In my long post below, Celts to Anglo-Saxons, in light of updated assumptions, I had a “cartoon” demographic model in mind which I attempted to sketch out in words. But sometimes prose isn’t the best in terms of precision, and almost always lacks in economy.
In particular I wanted to emphasize how genes and memes may transmit differently, and, the importance of the steps of going between A to Z in determining the shape of things in the end state. To illustrate more clearly what I have in mind I thought it might be useful to put up a post with my cartoon model in charts and figures.
First, you start out with a large “source” population and a smaller “target” population. Genetically only the migration from the source to the target really has an effect, because the source is so huge that migration from the target is irrelevant. So we’ll be focusing on the impact upon the target of migration both genetically and culturally.
To simplify the model we’ll imagine a character, whether genetic or memetic, where the source and target are absolutely different at t = 0, or generation 1. Also, these are discrete generations, and the population is fixed, so you can presume that it’s at carrying capacity. Migration of the outsiders into the target population from the source means less of the original native population in absolute terms (to be realistic this is bidirectional, so people are leaving the target too, but that’s not our concern here).
There are two time series which illustrate the divergent dynamics on both the genetic and memetic dimensions. In one series you see gradual and continuous migration from the source to the target population over 13 generations. In another there are two generations of massive migration, before and after which there is no migration. For the genetic character, imagine disjoint allele frequencies at generation 1. So at generation 1 the target population is at 100% for allele A, while the source is at 100% for allele B. Therefore migration of from the source to the target results in a decrease in the proportion of allele A, which is what is being measured on the y-axis. For the memetic character, imagine that it’s language. So at generation 1 100% in the target zone speak language A, while everyone in the source zone speak language B. Again, the frequency on the y-axis is of the proportion who speak language A in the target zone.
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