## 1. Terminological issues



The term "heritable" applies to traits that vary in the
population and are more similar in parents and offspring than they are
in randomly selected individuals in the population. We inherit
numerous attributes from our parents including their religious beliefs
and, if we are lucky, their vast fortunes. The kinds of hereditary
traits that biologists are interested in are those that are reliably
transmitted from one generation to the next as a matter of
biology. Darwin (1859 [1968]), working without the advantages that
genetics would later bring, discussed hereditary traits at the level
of phenotypes. Darwin demonstrated that natural selection sorts among
hereditary variations, for example, the height of an organism, its
weight, the color of its coat and so on. Most contemporary discussions
of heredity constrain hereditary traits to those that can be
demonstrated to be passed on genetically. The concept of
"heritability" was introduced "to quantify the level
of predictability of passage of a biologically interesting phenotype
from parent to offspring" (Feldman, 151). Heritability is
usually assessed by complex statistical analysis, careful
experimentation or both.



Discussions of heredity invite confusions between mechanisms
responsible for individual development and mechanisms responsible for
the transmission of traits from one generation to the next. Genes are
the standard units of inheritance discussed in biology. Genes are also
taken to be the most important causal component in the development of
an organism's traits. Methods derived from population genetics
to assess heritability provide no information about the causal
mechanisms contributing to the development of an individual's
traits. Population geneticists study the patterns of transmission of
traits in populations from one generation to the next. Molecular
biologists identify coding sequences of DNA and hence the proteins
that these sequences produce in the developing organism. Working
together, molecular biologists and population geneticists can produce
a convergent account of a particular gene, providing both its pattern
of transmission and an account of its role in development. For
example, medical geneticists may discover a pattern of inheritance for
a disease in a family that leads them to hypothesize that there is a
gene (or a number of genes) responsible for the development of the
trait in individual humans. Molecular analysis may then lead to the
discovery of a sequence of DNA that codes for an unusual protein that
is in part responsible for the development of the symptoms of the
disease. Finally, population genetics techniques, such as heritability
analysis, may then be applied to mechanisms discovered by molecular
biologists.


## 2. Heritability and Population Genetics



Mendelian genetics provides laws that govern the passing on of
discrete traits from one generation to the next. For example, Mendel
experimentally demonstrated particular patterns of inheritance for
smooth and wrinkled peas in a population of pea plants. Discrete or
discontinuous traits contrast with continuous or quantitative traits.
Height in humans and leaf number in trees are continuous traits.
Continuous traits vary on a continuum that can be represented as a
normal distribution, graphed as a bell curve. Most philosophical
discussion about heredity and heritability arises from the study of
continuous traits.



The study of quantitative or continuous traits can be carried out by
looking simply at phenotypes. For example, if a population of plants
varies in height we can ask how much of this variation is due to
genes. Assessing the proportion of the variation of a trait in a
population that is due to genes is achieved by a statistical method
called the analysis of variance. Once this analysis has been carried
out a simple formula provides a number between 0 and 1 that is the
heritability measure for the trait in question. We use a few simple
examples to illustrate the important concepts involved in producing
heritability measures.



Before we consider the analysis of variance and its contribution to
heritability measures, it is helpful to understand the general concept
of heritability. Heritability is a measure of genetic influence on
variation. If a trait has high heritability, its varying from
individual to individual in a population can be explained genetically.
An imaginary example illustrates one way of assessing heritability.
Say we have two students from a class and student *a* is
6'2'' and student *b* is 4'2''. To discover
the influence of genes on height, we could clone both students and
then swap the clones' environments and see what happens. In the
figure below, the environments that *a* and *b* grew up in
are \(\rE a\) and \(\rE b\). Clones of *a* and *b* are \(\rC
a\) and \(\rC b\).

 

\[
\begin{array}{cccl} 
& \rE a & \rE b & \text{Height results} \ldots \\\hline 
1 & \rC b=4^{\prime}2^{\prime\prime} & \rC a=6^{\prime}2^{\prime\prime} & \text{from genes} \\\hline 
2 & \rC b=5^{\prime}8^{\prime\prime} & \rC a=5^{\prime}8^{\prime\prime} & \text{from genes and environment} \\\hline 
3 & \rC b=6^{\prime}2^{\prime\prime} & \rC a=4^{\prime}2^{\prime\prime} & \text{entirely from environment} \\\hline 
\end{array}
\]


A scenario like 2 is the most likely outcome. Of course we can't
clone humans (or faithfully replicate the environments they grow up
in). We can, however, do this with plants and other kinds of
experimental organisms and as a result we can get a good sense of the
contribution of genes to variation in a phenotypic trait.



Heritability can be estimated in humans by comparing resemblance in
the phenotypic traits of twins (See Section 4. For a more detailed
discussion of twin studies.). Twin studies make the following
assumptions: Monozygotic, (identical), twins share all their genes and
their environment but dizygotic, (fraternal), twins share half their
genes and their environment. For any given trait, say height, we get
the following results:



> 
> *If heritability is high and variation is due mostly to genes, then
> monozygotic twins will be closer in height than fraternal twins.*
> 



If heritability is low and variation in height is due mostly to the
environment, then monozygotic twins will be as different in height
from one another as dizygotic twins.



Finally, we can get a sense of the heritability of a trait by finding
the slope of the regression line on the plots of offspring value for a
trait graphed with parental value. If the slope is 1, the trait is
entirely genetic and if the slope is 0, then the trait is not genetic
at all. If the variation among individuals is due to variation in
their genes, then offspring ought to resemble their parents.
Heritability is always a value between 1 and 0. In the graph below
values for mid-parent height and mid-offspring height are plotted for
a small sample population (mid-parent height is the average of the
height of both parents). The slope of the regression line is .75,
which indicates high heritability. (It should be stressed that this is
a very informal presentation of this kind of estimation of
heritability and for this approach to provide any useful results
important constraints on the nature of the population and the relevant
environment would have to be satisfied.)



![image](heritability-height.png)

Figure 1.




So far we have introduced methods of measuring or calculating
heritability that are somewhat intuitive. The problem is that these
methods do not acknowledge all that is involved in the production of
variation in the quantitative traits of organisms in a population. If
we stick to the example of variation in height in a sample population
of humans, we will discover that in most representative samples,
heights are distributed more or less normally. The variance in height
is defined as the average of the squared difference between each
measured height and the mean height for the population. Variance in
phenotype or phenotypic variance is symbolized as \(V\_P\). (From here
until the end of this section we adopt a specific strategy for
presenting the equations used in spelling out heritability relations.
We start out, with equation (1) below, by presenting the simplest
version of the relevant equations. Simple equations such as (1) below
are rarely ever satisfied but are routinely presented as adequate in
elementary introductions to behavioral genetics. Subsequent equations
in the sequence below render the relevant situation more accurately.
Population geneticists endorse variants of (1') below and do not
endorse (1).)

 

\[\tag{1} V\_P = V\_G + V\_E \]


Equation (1) simply says that the phenotypic variance is the variance
due to genes plus the variance due to the organisms'
environment. Behavioral geneticists and psychologists introduce
heritability in the following way: Heritability is the proportion of
phenotypic variance that is attributable to genotypic variance:
heritability \(= \bfrac{V\_G}{V\_P}\) (Biologists will also sometimes
talk of "environmentability", which is
\(\bfrac{V\_E}{V\_P}\).)



This notion of heritability is called broad sense heritability,
\(h\_b^2\) , and is "the proportion of phenotypic differences due
to all sources of genetic variance" (Plomin 1990, 234). Narrow
sense heritability, \(h^2\), is "the proportion of phenotypic
variance due solely to additive genetic variance" (Plomin 1990,
234).

 

\[\tag{2} h\_b^2 = \frac{V\_G}{V\_P} \] \[\tag{3} h^2 = \frac{V\_A}{V\_P} \]


"Additive genetic variation \((V\_{A})\) is variation among
individuals due to the additive effects of genes" (Freeman and
Heron, 206). For example, variation in height of organisms could
result from the contribution of several alleles at a locus where each
allele contributes more height to the organism. More precisely, allele
*A* could contribute .5 units to an organism's height,
allele *a* another .5 units and so on. A contrast with additive
genetic variance is dominance variance \((V\_{D})\). In this case, say
two alleles (*A* and *a*) are responsible for the
organism's height. An organism with *aa* is 1.0 units high,
an organism with *AA* is 2.0 units high but an organism with
*Aa* is also 2.0 units high. Total genetic variance,
\(V\_G\), is actually the sum of all the genetic variance. In the
simplified case presented here this is

 

\[\tag{4} V\_G = V\_A + V\_D \]


The implied equation for \(V\_P\) from the discussion so far is



\[\tag{\(1^{\prime}\)} V\_P = V\_A + V\_D + V\_E \]


But this equation still oversimplifies the situation and requires more
refining to deal with quantitative traits. Variance in phenotype can
result from gene interaction effects, or epistatic variance,
\(V\_{I}\). This occurs when alleles at one locus have an effect on the
phenotype that is dependent upon alleles at one or more other loci.
Further, there may be a contribution to phenotypic variance from
gene/environment interaction, \(V\_{G\times E}\) (See Tabery 2014 for a
detailed discussion of gene/environment interaction.). This occurs
when the effect of the environment on the phenotype differs between
genotypes. Finally, \(V\_P\) can be affected by non-random correlations
between genotypes and environments referred to as gene-environment
covariation, \(\COV(G,E)\). For example, if plants with a genotype
that tends to produce large plants also select nutrient- rich
environments, by root growth or seed dispersal, and plants with a
genotype that tends to produce small plants also select nutrient- poor
environments, the variance in height would be increased. If the
relation were switched the variance would decrease (Futuyma
1998). Factoring all the above in we now have the following:



\[\tag{\(1^{\prime}\)} V\_P = V\_A + V\_D + V\_I + V\_E + V\_{G\times E} + \COV(G,E) \]


And

 

\[\tag{\(4^{\prime}\)} V\_G = V\_A + V\_D + V\_I \]


The assumption made by many evolutionary biologists is that \(V\_I,
V\_{G\times E}\) and \(\COV(G,E)\) are generally small and the most
important component of variance from an evolutionary standpoint is
\(V\_A\). As a result, evolutionary biologists are usually interested
in \(h^2 (= \bfrac{V\_A}{V\_P})\). In contrast, psychologists and
behavioral geneticists are more interested in \(h\_b^2 (=
\bfrac{V\_G}{V\_P})\). Psychologists are interested in the contribution
of genes to human psychological traits whereas evolutionary biologists
use heritability measures to predict and measure the response of a
trait to selection. The relevant equation here is

 

\[\tag{5} h^2 = \frac{R}{S} \]


where, *R* is response to selection and *S* is the selection
differential. Heritability in this context is referred to as realized
heritability.



Philosophical discussion over measuring heritability has arisen mostly
from the use of \(h\_b^2\) measures in behavioral genetics and
psychology. Much of this discussion takes off from a paper by Lewontin
(1974) in which he argues that the analysis of variance cannot provide
us with answers to questions about how much genes contribute to
variance in a given trait. Before we turn to this and related
discussions, we provide more detail on how heritability is measured in
humans.


## 3. Measuring heritability: From Galton to GWAS



Francis Galton promoted a version of Darwin's account of
inheritance that clearly identified an internal, material contribution
to hereditary traits. He proposed the distinction between nature and
nurture, arguing that traits due to nature were the products of
inherited biological material. He also was the first to propose the
study of human twins as a way of understanding the contribution of
nature, as opposed to nurture, to human traits (Burbridge 2001; see
also Kronfeldner 2018). Galton's early work set the basis for a
paradigm in behavior genetics: twin and family studies. In studies of
plants and other organisms, genetic makeup and environment can be
systematically varied to assess the relative impact of genes and
environment on phenotypic traits. Twin studies are human behavioral
geneticists' analogue to such experiments (See, e.g.,
Shaffner 2016). By tracking similarities and differences between
groups of genetically related individuals reared in similar
environments, twin and family studies permit some scientific
investigation into sources of variance attributable to genetics and
environment. The predominant tool for practitioners in the field is
the statistical 'ACE model' (figure X)



> 
> ![TO BE SUPPLIED](fig2.png)
> 



The ACE model is a factor analytic model that partitions phenotypic
variance (represented with boxes) into three latent components
(represented with circles). The first latent factor, 'A'
represents 'additive' genetic variance and captures
genetic similarities and dissimilarities between twin pairs, as
monozygotic (MZ) 'identical' twins share roughly 100% of
their DNA while dizygotic (DZ) 'fraternal' twins share
roughly 50% of their DNA, just like normal siblings. The component
'*C*' represents 'common' environment,
signifying environmental variance that is shared by twin pairs reared
together. For example, because both MZ and DZ twin pairs live in the
same home, the correlation between their shared environment equals 1.
Finally, '*E*' represents 'unique' or
non-shared environmental variance, capturing environmental variables
that vary between twin pairs. In effect, it is the environmental
variation that is not shared by twins outside the home which ends up
getting couched as '*E*', as is the case when twins
attend different institutions or undergo different life events. 



The ACE model is effectively a visual representation--in the form
of a path analysis--of the underlying mathematics of heritability
estimation, known as 'Falconer's formula' (Falconer
and McKay 1998). The formula is derived from an observed population
statistic: the phenotypic correlation between pairs of MZ and DZ
twins. For any phenotype the MZ correlation or
'\(r\_{\MZ}\)' is typically higher than the DZ correlation
or '\(r\_{\DZ}\)'. Perhaps unsurprisingly, genetically
identical twins are more similar than fraternal twins. The implication
is that the greater the genetic similarity, the greater the phenotypic
similarity. Thus, narrow-sense, quantitative genetic heritability is
intuitively defined as the *difference* between MZ and DZ
correlations: the greater the difference, the higher the heritability.
On the flip side, if there is minimal difference between MZ and DZ
correlations, it would imply that genetics have little to do with
variance in the trait in question, and result in a low heritability
estimate.



Falconer's formula starts from the simple observation that MZ
twin pairs share two of the three components in common: 100% of their
genes and 100% of their common environment. Thus, MZ correlation are
treated as the sum of A and C:

 

\[ r\_{\MZ} = A + C\]


Similarly, DZ twin pares share 100% of their common environment, but
only half their genetic relatedness. Thus, the DZ correlation is the
sum of half additive genetic variance and common environment:



\[r\_{\DZ} = \frac{A}{2} + C\]


With these definitions in place, Falconer's formula permits
heritability estimation by calculating the difference between MZ and
DZ correlations:

 

\[
\begin{align}
r\_{\MZ} - r \_{\DZ} & = A - \frac{A}{2} + C - C\\
r\_{\MZ} - r \_{\DZ} & = A - \frac{A}{2}\\
\therefore A & = 2\left (r\_{\MZ} - r\_{\DZ}\right)
\end{align}
\]


With narrow-sense heritability defined, one may deduce the formulas
for estimating shared (*C*):

 

\[
\begin{align}
r\_{\DZ} & = \frac{A}{2} +C \\
r\_{\DZ} &= \frac{r\_{\MZ} -C}{2} + C\\
2 r\_{\DZ} & = r\_{\MZ} - C + 2C\\
2 r\_{\DZ} & = r\_{\MZ} + C\\
\therefore C&= 2 r\_{\DZ} - r\_{\MZ}\\
\end{align}
\]


Finally, non-shared environment may be derived from the assumption
that genetic similarity, shared environment, and non-shared
environment comprise the total variance in an observed trait:



\[
\begin{align}
A + C + E & =1 \\
[ 2(r\_{\MZ} - r\_{\DZ})] + [2(r\_{\MZ} - r\_{\DZ})] + E & = 1\\
r\_{\MZ} + E & = 1\\
\therefore E & = 1- r\_{\MZ}\\
\end{align}
\]


Consider the following example. In a twin study, one conducts a study
of height, revealing that \(r\_{\MZ} = .95\) and \(r\_{\DZ} = .55.\)
With this information, the basic techniques of quantitative genetics
may be used to partition said variance into sources attributable to
shared genetics or environments. Starting with heritability:



\[
\begin{align}
A & = 2(r\_{\MZ} - r\_{\DZ})\\
A & = 2(.95-.55)\\
A & = 2(.4) \\
A & = .8 \\
\end{align}
\]


Although philosophically contentious (for reasons discussed elsewhere
in this entry), the outcome above suggests that 80% of the variance in
height in the studied population of twins reared together is
attributable to genetic differences. To estimate non-shared
environment (*C*), recall the formula derived earlier:



\[
\begin{align}
C & = 2r\_{\DZ} - r\_{\MZ}\\
C & = 2(.55) - .95\\
C & = .15\\
\end{align}
\]


Finally, total variance in height attributable to non-shared
environment:

 

\[
\begin{align}
E & = 1 - r\_{\MZ}\\
E & = 1 - .95 \\
E & = .05\\
\end{align}
\]


In this example, 80% of the variance in height is attributable to
additive genetics (*A* = .8), 15% to shared environment (*C*
= .15), and 5% to non-shared environment (*E* = .05).



Research on heritability is currently undergoing a major transition.
For nearly a century, heritability has been estimated in the
'traditional' sense, through twin and family studies,
which are silent with respect to the underlying biological units of
genetic transmission. Twin and family studies and the ACE model, that
is, proceed from coarse-grained assumptions about genetic relatedness:
MZ twin share roughly 100% of their genetic material, DZ just half. It
wasn't until Watson and Crick's co-discovery of the double
helical model of DNA that geneticists could refine heritability
estimation with attention to biological details. Too much has happened
since the discovery of DNA to detail here, such as linkage analysis
and candidate gene studies, but a few key developments are integral to
understanding the most recent approaches to estimating
heritability.



First, all modern approaches to heritability estimation are
constructed from empirical data on Single Nucleotide Polymorphisms
(SNPs). In effect, SNPs are the fundamental units of genetic
differences that occur between individuals. While genetic sequences
between humans are greater than 99% identical, SNPs are the points that
differ. From a blood or saliva sample, 'SNP chips' allow
researchers to acquire a large set of SNPs for an individual. Early
SNP chips tracked 500,000 variants across the genome; recent
technology allows SNP detection in the excess of millions. With the
development of fast and cheap SNP chips within the past ten years, one
now has the ability to assess large populations of minute DNA-based
differences between individuals, which confers a new approach to
estimating heritability. Through a large family of approaches, Genome
Wide Association Studies (GWAS) identify statistical associations
between SNPs and thousands of phenotypes, from physical traits (e.g.,
height, weight, BMI, etc.) to behavioral and psychiatric traits (e.g.,
IQ, schizophrenia, depression, etc.). Historically, GWAS are conducted
as case-control studies: SNP profiles are collected from one
population of individuals who share a trait (such as high ADHD or
macular degeneration) and are compared to SNP profiles of a control
population lacking in the trait under investigation. If it turns out
that populations, on average, with the trait of interest also share
genetic similarities, then GWAS will flag the relevant SNPs as
statistically significant.



GWAS identify SNPs that are statistically correlated with phenotypes
of interest. After nearly a century of twin and family studies
consistently demonstrating relatively high heritability of traits,
there was some expectation that early GWAS would find a few genes of
large effect. GWAS results in this respect have been disappointing.
While twin studies indicate that roughly 50% of the total variance in
cognitive ability is explained by genetic differences, individual SNPs
associated with cognitive ability typically explain less than .04%
total variance.



One simple method of increasing the amount of phenotypic variance
accounted for by GWAS (sometimes referred to as
'h2GWAS') is to sum the total
effects of genome-wide significant SNP hits. The first efforts to do
this were met with disappointing results as well. Weedon et al. (2008)
conducted a GWAS of height which identified 20 SNPs with a combined
effect of 3%. These meager results inspired an impetus in the GWAS
community to conduct bigger and better studies that would be required
to power the small effect sizes of individual SNPs. Bigger data meant
more SNPs, which meant more variance explained and, consequently,
increased h2GWAS. Even when summing the small
effects of hundreds of genome-wide significant SNPs, variance
explained by GWAS results are still quite small. For example, the
traditional heritability of IQ is 50%, while the largest GWAS of IQ to
date explains less than 5% total variance (Plomin and von Stumm
2018).



In an effort to increase the amount of phenotypic variance accounted
for by GWAS results, Yang et al. (2015) developed genome complex trait
analysis (GCTA), now referred to as 'SNP heritability' (or
h2SNP). While traditional heritability is
estimated from coarse-grain genetic similarity of related individuals,
SNP heritability is estimated from fine-grain genetic similarity of
unrelated individuals. SNP heritability now comprises a family of
highly sophisticated statistical techniques that seek to maximize
proportions of phenotypic variance attributable to observed or imputed
SNP variants. SNP heritability exhibits a few features worth
attention. First, instead of limiting analysis to SNPs who meet the
strict *p*-value GWAS significance threshold, SNP heritability is
derived by analyzing the complete set of SNPs for each participant
sample--even those that are not associated with the trait of
interest. To this end, SNP heritability is biologically non-obvious.
Second, SNP heritability assumes linear additivity of SNP effects.
Third, SNP heritability represents the current limit on the total
variance that could be explained by SNPs, for any given phenotype. So,
for example, if a polygenic score were maximally predictive, it would
be equivalent to SNP heritability. Fourth, SNP heritability is
consistently lower than twin heritability, for any behavioral trait.
This gap between twin heritability and SNP heritability is sometimes
referred to as the missing heritability problem, which we discuss in
Section 5.


## 4. Philosophical issues arising from twin studies and heritability analysis



Discussions of the viability of heritability measures were most heated
in the 1970s and 1980s. In the 1970s discussions about IQ and race
came to a head (this issue was revisited in the 1990s with the
publication of Herrnstein and Murray (1994)), and in the late 1970s
and early 1980s sociobiology came under critical scrutiny. Both
proponents of the hereditary nature of IQ and sociobiologists made a
connection between human behavioral traits and genes. Hereditarians in
the IQ debates explicitly relied upon twin heritability analyses such
as those introduced above. Critics of sociobiology and hereditarianism
over IQ included biologists, philosophers and many social scientists
as well as many left-leaning political and social activists (See Gould
(1981), Paul (1998) and Segerstrale (2000) for some of the
relevant history here).



The point of departure for many philosophers criticizing heritability
analysis is Lewontin's (1974) paper on the analysis of variance.
(It is worth noting that Lewontin's paper is somewhat informal
and should perhaps be best viewed as Lewontin's attempt to pass
on the received wisdom among population geneticists at the time to a
wider audience. The formal arguments Lewontin alludes to are presented
in a number of places including Layzer (1974) (and later Kempthorne
(1978)) and precursors to these arguments can be found in Hogben
(1933) and can also be found in R.A. Fisher's work.) Lewontin
claims that equation \((1')\) above presents the most accurate
picture of the contributions to phenotypic variance. He goes on to
argue that \(V\_{I}, V\_{G\times E}\) and \(\COV(G,E)\) are not
negligible. In fact, he argues that these are always part and parcel
of the variance in traits. As a result, apportioning the phenotypic
variance between genes and environment is no easy matter and standard
analyses of variance simply cannot come up with useful and informative
values for \(h\_b^2\) and \(h^2\). Lewontin also points out that many
proponents of heritability measures mistakenly attribute the
heritability values to individuals rather than populations. Further,
he argues that norms of reaction gave a more accurate picture of the
relations between genes, environment and phenotypic traits. A norm of
reaction is a graph of a quantitative phenotype plotted as a function
of environment for different genotypes. Many philosophers and
biologists have extended and refined Lewontin's criticism of the
analysis of variance (e.g. Block 1995, Kitcher 1985, Sarkar 1998,
Sober 1988, Northcott 2006) and most share his conclusions that
heritability measures are hard to come by and that norms of reaction
are a superior way to examine gene/environment interactions.


 Lewontin (2006) later adds "The point of the (1974) paper
was to explain why the statistical partitioning of observed variation
in phenotype into variance associated with variation in genetic
relationship as opposed to variance assigned to environmental
dissimilarities does not, in fact, separate genetic and environmental
causes in development" (2006, 536). He adds that advances in
molecular genetics now make it "possible to provide a detailed
molecular analysis of the chain of causation between nucleotide
substitution and cell development and function" (Lewontin, 2006,
536). (Sober (1988) also emphasizes this aspect of Lewontin's
criticism of the analysis of variance.) Lewontin makes clear what he
takes genetic causation to be: the causal chain from a DNA sequence to
a protein product taking place within cells of organisms. His point is
that statistical methods of population genetics and behavioral
genetics alone are not appropriate to the task of revealing genetic
causes construed this way. We revisit this issue in Section 5. recast
in light of GWAS and other "molecular" techniques of
measuring heritability.



One response to these kinds of criticisms is to emphasize caution in
the use of heritability measures and to re-emphasize Lewontin's
point that such measures do not provide information about the traits
of individuals (See e.g. Plomin et al. 1990; 1997, Hamer and Copeland
1998). Kitcher (1985) pointed out in response to this line of defense
that words of caution do not seem to be enough and many behavioral
geneticists and psychologists still talk as if they can discover the
genetic components of human behavioral traits by using heritability
analyses. A second line of response is to argue that norms of reaction
are almost impossible to generate for complex human traits and, as a
result, are not a serious contender in the business of ascertaining
the genetic causes of human traits. Lewontin himself introduced this
problem for norms of reaction. In organisms whose genotypes and
environments can be exhaustively manipulated, a norm of reaction for a
particular trait can be produced. Lewontin cites early work on
*Drosophila* larvae's responses to temperature as
pioneering work of this kind. The problem for most human traits,
particularly human behavioral traits, is that we have no clear sense
of either what the relevant genes to examine are or what the range of
relevant environments is. This response need not necessarily blunt
Lewontin's critical attack on heritability measures, as in cases
where a norm of reaction can be reliably produced, we do have more
information about the relations between genes and environment than can
be provided by a standard analysis of variance. Further, attempts to
experimentally partition the contribution of genetic variance to
phenotypic variance run into problems for human traits similar to the
problems presented by attempts to generate norms of reaction. The
examples in Section 2. above are artificial for a reason: it is hard
to establish the relevant genotypes and environments that lead to
variance in human traits. The current consensus among philosophers of
biology is that heritability analyses are misleading about the genetic
causes of human traits but Pearson (2007) provides a cautious defense
of the explanatory usefulness of heritability analyses. Omri Tal also
presents modest defenses of heritability via his application of
probability to heritability analysis. He does this both in cases in
which there is assumed to be no gene-environment interaction (2009)
and in cases in which there is gene-environment interaction (2011).
Sesardic's (1993 and 2005) work stands in stark contrast both
the anti-heritability consensus and the moderate and carefully
measured support for heritability provided by Pearson and Tal.
Sesardic strongly supports heritability analyses and vehemently
criticizes critics of heritability analysis. Finally, work on norms of
reaction (see e.g. Pigliucci 2001) since Lewontin's invoking of
the measure reinforces his point about the information that can be
gained from such analyses.



There is something of a consensus in most fields (e.g. philosophy of
biology, evolutionary biology, psychology and behavioral genetics)
that heritability measures (particularly \(h\_b^2\) measures) only have
a very limited use. The consensus among philosophers of biology is
that broad heritability measures are uninformative but there are a few
dissenting voices (e.g. Sesardic 1993 and 2005, Pearson 2007 and Tal
2009 and 2011). (The notion of consensus used here is informal,
techniques in science studies and experimental philosophy of science
could be used to test claims of consensus.) Kaplan (2000) provides an
introduction to heritability and its use in behavioral genetics.
Sarkar (1998) presents a sophisticated (and technically quite
difficult) treatment of arguments against heritability. Freeman and
Heron (1998) present a clear analysis of the problems with the use of
heritability measures by proponents of the connection between IQ and
race (understanding this analysis requires some knowledge of
statistics). Block (1995) presents an overview of arguments against
the use of heritability measures in the IQ and race literature. This
overview is helpful and specifically designed for a non-technical
audience. Sober (1988) presents a defense of Lewontin's (1974)
criticism of the use of the analysis of variance in assessing the role
of genes in the formation of traits of individuals and Northcott
(2006) provides further helpful analysis of Lewontin's and
Sober's work. Both Tabery (2014 and Taylor (2014 ) provide
sustained criticism of heritability analysis via their alternate
reflections on the nature/nurture debates.



Sesardic's recent work is a criticism of those who invoke
Lewontin-style arguments against heritability analyses. He argues in
favor of hereditarianism by attacking its critics. He summarizes his
complaint as follows: "For some reason in [the heritability]
debate philosophers have displayed a surprising lack of intellectual
curiosity and analytical acuity" (2005, 9). This is because
"they hastily accepted anti-hereditarian arguments that
possessed only superficial plausibility" and "are often
poorly informed about basic scientific facts in the very domain of
their explorations" (2005, 9). Sesardic's criticism is
polemical and does not introduce any new techniques in heritability
analysis to the philosophical audience. Rather, he relies on a
recapitulation of earlier views, such as those of Jensen, one of the
original targets of Lewontin's critique. There are several
spirited responses to Sesardic's book (Tabery's 2006 and
2009b reviews are examples) and Gri Oftedal (2005) presents a
clarification of the issues at stake between Sesardic and
Lewontin.


 Part of what is at stake between followers of Lewontin and
Sesardic is whether or not \(V\_{GxE}\) and other components of
variance are negligible or significant. This issue is not purely
philosophical and can and has been tackled experimentally. Tabery
(2009a and 2014) draws attention to a longitudinal study by
psychologists Caspi and Moffitt, who show GxE effects in a
longitudinal study of human anti-social behavior disorders, in support
of a view in line with Lewontin's. Douglas Wahlsten also pursues
this issue in much of his experimental work (Wahlsten 1990 summarizes
his theoretical views and Wahlsten and Gottfried 1997 is a good survey
of some of the relevant experimental work on animals). Further,
understanding gene-environment covariance, \(\COV(G,E)\), as part of
heritability has led some to incorrectly attribute environmental
effects on phenotype to genes. Dickens and Flynn (2001) use an
example of basketball playing ability, which they label BP, to make
this point. They argue that if we assume that BP is highly heritable,
there still appears to be a large environmental component to BP. On
their account, this makes sense is we take gene/environment covariance
seriously. Just as our tall plants, in Section 2. above, can end up
in nutrient rich environments that shorter plants do not, tall,
athletic individuals are often placed in environments that enhance
their BP. As Dickens and Flynn point out, identical twins who are tall
and athletic, including those separated at birth, could have parents
who play basketball with them or could be placed in basketball
training regimens in school or college. In these situations each
individual's BP would increase but it is wrong to attribute this
increase in BP to genes for height and athleticism, since the relevant
environment has a significant influence on the phenotype. 



There is some irony in the fact that philosophers of biology, who
focus their attention almost exclusively on evolutionary biology, are
critics of heritability. Heredity is a central component to
evolutionary change and heritability analysis, particularly via the
notion of realized heritability (see equation 5 above), is an
important component of theoretical evolutionary biology. The critical
attack on heritability arises against the background of nature/nurture
debates (see e.g. Tabery 2014) and concerns over genetic determinism
and is best understood as a critical appraisal of behavioral
geneticists in psychology. There is growing interest among
philosophers in critically assessing the notion of heritability in its
evolutionary context. The notion of realized heritability is briefly
discussed by Samir Okasha (2006) (See also Downes 2010) and by Sober
(2008). Until recently, thorough discussion of the relations between
heritability and other central concepts of evolutionary theory was
pursued exclusively by evolutionary biologists (e.g. Lynch and Walsh
1998 and Rice 2004). Peter Visscher *et al*.'s (2008)
review article is a nice introduction to much of the work in this
area. Philosophers have now presented and defended some radical claims
about heritability and heredity including the claim that evolution can
occur without heredity (see e.g. Earnshaw-Whyte 2012 and Bourrat
2013). Focusing on heritability in the context of evolutionary theory
is a productive area for philosophical research as evidenced by
Bourrat's (2014) examination of the role of heritability in the
recipe approach to evolution by natural selection.


## 5. Missing Heritability and related philosophical issues arising from GWAS



The development of alternative methods of estimating heritability
(e.g., GWAS and SNP heritability) has given rise to what is commonly
referred to as the 'missing heritability problem', which
has seen ample attention by behavioral geneticists and some attention
by philosophers of science and biology. At face value, the missing
heritability arises out of a numerical gap between traditional
heritability estimates and SNP-based heritability estimates of the
same trait. For example, traditional heritability estimates for IQ
obtained using twin and family studies range between .5 and .7 while
SNP-based heritability estimates of IQ are currently no greater than
.25 (Plomin and von stumm 2018). Missing heritability is greatest
among complex, behavioral traits.



Since Maher (2008) first coined the term "missing
heritability," statisticians and geneticists have written
extensively about the issue. In nearly all cases, contributors speak
to possible explanations for why there is missing heritability and
emphasize technological and methodological solutions that should close
the numerical gap between traditional and SNP heritability estimates.
Explanations for missing heritability typically focus on various
manners in which standard format GWAS are unable to track genetic
effects that are unavoidably part and parcel of twin and family
studies. Notably, contributors appeal to non-linear interactions
between genetic variants ('GxG interaction', or
epistasis). Epistatic interactions between SNPs entail that the effect
of a given SNP will be modified (enhanced or diminished, for example)
in the presence of another SNP, which violates the additivity
assumption of SNP heritability. Similarly, gene-environment
interaction and epigenesis have been proposed as explanations for
missing heritability (Zuk et al. 2012). Specific variants or groups of
variants may have effects that are enhanced, diminished, or even muted
with different environments, again violating the additivity assumption
of SNP heritability. Some missing heritability may be attributable to
the presenence of low-frequency, high-penetrance variants, which
require massive samples to detect (Zuk et al. 2014). (See Eric
Turkheimer (2011, 2012) and Matthews & Turkheimer (forthcoming) for a
more thorough review of explanations of and solutions to missing
heritability.)



The missing heritability problem is an example of a conflict between
two seemingly compatible scientific methods that give conflicting
results and thus has rich implications for philosophy of science. One
of these implications is pursued by Bourrat and Lu (2017), who argue
that the missing heritability problem is largely
'dissolved' in two complementary steps. On the one hand,
Bourrat and Lu indicate that the numerical gap between alternative
methods of estimating heritability may be partially narrowed by
decreasing traditional estimates, which have historically been charged
as being overestimated. On the other hand, Bourrat and Lu argue that
the numerical gap may be closed even more by altering SNP heritability
techniques so as to include non-linear and epigenetic factors that
they claim are currently untracked by GWAS.



To the contrary, Matthews & Turkheimer (forthcoming) argue that the
missing heritability problem is much more severe and prospective
dissolutions are out of sight. Their analysis tracks the historical
introduction of missing heritability by Maher, who commented on a
broader challenge facing behavioral geneticists in the ongoing effort
to explain, understand, and accurately predict the overwhelming
complex relationships between genetic differences and complex
behavioral differences, such as schizophrenia, depression, and
intelligence. Matthews & Turkheimer offer a tripartite
characterization of the problem, which treats the numerical gap
between traditional and SNP heritability as just one quantitative and
independent leg of a multi-faceted problem. On their view, the
remaining two legs of the problem regard prediction (the challenge of
accurately predicting complex behavioral phenotype from molecular
genotype) and mechanism (the challenge of elucidating meaningful
causal-mechanical stories that link molecular genetic differences to
complex behavioral differences). Although most behavioral geneticists,
as well as Bourrat and Liu, focus their efforts on the numerical gap
between alternative methods of estimating heritability, Matthews and
Turkheimer emphasize the fact that resolving the statistical problem
will not advance prediction nor explanation of the heritability of
human behavior.



The development of GWAS and SNP heritability raises anew old
philosophical questions regarding causal relationships. Researchers in
the field are well aware of a handful of conceptual issues that
provoke skepticism regarding the question of whether or not SNPs
identified by GWAS are causal or not. John Dupre identifies
GWAS as one among several approaches in the increasingly large effort
to correlate genetic differences with phenotypic differences. He says
that GWAS "uses the large amount of genetic data we now have
about human populations to find correlations with medical
outcomes--physiological and psychological disease" (2013,
285). Dupre goes on to say "as everyone involved in such
research is aware, this is hardly a search for sufficient causes. GWAS
will at best provide clues to the detailed causal processes involved
in pathology" (2013, 286). Some GWAS researchers are more
bullish on causation that Dupre indicates (See e.g. Plomin
2018). A well-known issue in population genetics, linkage
disequilibrium, occurs when there is non-random association of alleles
at different loci. GWAS researchers acknowledge that many of the SNPs
of interest today are in linkage with many other SNPs in the genome.
The implication is that it remains underdetermined whether SNPs are
causal variants, or merely in linkage with causal variants (perhaps
through evolutionary drift).



There is also strong evidence that current GWAS are susceptible to
population stratification. Because human populations exhibit ethnic or
cultural subgroups with distinct allele frequencies, population
stratification increases the likelihood that GWAS identify false
positive SNPs. Not only is there evidence of population stratification
among large groups of individuals of different biogeographic
ancestries (Europeans, Asians, Africans), but populations are
stratified within groups as well. For example, individuals of European
descent would include both Parisians as well as English immigrants.



What may be the greatest impediment to causal interpretations of SNP
heritability is that it is biologically vacuous. SNP heritability is
constructed using all genetic variants included in any given SNP chip,
a significant portion of which are statistically insignificant.
Moreover, although SNP heritability represents another figure of
phenotypic variance 'explained' by genetic differences,
SNP heritability has not led to the discovery of meaningful
biological stories or etiologies that would causally link patterns of
nucleotides to patterns of complex human behaviors. Judea Pearl and
Dana MacKenzie refer to GWAS as a "prototypical 'big
data' method that allows researchers to comb through the whole
genome statistically, looking for genes that happen to show up more in
people with a certain disease" (2018, 339-340). They go on to
say "It is important to notice the word
'association' in the term GWAS. This method does not prove
causality; it only identifies genes associated with a certain disease
in the given sample" (340). They echo our point here, in saying
that the methods used in GWAS hamper efforts at making causal
inferences.


## 6. Looking forward



The study of heritability has a long and rich history. Many scientific
developments have led to refined techniques for estimating
heritability and each of these scientific developments has been the
focus of philosophical analysis. In recent
years, empirical approaches toward the investigation and construction
of heritability estimates have undergone great changes, especially
with the introduction of GWAS, SNP chips, and SNP heritability. These
recent developments are beginning to see more attention from
philosophers. At the forefront of debates about SNP heritability is
the issue of causation we raised above: are SNPs causal? Bourrat
(forthcoming) addresses the question of whether SNPs are causal under
an interventionist framework, but there is more work to be done here.
Methodologically, twin and heritability and SNP heritability are
estimated very differently. There is need for more philosophical
analysis regarding the nature of heritability and a fine-grained
perspective of the differences between twin and SNP heritability. In
addition to philosophical arguments for or against causal
interpretations of SNPs and heritability, scientists present their own
cases, often appealing to sophisticated statistical techniques as
sufficing for the identification of causal relationships in human
genetics. Philosophers could profitably address such
techniques--notably Mendelian randomization--with an eye for
how they align with broader philosophical frameworks such as alternate
accounts of causation.



As mentioned previously, the advent of SNP heritability gives rise to
a new and interesting issue: the missing heritability problem.
Although Matthews and Turkheimer (forthcoming) have considered the
implications of the missing heritability problem for debates about
scientific pluralism, we expect that the implications are broader.
More philosophical work here should prove to be productive.



Finally, heritability is unequivocally tethered to bioethics. To the
extent that twin heritability estimates played a central role in
debates about race science from the 70s through the 90s, the advent of
SNP heritability warrants a renewed assessment. Just as it was for
twin heritability, SNP heritability is now being used to assess old,
controversial questions about the genetic basis of racial differences
in intelligence and cognitive ability. Presumably because twin
heritability and SNP heritability are conceptually and
methodologically distinct, there is demand for philosophers and
scientists to re-assess the legitimacy of group-difference
investigations that appeal to SNP heritability.