = VG / (VG + VE)
• Note: if a population consists of a single
clone, all individuals have the same
genotype, and VG = 0, so H2 = 0
• On the other hand, if individuals have
different genotypes, but environment has no
effect on the trait, then VE = 0, and H2 = 1
• The theoretical range of heritability is 0 to 1
34
Additive and dominance genetic variance
• The genetic variance can be further decomposed into
additive genetic variance, VA, and dominance variance, VD
• VG = VA + VD
• The additive genetic variance is the part of the phenotypic
variation that results from the average effects of alleles
when combined at random with other alleles in the
population.
• The dominance variance is the part of the phenotypic
variation that results from the dominance interaction
between a pair of alleles at a locus.
35
Additive variance and narrow-sense
heritability, h2
• Additive variance is important in sexually
reproducing organisms because parents pass
on only 1 allele of each gene to offspring —
not both alleles
• This means that they do not pass on the part
of their phenotype that is due to dominance
• h2 = VA / VP = VA / (VA + VD + VE)
• h 2 ≤ H2
36
Estimating heritability
• The every day sense of heritability is that it
describes resemblance between relatives. If a trait
is highly heritable, we expect children to strongly
resemble their parents
• In fact, resemblance between parents and offspring
is one way of estimating heritability
• In offspring - midparent regression, the slope of
the regression line is an estimate of h2
37
Midoffspring height (average height of offspring)
Estimating heritability by offspring-parent
regression (Fig. 8.11a-c)
Heritabilit
approximately 0
Midparent height
(average height of
mother and father
Midparent height
(average height of
mother and father
38