1. Heritability Revisited
Zinhle Mncube

2. What is heritability?
Heritability estimates “have been regarded as important primarily on the expectation that they would furnish valuable information about the causal strength of genetic influence on phenotypic differences” (Sesardic, 1993:399)
h2 (in the broad sense) = proportion of total phenotypic variance in a population (VP ) attributable to genetic variance (VG)
h 2 = VG / VP
E.g. Height differs among people
If height has a high h2 in a population, then differences in height in that population are mostly due to genetic differences in the population rather than any environmental differences
Heritability estimates = based on family and twin studies. Phenotype = observed traits and behaviours (e.g. height, intelligence, criminality)
Variation = any differences between groups of organisms of any species. Genetic variation = differences in alleles because of genes
Genotype = genetic make-up of organism.
Environment variation = differences that can result from climate, food supply, actions of other organisms, etc., or combination of these
Heritability = proportion of total phenotypic variation attributable to genetic differences

3. Why should we care about h2?
h2 is widely used in human disease genetics, amongst other fields, for e.g.
Tenesa and Haley (2013:147) explain: “Estimates of heritability quantify how much of the variation in disease liability in a population can be attributed to genetic variation”
Vissher et al. (2008:258-9) argue that h2 is ”so enduring and useful” because, amongst other reasons, it is useful in understanding “the genetic component of risk to disease, independently of known environmental risk factors”. More specifically, it useful “in determining the efficiency of prediction of the genetic risk of disease” (ibid.).
Liability is a term used to collectively describe all the genetic and environmental factors that contribute to the development of a multifactoral disorder. (Multifactoral disorders, like diabetes, alcoholism, mental illnesses, are associated with the effects of multiple genes in combination with lifestyle and environmental factors).
Familial recurrence risk - the chance that an inherited disease that is present in a family will recur in that family, affecting another person or  persons.

4. Heritability today
Despite this kind of use of heritability estimates, widely held view among philosophers today = heritability estimates do not indicate the causal strength of genes on phenotypic variance (Oftedal, 2005; Downes, 2016)
Specifically 3 main lines of arguments are used to undermine the causal construal of some heritability claims:
gene-environment interaction
gene-environment correlation
locality

5. On heritability
In this talk I argue that the widely held view that “heritability estimates are devoid of causal implications” (Sesardic, 2005:10) is too quick
It is possible to reply to each of the main lines of argument used to establish that heritability estimates are causally uninterpretable
In particular, these 3 challenges to heritability analysis express conditions under which heritability claims can be well-justified, possibly generalizable, depending on empirical matters that cannot be spelt out in advance

6. The gene-environment challenge
There are in fact 2 different notions of gene-environment interaction (Tabery, 2007a; 2007b; 2008, 2014; Griffiths and Tabery, 2008), each with different problems for causal construal of h2
First notion = biometric notion of gene-environment interaction, G×EB
“The concept of G×E [G×EB] refers to cases where different genotypic groups phenotypically respond differently to the same array of environments.” (Tabery, 2007a:2)

7. (From Kaplan, 2006:60, Figure 1)
“when different genetic groups respond differently to the same array of environments, the additivity between VG and VE breaks down, requiring an addition to the equation in the form of G×E [G×EB]. G×E creates a potential problem for biometricians because it generates its own variation [G×EB] ... eliminating the ability to calculate the heritability of a trait” (Tabery, 2007a:120).
Additivity = separate acting of, the genotype and environment influences on phenotypes. Cooper and Zubek bred several groups of rats and exposed them to several Hebb-Williams (1946) maze tests where they had to make their way from the start of a maze to a food source at the end of the maze. The rats were then scored on the number of errors they made – that is, the number of times the rats followed an incorrect path and crossed any of the dotted lines in Figure 1 (Tabery 2007a:161). The rats that were relatively good at running these mazes after several attempts were classed as “maze-bright”, and the rats that were relatively bad were classed as “maze-dull” (Kaplan, 2006:60).

8. The G×EB challenge
(B1): h2 analysis is based on the assumption of additivity (differences in genotype and differences in environments act separately on total phenotypic variance);
(B2): G×EB complicates the calculation of h2 because it generates a separate source of variation in the total phenotypic variance sum (Tabery, 2007a);
(B3): If there is strong G×EB, then heritability cannot be easily calculated for a particular trait (ibid.);
(B4): Non-additivity is rampant in nature (e.g. Lewontin, 1974, 1975; Layzer, 1974; Block & Dworkin, 1974b; Dick & Rose, 2002); G×EB is pervasive in nature;
(B5): Therefore, heritability estimates cannot have a causal interpretation, let alone a useful one (Lewontin, 1974; Northcott, 2008:22); or heritability is “meaningless in terms of its causal explanatory content” (Tal, 2011)
(2 implications of GxEB for heritability) B3 - if we calculate heritability when the is GxEB, heritability will be inflated because it will include this GxEB. Second implication = how one genoype responds to other set of environments (beyond those studied) is unpredicatable (locality objection). Brings use and even ability to calculate heritability in question.

9. Reply to the GxEB challenge
A) The additivity reply:
the question of additivity, of the actual pervasiveness of G×EB in nature, is an empirical one
Heritability estimates can have a causal interpretation when there is no statistical gene-environment interaction (amongst other conditions).
The G×EB challenge turns on the pervasiveness of G×EB in nature. But if the question of non-additivity is an empirical one (one that cannot be decided a priori), if significant G×EB is rare, then the G×EB can be dissolved
The question we now have to consider is, is it true that non-additivity is rampant in nature?
G×EB IS NOT INTERACTIONIST CONSENSUS. Consensus is about causes of traits; heritability is about differences. (fire)

10. Reply to the G×EB challenge
Like Jensen (1969), Levin (1997), Sesardic (2005), Oftedal (2005), and Tal (2009, 2011), I agree that we cannot answer the question of the pervasiveness of G×EB and non-additivity in biology in a non-empirical way
To the effect that step 4 (B4) in the G×EB challenge to heritability (non-additivity is rampant in nature) is defended in an aprioristic manner (for e.g. by Gray (1999) & Sterelny and Griffiths (1999)), it cannot be used to establish the strong conclusion that heritability estimates have no causal import
If G×EB is substantial in a particular study, then calculating heritability will be futile (Tal, 2009, 2011) - uncontroversial
But when there is no G×EB , it makes sense to causally interpret the heritability estimate (Sesardic, 2005; Tal, 2011)
In other words, we can say only of the particular situation that there is, or is not statistical gene-environment interaction, and therefore, whether we can or cannot calculate heritability in a meaningful way:

11. Lessons on heritability
Possible problems?
1) At exactly which point or which percentage (of total phenotypic variance) does statistical gene-environment interaction become problematic for heritability?
2) Methodological issue that the analysis of variance cannot detect some statistical gene-environment interaction effects
Challenges to heritability analysis express conditions under which heritability claims can be well-justified, possibly generalizable, depending on empirical matters that cannot be spelt out in advance
Once we deal with the question, does it ever make sense to causally interpret heritability claims?
We can now ask, what non-statistical reality underlies heritability claims?
Despite challenges, important point is that we do not know beforehand whether there will or will not be significant statistical gene-environment interaction in a particular study

12. Thank you Heritability Revisited What is heritability?
Why should we care about heritability?
The gene-environment challenge to heritability analysis
Lessons on heritability
Thank you