Fig 1.
An illustration of the model, showing four local and four global connections of an individual with identity A. Positive feedback is received from connections to individuals with the same identity (solid) and negative feedback from those to dissimilar identities (dashed). Local connections represent externally constrained interactions (geography, workplace, etc.) and may be heterogeneously positive and negative. Global connections represent interactions afforded by technology. These are selected to be positive and are thereby homogenously positive. The magnitude of the feedback is the product of the strength of the identity of both individuals.
Fig 2.
The transition to a dominating identity is illustrated in a simulation where individuals have 3 global and 5 local connections. In each time step, the average strengths of the 4 possible identities are plotted. The simulation is based on a system of N = 200 individuals, and 50,000 individual learning updates are applied. The M = 4 different identities are represented by full to dotted lines in their order of dominance.
Fig 3.
Transitions to one or several dominating identities are shown as a function of the number of global connections (nglob). The plot is based on 50 simulations for each value of nglob, with averages of final strength values plotted in the graph. We use N = 200 individuals and each run is 200,000 time steps, i.e., individual reinforcement learning steps. For each run, the M = 4 different identities are represented by full to dotted lines in their order of dominance. The graph illustrates that, when the local neighborhoods are dominating (smaller number of global connections), only zero or one of the identities develops towards high identity strengths. When connections can be chosen freely (larger number of global connections), a larger number of the identities achieve higher strength values.
Fig 4.
Hysteresis is illustrated by the difference in transition points, between weak and strong identities, when increasing (full line) and decreasing (dashed line), the number of global connections. The panels are based on a model experiment in which we (i) start with 0 global connections, (ii) let the identity dynamics run to an essentially stationary situation and store the strengths of the 4 different identities, and (iii) from this situation the global connections is increased by 1, and the identity dynamics continues, and so on. This is continued up to 8 global connections, after which the procedure is continued, but with a decreasing number of global connections down to 0. The identity strengths are calculated as averages from 50 simulations. The different panels (a-d) show the identity strength for the strongest identity (a) to the weakest identity (d). The full lines show the average strengths when we have an increasing number of global connections, while the dashed lines show the average strengths when going back with decreasing number of connections. As in Fig 3, we see that the more global connections, the more identities may develop to a maximum expression level. It is clearly seen that transitions back to lower expression levels do not occur until significantly lower values of nglob are reached, and for the strongest identity (a) it does not even happen at nglob = 0. The size of the system is N = 200 individuals.