USS don't accumulate because the bias is much too weak

In our very-preliminary version of the USS evolution model, we've been using a very simple scheme to score the similarity of DNA sequences to the USS motif. We just count the number of matches to the 10bp core USS sequence. Right now I'm keeping everything simple by running the model with DNA fragments that are only 13 bp long (and a genome that's 200-1000 bp long).

So a fragment with a perfect 10 bp match to the motif is only twice as likely to recombine back into the genome as a fragment with only 5 bp matching. We know from our earlier model, and from a calculation I did years ago, that the bias favouring USS needs to be much stronger than this if it is to overcome the randomizing effects of mutation. For example, (ignoring the effects of base composition) a sequence that matches the motif at 9 positions has 27 different ways to mutate into a fragment that matches at only 8 positions, and only one way to mutate into a fragment that matches at 10 positions. To overcome this disproportion, the bias favouring 9 over 8 (or is it 10 over 9?) has to be proportionally strong (i.e. 27-fold).

Now I need to find that old calculation - I think it might be with my 1999 NIH proposal.