It now looks as if everyone outside of sub-Saharan African has two or three percent Neanderthal ancestry. Australoids have, in addition, somewhat more Denisovan admixture, while Pygmies and Bushmen have a couple percent admixture from an unknown, very divergent African archaic population. The question is, what kind of effect – if any – might such admixture have had?
The first-cut answer is that anatomically modern humans, the invasive population, picked up adaptive alleles from those archaics. Such a new allele is like a favorable mutation: a single copy with a fitness of s has a 2s probability of fixation. Admixture at the few-percent level would have allowed the expanding mostly-AMH population to pick up most such alleles. The most obvious kind of beneficial archaic allele would be one that conferred some kind of local adaptation. After all, the mostly-AMH population was moving into areas that been occupied by those archaic humans for hundreds of thousands of years: obviously the archaics were well-adapted to local circumstances. Loci involved in defense against regional pathogens ought to have been acquired by the invaders: Parham thinks he has found that kind of adaptive introgression in HLA loci, and he may be right.
It’s also possible that some archaics had some alleles that were better generally, not just in their locale. Even though these archaic humans were competitively inferior, since they were largely replaced, they could have had, indeed almost certainly did have generally superior versions of some genes. Some people find this incomprehensible. For example, they don’t see how a presumably dumber human subspecies could possibly have an allele that could boost human intelligence in AMH. Well, a T-34 was a better tank overall than a PZ-III, but would have been been better yet with a German radio. Adaptive introgression can combine the best of both designs: we see this in agriculture every day.
In the short run, admixture almost certainly increased fitness, at least after natural selection and recombination had winnowed out the advantageous alleles. I say almost certainly because AMH likely picked up any and all archaic driving genes in this assimilation process: some might have been harmful.
In the longer run, the effects are unpredictable. In principle, alleles entering via admixture might change the contours of the adaptive landscape, changing the long-term direction of adaptive evolution. Changes that strongly increase fitness in the short run can dead-end: others that yield smaller fitness advantages in the short run can have a better upgrade path. Natural selection can’t tell and we’re not that good at it ourselves.