Accepted_test

We explore the dynamics of genetic admixture and expansion, as well as language assimilation, through mathematical-demographic modeling. Our primary goal is to address the population-genetics 'paradox' wherein autosomes and allosomes present markedly different, if not contradictory, pictures of past migrations. We demonstrate that this paradox may find a purely demographic explanation, as single-sex and two-sex reproduction models exhibit markedly distinct dynamics. We illustrate that the three processes—allosomal expansion, autosomal admixture, and language assimilation—occur at significantly different modes, potentially explaining the varied outcomes of these processes upon the completion of ethnogenetic transitions. After developing the formalism for the proposed demographic models, we perform numerical simulations aimed at emulating two scenarios stylised after two empirical populations. Building upon formal results and numerical simulations, we propose several qualitative indicators of modes of social transformation in historical populations. A large disparity between the proportions of invading genome in allosomes and autosomes serves as an indicator of quick admixture, suggesting minimal obstacles to interethnic marriages. Conversely, similar proportions of invading genome in allosomes and autosomes indicate lack of mixed marriages. A limited eventual proportion of invading allosomes suggests quick social assimilation and ethno-genesis, highlighting the rapid integration of immigrant populations into the existing social fabric.