(no subject)

[impossiblewizardry]

Rick Durrett:

The results for E[η_{n,m}] are useful for population genetics, but are not really relevant to cancer modeling. To investigate genetic diversity in the exponentially growing population of humans, you would sequence the DNA of a sample of individuals from the population. However, in the study of cancer each patient has their own exponentially growing cell population, so it is more interesting to have the information provided by Theorem 1 about the fraction of cells in the population with a given mutation.

The results he seems to think are so useless still seem to be the only results in the paper that has been used in data analysis (in this paper).

What Rick Durrett doesn’t seem to have realized is that, two years prior to the publication of this paper, people started doing DNA sequencing of individual cells from patient’s tumors. So, the study of a single patient became a population genetics problem, and results from a population genetics perspective were exactly what was needed.

Rick Durrett can be forgiven for not noticing that. He’s a mathematician, and can’t be expected to keep up with the latest advances in genomics. But as a consequence he should worry less about whether his results are applicable to the few problems he’s familiar with from his collaborators.

I prefer the spirit he demonstrated in this paper with Foo and Leder, where they provide extensive information about the growth of cancer in a space of 3 or more dimensions.