My mother in DNA.LAND

My mother, Beryl Seel, died on the 3rd of December 2015 aged 92. In August the previous year I had persuaded her to spit into the 23andMe sample collection tube and get sequenced.

"Now we can bring you back," I murmured, but she didn't seem keen.

I understand 23andMe pussyfooting around, not wishing to fall foul of the US regulators yet again. This means DNA.LAND if you want to play with polygenic scores. I uploaded her genome subset (the 23andMe downloaded text file) and here are some of the results.

As usual, click on an image to make it large enough to read.

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This is the top-level screen showing some of the traits they can begin to predict

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Educational attainment

My mother was predicted to have 14.7 years of schooling (two years at university). In fact she had 9, leaving school in 1937 as a 14 year old.

My prediction from DNA.LAND is also 14.7 years but in fact I had 19 years equivalent full-time education. Clare was predicted to have 14.4 years yet she is a graduate with an additional teacher-training qualification.

Heritability of EA is low and the small numbers of relevant SNPs available to DNA.LAND makes even the genetic component estimate a very noisy measure. See the discussion below.

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Intelligence and IQ

This is marked as 'very preliminary' which - as they are quoting only 16 SNPs - seems about right.

Heritability of IQ is of the order of 80% but given this few genetic markers the signal will be swamped by the effects of all the other relevant SNPs which are unknown and whose contributions are therefore unmeasured.

About all you can say in favour of the exercise is that correlations between IQ-enhancing alleles based on an underlying soft sweep probably gives this slightly more predictive power than one might naively expect.

Note also we don't get a central IQ estimate with error bars. The normal distribution curve above is referenced to the DNA.LAND sign-up population, with unknown IQ parameters.

Anyway, FWIW, my mother seems to be one IQ point above the DNA.LAND average based on a super-noisy regression line.

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Neuroticism

Neuroticism (emotionalism, anxiety) is one of the 'five factor' personality traits and is the opposite to emotional stability, calmness on this dimension. There are strong gender differences in this factor, women scoring as more emotional.

I have memories of a fair degree of maternal emotionalism, but perhaps that was par for the course.

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Height

My DNA.LAND polygenic score was 182 cm, which is exactly right. My mother's (above) equates to 5' 7". That is taller than I remember, perhaps by an inch. I recall that growing up in the 1930s was not a picnic. My father was just under six foot.

My parents on their engagement: is she taller than average?

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Discussion

How seriously should we take all this? Not very, at this point (except for height, where PGS scores are accurate predictors of genomic potential - although DNA.LAND aren't using the latest estimators).

Example regression line for scatter plot with correlation 0.38

The correlations between the small numbers of SNPs currently being used by DNA.LAND and the physical/cognitive variables they're trying to predict are very low. Educational attainment was discussed on their website as follows:

"Overall, educational attainment is estimated to have a heritability of around 20%. This means that in a population of individuals with varying years of education, 20% of that variation can be explained by variants in the individuals' genomes."

So the polygenic score will give the phenotype value on the regression line, but the true value could be a long way up or down depending on life events. My mother, a working class girl, left school at 14 for example. Nobody does that today.

Thousands of SNPs are implicated in complex polygenic traits like those listed above, yet relatively few are currently known (except for height) .. and DNA.LAND uses only those publicly available (a tiny subset). So their regression lines will be pretty inaccurate.

Finally, note that my mother is positioned with respect to DNA.LAND's user population which is self-selected. We don't know how the norms for this group compare to the general population.

It will get better, even if we're a way from the option of bringing her back.

Heritability, correlation and prediction

We're told that intelligence is 60-80% heritable, and that personality is 40-60% heritable. In some hand-wavy way, we know that heritability captures the nature side of the nature-nurture contribution to traits.

But what does heritability really mean? It's a rather slippery concept. We'll get there by stages.

1. The contribution of genes to a phenotype

Let's take height as our running example (pretty much the same heritability as intelligence). Let's take a person with height P (P stands for phenotype - the measured trait). P is measured in inches away from the population mean height.

How did a person get to be that height? Nature and nurture, right?

We assume that the alleles the person got from their father contributes X_father inches of height, X_mother counts the inches they received from their mother's alleles they inherited, and then there is a nurture - or environmental - term E inches. So their total height,

P = X_father + X_mother + E.

Note these are genetic additive effects: each additional allele is plausibly assumed to make its independent contribution into raising or lowering X a fraction. Dominance and epistatic effects are neglected in this simplified conceptual model (in a polygenic trait, they tend not to be large).

Since we're measuring deviations from the mean, the average values across the population of X_father, X_mother and E must all be zero. And so, therefore, must be the average value of P.

So without loss of generality, we assume X_father, X_mother and E are normally distributed random variables with mean zero and variances as follows:

Var(X_father) = V_additive/2    -- each parent provides half the additive genetic 'input'

Var(X_mother) = V_additive/2   -- each parent provides half the additive genetic 'input'

Var(E) = V_environment.

So what is Var(P), the variance of height as we observe it in the population?

Var(P) = Var(X_father) + Var(X_mother) + Var(E) +

        2Cov(X_father, X_mother) + 2Cov(X_father, E) + 2Cov(X_mother, E).

Messy, but if we assume X_father, X_mother and E are independent, their covariances are zero, so

Var(P) = Var(X_father) + Var(X_mother) + Var(E),

V_phenotype  = V_additive + V_environment

The fraction of the population phenotypic variation due to genetic, additive effects is then simply

h² = V_additive/V_phenotype = V_additive/(V_additive + V_environment).

This is the definition of heritability, h².

So if h² is 0.5, then 50% of the variance in the phenotype is genetic in origin (additive-genetic, that is) and 50% is environmental (everything else).

Note that the more you reduce environmental variance, for example making sure that everyone's well-fed, properly educated and not knocked about, the more genetic differences predominate .. and heritability goes up. Not what the SJWs really want to hear!

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2. Correlations

What is the correlation, ρ, between a parent and child for height?

If we have two random variables, A and B, the correlation between them is defined as follows:

ρ =  Cov(A,B)/√(Var(A) * Var(B)).

This is the standard definition.

In the case of one parent and their offspring, under some simplifying assumptions,

Cov(parent,offspring) = V_additive/2

- this takes a few lines to work out, setting most of the X_father, X_mother and E cross-terms to zero. It reflects the 50% of genetic material they have in common.

More obviously,

Var(parent) = Var(offspring) = V_phenotype,

So using the formula for ρ above,

ρ = (V_additive/2) / V_phenotype = h²/2.

This shows that heritability is not the same as the correlation between a child and one of its parents.

In general, the correlation, ρ, on a trait between relatives is equal to the coefficient of relatedness times the heritability, ie ρ = rh².

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3. Predictions

If we know the height of both the parents, what's our best prediction of the height of their offspring? In our mind, we draw the best-fit regression line on the scatter-plot of parental-midpoint and offspring heights measured across the population.

If we centre the graph-axes at the mean values of the two populations (parental mid-point heights and offspring heights) then the regression line goes through the origin, with slope β. Then the equation of the regression line takes this simple form:

predicted-offspring-height = β * parental-midpoint-height

with both heights measured as inches in deviation from the respective means.

How do we compute β?

In this special case it turns out that β equals the heritability, so β  = h². *

This should remind you of the Breeder's Equation.

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Example: suppose the heritability of height is 0.673 and we know that one parent is 3 inches above the population mean while the other parent is 1 inch above the mean, what's the predicted (expected) height deviation from the mean for their child?

Answer: predicted-offspring-height = β * (3 + 1)/2 = 2h² = 1.35 inches.

Yes, the child has regressed towards the mean.

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This is problem 6.3 (p. 149) from 'Population Genetics: a concise guide' by John H. Gillespie, from which all the material above has been summarised.

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* In general, β = ρ * (σ_y/σ_x) where x is the independent variable.

You're similar to your spouse in so many ways ...

You already knew that spouses were correlated for intelligence.

R Plomin and I J Deary have this to say:

" ... Assortative mating is greater for intelligence (spouse correlations ~0.40) than for other behavioural traits such as personality and psychopathology (~0.10) or physical traits such as height and weight (~0.20)."

Here's what a correlation of 0.4 looks like (top right).

Marginal Revolution gets excited about this result though:

"Nordsletten and colleagues find an amazing amount of assortative mating within psychiatric disorders.

"Spouse tetrachoric correlations are greater than 0.40 for attention-deficit/hyperactivity disorder (ADHD), autism spectrum disorder (ASD), and schizophrenia.

"The next highest spouse correlation emerged for substance abuse (range, 0.36-0.39).

"Assortative mating was significant but far less substantial for other disorders, such as affective disorders (range, 0.14-0.19)."

They conclude:

"Beyond genetics and genomics, assortative mating matters because it means that the person closest to an individual with a psychiatric disorder is also likely to have psychiatric problems, which could exacerbate problems for both spouses and their offspring."

The ubiquity of assortative mating - who knew?