Complex self-replicating programs still emerge in the BFF experiment even when the mutation rate is set to zero, contradicting the assumption that mutation is the source of evolutionary novelty.

24:26the mutation rate cranked all the way down to zero, you still get the same exact phenomenon. And that is very mysterious because if you crank mutation down to zero, you should have no source of novelty. You should have no evolution. Why do you still get this apparent complexification even with zero mutation? Uh so let's let's go into some of the some of the theory of this. By

24:45the end uh we have a replicating entity. It can engage in standard sort of population evolution dynamics. This is the kind of of differential equation that that one generally writes for this sort of thing. It's a very general unsat. Uh this is for you know uh species uh I let's say they're n species. They could be chemical species. They could be biological species whatever. Here's a classic example of of

25:07such an ansat. This is the uh the lotka volta equations for predator and prey which I'm sure many of you are very familiar with. They were co-invented or or invented independently by Alfred Lotka and Vto Volatera near the beginning of the 20th century. This is what the classic lota equations look like. There are two species. There is a prey species and a predator species. And those four terms are uh reproduction,

25:30getting eaten, uh eating to reproduce and background death rate. So uh if you got those four terms, you get these nice oscillatory solutions uh you know between your predators and your prey that arise. Okay. So this is a slightly more general form of those lotka volta equations. There is a linear part which we'll call rx and uh in lotka volta that linear part is diagonal. Uh so you know

25:54the the uh the wolf can't turn into a rabbit, the rabbit can't turn into a wolf. So so the reproduction is diagonal. And then there's also a bilinear term which is the the part where predation, competition and the fact that niches are finite uh gets implemented. So the the the right part is suppressive. The left part makes things grow. The right part makes things uh um squish squish down. Keeps them

26:15finite. But this can't be the whole story of evolution. Why can't it be the whole story of evolution? Well, of course, because it's closed-ended. Uh you know, we only have two species here. It doesn't matter how long you run this damn thing. You're not going to get a third species. Uh and uh and you're not going to change the design space either. uh you can have you know very