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Even with Heritability Outcomes Are Unpredictable
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Credit: John Hawks

Credit: John Hawks

In the comments below there was a question as to why outcomes for offspring from parents can vary a great deal even without regression toward the mean. First, about regression. It’s a confusing and misunderstood concept. There is a general statistical phenomenon here, but let’s focus on genetics. Often in the comments of this weblog I’ll get the rhetorical question which has the general form of “but what about regression toward the mean?” Usually this is a good clue that the person has no idea what they are talking about. What about regression toward the mean? It’s not a magical force which shifts populations back toward a set point in an orthogenetic fashion. Basically when you select an individual based on their traits, and infer about the likely character of their offspring, you can predict the expected impact of genes on the outcome. The phenotype is an intelligible signal of the nature of genes in a heritable trait, and genes are predictably transmitted to offspring. In contrast there is an “environmental”* component which you don’t understand, can’t control, and can’t account for. This component is often not transmitted across the generations, so fluke contingencies which lead to individuals who are sharply deviated from the average of a population are not replicated in subsequent generations, and individuals are expected to be more typical. A perfectly heritable trait would not regress at all on the population level.

But you can predict only so much from heritability. The above plot is from John Hawks’ anthropology class. You see that the regression line is 0.72, so the heritability as inferred from these data is such. That means that 72% of the variance in the phenotype, height, can be accounted for by variance in genes. That’s a population wide statistic. That doesn’t mean that height is “72% genetic” on the individual level. That’s not even wrong. Since heritability is a population wide measure, so you need to be judicious when inferring toward individuals.

Yet still tall parents tend to have tall children. If two tall parents had hundreds of children, then you could make some inferences about the average height of the children using the breeder’s equation. But observe that there’s still noise in the prediction. There’s going to be a distribution of outcomes. Height in the developed world is 80 to 90 percent heritable, but the correlation in heights between siblings is on the order of 0.5. Similarly, IQ is on the order of 50 percent heritable, but the correlation between siblings is on the order of 0.5. Presumably segregation and recombination are working in a fashion to mix and match the genomes of individuals so that even heritable polygenic traits aren’t quite as predictable as you’d think.

* Before someone points it out, I am aware this component often collapses non-additive genetic variance, such as epistasis.

 
• Category: Science • Tags: Heritability 
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  1. I don’t follow the conclusion: “That means that 72% of the variance in the phenotype, height, can be accounted for by variance in genes.” A priori, couldn’t such variance be accounted for by shared environmental factors among parents and their offspring. Isn’t this why twin studies are required to tease out genetic components?

  2. Actually, IQ is also about 80% (or more) heritable. But the narrow-sense heritability, which is what you need for the breeder’s equation, appears to be about 60%.

  3. Perhaps you could answer this question from an ignoramus on statistical matters. Say we have some towers made of blocks piled one on top of another. Each tower consists of 50 black blocks and 50 white blocks. Each black block and each white block can be tall or short. If every tower has the same amount of tall and short black blocks but a random selection of tall and short white blocks, 100% of the variance can be accounted for by the white blocks, right? Whereas if every tower has a random selection of short and tall for both colours of block, the variance accounted for by the white blocks would be 50%, right? But what if the number of tall and short black blocks in each tower exactly mirrored the number of tall and short white blocks, how much of the variance is then accounted for by the white blocks? 50%? 100%? What if the number of tall black blocks does not exactly correlate with the number of tall white blocks but is positively correlated with the number of white blocks to some degree? It seems to me there is a distinction here between the amount of the variance ‘physically due to the white blocks’ and the amount of the variance ‘which can be accounted for by knowledge of the white blocks’. Right?

  4. Whoops! The variance I mean is in the overall height of the towers.

  5. I wish the graph included one more bit of information: the height difference of each subject’s parents (expressed, e.g. by the color of dots). Would be interesting to see if the low-difference dots cluster near the straight line, and those who, perhaps, inherited most of their height genes from one ( taller or shorter) parent, deviating more from the average.

  6. I don’t follow the conclusion: “That means that 72% of the variance in the phenotype, height, can be accounted for by variance in genes.” A priori, couldn’t such variance be accounted for by shared environmental factors among parents and their offspring. Isn’t this why twin studies are required to tease out genetic components?

    yeah. i got priors. in developed world heritability is .8 or .9.

    inherited most of their height genes from one ( taller or shorter) parent, deviating more from the average.

    well, you’re really talking about grandparents. though you are right that parents can contribute different aspects of their genome….

    #3, i’ll get back to you. i don’t have time for word problems right now 🙂

  7. I interpret #5’s comment to be about sampling drift from a diverse mix of rare and high-magnitude alleles rather than about grandparents. Imagine that height is determined by a single gene, with a recessive common allele (average height) and two rare dominant alleles (one tall, one short). When two homozygous average people mate all of their children will be average. When a heterozygous tall mates with a heterozygous short then 1/4 of their offspring will be tall, 1/4 will be short, 1/4 will be homozygous average, and 1/4 will be heterozygous average. Thus the tall and the short couple have more variation. Height is of course highly polygenic, so this effect is going to be attenuated.

  8. “If two tall parents had hundreds of children, then you could make some inferences about the average height of the children” This is the key aspect.
    If the tall parents have only one child there are good chances that he will be tall, but he may be shorter than the average if he has an unfavorable combination of genes. If the parents have hundred of children they are guaranteed to hit the entire range of possible child heights for that particular couple with tall kids being more frequent.
    That’s why embryo selection could possibly be such an effective technique. If your goal is to have a tall child it’s impractical to raise 100 children, but, in theory, you can create 100 embryos, determine which one will result in the tallest child and implant it.

  9. “You see that the regression line is 0.72, so the heritability as inferred from these data is such. ”

    (Probably out of my depth here:) Wouldn’t that be .72 squared ?

  10. As Jayman stated above, I was also under the impression a properly measured “g” was on the order of 70-90% heritable.

  11. #9, it’s not the same as the r^2. if it was so then traits like height would exhibit much tighter correlation between parents and offspring than they do. see this and control-f correlation

    http://www.nature.com/scitable/topicpage/estimating-trait-heritability-46889

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