Heritability vs. Penetrance - a ChatGPT tutorial

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Heritability, Penetrance, and Genetic Control

When you first encounter the term heritability in genetics, it is natural to assume it means “how genetic” a trait is. But that is not quite right. Heritability has a very specific technical meaning: it is the proportion of the variation in a trait, within a population, that can be attributed to genetic differences between individuals (genetically-induced variance over total variance).

(See the definition of heritability at the end of this post, below).

Notice the emphasis: heritability is about trait variation in a group, not about whether a trait is caused by genes in the first place.

Take the example of having two eyes. The development of two eyes is tightly controlled by genes. The biological mechanism is overwhelmingly genetic. But in most human populations there is no meaningful variation here: virtually everyone has two eyes and any variation is likely to be environmentally-induced. Since heritability measures genetic contribution to observed variation, the heritability of “having two eyes” is close to zero. Yet no one would doubt that the trait itself is genetically determined.

Now compare this with height. In a given population, some of the variation in height is due to genetics, and some is due to environment (nutrition, illness, socioeconomic status). If careful statistical studies show that 80% of the variation in height is explained by genetic differences, then we say the heritability of height is 0.8 in that population at that time.

But change the environment (for example, move the same genotypes to a famine-stricken region), and the heritability estimate will sharply drop, because environmental variation now explains so much more of the differences.

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More Direct Measures of Genetic Influence

Heritability does not tell us how a trait is controlled at the level of the individual or the mechanism. For that, biologists use different concepts:

• Penetrance: For a specific genotype, what is the probability that the phenotype will appear? For example, a BRCA1 mutation carries high but not complete penetrance for breast cancer. This is a direct, causal measure at the level of an individual genotype.
• Expressivity: Given that a trait is present, how strongly or in what form is it expressed? Cystic fibrosis mutations can vary in severity, even within the same family. Expressivity captures this.
• Functional impact of alleles: Molecular biology can measure how a specific mutation changes protein function or disrupts a developmental pathway. This connects genotype to mechanism. For example, the sickle cell mutation changes a single amino acid in hemoglobin, altering how red blood cells form under low oxygen.
• Variance explained by identified loci: Genome-wide association studies (GWAS) can estimate how much of the variance in a trait is accounted for by the set of variants we have actually identified so far. This is still a population-level measure but closer to causal genetics than broad heritability.

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Contexts of Use

Heritability is most useful in population genetics, plant and animal breeding, and public health studies. It tells us how much of the observed variation we can expect to respond to selection - given current conditions. But it should never be taken as a timeless or universal measure of “genetic determination”.

Penetrance, expressivity, and functional impact are more useful in medical genetics and molecular biology. They help clinicians predict risk for individual patients, and they help researchers understand mechanisms.

In short: heritability is a statistical lens on variation within a group. Penetrance and related concepts are causal lenses on individuals and mechanisms. Both are valuable, but they answer different questions.

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Key Takeaway

Always ask: are we talking about variation in a population (heritability), or are we talking about causal pathways in an individual (penetrance, expressivity, functional effect)? Mixing them up is a common beginner’s mistake. Once you see the distinction, the field of genetics becomes far less confusing.

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Mathematical definition of heritability

Broad-sense heritability is the fraction of phenotypic variance in a population attributable to all genetic sources (G - total-genetic; P - population):

H² = V_G / V_P

Narrow-sense heritability is the fraction of phenotypic variance attributable to additive genetic effects only:

h² = V_A / V_P

Variance decomposition (standard model)

V_P = V_G + V_E + 2COV(G,E) + V_GE

and

V_G = V_A + V_D + V_I

Variables

• V_P: phenotypic variance of the trait in the specified population and environment.
• V_G: total genetic variance (all genetic contributions combined).
• V_A: additive genetic variance (sum of average effects of alleles; component that responds predictably to selection).
• V_D: dominance variance (interactions between alleles at the same locus).
• V_I: epistatic variance (interactions among loci).
• V_E: environmental variance (all non-genetic sources of variation).
• COV(G,E): covariance between genotype and environment (nonzero when genotypes systematically experience different environments).
• V_GE: genotype-by-environment interaction variance (genetic effects that change with environment).

Notes

• H² and h² are properties of a particular population in a particular environment; they are not trait constants.
• When COV(G,E) and V_GE are negligible, many texts simplify to V_P = V_G + V_E.

Optional estimator (selection response)

Under the breeder’s equation, an empirical estimate of narrow-sense heritability is:

h² ≈ R / S

• R: response to selection (mean of offspring minus mean of base population).
• S: selection differential (mean of selected parents minus mean of base population).

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