Quantitative Inheritance - Pt.1

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Quantitative Inheritance - Pt.1

• Chapter 8

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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

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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 31 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

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Some quantitative traits in humans (Fig. 8.1)
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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

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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

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Inheritance of corolla height in longflower
tobacco under the assumption of a single
controlling gene and incomplete dominance (Fig.
8.2a)
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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)
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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)
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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

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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

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Selection on corolla length in longflower tobacco
is consistent with Mendelian inheritance (Fig.
8.3)
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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
  dont all have exactly the same phenotype their
  variation reflects environmental effects on the
  phenotype (assuming that they are highly inbred
  and homozygous)

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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

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QTL Mapping

• Life span in Drosophila melanogaster

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A hypothetical map of 2 QTLs and 7 markers on a
chromosome
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
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Interval Mapping QTL in interval (1)
Short-lived inbred line, S
Long-lived inbred line, L
P
F1
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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

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Interval Mapping QTL in interval (3)
F2 marker genotype Likely F2 QTL Likely F2
genotype phenotype Non-crossovers M1M2/M1M2
QS / QS short life M1M2/m1m2 QS /
QL ? m1m2/m1m2 QL /
QL long life QTL close to M1
QTL close to M2 Crossovers M1m2/M1M2
QS/ QS QL / QS M1m2/m1m2 QS /QL QL
/ QL m1M2/M1M2 QL / QS QS /
QS m1M2/m1m2 QL / QL QS / QL
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Interval Mapping no QTL in interval (1)
Short-lived inbred line, S
Long-lived inbred line, L
P
F1
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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

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Interval Mapping no QTL in interval (3)
F2 marker genotype Likely F2 QTL Likely F2
genotype phenotype Non-crossovers M3M4/M3M4
null average M3M4/m3m4 null
average m3m4/m3m4 null average Crossov
ers M3m4/M3M4 null average M3m4/m3m4
null average m3M4/M3M4 null
average m3M4/m3m4 null average
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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

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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 168301-311.
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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 168301-311.
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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

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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

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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

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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

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Association between genotypes at the D4 dopamine
receptor (D4DR) gene and novelty-seeking score
(Fig 8.10)
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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
• Thats not very much. If novelty seeking has
  reasonably high heritability, we expect that
  there are other genes that affect it.

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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?

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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

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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

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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.

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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)
• h2 H2

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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

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Estimating heritability by offspring-parent
regression (Fig. 8.11a-c)
Heritabilit approximately 0
Midoffspring height (average height of offspring)
Midparent height (average height of mother and
father
Midparent height (average height of mother and
father