NetLogo Models Library:
This model explores how the properties of language users and the structure of their social networks can affect the course of language change.
In this model, there are two linguistic variants in competition within the social network -- one variant generated by grammar 0 and the other generated by grammar 1. Language users interact with each other based on whom they are connected to in the network. At each iteration, each individual speaks by passing an utterance using either grammar 0 or grammar 1 to the neighbors in the network. Individuals then listen to their neighbors and change their grammars based on what they heard.
The networks in this model are constructed through the process of "preferential attachment" in which individuals enter the network one by one, and prefer to connect to those language users who already have many connections. This leads to the emergence of a few "hubs", or language users who are very well connected; most other language users have very few connections.
There are three different options to control how language users listen and learn from their neighbors, listed in the UPDATE-ALGORITHM chooser. For two of these options, INDIVIDUAL and THRESHOLD, language users can only access one grammar at a time. Those that can only access grammar 1 are white in color, and those that can access only grammar 0 are black. For the third option, REWARD, each grammar is associated with a weight, which determines the language user's probability of accessing that grammar. Because there are only two grammars in competition here, the weights are represented with a single value - the weight of grammar 1. The color of the nodes reflect this probability; the larger the weight of grammar 1, the lighter the node.
INDIVIDUAL: Language users choose one of their neighbors randomly, and adopt that neighbor's grammar.
THRESHOLD: Language users adopt grammar 1 if some proportion of their neighbors is already using grammar 1. This proportion is set with the THRESHOLD-VAL slider. For example, if THRESHOLD-VAL is 0.30, then an individual will adopt grammar 1 if at least 30% of his neighbors have grammar 1.
REWARD: Language users update their probability of using one grammar or the other. In this algorithm, if an individual hears an utterance from grammar 1, the individual's weight of grammar 1 is increased, and they will be more likely to use that grammar in the next iteration. Similarly, hearing an utterance from grammar 0 increases the likelihood of using grammar 0 in the next iteration.
The NUM-NODES slider determines the number of nodes (or individuals) to be included in the network population. PERCENT-GRAMMAR-1 determines the proportion of these language learners who will be initialized to use grammar 1. The remaining nodes will be initialized to use grammar 0.
Press SETUP-EVERYTHING to generate a new network based on NUM-NODES and PERCENT-GRAMMAR-1.
Press GO ONCE to allow all language users to "speak" and "listen" only once, according to the algorithm in the UPDATE-ALGORITHM dropdown menu (see the above section for more about these options). Press GO for the simulation to run continuously; pressing GO again will halt the simulation.
Press LAYOUT to move the nodes around so that the structure of the network easier to see.
When the HIGHLIGHT button is pressed, rolling over a node in the network will highlight the nodes to which it is connected. Additionally, the node's initial and current grammar state will be displayed in the output area.
Press REDISTRIBUTE-GRAMMARS to reassign grammars to all language users, under the same initial condition. For example, if 20% of the nodes were initialized with grammar 1, pressing REDISTRIBUTE-GRAMMARS will assign grammar 1 to a new sample of 20% of the population.
Press RESET-STATES to reinitialize all language users to their original grammars. This allows you to run the model multiple times without generating a new network structure.
The SINK-STATE-1? switch applies only for the INDIVIDUAL and THRESHOLD updating algorithms. If on, once an individual adopts grammar 1, then he can never go back to grammar 0.
The LOGISTIC? switch applies only for the REWARD updating algorithm. If on, an individual's probability of using one of the grammars is pushed to the extremes (closer to 0% or 100%), based on the output of the logistic function. For more details, see https://en.wikipedia.org/wiki/Logistic_function.
The ALPHA slider also applies only for the REWARD updating algorithm, and only when LOGISTIC? is turned on. ALPHA represents a bias in favor of grammar 1. Probabilities are pushed to the extremes, and shifted toward selecting grammar 1. The larger the value of ALPHA, the more likely a language user will speak using grammar 1.
The plot "Mean state of language users in the network" calculates the average weight of grammar 1 for all nodes in the network, at each iteration.
Over time, language users tend to arrive at using just one grammar all of the time. However, they may not all converge to the same grammar. It is possible for sub-groups to emerge, which may be seen as the formation of different dialects.
Under what conditions is it possible to get one grammar to spread through the entire network? Try manipulating PERCENT-GRAMMAR-1, the updating algorithm, and the various other parameters. Does the number of nodes matter?
Whether or not two language users interact with each other is determined by the network structure. How would the model behave if language users were connected by a small-world network rather than a preferential attachment network?
In this model, only two grammars are in competition in the network. Try extending the model to allow competition between three grammars.
The updating algorithm currently has agents updating asynchronously. Currently, the grammar may spread one step or several within one tick, depending on the links. Try implementing synchronous updating.
Regardless of the updating algorithm, language users always start out using one grammar categorically (that is, with a weight of 0 or 1). Edit the model to allow some language users to be initialized to an intermediate weight (e.g., 0.5).
Networks are represented using turtles (nodes) and links. In NetLogo, both turtles and links are agents.
This model was also described in Troutman, Celina; Clark, Brady; and Goldrick, Matthew (2008) "Social networks and intraspeaker variation during periods of language change," University of Pennsylvania Working Papers in Linguistics: Vol. 14: Issue 1, Article 25. http://repository.upenn.edu/pwpl/vol14/iss1/25/
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Copyright 2007 Uri Wilensky.
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