On heritability (3): Non-additive effects – dominance

Dominance is a just a fancy-schmancy way of saying that the phenotypic effects of alleles at a single locus are not additive 💁. Ok, but what does that mean?

To illustrate, let’s go back to the example of differences in milk-yield among a bunch of cows 🐮🐮 (Fig. 1). As I mentioned in a previous post, some of these differences are due to genetic differences among the cows and some are due to environmental differences. For example, there could be (average) differences between the milk yield of cows with AA genotype (30 liters) vs cows with Aa genotype (20 liters) vs cows with aa genotype (10 liters). In this example, each additional A allele results in an (average) increase of 10 liters of milk (Fig. 1A). This may not always be the case if, for example, cows with the Aa genotype and AA genotype have the same average milk yield: 30 liters (Fig 1B). If this is the case, we say that the effect of alleles at this locus are non-additive or that there is dominance at this locus.


Fig. 1: A) Additivity is when each additional allele adds a fixed value to the phenotype. B) Things are not that symmetric when there’s dominance. In this example, the average phenotype is the same for the AA and Aa genotypes.

When you were learning genetics in school 🏫, you probably came across terms like “dominant” and “recessive”, which are often used to refer to Mendelian traits such as the presence/absence of cleft chin 🍑 in humans. These terms are ok for simple Mendelian traits but quite limiting for quantitative traits. Also limiting are terms like complete dominance, a special case of dominance in which the phenotypic distributions of AA and Aa genotypes are indistinguishable (Fig. 1B). There is a more flexible way to describe dominance: d.

The dominance deviation, d, describes the degree (and direction) in which genotypic values deviate from additivity.

🔴✋Sidebar: It’s useful to define genotypic value here as it is an important concept in quantitative genetics. The genotypic value is the average phenotype of a specific genotype. For example, the genotypic value of the Aa genotype in Fig. 1A is 20 liters. So even though some individuals carrying the Aa genotype have higher or lower milk yields because of environmental differences among them, they all yield, on average, 20 liters of milk. Thus, the genotypic value is supposed to represent the ‘true’ phenotypic effect of the genotype. It is often convenient to represent genotypic values as deviations from the mean of the population. For example, the genotypic value of the aa genotype in Fig. 1A can be written as 10 – 20 = -10 (instead of 10) if we assume the average milk yield in the population is 20 liters. This is mostly for convenience sake in calculations so don’t worry too much about this. Sidebar over. 👍

Now take a look at Fig. 2 and give it some time. 🤔

Fig. 2: Different values of d describe different cases of dominance. The scale represents the genotypic values, where +1 and -1 refer to the genotypic values of AA and aa, respectively, expressed as scaled deviations from the mean. The red line, which represents the scaled dominance deviation, shows the extent to which the genotypic value of the heterozygote Aa deviates from what we expect had the allelic effects been completely additive.

Can you see how the dominance deviation flexibly and quantitatively describes the different cases of dominance (including no dominance!)? The meaning of the different values of d are further explained below:

d = 0: no dominance. The allelic effects are completely additive and the average phenotype of Aa is smack dab in the middle between AA and aa.

d = 1: complete dominance. AA has the same genotypic value as Aa. Note that this is the same as the example of milk yield in Fig. 1B.

0 > d > 1: partial dominance. The genotypic value of Aa lies somewhere between that of AA and aa. As d gets closer to 1, the genotypic value of Aa gets closer to that of AA.

d > 1: overdominance. This is when the genotypic value of Aa is greater than that of either homozygote. So, for example, the average milk yield of cows carrying the Aa genotype might greater than the average milk yield of cows carrying the AA or aa genotype. This is sometimes referred to as hybrid vigor.

d < -1: underdominance. The genotypic value of Aa is less than that of either homozygote.

🚨 There is one common misconception regarding dominance that I want to clear up: dominance does not tell us anything about how frequent the allele is in the population. For example, the A allele in Fig. 1B, even though it is ‘dominant’, might only be present at 10% frequency in the population.

Dominance is only one example of non-additive effects of alleles on the phenotype. So far I have only talked about the phenotypic effects of alleles at a single locus. What happens if we consider alleles at two or more loci? We’re faced with non-additive effects of alleles across loci. Non-additive effects of alleles at two or more loci are called epistasis and I plan to talk about this next time. See you in a couple of months…📆

On heritability (2): narrow and broad sense heritability

Quick recap: I mentioned last time that heritability = Vg / Vp, where Vg is the genetic variance among individuals and Vp is the total phenotypic difference among individuals. Furthermore, Vp = Vg + Ve, where Ve is the environmental variance contributing to phenotypic differences.

There are two different types of heritability: broad-sense heritability and narrow-sense heritability. What we’ve been discussing so far is broad-sense heritability: the proportion of phenotypic variance that can be explained by ALL genetic differences among individuals. Geneticists often like to split Vg, the genetic variance, into two: additive genetic variance and non-additive genetic variance. There is a reason for this split (besides a masochistic need to make life harder for everyone 🤦🏽‍♂️), which I will talk about later but first let’s talk about what these things are.

Additive genetic variance first since that’s easier. Suppose there is a gene called A (very creative, I know 😛) involved in milk production in cows 🐮. Further suppose that a cow can have the genotype AAAa, or aa at gene A because cows are diploid. Cows with genotype aa produce, on average, 10 liters of milk everyday. I don’t know if that’s a normal amount or not so don’t judge me if you’re a farmer 👨🏻‍🌾 and you’ve chanced upon this blog. Cows with a single A allele in their genotype (i.e. genotype Aa or aA) produce, on average, 20 liters of milk and cows with genotype AA produce 30 (Fig. 1).


Figure 1: Cows with different genotypes can have different means for milk yield. This variation is due to a combination of genetic and environmental differences. However, among cows with the same genotype, differences in milk yield are purely due to environmental differences.

There are a couple of interesting things happening here (if we play fast and loose with the word ‘interesting’ 😅):

  1. There are differences in milk yield among cows of the same genotype even though there are no genetic differences among them (Vg = 0) (Fig. 1). Remember from the last post that these differences arise solely because of environmental differences. This is why I keep saying things like “cows with a single A allele produce, on average, 20 liters of milk” as there are some that might produce 22 and some that might produce 18, because of small environmental differences. Note also that this means that heritability among cows of the same genotype is 0. Ok, I think I’ve hammered 🔨 this point hard enough.
  2. The differences among groups of cows with different genotypes (AA vs Aa vs aa) arise not only due to environmental differences, but also due to genetic differences (i.e. Vg > 0). Because Vg > 0, Heritability > 0 and we can say that milk yield is heritable in this specific herd of cows (Fig. 1).
  3. It seems that each additional A allele that a cow carries, on average, increases the milk production by 10 liters (aa = 10, Aa = 20, AA = 30, Fig. 1). There is no dominant or recessive allele, despite my poor use of the letters. We say that the effect of A (and a if we look at it as decreasing milk yield) is additive. If one of the alleles were dominant/recessive, we would say the allelic effects are non-additive because we couldn’t just figure out the average milk yield by adding up the number of A alleles. (Side exercise: if A is the dominant allele and a is recessive, what would the average milk yields be for the three genotypes?).

The last point can be extended from one gene/ locus to two (or more) genes/loci. Different alleles at the two loci might contribute additively to milk yield (Fig. 2). This additivity has everything to do with the difference between narrow-sense and broad-sense heritability. If broad-sense heritability is the proportion of phenotypic variance that is due to ALL genetic effects (additive + non-additive), narrow-sense heritability is the proportion of phenotypic variation only due to additive genetic effects. What are non-additive effects? Why are they important? Why does this distinction matter? What is the meaning of life 🌄🤔? There’s a whole post about this (ok, not the last question), so stay tuned 😎🍿.


Figure 2: The effect of alleles on milk yield (numbers) in this example is additive. Doesn’t matter if we look at each gene separately, or combine effects across them.

Primary source: Lynch M, Walsh B. 1998. Genetics and analysis of quantitative traits. Sunderland, MA: Sinauer Associates, Inc.

On heritability (1): How ‘genetic’ is a trait?

One of the reasons I’ve come to write about this is because recently I’ve been asked a lot about “how genetic is this trait or that trait?”. And I find myself responding with another question (yeah I’m that guy 👨🏽‍🏫, get over it): “What do you mean by genetic?”. I ask this because I think there is often a confusion between the term ‘genetic’ and ‘heritable’, and that distinction is extremely important to understand.

Maybe you’ve heard this before: Every trait is genetic. There are genes involved in the development of every trait. Nothing pops out of the environment (unless it’s a spray tan or something?🤔). Is height genetic? Yes. Is hair color genetic? Yes. If you go work out a lot🏋🏽‍♂️, are your bulging biceps genetic? Yes, because there are genes that respond to the body’s need by triggering a cascade of biochemical processes that result in muscle production. The question, “How genetic?”, is not a legit question. What one really means to ask is “How heritable?“.

Cutting to the chase and then I’ll explain: Heritability is the proportion of variation in a trait (Vp) explained by genetic differences among individuals (Vg).

Heritability = Vg/Vp

Vp = Vg + Ve. This is the classic equation which, in english, reads: Variation in the phenotype/trait can be explained by the sum of the variation in the genotype (Vg) and variation in the environment (Ve), where environment is everything that is not ‘genetic’. It becomes clear from the definition of heritability that it cannot be defined for a trait in a single individual. That’s not a thing. It can only be defined for differences between two or more individuals.

Let’s expand on this. Imagine there are 10 cows 🐮☘️ grazing on a pasture. They’re all clones of each other, i.e., they are all exactly the same genetically. If you milk all of them, the milk yield 🥛 will vary among them (Figure 1). How much it varies (the variance) is Vp. Is the milk yield of a cow genetic? There are genes involved in milk production, so yeah. Is the milk yield among the cows heritable? Nope. Think about it. Since the cows are clones of one another, there are no genetic differences among them (i.e. Vg = 0 👌🏽) . So any differences in milk yield have to be because of the environment (Vp = Ve). Maybe they were grazing on different regions of the pasture or maybe some of them were being tipped more than others 🙌🐄 (it’s a real thing). The heritability of milk yield among the cows is 0.


Figure 1: Variation in milk yield in a hypothetical herd of cloned cows. Since there is no genetic variation among cows, heritability of milk production in THIS set of cows is zero.

There are some other things about the concept of heritability that make it tricky. One thing that I’ll mention now and leave the rest for some other time is that heritability is not a fundamental property of the trait itself. It is context specific and is a property of the sample you are looking at. If I tried to measure the heritability of milk yield in another set of 10 cows grazing in the same pasture, who are genetically different from one another, the heritability of milk yield will likely not be zero since Vg > 0.

So when most people ask “how genetic is skin pigmentation” or “how genetic is intelligence” (that’s a whole can of worms that I hope to address at some point), they’re really asking “how heritable are they?”.