The biological consequences of the classical theory of competition are shown to be at least partly a function of a very special way of interpreting particular constants in simple equations. Ii is shown how altered consequences may be obtained by different, but equally plausible, interpretations of those constants.

Starting from 12,000 years ago in the Middle East, the Neolithic lifestyle spread across Europe via separate continental and Mediterranean routes. Genomes from early European farmers have shown a clear Near Eastern/Anatolian genetic affinity with limited contribution from hunter-gatherers. However, no genomic data are available from modern-day France, where both routes converged, as evidenced by a mosaic cultural pattern. Here, we present genome-wide data from 101 individuals from 12 sites covering today’s France and Germany from the Mesolithic (N = 3) to the Neolithic (N = 98) (7000–3000 BCE). Using the genetic substructure observed in European hunter-gatherers, we characterize diverse patterns of admixture in different regions, consistent with both routes of expansion. Early western European farmers show a higher proportion of distinctly western hunter-gatherer ancestry compared to central/southeastern farmers. Our data highlight the complexity of the biological interactions during the Neolithic expansion by revealing major regional variations.