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Cultural Drift_Neutral Model

by Hartmut Derler (Submitted: 09/18/2017)

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## WHAT IS IT?

In evolution frequencies of variants in a population change over time. This holds both for biological and cultural phenomena (e.g. names). Similar to genetic variants the number of cultural variants may change in frequency over time, resulting from evolutionary mechanisms like natural selection or genetic drift. This model simulates the classic phenomenon 'random genetic drift', "which describes how the diversity of variants evolve when the dominant process is one of random copying" (Bentley et al. 2004, p. 1443). Such a model is also known as the 'neutral model' due to the fact that variants are neutral regarding the success of the individual (see Kimura 1968).

## HOW IT WORKS

N individuals (N = number of individuals) setup with a unique cultural variant v. Per tick each individual randomly copies an individual's variant v from the previous tick. However, there is a certain chance that the individual chooses an alternative variant I (= innovation), which is given by the mutation rate m. Consequently, new unique variants appear and old disappear. Under certain conditions this can lead to a power law distribution of the frequencies of the variants (m < 0.1).

## HOW TO USE IT

Change the parameters I, N and the mutation rate m. Click on 'Setup' to initialize the model. Click on 'go' or 'go once' and check the monitors to see the frequency of the chosen variables per tick and how they change over time. The first monitor reports all variants and their occurrences, the second monitor reports a pair of two values. The first value indicates the occurrence of the second value, which is the respective variant, starting with the variant with the highest occurrence. The plot represents the frequency distribution of the variants. Further statistical processing of the data is necessary to show how well the data fits a power law distribution.

## THINGS TO NOTICE

Change the mutation rate m and the number of individuals N and see how this affects the frequency distribution of the variants. Under which conditions is it more likely that the model produces a power law distribution of the frequency of the variants?

## THINGS TO TRY

See 'How to use it'.

## EXTENDING THE MODEL

## NETLOGO FEATURES

Note that elements are added to the respective list with lput. It doesn't make a difference (also with regarding the performance) whether one uses fput or lput, since the frequency reporter will report the number of occurrences starting from 0 and ending with N + I, irrespectively of the order of the elements in the given list.

## RELATED MODELS

See 'Genetic Drift' in the models library.

## CREDITS AND REFERENCES

Bentley, R., Hahn, M., & Shennan, S. (2004): Random drift and culture change. Proceedings. Biological sciences / The Royal Society, 271(1547), 1443–1450. doi:10.1098/rspb.2004.2746

KIMURA, MOTOO (1983): The neutral theory of molecular evolution. Cambridge [Cambridgeshire], New York: Cambridge University Press.

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