Simulation of linguistic change

Simulation of language change

Social Impact Model

• The age of each speaker is divided into five stages labeled 1 to 5.
• The speech community is designed as a 2D toroidal space to avoid "edge effects".
• The distance in this 2D space is interpreted as the social distance between two speakers.
• Speakers are distributed by their age in a homogene (vertical) as well as hierarchical (horizontal) way to represent both family bounds and friends. In General the sequence of speakers in the toroidal space is 5 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 5 (for a population of 400 this would be one "line of speakers").
• Each scenario starts with 100% of the population speaking the same variation. Thus a mutation rate of zero can never produce a language change! Note, that a Mutation rate of 1.0 (=100%) means that language acquisition is at chance.
• The standard settings of the applet presented below are: population size is 100, 50 generations, a mutation rate of 5%, an impact factor of 0.8 for the number of people speaking a certain variation and a Possoin curve distribution of social influence among the speakers with some hyper-influential individuals.
• In this version of the applet the functional bias (see Nettle 1999) is equal for the two competing variations, but the code of ImpSoc is designed for a variable number of competing variations as well as different functional biases for each of them.

Complexity of this Simulation

• The initialization has a complexity of O(3 x N) = O(N)
• Each cycle has a complexity of O(N) + O(2 x N²) = O(N²)
• The program consists of 2 x G cycles.
• A lot of exceptions had to be considered...

Simulation of language change

Social Impact Model

• The age of each speaker is divided into five stages labeled 1 to 5.
• The speech community is designed as a 2D toroidal space to avoid "edge effects".
• The distance in this 2D space is interpreted as the social distance between two speakers.
• Speakers are distributed by their age in a homogene (vertical) as well as hierarchical (horizontal) way to represent both family bounds and friends. In General the sequence of speakers in the toroidal space is 5 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 5 (for a population of 400 this would be one "line of speakers").
• Each scenario starts with 100% of the population speaking the same variation. Thus a mutation rate of zero can never produce a language change! Note, that a Mutation rate of 1.0 (=100%) means that language acquisition is at chance.
• The standard settings of the applet presented below are: population size is 100, 50 generations, a mutation rate of 5%, an impact factor of 0.8 for the number of people speaking a certain variation and a Possoin curve distribution of social influence among the speakers with some hyper-influential individuals.
• In this version of the applet the functional bias (see Nettle 1999) is equal for the two competing variations, but the code of ImpSoc is designed for a variable number of competing variations as well as different functional biases for each of them.

Complexity of this Simulation

• The initialization has a complexity of O(3 x N) = O(N)
• Each cycle has a complexity of O(N) + O(2 x N²) = O(N²)
• The program consists of 2 x G cycles.
• A lot of exceptions had to be considered...

Simulation of language change

Social Impact Model

• The age of each speaker is divided into five stages labeled 1 to 5.
• The speech community is designed as a 2D toroidal space to avoid "edge effects".
• The distance in this 2D space is interpreted as the social distance between two speakers.
• Speakers are distributed by their age in a homogene (vertical) as well as hierarchical (horizontal) way to represent both family bounds and friends. In General the sequence of speakers in the toroidal space is 5 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 5 (for a population of 400 this would be one "line of speakers").
• Each scenario starts with 100% of the population speaking the same variation. Thus a mutation rate of zero can never produce a language change! Note, that a Mutation rate of 1.0 (=100%) means that language acquisition is at chance.
• The standard settings of the applet presented below are: population size is 100, 50 generations, a mutation rate of 5%, an impact factor of 0.8 for the number of people speaking a certain variation and a Possoin curve distribution of social influence among the speakers with some hyper-influential individuals.
• In this version of the applet the functional bias (see Nettle 1999) is equal for the two competing variations, but the code of ImpSoc is designed for a variable number of competing variations as well as different functional biases for each of them.

Complexity of this Simulation

• The initialization has a complexity of O(3 x N) = O(N)
• Each cycle has a complexity of O(N) + O(2 x N²) = O(N²)
• The program consists of 2 x G cycles.
• A lot of exceptions had to be considered...

The formula

1. At a time (=generation) t calculate the variation used by the speaker s1 as follows:
1. Divide the social influence (=status) of any speaker s2 towards s1 by the squared social distance between them (measured by the euclidian distance in the toroidal space).
2. Sum up that weight average social influence (=status/distance^2) of all speakers for each variation.
3. Raise the number of speakers who actually use that variation to the power of a, where a is a constant for the impact of additional speakers of the same variation (see the form below).
4. Multiply the result of 3) with the result of 4).
5. Speaker s1 will now speak that variation with the highest impact on him (4).
2. Repeat until maximum of generations is reached.