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Migration instead of acculturation removes anywhere between-group adaptation.
Without acculturation, migration always eliminates between-group variation, just as in Wright’s original island model and specified by Eq 1. Fig 1 shows time series of FST for low (m = 0.01), typical (m = 0.1) and high (m = 0.3) migration rates. In all cases, the grey a = 0 lines fall to zero. Each trait in each population converges on the mean frequency of that trait across the whole population. Because each sub-population is equally sized, and each trait starts out at unity in one of these s sub-populations, this mean frequency = 1 / s for every trait. This can occur rapidly: for m = 0.01, the perfect between-group structure completely disappears within 300 timesteps, while for m = 0.1 it Los Angeles CA sugar baby disappears within 30, and for m = 0.3 within 10.
Time series showing changes in FST over time for (A) a low migration rate m = 0.01, (B) a typical migration rate m = 0.1, and (C) a high migration rate m = 0.3, at varying strengths of acculturation, a. Other parameters: s = 5, n = 5, r = 0.
Conformist acculturation is also maintain between-classification cultural adaptation.
Fig 1 shows that as conformist acculturation increases in strength, between-group cultural variation is maintained (FST > 0) at equilibrium. When migration is low or moderate then complete acculturation (a = 0, red lines) causes FST to remain at 1, indicating the maintenance of complete between-group cultural variation. Values of a between 0 and 1 generate equilibrium values of FST between 0 and 1, at a level at which migration and acculturation balance out. That is, the decrease in a common trait’s frequency due to migration is equal to the amount by which conformist acculturation increases the common trait’s frequency after migration. At low migration rates, even small amounts of acculturation can restore FST to realistically high values. In Fig 1, when m = 0.01, then a = 0.1, or an extra 10% chance of adopting majority traits per timestep, maintains FST at approximately 0.87, which is already higher than the highest FST found by . An FST of approximately 0.35 can be maintained with just a = 0.02. When m = 0.1, then higher acculturation rates are needed to maintain between-group structure, but an a of just 0.2 is needed to maintain FST at realistic levels of around 0.35. At high migration rates (m = 0.3), the maximum strength of conformist acculturation (a = 1) does not maintain complete between-group cultural variation, and higher values of a are needed to prevent the loss of all between-group cultural variation. Nevertheless, even with such high migration, conformist acculturation can still maintain plausible levels of between-group variation.
Fig 2 shows how the full range of conformist acculturation strength a affects FST, for three different migration rates and four different values of n. Fig 2 confirms that higher FST can be maintained with stronger acculturation (larger a) and lower migration (smaller m). For high migration rates (here, m = 0.1 and m = 0.3), equilibrium FST also increases with n. At low migration rates (m = 0.01), n = 3 is just as effective as larger values of n. This is because the migration rate is so low as to maintain homogeneity in demonstrators no matter how small the sample. When migration is high (m = 0.3), the minimum number of demonstrators that are required for conformity to work, n = 3, fails to maintain any between-group variation at any value of a. This shows that conformist acculturation crucially depends on n as well as a.