This post is based on a chapter of mine in Bouchard and Huneman’s book “From Groups to Individuals”. That chapter is were I first came up with the comparison between sickness and laziness.

]]>Just wanted to say that after finding and re-reading these posts, I found them just as interesting. Thank you!

P.S. I particularly enjoyed the comparison between “sick” and “lazy” in part 1.

Cheers,

Lucas ]]>

This should be ‘the within’.

]]>I just think the arithmetic mean is weird to use, because of the way we think about selection coefficients. They are relative increases in fitness, and so work on a multiplicative way. A mutation of s=0.1 increases fitness by 10 percent, and a second mutations with s=0.2 by another 20 percent (total w=1.1*1.2), so it just feels strange to use the arithmetic mean for the total fitness.

But whatever I feel about it, it’s very hard to measure individual fitness components, which you would have to do to test it.

]]>I put in the arithmetic mean mostly because I didn’t really think it through and have no opinion one way or another. For average effects the arithmetic mean is what Fisher (and Falconer) use. So, I am open to being corrected on that, but you would have to tell me why something else would be a better choice.

By the way, I can’t figure out the keys I need to spell your name correctly.

]]>I found something regarding heritability in Frank (1997) that I think deals with the artificially high covariance term. He starts with the other definition of heritability:

B_g’z = Cov(g’,z)/Var(z),

where g’ is the breeding value transmitted to offspring, and z is the phenotype of the parent. He showed that this could be further partitioned into

B_g’z = B_g’g * B_gz = (Cov(g’g) / Var(g)) * (Var(g) / Var(z)).

Thus, heritability has two components, the fidelity of transmission of breeding value B_g’g, which will be ~1 for clonal cells (like I said), and B_gz, which will be ~0 for clonal cells (like you said), since there is little genetic variance.

Ref:

Frank (1997) The Price Equation, Fisher’s Fundamental Theorem, Kin Selection, and Causal Analysis

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,

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.

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