A point of misunderstanding here, my fault for being unclear. I am STARTING from fixation in the population. My understanding is that new alleles arrive at roughly the mutation rate (all mutations, not just single nucleotide replacement). *Any negative selection has already occurred at the time of fixation, otherwise it wouldn’t be fixed.* Positive selection means it fixes more quickly but is not relevant - I am starting my clock at fixation.

Of course not every recombination results in improved fitness. My point is there are a truly astounding number of possible recombination of allele pairs, allele tripletes, etc., which have the potential to create a new trait.

For example, let’s say that only 200 genes are relevant to the differences between human and pan, ignoring the other 99% of genes. I feel this is being conservative. Now let a single new allele become fixed. It is unlikely to be a beneficial trait all by itself, but consider the potential trait that are allow by recombnination. There are …

200 (200 choose 2) possible allele pairs that may generate a new trait,

19,900 (200 choose 3) allele triplets that may generate a new trait,

1,313,400 (200 choose 4) quadruplets that may generate a new trait,

~6.5 million 5 allele tuples,

~2.5 trillion 6 allele tuples,

and this continues to increase by roughly an order of magnitude for each additional allele for quite a while.

[EDIT *Long after the fact*: I’m off by a step here. The first paring has 200 combinations (200 choose 1) with the new allele. There are 200 choose 2 existing pairs to form triplets with the new allele, 200 choose 3 triplets to form quadruplets, etc… Dan]

Now add a *second new allele* to the population and repeat. I’m willing to allow that more complex traits are less common, but it is undeniable that there are a hell of a lot of them (it’s a simplification to assume a small but equal probability for all). The question becomes, out of all of these possible combinations, what is the probability that no beneficial new traits will arise?

I’m sure you know this math already, but I’ve explained it to others so many times before I made a thread for it. For a convenient rule of thumb, the limiting probability of an event **X** with * probability 1/N and N trials* (here allele combinations), the probability

**X**will occur at least once in

**N**trials is ~0.63 (

*=1-1/e*). If the odds of

**X**are 1 in a million, and there have been a million trials, there is a good chance

**X**has happened already.

Now use whatever fixation rate, replication rate, and population size you like, and apply the proper recombination rate to the probability that *at least one* of those combinations is beneficial.

Thank you for the quote, this also makes my case.

Miscellaneous details:

- A single combination need not arrive at the final configuration of a new trait, it need only get “close enough” for positive selection to act. This will significantly increases the probability of arriving at beneficial traits, but it would be difficulty to calculate.
- Only considering single nucleotide replacement only makes the Sharpshooter Fallacy worse. There are also transposition, which don’t create anything new but may allow new combinations the other 99% of the genome I excluded from my example.