September 19, 2016 at 03:08AM

Today I Learned: 1) Hardy, of the Hardy-Weinberg equilibrium, was yet another example of a mathematician who was proud to never work on anything practically useful, but ended up being famous for deriving very practiacal, applied mathematics. 2) Single-population, two-allele evolutionary dynamics seem pretty simple at first blush. If the populations are big enough that genetic drift isn't a problem, then the one with the higher fitness grows in the population until the other one doesn't. Today I learned that that's only true if population growth is exponential, i.e. the rate of reproduction of each population is exactly proportional to the size of that population. If the rate of growth is *slower* than exponential, then there is a stable equilibrium between the two populations where both can coexist. If the rate of growth is *faster* than exponential, then fitness is actually more or less irrelevant -- there is an unstable nonzero equilibrium between the two species, and whichever species starts with a larger population than it has at that equilibrium will dominate regardless of the relative fitness of the two populations. When would you encounter sub- or super-exponential growth in a population? A nonreproducing population with immigration would be an example of subexponential growth -- there, population growth is entirely determined by a (potentially) constant immigration. A mix of reproduction and immigration also can result in subexponential population growth. An example would the release of sterile insect populations into the wild, which is done to bring down wild pest populations. Superexponential growth happens any time two organisms have to find each other to mate, as in sexually reproducing species -- the denser the population, the more likely it is that each individual reproduces, and the faster overall population growth. 3) I read a claim today that the terms transcription and translation (as in, transcription of RNA from DNA and translation of RNA into protein) were coined by John von Neumann, to refer to processes in an abstract self-replicating automata schema he had theorized. There wasn't a citation given, but context clues suggest that the term was, as I say, coined in "Theory of Self-Reproducing Automata", a classic 1966 work on, well, self-reproducing automata* **. Well, I read through a chapter (chapter 4: http://ift.tt/2cJdGxl) of that book looking for references to transcription and translation before realizing that I was just reading a chapter excerpted from a bit of a longer work than I wanted to read in one Sunday afternoon. In any case, I didn't see any reference to transcription and translation exactly, though it *did* contain a theoretical description of abstract machinery surprisingly like the transcriptional machinery of the cell... not surprising, since it was inspired by the same (although it was written before most of the details of either transcription or translation had been worked out, so there are some telling differences among the similarities). I eventually found a text version of the book (link available here, along with a bunch of other formats: http://ift.tt/2d9SVt4) and ctrl+f'ed for "transcrip" and "transl", and there was nothing quite resembling transcription and translation in the biological sense. Phoey. Would've been a great story. In any case, von Neumann is great. Go check out his works. The chapter linked above has, among other things, a really nice succinct little comparison of brains, computers, and theoretical thermodynamic limits. If you're interested in computation, this is a must-read. * Ever heard of a von Neumann machine? This is the book that defined it. ** I'm not sure if von Neumann actually penned anything in that book. It's "edited and completed" by Arthur W. Burks. What I read of it reads as a sort of "best of" compilation of von Neumann's best lectures, interspersed with some commentary and summarization by Burks.