1. 科学抑或哲学？—— 从“遗传率消失之谜”说起
哲学与好奇午餐会
陆俏颖

2. The fittest will survive.
生物学哲学的三种类型
The fittest will survive.
在生物学语境中处理科学 哲学的一般议题
对生物学内部的概念问题 进行哲学分析
借鉴或引用生物学来探讨 传统哲学问题
fittest
survive
还原，热现象还原为分子动力学，
适者生存，理论生物学
《圣经》曾经用来解释一切，而达尔文来了之后，神学受到了前所未有的冲击
Kenneth F. Schaffner
David L. Hull

3. 遗传率消失之谜
遗传率（heritability）：a measure of the variation of a trait of a population that can be attributed to genotypic variation.
谜：heritability estimates obtained in traditional quantitative methods are much larger than those obtained in genome-wide association studies (GWAS).
Human height: 0.8 Vs (0.45) → the missing heritability
Before presenting the details, let’s see briefly what the problem is.
The heritability of a trait or a phenotype is a measure of the variation of this trait * that can be attributed to genes. It refers to the contribution of genetic difference to phenotypic or trait difference of a population. If we assume Woodwoods’ account of causation, then heritability reveals loosely speaking genetic cause of a phenotype.
The missing heritability problem comes from the fact that different estimates of heritability obtained, namely those obtained from traditional quantitative methods are much larger than those obtained from GWAS.
For example, the heritability of human height measured by traditional methods is about 0.8, but the original estimates of GWAS were only of about More sophisticated statistical methods have reached an estimate of about Although improved, the difference in estimates between the two methods is still large and half of the heritability seems to be missing.
How shall we explain the missing heritability problem? Some methodological hypotheses have been made such as taking rare variants into account or increasing sample sizes of studies in GWAS.
Some authors have also suggested that heritable epigenetic factors might account for part of the missing heritability. But there seems to have a contradiction: how can epigenetic factors account for the missing heritability, if the heritability is about genes?
Our goal is to answer this question as well as to analyze the missing heritability problem.

4. Project: 1. Definitions of Heritability
2. Heritability in Traditional Studies
3. Heritability in GWAS
4. Dissolving the Missing Heritability
The following talk will be in four parts. First is the definitions of heritability. Then introduce the methods used to estimate heritability in traditional quantitative methods. Third, I will present how heritability is estimated in GWAS. Finally, by comparing these two methods, to a summary of how we can dissolve the missing heritability problem, at least partially.

5. 1. Definitions of Heritability
(Broad-sense heritability)
stably transmitted genetic effects
First, the heritability in quantitative genetics. According to the basic assumption of quantitative genetics, if we want to explain the trait difference in a population, individuals have different heights for example, it can be explained by two components, the difference in the genes and the difference in the environment. Using the analysis of variance, the phenotypic difference Vp in a population equals to V_G the genotypic variance, plus V_E the environment variance. If there is V_(G∗E) the interaction between genotype and environment, and the correlation variance of the two, they should also be added. V_G can be further portioned into V_A the additive genetic variance, V_D the dominance genetic variance and V_I the epistasis genetic variance. The dominant variance represents the interaction between alleles at one locus for diploid organisms, and the epistasis variance represents the interaction between alleles from different loci. These two together represents the effects on the phenotypic variance due to particular combinations of genes for an organism. Since with reproduction genotypes recombine every generation in sexual organisms, the effects of the dominance variance and the epistasis variance are not stably transmitted across generation. The additive genetic variance Va, without taking gene combination effects into account, represents the genetic effects that are transmitted across generations.
The narrow sense heritability equals to Va divides Vp. It measures to what extent variation in phenotypes is determined by the differences in genes transmitted from parent(s) to offspring. And the broad sense heritability equals to Vp divided by Vg, a measure of the total genetic influence on Vp. For behavioral geneticist, they are interested in knowing how much the total genotypic differences in a population influence differences in a trait, so the broad-sense heritability is often used. Evolutionary biologists are especially interested in making evolutionary projections of a trait within a population across generations. So they are more interested in the narrow sense heritability.
As we argued in the BJPS paper, additive genes whose influence on the phenotype is represented by the additive genetic variance, are defined solely by their effects on the phenotype. They are hypothetical or theoretical entities which are not restricted to specific physical entities. Traditionally, biologists think that additive genes are mostly DNA molecules, but if epigenes can play the same role in heredity and evolution, then epigenes can also be the additive genes in quantitative genetics. The traditional way to measure heritability can also confirm this claim. Now let’s see how the heritability is measured in practice in quantitative genetics.
(Narrow-sense heritability)

6. 2. Heritability in Traditional Studies
To measure the narrow sense heritability, according to the definition, we need to know VA and VP.
𝑉_𝑃, for most quantitative traits (including height), can be directly obtained by measuring phenotypes of individuals. However, traditional methods do not permit to obtain 𝑉_𝐴 directly. It is classically obtained by deduction. This deduction is based on two types of information.
First, we need one or several population-level measures of a phenotypic resemblance of family relative pairs. These measures are obtained by calculating the covariance of the phenotypic values for those pairs. Second, one needs the genetic relation between family pairs. It indicates the percentage of genetic materials the pairs are expected to share. Or the mean values of their class (e.g., offspring) depending on the particular method used.
Eliminate these terms: Different ways to do that with different types of pairs

7. 2. Heritability in Traditional Studies
Traditional methods usually assume that there is neither gene-environment interaction nor correlation. In such cases, the covariance between the phenotypic values of family pairs equals to the additive genetic covariance, dominant and epistasis genetic covariance, plus the environmental covariance.
The additive genetic covariance can be transformed into a term proportionate to VA when we know the percentage shared by A1 and A2. these three terms can be eliminated by different ways with different types of pairs.
Let’s see an example of parent-offspring pairs. This method also assumes neither gene-environment interaction nor correlation. Following these assumptions, we can deduce that the covariance between the height of parents and the mean of their offspring is equal to the additive genetic covariance, dominant covariance (the epistasis covariance is assumed to be small and is not included), plus environmental covariance between the heights of parents and offspring. “P” and “O” represent “parents” and “offspring”.
Three further assumptions are then made. The first one is that parents are not related and consequently no dominant effects are transmitted from the parents to the offspring, which means that 𝐶𝑜𝑣(𝐷_𝑃,𝐷_𝑂 ) is nil. The second one is that there is no correlation between the parents’ environment and the offspring’s environment so that 𝐶𝑜𝑣(𝐸_𝑃,𝐸_𝑂 ) is also nil. The third assumption is that there is no assortative mating between parents. Given these assumptions, parents share on average, in expectation 50% of their genes with their offspring, it leaves the equation with a result of half of the additive genetic variance (1/2 𝑉_𝐴).
But the above three assumptions might be violated. If we take these three factors into consideration, the covariance between the parents and their offspring is equal to half of the additive genetic variance, plus a term representing some effects due to dominance, similarities between environments and assortative mating.

8. 2. Heritability in Traditional Studies
“TM” is for “traditional methods”, o is for “other”

9. 3. Heritability in GWAS SNPs: single nucleotide polymorphisms;
Two variants of a SNP
"Dna-SNP" by SNP model by David Eccles (gringer). Licensed under CC BY 4.0 via Commons
SNPs: single nucleotide polymorphisms;
Common SNPs: p > 1%
If one variant of a common SNP, compared to another variant, is associated with a significant change on the trait studied, then this SNP is a marker for a DNA variation that associates with the trait.
Although any two unrelated individuals share about 99.5% of their DNA sequences, their genomes differ at specific nucleotide locations (Aguiar and Istrail 2013). Given two DNA fragments at the same locus of two individuals, if these fragments differ at a single nucleotide, they represent two variants of a Single Nucleotide Polymorphism (SNP). GWAS focus on SNPs across the whole genome that occur in the population with a probability larger than 1%. They are called common SNPs. If one variant of a common SNP, compared to another one, is associated with a significant change on the trait studied, then this SNP is a marker for a DNA region (or a gene) that leads to phenotypic variation, which is called causal DNA variant. For a polygenic trait like height, if we can detect all the SNPs that associate with it, then all the DNA difference makers that determine height difference can be located.
The development of commercial SNP chips makes it possible to rapidly detect common SNPs of DNA samples from all the participants involved in a study. For quantitative traits like height, the most common approach is to make an analysis of variance table and assess whether the mean height of a group with one variant at one nucleotide is significantly different from the group with another variant of the same SNP (Bush and Moore 2012). With all the SNPs associated with height being detected, data from the HapMap project, which provides a list of SNPs that are markers for most of the common DNA variants in human populations (Consortium, International HapMap ), is used to map the associated SNPs with causal DNA variants.
Based on the readings of SNP chips as well as further independent tests for SNPs, the effects of the associated SNPs (markers for causal DNA variants) on the trait can be calculated. By estimating the phenotypic variance contributed by these SNPs compared to the total phenotypic variance of the population, the heritability of causal DNA variants can be estimated (Weedon et al. 2008). Since it is common for biologists to assume that genes are only made up of pieces of DNA, it is thought that the variance obtained from all the causal DNA variants represent exactly the additive genetic variance, and the heritability estimated by GWAS should match narrow-sense heritability (ℎ^2) (Yang et al. 2010; Visscher et al. 2006). However, the assumption that additive genetic effects are solely based on DNA sequences is problematic when faced with the evidence of epigenetic inheritance.

10. 3. Heritability in GWAS VA
Although any two unrelated individuals share about 99.5% of their DNA sequences, their genomes differ at specific nucleotide locations (Aguiar and Istrail 2013). Given two DNA fragments at the same locus of two individuals, if these fragments differ at a single nucleotide, they represent two variants of a Single Nucleotide Polymorphism (SNP). GWAS focus on SNPs across the whole genome that occur in the population with a probability larger than 1%. They are called common SNPs. If one variant of a common SNP, compared to another one, is associated with a significant change on the trait studied, then this SNP is a marker for a DNA region (or a gene) that leads to phenotypic variation, which is called causal DNA variant. For a polygenic trait like height, if we can detect all the SNPs that associate with it, then all the DNA difference makers that determine height difference can be located.
The development of commercial SNP chips makes it possible to rapidly detect common SNPs of DNA samples from all the participants involved in a study. For quantitative traits like height, the most common approach is to make an analysis of variance table and assess whether the mean height of a group with one variant at one nucleotide is significantly different from the group with another variant of the same SNP (Bush and Moore 2012). With all the SNPs associated with height being detected, data from the HapMap project, which provides a list of SNPs that are markers for most of the common DNA variants in human populations (Consortium, International HapMap ), is used to map the associated SNPs with causal DNA variants.
Based on the readings of SNP chips as well as further independent tests for SNPs, the effects of the associated SNPs (markers for causal DNA variants) on the trait can be calculated. By estimating the phenotypic variance contributed by these SNPs compared to the total phenotypic variance of the population, the heritability of causal DNA variants can be estimated (Weedon et al. 2008). Since it is common for biologists to assume that genes are only made up of pieces of DNA, it is thought that the variance obtained from all the causal DNA variants represent exactly the additive genetic variance, and the heritability estimated by GWAS should match narrow-sense heritability (ℎ^2) (Yang et al. 2010; Visscher et al. 2006). However, the assumption that additive genetic effects are solely based on DNA sequences is problematic when faced with the evidence of epigenetic inheritance. VA

11. Where is the missing heritability?
Examples include:
increasing the sample sizes (e.g., Wood et al. 2014),
considering all common SNPs simultaneously instead of one by one which has increased the heritability estimates of height from 0.05 to 0.45 (see Yang et al )
conducting meta-analyses (see Bush and Moore 2012).
searching for SNPs with lower frequencies than 1% in order to account for a wider range of possible causal variants (Schork et al. 2009).
Some authors have also suggested that heritable epigenetic factors might account for part of the missing heritability. ➔ how can epigenetic factors account for the missing heritability, if the heritability is about genes?

12. Epigenetic additive effects
(Morgan HD, Sutherland HG, Martin DI, Whitelaw E 1999)
In traditional quantitative methods, the genes are not defined physically, but functionally as heritable difference makers (Falconer and Mackay 1996, 123). In other words, they are theoretical units defined by their effects on the phenotype. With the discovery of DNA structure in 1953, it was thought that the originally theoretical genes were found in the physical DNA molecules. Since then, biologists commonly refer to genes as DNA molecules and this assumption is also made by researchers of GWAS. As [author] claim, this step was taken too hastily.
The increasing evidence of epigenetic inheritance seriously challenges the restriction of the concept of the gene in the evolutionary sense to be materialized only in DNA. Relying on traditional quantitative methods, it is impossible to distinguish whether additive genetic variance is DNA based or based on other material(s). Some transmissible epigenetic factors, which are not DNA based, might de facto be included into the additive genetic variance used to estimate ℎ².

13. 3. Heritability in GWAS
To apply the idea that some epigenetic factors can lead to additive genetic effects, the additive variance of them (𝑉_(𝐴_𝑒𝑝𝑖 )) should be added to the additive variance of DNA sequences (𝑉_(𝐴_𝐷𝑁𝐴 )) to obtain 𝑉_𝐴. Assuming there is no interaction between 𝑉_(𝐴_𝑒𝑝𝑖 ) and 𝑉_(𝐴_𝐷𝑁𝐴 ), we have:
𝑉_𝐴=𝑉_(𝐴_𝐷𝑁𝐴 )+𝑉_(𝐴_𝑒𝑝𝑖 ) (15)
Inserting Equation (15) to Equation (4) leads to:
ℎ^2=𝑉_(𝐴_𝐷𝑁𝐴 )/𝑉_𝑃 +𝑉_(𝐴_𝑒𝑝𝑖 )/𝑉_𝑃 (16)
Here we term the first term on the right side of Equation (16) “DNA-based narrow-sense heritability” (ℎ_𝐷𝑁𝐴^2), and the second term “epigenetic-based narrow-sense heritability” (ℎ_𝑒𝑝𝑖^2), we thus have:
ℎ_𝐷𝑁𝐴^2=ℎ^2−ℎ_𝑒𝑝𝑖^ (17)

14. 4. Dissolving the missing heritability
Two reasons explaining away (at least partially) the missing heritability (MH)：
In traditional studies, overestimation of heritability (dominance, G-E correlation, interaction, assortative mating etc.) ;
In GWAS, heritability is estimated solely from DNA variants, not include epigenetic difference makers.
our analysis reveals two other reasons explaining away the missing heritability problem:
in traditional quantitative methods heritability is overestimated because the methods used cannot fully isolate the additive genetic variance from other components of variance, and
in GWAS, heritability is estimated based on causal DNA variants only, while in traditional quantitative methods the additive effects contributed by epigenetic difference (VAepi ) are de facto included in the estimates.
This means that the missing heritability, excluding potential methodological flaws in GWAS, results from the part of heritability originating from additive epigenetic factors, plus the overestimation obtained from family studies, in which the additive genetic term cannot be fully isolated from other terms. Those other terms include nonadditive terms and terms coming from assortative mating.

15. Science or philosophy?