1. 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)

2. 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

3. Why cookbooks? Recipes = cultural replicators (memes)
Recipes in standard algorithmic form
Cookbooks provide judicious (non-random) selection of recipes

4. Ingredients and Recipes Bipartite network

5. Cultural invariance

6. Temporal invariance

7. Complementary Cumulative Distribution

8. Recipe degree distribution

9. Copy-mutate model

10. Fitness selection Fitness fi interval [0,1] Substitute if fj > fi
Recipe with K ingredients fi
Fitness fi interval [0,1]
Substitute if fj > fi fj
Ingredient pool

11. Model results

12. Founder Effect

13. Founder Effect (II)

14. Fitness functions

15. Slow dynamics
1-F(t) = c t-g

16. Conclusions
Bipartite network of ingredients and recipes is scale free with non-trivial exponent a  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

17. Acknowledgments: CNPq

18. Rank Entropy

19. Rank Entropy