Limits...
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 in the simple Axelrod model plotted against number of connected components in the culture graph of initial conditions for three different schemes to generate initial culture vectors for various initial perturbation probabilities p.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 at the absorbing state is shown on the y axis. F = 100, q = 10, N = 125.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4007089&req=5

f4: Number of cultures at the absorbing state in the simple Axelrod model plotted against number of connected components in the culture graph of initial conditions for three different schemes to generate initial culture vectors for various initial perturbation probabilities p.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 at the absorbing state is shown on the y axis. F = 100, q = 10, N = 125.

Mentions: Fig. 4 shows, for all three schemes in the simple Axelrod model, the number of cultures at the absorbing state against the number of connected components in the initial culture graph. Both neutral evolution and the trivial ultrametric scheme show similar results to real data in the simple model; the most ultrametric data is approximately on the diagonal, with the curve further below the diagonal in the lower triangle as the degree of ultrametricity decreases. Surprisingly, however, prototype evolution shows the most ultrametric curve well above the diagonal in the upper triangle, and the curves for initial data with lower degrees of ultrametricity successively beneath it, with the p = 0.4 curve approximately on the diagonal. As we previously mentioned, this result may seem impossible if we believe that the largest possible number of cultures at the absorbing state is along the diagonal. However (as is evident from this result), given the right distribution of initial culture vectors, curves above the diagonal are indeed possible, even in the simple model. We show how this is possible by constructing the simplest case in the Supplementary Information.


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 in the simple Axelrod model plotted against number of connected components in the culture graph of initial conditions for three different schemes to generate initial culture vectors for various initial perturbation probabilities p.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 at the absorbing state is shown on the y axis. F = 100, q = 10, N = 125.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f4: Number of cultures at the absorbing state in the simple Axelrod model plotted against number of connected components in the culture graph of initial conditions for three different schemes to generate initial culture vectors for various initial perturbation probabilities p.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 at the absorbing state is shown on the y axis. F = 100, q = 10, N = 125.
Mentions: Fig. 4 shows, for all three schemes in the simple Axelrod model, the number of cultures at the absorbing state against the number of connected components in the initial culture graph. Both neutral evolution and the trivial ultrametric scheme show similar results to real data in the simple model; the most ultrametric data is approximately on the diagonal, with the curve further below the diagonal in the lower triangle as the degree of ultrametricity decreases. Surprisingly, however, prototype evolution shows the most ultrametric curve well above the diagonal in the upper triangle, and the curves for initial data with lower degrees of ultrametricity successively beneath it, with the p = 0.4 curve approximately on the diagonal. As we previously mentioned, this result may seem impossible if we believe that the largest possible number of cultures at the absorbing state is along the diagonal. However (as is evident from this result), given the right distribution of initial culture vectors, curves above the diagonal are indeed possible, even in the simple model. We show how this is possible by constructing the simplest case in the Supplementary Information.

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.