Quantitative Genetics
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A loose distinction
“Qualitative” traits:
• Blood groups (ABO)
• Coat color in cats
• Color vision
Quantitative traits:
• Height
• Weight
• Facial features
Difference between
phenotypes of two
individuals can be explained
by difference in genotype at
a small number of loci (for
example, 1 or 2).
Mendelian ratios in F1
The phenotype is
determined – to some
extent – by genotype, but
phenotypic difference
between individuals is due
to difference in genotype at
a large number of loci.
No Mendelian ratios in F1
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Gene for starting businesses
“If you belong to a certain extended family in Seattle, you're
probably an entrepreneur. It seems to be about the only
career many of the members ever considered. ''It's in our
blood'' said Brian Jacobsen, president of Madison Park
Greetings, a stationery and gifts company. Mr. Jacobsen's
brother, mother, grandfather, two uncles, two cousins and
an aunt all started and ran their own companies and say
they cannot imagine any other livelihood.
Why are so many people in the same clan hooked? Some
of them have a theory. They believe that somewhere in
their chromosomes lurks an actual entrepreneurial gene -that their bent for business really is in their blood.”
New York Times, Nov. 20, 2003 – p. C8
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New York Times,
Nov. 20, 2003 – p. C8
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Gene for metaphors
“AG: Many of your songs include clear, visual images. Do
these images come from dreams?
Suzanne Vega: My mind works in a
metaphorical way. It’s easier for me to say
what I see than what I feel. The emotions
are expressed in the images.
I think it must be genetic, because my
daughter, Ruby, thinks the same way.
She’ll see smoke coming out of the back
end of a car and say, "The smoke is tapdancing." And if you look at it, you can see
what she means.
http://www.acousticguitar.com/issues/ag110/feature110.html
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The God Gene
“Modern science is turning up a possible
reason why the religious right is flourishing
and secular liberals aren’t: instinct. It turns
out that our DNA may predispose humans
towards religious faith. … Dean Hamer, a
prominent American geneticist, even
identifies a particular gene, VMAT2, that
he says may be involved. People with one
variant of this gene tend to be more
spiritual, he found.”
N. Kristof, New York Times, 2-12-05
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“Nature vs. nurture”:
the curse of “folk wisdom”
Is a given human trait in a given person the
result of “genes or the environment”?
• “She got her brains from her Dad”
• “Crime runs in his family – it’s genetic…”
• “All Klingons are bellicose” (“Blood tells”)
• “… is genetically predisposed to …”
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In a population, phenotypes of
individuals for a quantitative trait
tend to be normally distributed
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Central limit theorem
Carl Friedrich Gauss 
If a variable is the sum of many independent
variables, then its distribution will be normal:
e
x
2
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In this example, a trait (color) is
controlled by three loci, A, B,
and C, each of which occurs in
only 2 alleles.
The actions of the alleles is
somewhat additive, in other
words, an aabbcc organism is all
white, whereas an AABBCC
organism is dark red.
The remarkable thing is, even
with such a simple system (three
loci with two alleles each!), we
can get a remarkably “smooth”
distribution of phenotypes!
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Crisper distinction between Mendelian and quantitative traits:
For a quantitative trait, the range of phenotypes exhibited by
individuals in any given genotypic class is BROADER than the
difference between two average individuals of two different
genotypes. In contrast, for a Mendelian trait, two individuals of the
same genotype will tend to be relatively similar, and all quite
strikingly distinct from individuals of a different genotypic class.
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Is trait X heritable?
Height – yes.
Language – no.
Neuroticism – ?
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Pellagra
Disorder caused in large part by ???, and characterized by skin lesions
and by gastrointestinal and neurological disturbances--the so-called
classical three Ds of pellagra: dermatitis, diarrhea, and dementia.
Pellagra Commission (1910s): simple Mendelian inheritance of pellagra
in the US South. “Controversy over the origins of pellagra continued
until the mid-1930's…”
Pellagra is caused by a dietary deficiency of
niacin (nicotinamide and nicotinic acid) –
precursor to NAD and NADP
Pellagra ran in families because poverty ran in families, and poor
families in the South subsisted on corn, which is low in niacin.
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Is a trait heritable?
Well, let’s mate individuals from
the two extremes of the
distribution, place their progeny
into a common, controlled
environment, and look.
If the progeny follow a
distribution that is skewed from
the parental one towards the
end of the curve their parents
came from, the trait is heritable.
If the progeny follow the same
distribution as the original one,
the trait is not heritable.
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Mapping of quantitative trait
loci (QTLs)
“Search for genes responsible for
variance in quantitative traits”
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Ulrike Heberlein:
the inebriometer 
Moore et al. (1998)
Cell 93: 997.
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QTL mapping, version 1
Testing alleles of candidate genes (forward
genetics): pick a gene (serotonin receptor)
that may have something to do with the trait
under study (neuroticism) and look for allelic
forms thereof that may occur more
frequently in individuals who are neurotic.
How do you measure someone’s level of
neuroticism?
http://cac.psu.edu/~j5j/test/ipipneo1.htm
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“Mood disorders”: anxiety
• Serotonin (5-HT) – neurotransmitter (motor
activity, food intake, sleep, reproductive activity,
cognition, emotional states, including mood and
anxiety).
• Serotonin transporter (5-HT uptake) – two alleles
(long and short) – former transcribed more
efficiently
• “NEO personality inventory” – people with short
allele have greater anxiety-related personality
characteristics
• Polymorphism explains 7-9% of genetic variance
Lesch et al. (1996) Science 274: 1527.
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“Serotonin transporter genetic variation and
the response of the human amygdala”
“Individuals with one or two copies of the short
allele of the serotonin transporter (5-HTT)
promoter polymorphism, which has been
associated with reduced 5-HTT expression
and function and increased fear and anxietyrelated behaviors, exhibit greater amygdala
neuronal activity, as assessed by BOLD
functional magnetic resonance imaging, in
response to fearful stimuli compared with
individuals homozygous for the long allele.
These results demonstrate genetically driven
variation in the response of brain regions
underlying human emotional behavior and
suggest that differential excitability of the
amygdala to emotional stimuli may contribute
to the increased fear and anxiety typically
Hariri et al (2002) Science 297: 400.
associated with the short SLC6A4 allele.”
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Willis-Owen Biol. Psychiatry 2005
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Willis-Owen Biol. Psychiatry 2005
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Living With Our Genes
D. Hamer and P. Copeland (1998)
“In the future, a person who complains of depression or
anxiety could have a DNA test to check the serotonin
genes. People with compulsive behaviour such as
gambling, drinking, drugs, or promiscuous sex, would be
checked for dopamine genes. Eating disorder or obesity?
Look at the genes for leptin, the leptin receptor, or its
targets. …
Doctors won’t be the only ones to read this information.
Insurance companies … would be very interested in
genetic predispositions toward addiction or mental
disorders. The military … might want to know about genes
for rebellious temperament. Employers might be interested
in genes for loyalty. Religious orders would be wise to
discourage high novelty seekers, while the maker of sports
cars would want to target them with ads. Dating services
would have revealing new ways to match people. Imagine
how excited certain school administrators would be to track
students who are bright, troubled, or aggressive.”
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QTL mapping, version 2
Mapping by linkage:
Take pedigrees with some frequency of
individuals affected by a trait (e.g.,
schizophrenia), and scan their entire
genome for “linkage” with some
polymorphic marker (e.g., a RFLP).
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Mapping a qualitative trait by linkage
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11.24
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Brockmann and Bevova (2002). Trends Genet. 18: 367.
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The ob mouse
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Well-said
“The fact that single genes can be modified
and produce obese mice conclusively
shows that genes contribute to obesity.
However, the effect of a tested gene –
especially if it contributes to complex traits
– depends on the genetic background (i.e.,
the effects of other genes – and thus might
or might not produce the expected
phenotype, or a milder phenotype.”
Brockmann and Bevova (2002). Trends Genet. 18: 367.
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Problem
For “simple” traits, the genotype-phenotype relationship is
fairly unambigious, issues of penetrance and expressivity
aside. If you are homozygous for HbS, you will get SCA, no
question about it. It is largely irrelevant, what environment
you grow up in – you’ll get anemia (although medical care
will help you lead a better life, no question about that).
For qualitative traits, the relationship between genotype
and phenotype is impossible to express in a simple
statement, so the general public, eager for simple solutions
that fit its short attention span, has become enamored of
the word “tendency.”
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Sigh
“Genetic predisposition to…”:
(you name it)
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A pernicious line of reasoning
I did X
(or “I am Y”)

I have a gene that caused me to do X
(or to become Y)

It’s not my fault, it’s the gene’s fault
(or, “I am genetically superior”)
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Misunderstanding a fundamental distinction
between quantitative and qualitative traits
Let’s say a driver with colorblindness (a mutation on the X
chromosome) ran a streetlight and killed a person.
Well, on some level, we will be less prone to blame that
person (“he can’t help being colorblind”) for that act than
someone with normal color vision who got drunk and ran
that light.
The leap here is to go from such “assignment of blame” in
the case of qualitative traits, with their fairly
unambiguous genotypephenotype relationship, to
similar logic for quantitative traits (“I ran the streetlight
because I was scared of being late to work, and I carry
the allele of the serotonin receptor gene that makes me
genetically scared”).
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Norm of reaction
A plot of carefully measured phenotype
in large pool of genetically identical
individuals grown under a range of
environments.
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Achillea millefollium (yarrow)
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Take 7 yarrow plants,
grow cuttings from
each one at different
elevations.
Measure each “child”
at each elevation.
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Risk of breast cancer and physical exercise in
BRCA1/2 mutation carriers: an example of how the
norm of reaction illuminates the modification of a
“genetic tendency” by environment
“Physical exercise and lack of
obesity in adolescence were
associated with significantly
delayed breast cancer onset.”
M.-C. King et al. Science 2003
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The reality of “Nature vs. nurture”: a group of individual of identical genotype,
when placed in a normally distributed range of environments (X axis) will yield a
population with a normally distributed range of phenotypes (Y axis), but the shape
of the distribution will be a function BOTH of that genotype’s norm of reaction and
of the distribution of environments.
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Nature vs. Nurture: Wrong Question!
1.
2.
Each organism is the subject of continuous
development throughout its life. The environment’s
effects on the organism will vary depending on when in
development the effect is exerted (e.g., PKU).
The developing organism is not under the effect of
genes and the environment acting separately. It is
under the effect of mutually interacting genes and the
environment. In the resulting organism, the effects of
nature and nurture are as “separable” as effects of
flour and of the oven in the baked muffin.
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And therefore …
For any given individual, assigning percentages to “genes” and
“environment” in determining the phenotype for a given quantitative
trait has no meaning.
For each given quantitative trait, each human being (a specific,
given genotype), has a norm of reaction. The “norm of reaction”
describes exactly how the trait will develop when very many
individuals of exactly identical genotype will be placed in many
different, very carefully controlled environments. Careful analysis of
the norm of reaction may, perhaps, tell us a little bit about how the
genes responsible for that quantitative trait interact with the
environment in that trait’s development. No percentage values will
be assigned to “nature or nurture” at any point in time—they are
meaningless in this context.
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Genetics of “intelligence”
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“The Bell Curve” (1994)
R.J. Herrnstein and C. Murray
Claims (according to HnM, based on data they present):
1. African-American and Latinos in the US score on the
average lower on IQ tests that whites or AsianAmericans, and lower IQ contributes to greater crime,
poverty, illegitimacy, welfare dependency,
unemployment, workplace injury.
2. IQ is substantially heritable and the higher fecundity of
Blacks and Latinos leads to dysgenesis – a decline in
the population’s potential for high IQ.
3. Forecast: establishment of a caste-like, reproductively
isolated, cognitive elite, maintained through
intermarriage, and ruling over the cognitively limited
masses.
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Public vs. private dialogue
HM: “Here was a case of stumbling onto a subject
that had all the allure of the forbidden. Some of
the things we read to do this work, we literally
had to hide when we were on planes and trains.”
In other words, the data really support all the
claims, and people are afraid to admit it.
Problem: >99% of all people in the US are not
qualified to understand whether the data support
the claims. New York Times: “But this reviewer is
not a biologist and will leave the arguments to
the experts” (10/27/94).
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Calling a spade a spade
“[The] taboo being violated is … that of the
great war against Nazi Germany. It’s not the
taboo against unflinching scientific inquiry,
but against pseudoscientific racism. Of all
the world’s taboos, it is the one most
deserving of retention.”
John Judis Hearts of Darkness (The Bell
Curve Wars, New York, Basic Books 1995)
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For the record
1. In my opinion, Drs. Herrnstein and Murray are
pseudoscientific racists. That is, they just don’t
like people of other races, and hide that dislike
behind data, or what they claim to be data.
2. In addition, they deliberately misinterpret those
data, and their conclusions, therefore, are
wrong.
3. Problem: while no education is necessary to
see the validity of item 1, item 2 requires a
large amount of specialized knowledge.
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What do the data show?
What is IQ and how heritable is it? How severe is
the threat of dysgenesis for IQ? What is the
correlation between low IQ and societal ills?
To answer these question, we must examine the
scientific meanings of the words “IQ” and
“heritable,” the procedures for measuring IQ
heritability in human populations, or the heritability
of anything in any population, and how correlations
between things are actually measured.
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Point 1 – the reification of IQ
“Among the experts, it is by now beyond much
technical dispute that there is such a thing as a
general factor of cognitive ability on which
human beings differ and that this general factor
is measured reasonably well by a variety of
standardized tests, best of all by IQ tests
designed for the purpose” H+M
“Extraordinary obfuscation”
(SJG, The Mismeasure of Man)
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“The tendency has always been strong to
believe that whatever received a name must
be an entity or a being, having an
independent existence of its own. And if no
real entity answering to the name could be
found, men did not for that reason suppose
that none existed, but imagined that it was
something peculiarly abstruse and
mysterious.” John Stuart Mill
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Speed
Rodgers Rop (Kenya)
2 hrs. 9 min. marathon
Tim Montgomery (USA)
9.78 sec. 100 m
Nolan Ryan (USA)
100.9 mph 8/20/74
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Point 2 – the heritability of the “trait”
that IQ tests measure
“The genetic component of IQ is unlikely
to be smaller than 40% or higher than
80%. … We will adopt a middling
estimate of 60% heritability … the
balance of the evidence suggests that
60% may err on the low side” (p. 105)
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Environmental
vs. genetic variance
in quantitative traits
aka “How extremely technical it
will very rapidly get”
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20.13
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20.13
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Two sources of variance
In a given population, variance will be due to individuals
having different genotypes (genetic variance) and
experiencing different environments:
s s s
2
p
2
g
2
e
Please note, though, that the equation makes a claim about
the population and NOT about the “relative contributions
of genes and environment” to the phenotype of an
individual.
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Broad heritability is NOT,
repeat, Nancy, Oliver, Tango, a
general characteristic of this
trait. In fact, for a trait, heritability
can be 0 (if no genetic variation
exists).
Note that broad heritability
being equal to zero does NOT,
repeat, November, October,
Typhoon, imply that the trait has
no genetic basis. If H2=0, then
there is no variation in this
population for genotypes that
affect this trait, that’s all. Nothing
can be said about whether this
trait “is in the genes” or not.
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… and therefore
It is scientifically incorrect to use high withingroup broad-sense heritability of a trait to
make claims about the “reasons” for
differences between groups.
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What H2 does NOT mean
Highly heritable traits (height, for example)
are not necessarily “set in stone.”
For example, height is highly heritable. In
the third world, people tend to be shorter
due to malnutrition. If we take those
children and move them to Marin county,
they will grow much taller.
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Problem
H2 is simply not a very useful number, however
wide attempts at its (mis)use may be. It does not
say much except something about the amount of
genetic variation in a given population for a trait.
Note that Fig. 20.15 talks about how to measure
H2 in humans using twin studies.
What one would really like is some quasiexperimental measure of the extent to which we
can expect a given trait to vary when we vary the
genotype of the organism.
I.e., can we breed “a bigger artichoke”?
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Narrow-sense heritability, h2
= a really useful number that is
really hard to measure properly
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A closer look at genetic variance
In a population, the total variance is due to
individuals differing in genotype, and to
individuals experiencing different
environments:
s s s
2
p
2
g
2
e
This sg2 term, in fact, hides 3 different things!
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Let’s take a “complex” trait controlled by 10 loci (A through J), each with two alleles
(A and a through J and j). For any given locus, variation between individuals for this
trait can be attributed to 3 different things:
1.The particular allele the individual inherited (e.g., A tends to make you taller, and
a tends to make you shorter).
2.The overall genotype for this locus (if you’re AA, you’ll be very tall; if you’re Aa,
intermediate; if aa, short).
3.The genotype for the other loci – there always are epistatic interactions (for
example, an AA BB person will tend to be taller than an AA bb person).
Different traits – i.e., height vs. neuroticism – may be expected to experience these
3 different variances differently. For example (hypothetical), neuroticism may be
particularly susceptible to epistasis (item 3) – that is, it doesn’t really matter what
specific allele of any given gene you’ve inherited, what you need is a particular
combination. On the other hand, other traits may be more “additive” –
hypothetically, height may be due to algebraic additive effects of individual genes –
if you’re AA for the first gene pair and homozygous recessive for the other 9 loci,
you’re 5 inches shorter that an AA BB person, and that person is 5 inches shorter
than an AA BB CC person, etc.
From an agricultural perspective, traits amenable to change by selective breeding
are those that are susceptible to the “additive” process (“the more right alleles of
different genes you get, the bigger the artichoke”). Items 2 and 3 reflect individual
genotypes, on different chromosomes, are ripped apart by meiosis, and are
impossible to systematically recreate in agriculture. Thus, traits in which it’s
important what allele pair occurs at a given locus, or what combination of alleles
are found at a number of different loci, are hard to manage via selective breeding,
unless they all occur on the same short stretch of 1 chromosome!
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Components of variance
1. Additive: what allele of what gene you
inherited.
2. Dominance: what is the other allele for
that locus.
3. Interaction: what other alleles of other
genes you inherited.



sg sa sd si
2
2
2
2
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The useful part of genetic variance



sg sa sd si
2
2
2
2
In quantitative genetics, how extensive is the
additive genetic variance for a trait is a
measure of how much we can expect the
trait to respond to changes in genotypic
composition.
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A definition of narrow-sense
heritability
The fraction of total variance in the population that
is due to additive genetic variance:
2
2 sa
h 2
sp
By the way, did anyone notice how rapidly technical it got, and away
from “This kid is real bright, just like his old man was. Must be
genetic…” ?
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Fact and problem
In agriculture, narrow-sense heritability is a
valuable number to know, because it
illuminates the extent to which a
quantitative trait may respond to selective
breeding. For example, is it feasible to
breed a cow that gives more milk?
How on Earth do you measure “additive
genetic variance”?
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Estimates of narrow-sense
heritability from regression of
offspring on parents
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Regression of y on x
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For a given quantitative trait, regression of
offspring on parents yields a numerical
estimate of additive genetic variance, i.e.,
the elusive and highly interesting narrowsense heritability, h2.
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Gasp! Regression of offspring on midparents
yields a line the slope of which is the elusive
narrow-sense heritability!!!
20.16
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Resemblance between relatives
(a simplification)
1.
2.
3.
Resemblance between relatives is one of the basic genetic
phenomena displayed by metric characters. It is, of course, due to
shared genes and shared environment.
In a given population, however, if a parent-child pair diverges from
the population mean (the taller person in the village has a taller
child), this may be due to the fact that they are the only ones with
access to lead-free water, but, in a general, averaged sense, it’s
more likely that their divergence is due to sharing of alleles of
genes that contribute to the development of the trait.
This means that the covariance of parents and their offspring for a
given trait – i.e., the tendency of both parents and their children to
diverge from the population mean to the same extent in the same
direction – is reflective of their common genetic makeup.
D. Falconer Quantitative Genetics
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20.14
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The importance of the womb
What Herrnstein and Murray
“overlooked” in “calculating” the
narrow-sense heritability of IQ
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Nature, July ’97: “The heritability of IQ”
IQ heritability, the portion of a population's IQ variability attributable
to the effects of genes, has been investigated for nearly a century,
yet it remains controversial. Covariance between relatives may be
due not only to genes, but also to shared environments, and most
previous models have assumed different degrees of similarity
induced by environments specific to twins, to non-twin siblings
(henceforth siblings), and to parents and offspring. We now evaluate
an alternative model that replaces these three environments by two
maternal womb environments, one for twins and another for
siblings, along with a common home environment. Meta-analysis of
212 previous studies shows that our 'maternal-effects' model fits the
data better than the 'family-environments' model. Maternal effects,
often assumed to be negligible, account for 20% of covariance
between twins and 5% between siblings, and the effects of genes
are correspondingly reduced, with two measures of heritability being
less than 50%. The shared maternal environment may explain the
striking correlation between the IQs of twins, especially those of
adult twins that were reared apart.
Devlin et al. (1997) Nature 388: 468.
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Devlin et al. (1997) Nature 388: 468.
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Hmmmm….
“Adoption designs are a popular means of estimating IQ heritability.
Associated analyses, however, usually assume negligible maternal
effects. By contrast, our results show that 20% of twin and 5% of sibling
covariance may be attributable to maternal effects. These results have
two implications: a new model may be required regarding the influence
of genes and environment on cognitive function; and interventions
aimed at improving the prenatal environment could lead to a significant
increase in the population's IQ. Moreover, some of Herrnstein and
Murray's conclusions regarding human evolution such as the
development of cognitive castes and IQ dysgenics, arise from their
belief that IQ heritability is at least 60%, and is probably closer to the
80% values obtained from adoption studies. Our results suggest far
smaller heritabilities: broad-sense heritability, which measures the total
effect of genes on IQ, is perhaps 48%; narrow-sense heritability, the
relevant quantity for evolutionary arguments because it measures the
additive effects of genes, is about 34%. Herrnstein and Murray's
evolutionary conclusions are tenuous in light of these heritabilities.”
Devlin et al. (1997) Nature 388: 468.
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Dysgenesis, huh?
Amount that phenotype changes from
generation to generation: R
Selection differential: difference between the
mean phenotype of the selected parents
and the mean phenotype of the population
before selection – s
R = h2 · s
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A perspective on the allure of the
“dream of blue blood”
Why does it matter so much to people whether IQ
is “hereditary” or not?
E.L. Thorndike (1905): “In the actual race of life,
which is not to get ahead, but to get ahead of
somebody, the chief determining factor is
heredity” [emphasis added]
R. Lewontin (1995): “In the three-quarters of a
century that have since passed, the central effort
of human behavioral and psychological genetics
has been to put a firm foundation under
Thorndike’s claim.”
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Further reading on this subject
1.
2.
3.
4.
D. Falconer Quantitative Genetics
M.G. Bulmer Principles of Statistics
R. Lewontin The Triple Helix
S.J. Gould Mismeasure of Man
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