Somebody check me here, because I’m better at math than biology.
Let’s says the MRCA of Humans and Pan had 20000 genes. there will be variation in alleles too, but setting that aside for now.
New mutations or alleles enters the diploid population at the mutation rate.
New traits are driven by new allele, OR by new combinations of alleles, is this correct?
If correct, then each new allele has potential to create ~20000 new traits either directly or by interaction with other genes. But since humans and pan are 99% similar I will cut that down to 200 gene that matter. Even then most other gene won’t have any interaction (I think?) so the actual number of potential new traits is much smaller. Let’s say 1 in 10,000.
Of those new traits, most still won’t be beneficial, so I’ll use 1 in 10,000 again.
New mutations or alleles enter the population predictably. and with each new trait the number of new combinations expands combinatorially. At the time 4 new alleles have entered the population there are some 200 choose 4 combinations (~=6.5 million), and dividing by 10,000, twice, gives us an expected ~0.65 beneficial new traits.
With 5 new alleles this gives ~25 new beneficial traits, 8 new alleles give over half a million. I reworked this a few times to be less generous, but combinatorial grown is overwhelming. This still ignores existing variation in the population, or gene interactions with 99% of genes common to the MRCA, which could be huge. I’m certain my numbers are not exactly right, but I don’t think I am exaggerating the combinatorial power of sexual reproduction.
I’m treating traits as completely independent, which can’t be right. Likely there are fewer beneficial traits to be found, but more possible combinations that would allow selection toward these traits (making them easier to find). Not knowing any better, I’ll call that a wash.
edit: “200 choose 4”, not “2000 choose 4”.
