By constraining Denisovan admixture as having occurred before the Aboriginal Australian–Papuan divergence, the SFS-based approach results in an admixture estimate of ~4.0% (95% CI 3.3–5.0%, Fig. 4, Supplementary Information section S07), similar to that obtained by D-statistics (~5%, Supplementary Information section S09). The SFS analyses further suggest that Denisovan/Australo-Papuan admixture took place ~44 kya (95% CI 31–50 kya, Supplementary Information section S07), a date that overlaps with an estimate from a more recent study54.
The SFS analysis also provides evidence for a primary Neanderthal admixture event (~2.3%, 95% CI 1.1–3.5%) taking place in the ancestral population of all non-Africans ~60 kya (95% CI 55–84 kya, Fig. 4, Supplementary Information section S07). Although we cannot estimate absolute dates of archaic admixture from the lengths of PDHs and putative Neanderthal-derived haplotypes (PNHs) in our samples, we can obtain a relative date. We found that, for putatively unadmixed Aboriginal Australians and HGDP-Papuans, the average PNH and PDH lengths are 33.8 kb and 37.4 kb, respectively (Extended Data Fig. 3b). These are significantly different from each other (P= 9.65×10−6 using a conservative sign test), and suggest that the time since Neanderthal admixture was about 11% greater than the time since Denisovan admixture, roughly in line with our SFS-based estimates for the Denisovan pulse (31–50 kya, Fig. 4) versus the primary pulse of Neanderthal admixture (55–84 kya).
The SFS analysis also indicates that the main Neanderthal pulse was followed by a further 1.1% (95% CI 0.2–2.7%, Fig. 4, Supplementary Information section S07) pulse of Neanderthal gene flow into the ancestors of Eurasians.
Finally, using our SFS- and haplotype-based approaches, we explored additional models involving complex structure among the archaic populations. We found suggestive evidence that the archaic contribution could be more complex than the model involving the discrete Denisovan and Neanderthal admixture pulses8,9 shown in Fig. 4 (Supplementary Information sections S07, S10).
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