A Self-Organized Tower of Babel: Diversification through Competition

TL;DR

A minimal evolutionary model is introduced to show how local cooperation and global competition can create a transition to the diversity of communities such as linguistic groups, and provides a simple mechanism for the diversification of culture.

Abstract

We introduce a minimal evolutionary model to show how local cooperation and global competition can create a transition to the diversity of communities such as linguistic groups. By using a lattice model with high-dimensional state agents and evolution under a fitness that depends on an agent's local neighborhood and global dissimilarity, clusters of diverse communities with different fitness are organized by equalizing the finesses on the boundaries, where their numbers and sizes are robust to parameters. We observe successive transitions over quasi-stationary states, as triggered by the emergence of new communities on the boundaries. Our abstract framework provides a simple mechanism for the diversification of culture.

Figures (4)

• Figure 1: (A): Snapshots showing the state of the 2D lattice for varying alignment strength $\alpha$, for $\gamma$=1 $L$=256, $B$=16, $\mu$=0.001. Agents are colored randomly by their language. (B): Phase diagrams for the mean number of clusters Note3 (B1) and the largest cluster size divided by $L^2$ (B2) over $\alpha$ and $L$. We observe $\approx 20$-$30$ clusters, with the largest around $25\%$ of the system size robust to changing parameters, as long as $\alpha>0$ and is before the transition. (C): A schematic diagram of the boundary between two languages. The small rows represent the languages (011 and 100) and their heights represent their fitnesses. The $\alpha$ term of the fitness can be seen to drop, from 4 to 2 for the left language, and from 2 to 1 for the right language. This asymmetric dropoff allows languages with different bulk fitnesses to coexist, as long as their boundary fitnesses are equalized.
• Figure 2: (A): The number of agents speaking a given language in the 2D lattice model, over time. For low $\mu$ ($\mu$=$10^-5$ in the figure), the system appears to stay in mostly 'metastable' states, which can be destabilized in a quick transition. This transition moves the system to a new steady state, where populations remain roughly constant (reminiscent of punctuated equilibria bak1993punctuatedgould1993punctuated). (B): Snapshots of the time evolution, showing the emergence of a new cluster. A mutation (cyan) forms on the boundary of three clusters, which proceeds to expand and 'invade' its neighbors. Mutations in the bulk of a cluster are often unfit due to non-alignment with the neighbors, but cluster boundaries have lower fitness from alignment and thus are more vulnerable. (C): A schematic diagram for new community creation. Although the cyan language (1101) is created as a mutation from the blue (1100) in the top right, it contains 'borrowed' features from the other languages, as that would increase the mutants fitness over one which lacks them (eg: if 1110 was mutated instead, it would have a lower fitness and promptly be eliminated).
• Figure 3: (A): Snapshots of a $L$=256 lattice with $B$=16 at $\alpha$=1.4 ($\gamma$=1), just above the transition point, showing the behavior for increasing mutation rate $\mu$. The homogeneous cluster can be destabilized by increasing $\mu$ (on a log scale for $\mu$), forming clusters that collapse into uncorrelated languages on further increasing $\mu$. (B): A phase diagram for the same parameters over alignment term $\alpha$ and mutation rate $\mu$ showing the number of clusters Note3 observed. While $\alpha$ does not appear to significantly change the number of clusters (similar to \ref{['fig:2D-lattice-raster']}) increasing $\mu$ appears to increase the cluster number. (C): Plots of the number of clusters Note3 (C1) and the size of the largest cluster (C2) as a function of $\mu$. The scaling seems similar, robust to changes in $\alpha/\gamma$, and only weakly dependent on $L$ and $B$ (for $B$, assuming $\mu$ is scaled inversely: See supplement Fig.8,9).
• Figure 4: A plot of the 1D lattice over time, from the same initial condition, for different values of mutation rate $\mu$, for $L$=512, $B$=16. $\mu$=0 has stable boundaries which remain in place. Increasing $\mu$ leads to faster moving boundaries, the emergence of new langauges, and finally a collapse into an unstructured state.