She asked whether the positions of uptake sequences were stable once the score had reached equilibrium. Another way to say this is to ask whether the equilibrium is dynamic, with old uptake sequences lost to random mutation and new ones appearing in new places, or whether once an uptake sequence has arisen it tends to persist, presumably because mutant versions are efficiently restored by recombination. In real genomes of the same genus or family we tend to find the latter - uptake sequences are in homologous positions.
So I set up some runs that started with 200kb sequences that had evolved to equilibrium under more-or-less standard simulation conditions and would run for between 5000 and 200,000 additional cycles. The first results are done (just the 5000-cycle runs) and already the results are interesting.
The analysis will need to be redone because I'm not using the correct (10-mer) version of the US-locating perl script, but a 9-mer version intended for perfect USS cores. I'm also doing the analysis inefficiently in Excel using VLOOKUP; maybe my coauthor can write a little perl script to do it.
When the bias of the uptake machinery was fairly weak (because the matrix was applied additively), only one of the 44 perfect 9-mer uptake sequences in the input sequence was in the same location in the output sequence. But when the bias was strong (because the matrix was applied multiplicatively), 145 of the 205 original uptake sequences were present in the same positions in the output sequence.
This is a pleasing result. When the bias is strong, uptake sequences that acquire random mutations are restored by recombination before they can diverge (does this mean within a single cycle?). But when bias is weaker they often diverge before recombination can catch them. I'll have lots more data in a few days - I think some of the runs also test the effect of mutation rate.