Copy-mutate processes for growth of bipartite networks: an application to

cultural evolution

Osame Kinouchi, Antônio Carlos Roque

Adriano de Jesus Holanda (FFCLRP-USP)

Rosa Wanda Diez Garcia (FMRP)

Pedro Zambianchi (Faculdade Bandeirantes)

Why culinary?

• Physicists like to explain and model interesting statistical patterns (power laws)

• New application of complex networks ideas

• Database relatively easy to construct

• Analogy to biological evolution: growth network algorithm

• Similar to other humans, physicists like to eat

Why cookbooks?

• Recipes = cultural replicators (memes)

• Recipes in standard algorithmic form

• Cookbooks provide judicious (non-random) selection of recipes

Ingredients and RecipesBipartite network

Recipes

Ingredients

Cultural invariance

Temporal invariance

Complementary Cumulative

Distribution

72.1)(:pdf kkp

Recipe degree distribution

Copy-mutate model

Fitness selection

fi

fj

Substitute if fj > fi

Fitness fi interval [0,1]

Ingredient pool

Recipe with K ingredients

Model results

)/exp()( 0rrrA

CrF

Founder Effect

Founder Effect (II)

Fitness functions

fitnessculinary )(

1)(

fitness recipe1

fitness ingredient

)(

1

1

tR

k

k

K

i

ki

k

i

FtR

tF

fK

F

f

Slow dynamics

1F(t) = c t-

Conclusions

• Bipartite network of ingredients and recipes is scale free with non-trivial exponent 1.7 (out of range of generalized Yule process)

• Rank-frequency plot can be fitted by Darwinian copy-mutate process with ingredient fitness

• Model suggests presence of “founder effect” and slow (glassy) dynamics in cultural evolution

Acknowledgments: CNPq

Rank Entropy

)(ln)( rfrfSr

Rank Entropy