A phenotypic view of evolution Evolution in Structured Populations

Heritability and the individual

First off, an ad from a former graduate student I used to work with. Josh Payne, who was an author on the speciation in continuous populations paper I discussed some time ago , is looking for students and a postdoc to study evolution and robustness. Check out his ad if you are interested.

To summarize to this point, I first defined an individual as that which you define to be an individual, or more specifically, the level at which you assign fitness. This definition makes sense since there may be constraints on what can be measured. There are a trillion some odd cells in our bodies. Assigning fitness at the level of the cell would be a huge chore unless there was some compelling reason to do otherwise. On the other end, a paleontologist may have access to presence or absence data for species in a fossil assemblage, but no way of assigning fitness to individual organisms, or even knowing how many individuals there are in the population. Thus, they may forced to assign fitness at the level of the species. This first definition is entirely consistent with the pragmatic needs of research.

At this point an admonition to paleontologists: Do not apologize for studying “species selection”. In your world species ARE individuals. From this perspective, the waxing and waning of the range of a species, or anagenesis of the species is simply “species development”. It may well be that if we had a time machine, and ear tagged all of the mastodons, and measured traits and their reproductive success we would discover that the change in their distribution was due to selection at the level of the organism, but we can’t and because we can’t we cannot study it as evolution, and we need to let go of that and be happy with the evolution we can study. By the way, this also means that two investigators could choose to assign fitness at different levels, and as a result come to very different conclusions about how evolution works. It being the nature of biologists, they will almost certainly argue about which one is “right” when in fact, since they are using different definitions of what the individual is, they can both be correct.

My second definition is that the individual is the level at which selection is acting. I like this definition a lot since it is logically appealing that selection should define the individual. It also suggests that metazoans are metazoans because groups of cells have higher fitness than individual cells. Following this through, it logically also suggests that under some circumstances groups of organisms have higher fitness than individual organisms. We actually see that eusocial organisms often exploit environments and resources that solitary organisms can’t. Thus, naked mole rats can live in an environment that is too harsh for other rodents.   Social wasps can have open nests even though their larvae are extremely attractive food sources.   And ants have virtually taken over the world. It also suggests that there are times when social living may not improve an organism’s fitness. Just as there are environments where naked mole rats out compete all other rodents, there are many other environments where naked mole rats cannot compete. Presumably, in these richer environments the strength of group selection is lower and individual selection higher and as a result the naked mole rat cannot compete with its solitary brethren.

naked mole rats

Naked mole rats live in a harsh environment where other rodents cannot survive, but have not spread into more benign environments. Presumably this is because the balance of selection tips towards group selection in harsh environments. (http://adarwinstudygroup.org/illustrations/#img-01-2402 )

There is one last concept of individuality that needs to be discussed. This is the classic one that is the subject of books such as Maynard-Smith’s book supporting group selection (he said laughing in his hat five ways*), “The Major Transitions in Evolution“. That is the observation that selection at the group level can overwhelm individual selection, and effectively suppress evolution at the lower level.

The interesting thing about metazoans is that they rather famously start from a single fertilized egg, and eventually divide into trillions of cells. Importantly, the cell division is via mitosis, which has almost unbelievable fidelity. Thus, all of the cells are genetically virtually identical. From the perspective of individuality, what this does is that it lowers the heritability at the cellular level to nearly zero. To remind you, the breeder’s equation is:

R = h2S

Which basically means that if we are going to get evolution by natural selection we need both selection and heritability. In my second definition I identified the individual as the level at which selection is acting. Lowering the heritability has exactly the same effect. Thus a reasonable definition of individuality is the lowest level at which there is heritable variation for a trait under selection acting at that level.

It is important to recognize that mitosis is but one way that heritability can be minimized. In social insects you get the same minimization of heritability through “policing” behaviors. For example, in worker bees there is variation in their propensity to lay eggs (all haploid male eggs, of course); however, because workers eat eggs laid by other workers, this variation does not translate into reproductive success, and there is no variation among workers in offspring produced. Other mechanisms for reducing variation that have evolved are things such as having a single reproductive in a colony. Such reproductive behaviors increase relatedness within groups, having the effect of reducing heritability, and decreasing the response to selection.


A bee killing a worker laid egg. This policing effectively eliminates the heritability of fertility among worker bees. (from http://www.nature.com/news/2002/020425/full/news020422-16.html)

An interesting anecdote on this is that as good as mitosis is at making exact copies, there are mistakes. As a consequence there IS heritable variation among cells in metazoans. This would suggest that there should be strong selection, but low heritability, for cells becoming reproductive cells. So, why hasn’t your liver evolved to become a gonad? Obviously, part of this is the fidelity of mitosis, but another part is that the reproductive cells are isolated very early in development, and actually while development is still under maternal control. What I mean by that is that early cell division in vertebrates occurs far faster than is apparently possible based on normal rates of protein synthesis. The way this can occur is that the mother “packs” the cells with RNA and proteins before fertilization. Thus, the early cell division is under maternal control but after a few divisions the zygote derived gene products take over control of cell division. It turns out that in Drosophila for at least one important gene product, notch, isolation of the germ line occurs immediately before the shift from maternally derived notch to zygotically derived notch occurs. Of course I have no real idea, but as an adaptive story it is tempting to suggest that the maternal control of germ line segregation is similar to policing in social insects. (don’t ask me for references on this. Years ago I wrote a grant for this with somebody. We got the grant, but my collaborator left and I never saw the money or did the research. Also, this idea can be traced to Leo Buss [http://www.amazon.com/The-Evolution-Individuality-Leo-Buss/dp/0691084696], so I take no credit.)

Thus, the three definitions of individuality, and particularly, the second and third are really cut from the same cloth. An individual is an evolving unit. At the simplest, it is that which we recognize as an individual. Given that humans are good at recognizing patterns, it is hardly unreasonable that we intuitively identify “individuals” more or less correctly. The second and third are more formal definitions in the sense that we are saying that individuals are units of adaptation. They can be units of adaptation either because of the patterns of selection, or because of the patterns of heritability, or both.

* 10 points if you can identify that reference! The actual quote is “One little sniffer with his eyes half shut and a mitten on his nose, laughed in his hat five ways and said, ‘They are going to the moon and when they get there they will find everything is the same as it always was.’ ” And by the grace of the cosmos Disney never laid waste to those stories.

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  1. Hi Charles,

    Thanks very much for the blog post and your answer. I’ve been doing some research and I’ve managed to derive something that looks like GP^{-1}, using the ‘effective’ heritability. As you said, I’ve had to use least squares to get something useful out! I’m a bit rushed at the moment so don’t have time to properly respond to the ideas in your blog post, other than to say they sound interesting! I will have a proper read next week when I’m back off holiday and get back to you.

    Thanks again,


  2. Michael;

    I didn’t actually answer your specific question in my blog post. Basically, yes, in general matrices can be added together. If you want it to be meaningful they need to be orthogonal, however. This is why you need to do some form of least squares partitioning of the genetic effects. When you add them, you simply add the matching elements.

  3. Hi Charles,

    Thanks very much for your response. I’m currently trying to get my head around all these different definitions and what you said made a lot of sense. I’m wondering, do you know how the ‘effective’ heritability fits in with the framework of quantitative genetics? If I have multiple phenotypic traits of interest, the response to selection is

    delta z = GP^-1 s

    where G is the genetic variance-covariance matrix, P is a phenotpic variance-covariance matrix and s is a vector of trait-fitness covariances. I suppose the GP^-1 part here corresponds to heritability of the ‘Fisherian’ kind as you defined it? Is it legitimate to substitute G for a matrix of parent-offspring covariances to arrive at something of the ‘effective’ kind as I defined it?

    The reason I ask is that I’m currently working on developing a multicellularity model, and as you said the VA isn’t well defined in my model for within-organism selection.



  4. Michael;

    Yes, It is an interesting problem. Consider, in a world with no somatic mutations there is a very large phenotypic variance in the cells of a mammal (for example), ranging from liver cells, to nerve cells, to skin cells. However, since they are all genetically identical there is no additive genetic variance. Thus, the heritability is h^2 = VA/VP = 0/VP = 0. So using heritability in the sense defined by Fisher the heritability is zero. With somatic mutations that will presumably add a little VA, so it will be non-zero but small.

    The problem of course, is that Fisher’s definition of VA doesn’t really apply to non-sexual organisms, which is what a somatic cell is. What you are using is more consistent with a phenotypic definition of heritability, which is the extent to which offspring resemble their parents. In that case, yes, offspring cells do tend to resemble their parents, although that resemblance has almost nothing to do with genetics.

    I sometimes call these more general definitions of heritablity “effective heritability”. Fisher defined heritability, and as Ewens would say, if he defined it, his definition is the correct one. That definition is the covariance between the average effect and the average excess. Given that Fisher’s definition is useless in this situation we are stuck with effective heritability, and since you and I were thinking along different lines at the time we each used different definitions without being explicit about what those definitions were. My definition was the genetic variance divided by the phenotypic variance, yours was the parent offspring covariance divided by the phenotypic variance. Mine was more useful for the point I was trying to make, but honestly, I will admit that yours is more correct.

    Thanks for bringing up this important point, and in the process clarifying my thinking.

  5. Hi Charles,

    Please could I just clarify something you say in this piece, as it relates to something I’m working on at the moment. You say:

    ‘From the perspective of individuality, what this does is that it lowers the heritability at the cellular level to nearly zero.’

    This confused me, since the heritability at the cell level via mitosis is nearly one, not nearly zero, isn’t it? If we take h^2 = Cov(zi,zi’)\Var(zi), where zi is parent cell phenotype, and zi’ is offspring cell phenotype (we have regressed parent phenotype against offspring phenotype and taken the gradient of the regression line to be the heritability). Assuming high fidelity, we have Cov(zi,zi’) approx = Cov(zi,zi) = Var(zi). Putting this back in we get h^2 = Var(zi)/Var(zi) = 1, and thus h = 1.



  6. The quote is from Carl Sandburg’s “Rootabaga Stories” Hats off to people who even knows what a rootabaga is (definitely not a fast food).

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