Increase in complexity in evolution (questions, answers,

research programme)

Eörs Szathmáry

Collegium Budapest Eötvös University Budapest

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

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)

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

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

Cell count in a nematode

Bell and Mooers, 1997

Organism size and number of cell types (Bell)

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?

Genome size and gene number

Genome size and gene number II

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:

Protein functions

Genes for various functions

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

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)

Number of transcriptional activator families

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

Temporal complexity - yeast

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)

Increase in genetic complexity

(a) duplication and divergence(b) symbiosis(c) epigenesis

Animal phylogeny

* sequenced genomes

Hox gene duplications

ParaHox evolution

Some vertebrate proteins assembled from modules