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Ultrametric distribution of culture vectors in an extended Axelrod model of cultural dissemination.

Stivala A, Robins G, Kashima Y, Kirley M - Sci Rep (2014)

Bottom Line: A recent work used a real-world dataset of opinions as initial conditions, demonstrating the effects of the ultrametric distribution of empirical opinion vectors in promoting cultural diversity in the model.Unlike the simple model, ultrametricity alone is not sufficient to sustain long-term diversity in the extended Axelrod model; rather, the initial conditions must also have sufficiently large variance in intervector distances.Further, we find that a scheme for evolving synthetic opinion vectors from cultural "prototypes" shows the same behaviour as real opinion data in maintaining cultural diversity in the extended model; whereas neutral evolution of cultural vectors does not.

View Article: PubMed Central - PubMed

Affiliation: Melbourne School of Psychological Sciences, The University of Melbourne, 3010, Australia.

ABSTRACT
The Axelrod model of cultural diffusion is an apparently simple model that is capable of complex behaviour. A recent work used a real-world dataset of opinions as initial conditions, demonstrating the effects of the ultrametric distribution of empirical opinion vectors in promoting cultural diversity in the model. Here we quantify the degree of ultrametricity of the initial culture vectors and investigate the effect of varying degrees of ultrametricity on the absorbing state of both a simple and extended model. Unlike the simple model, ultrametricity alone is not sufficient to sustain long-term diversity in the extended Axelrod model; rather, the initial conditions must also have sufficiently large variance in intervector distances. Further, we find that a scheme for evolving synthetic opinion vectors from cultural "prototypes" shows the same behaviour as real opinion data in maintaining cultural diversity in the extended model; whereas neutral evolution of cultural vectors does not.

No MeSH data available.


Number of cultures at the absorbing state (y axis) in the simple Axelrod model versus number of initial connected culture components (x axis) for Eurobarometer and GSS data (N = 600), both real and simulated using random values with the same covariance as the real data.The value of θ is varied to obtain different numbers of initial connected components in the culture graphs along the x axis and the corresponding numbers of cultures (normalised to lie between 0 and 1 by dividing by N) at the absorbing state on the y axis.
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f1: Number of cultures at the absorbing state (y axis) in the simple Axelrod model versus number of initial connected culture components (x axis) for Eurobarometer and GSS data (N = 600), both real and simulated using random values with the same covariance as the real data.The value of θ is varied to obtain different numbers of initial connected components in the culture graphs along the x axis and the corresponding numbers of cultures (normalised to lie between 0 and 1 by dividing by N) at the absorbing state on the y axis.

Mentions: Fig. 1 shows results in the simple Axelrod model, reproducing the results described in Valori et al. (SI Text) [19] that the real data (for both Eurobarometer and GSS, as well as their simulated versions) has the largest number of cultures at the absorbing state for a given number of initially compatible agents. Fig. 2, for the extended Axelrod model, shows that, for a given number of initially compatible agents, real data again has the largest number of cultures at the absorbing state. Although the modified Axelrod model we use, incorporating social ties and geographical migration, with discrete values of cultural traits, is quite different from the simpler model used in Valori et al. [19], our result here is similar in this respect, although the effect is much smaller. We note that the real Eurobarometer data has a larger number of cultures at the absorbing state than the permuted and random data for a given number of initial connected cultural components, even though it has a smaller cophenetic correlation coefficient than the permuted data. It does, however, have a larger standard deviation of intervector distances (Table 1).


Ultrametric distribution of culture vectors in an extended Axelrod model of cultural dissemination.

Stivala A, Robins G, Kashima Y, Kirley M - Sci Rep (2014)

Number of cultures at the absorbing state (y axis) in the simple Axelrod model versus number of initial connected culture components (x axis) for Eurobarometer and GSS data (N = 600), both real and simulated using random values with the same covariance as the real data.The value of θ is varied to obtain different numbers of initial connected components in the culture graphs along the x axis and the corresponding numbers of cultures (normalised to lie between 0 and 1 by dividing by N) at the absorbing state on the y axis.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4007089&req=5

f1: Number of cultures at the absorbing state (y axis) in the simple Axelrod model versus number of initial connected culture components (x axis) for Eurobarometer and GSS data (N = 600), both real and simulated using random values with the same covariance as the real data.The value of θ is varied to obtain different numbers of initial connected components in the culture graphs along the x axis and the corresponding numbers of cultures (normalised to lie between 0 and 1 by dividing by N) at the absorbing state on the y axis.
Mentions: Fig. 1 shows results in the simple Axelrod model, reproducing the results described in Valori et al. (SI Text) [19] that the real data (for both Eurobarometer and GSS, as well as their simulated versions) has the largest number of cultures at the absorbing state for a given number of initially compatible agents. Fig. 2, for the extended Axelrod model, shows that, for a given number of initially compatible agents, real data again has the largest number of cultures at the absorbing state. Although the modified Axelrod model we use, incorporating social ties and geographical migration, with discrete values of cultural traits, is quite different from the simpler model used in Valori et al. [19], our result here is similar in this respect, although the effect is much smaller. We note that the real Eurobarometer data has a larger number of cultures at the absorbing state than the permuted and random data for a given number of initial connected cultural components, even though it has a smaller cophenetic correlation coefficient than the permuted data. It does, however, have a larger standard deviation of intervector distances (Table 1).

Bottom Line: A recent work used a real-world dataset of opinions as initial conditions, demonstrating the effects of the ultrametric distribution of empirical opinion vectors in promoting cultural diversity in the model.Unlike the simple model, ultrametricity alone is not sufficient to sustain long-term diversity in the extended Axelrod model; rather, the initial conditions must also have sufficiently large variance in intervector distances.Further, we find that a scheme for evolving synthetic opinion vectors from cultural "prototypes" shows the same behaviour as real opinion data in maintaining cultural diversity in the extended model; whereas neutral evolution of cultural vectors does not.

View Article: PubMed Central - PubMed

Affiliation: Melbourne School of Psychological Sciences, The University of Melbourne, 3010, Australia.

ABSTRACT
The Axelrod model of cultural diffusion is an apparently simple model that is capable of complex behaviour. A recent work used a real-world dataset of opinions as initial conditions, demonstrating the effects of the ultrametric distribution of empirical opinion vectors in promoting cultural diversity in the model. Here we quantify the degree of ultrametricity of the initial culture vectors and investigate the effect of varying degrees of ultrametricity on the absorbing state of both a simple and extended model. Unlike the simple model, ultrametricity alone is not sufficient to sustain long-term diversity in the extended Axelrod model; rather, the initial conditions must also have sufficiently large variance in intervector distances. Further, we find that a scheme for evolving synthetic opinion vectors from cultural "prototypes" shows the same behaviour as real opinion data in maintaining cultural diversity in the extended model; whereas neutral evolution of cultural vectors does not.

No MeSH data available.