A simple analytical model for Neanderthal disappearance due to genetic dilution by recurrent small-scale immigrations of modern humans

The disappearance of Neanderthals remains a subject of intense debate, with competing hypotheses attributing their demise to demographic decline, environmental change, competition with Homo sapiens, or genetic assimilation. Here, we present a mathematical model demonstrating that small-scale Homo sapiens immigrations into Neanderthal populations, providing recurrent gene mixing, could have led to almost complete genetic substitution over 10,000-30,000 years. Our model, grounded in neutral species drift, does not require selective advantage or catastrophic events but shows that sustained gene flow from a demographically larger species could account for Neanderthals' genetic absorption into modern humans within a time-frame consistent with archaeological evidence. This scenario aligns with growing evidence of interbreeding and genetic introgression through recurrent H. sapiens immigration waves, providing a parsimonious explanation for the observed patterns of Neanderthal ancestry in present-day Eurasian populations. Although other factors may have contributed to the decline of Neanderthals, our results highlight genetic admixture as a possible key mechanism driving their disappearance.