1. Increase in complexity in evolution (questions, answers, research programme) Eörs Szathmáry Collegium BudapestEötvös University Budapest

2. What are we interested in? Genetic basis of organismic complexity What is organismic complexity? Complex morphology? Complex behaviour? How do you quantify complexity for the different cases? An intuitive feel for complexity is widespread

3. Programme complexity S (spatial): storage space needed T (temporal): execution time P (programme): the size of the shortest programme with given input and output, given an agreed language Partly independent Short programmes with complicated dynamics (chaos, cellular automata)

4. Complexity II Kolmogorov: entirely random sequence has the highest complexity Another problem: in general one cannot prove that a given programme is the shortest possible A string is random if the minimal programme producing it is about as long as the string Randomness cannot be contracted

5. The number of cell types in an organism (Bonner) Countable at our present state of knowledge Can be refined with molecular techniques (microarrays) Fits the intuition rather well In the animal world there is a correlation between number of cell types and organism size, hence between size and complexity

6. Cell count in a nematode Bell and Mooers, 1997

7. Organism size and number of cell types (Bell)

8. Does complexity correlate with the number of genes? A few years ago this seemed to be the case There is no a priori reason why this should be so Algorithmic complexity: the length of the minimal programme, written in a specified language, that solves a particular problem Why should tinkered programmes be minimal?

9. Genome size and gene number

10. Genome size and gene number II

11. Gene number is not so good There is a correlation with complexity, but rather weak… Although there is an interesting pattern in the fraction of genes devoted to various functions:

12. Protein functions

13. Genes for various functions

14. Interaction density among genes is better (Szathmáry et al. 2001 Science) Cell types need genes to be switched on and off in an orderly manner Genes regulate other genes Once a gene is set, this state can be passed on to offspring in cell division Epigenetic inheritance (Jablonka & Lamb, 1995) systems

15. Complexity related to network properties of interacting genes? Networks are fashionable, but this by itself does not render them uninteresting Other areas in biology have a vast experience with network properties Food web theory in ecology Connectance = (number of existing links)/(number of possible links)

16. Number of transcriptional activator families

17. Egy gén számos más gént szabályozhat Az X gén terméke egy transzkripciós faktor Ez a fehérje az érintett gének szabályozó régiójához kötődik Aktiválás és gátlás egyaránt lehetséges

18. Temporal complexity - yeast

19. Complexity must be characterized slightly (?) better Delegated complexity: a generative system (genes, chemistry, language) can be launched with a finite number of discrete entities Immune and nervous systems: excellent examples Information carrying capacity of those systems should be quantified and combined Plants do not have a nervous/immune system, they use secondary metabolites, which must be coded explicitly (25,498 genes in Arabidopsis)

20. Increase in genetic complexity (a) duplication and divergence (b) symbiosis (c) epigenesis

21. Animal phylogeny * sequenced genomes

23. Hox gene duplications

24. ParaHox evolution

25. Some vertebrate proteins assembled from modules