Bill;

Great to hear that you read my drivel. I am just taking Fisher at his word. He explicitly states that the change in fitness is equal to the variance in fitness, so that is what I did. There is an implicit rate which is change per generation, but since that is not explicitly in the statement I left it out. The other thing is that I dislike that Fisher argues for “genetic variance”. In fact, since it is a mathematical truism, it works equally well for change within a generation. That is, consider that you have a set of individuals with differing probabilities of survival. Thus, the “differential fitness” is survivorship. Then, if we measure the number alive at some point in the future, and assign them a fitness of 1 if they are alive, and 0 if they are dead, and convert that to relative fitness we will find that the change in relative fitness in our experiment is equal to the phenotypic variance in relative fitness. Note genes are not involved, and the rate is determined by us — it is the time between when we started the experiment and everybody was alive, and the point where we ended the experiment, where some were dead. Obviously this is a silly experiment, but it shows that the “rate” is really set by us, and the basic equations make no statement about whether or not fitness is heritable.

Now that I think about if you could figure out how to do it there is no reason it wouldn’t work for a multiple generation period between the start of the experiment, and when the final fitnesses were calculated. Of course I have no idea how you would do that with anything other than a clonally reproducing organism, but again we see that the “rate” is of our choosing.

]]>I too enjoy simplicity, but I think Fisher was thinking in much broader terms, the selection theory of everything. My question is: why do you leave out “rate” in your treatment? This is of course a model for rates of change in fitness, and so many treatments explicitly include this (like the one Conrad Istock used in his lectures). Cheers

Bill

]]>Ryan Calsbeek: 2 questions: 1. What is the 1-squared for? and 2. Koalas?

My response:

Well, the 1-squared — I thought about leaving it out, but in calculating a variance you are supposed to subtract off the mean squared. Hence I was trying to be formally correct.

The Koalas? Saying FFT is about individuals instead of genes, or genes instead of individuals is silly and arbitrary, just like excluding koalas is silly and arbitrary. Plus Koalas are cute, and they have been in the news recently because of the fires in Australia.

Ken Spitze: Hi Charles – I enjoy your posts. Why do you want to delete “genetic” from FFT?

My response: For the simple reason that it works perfectly well if we apply it to individuals after selection, and before reproduction. In this case the trait need not be heritable, and it might not have any evolutionary repercussions, but you can still apply the equation.

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