agents. biology and complexity rob axtell external faculty member santa fe institute

Agents.Biology

and Complexity

Rob Axtell

External Faculty Member

Santa Fe Institute

Biology Economics

• Fitness• Selection (lethal)• Reproduction• Darwinian• DNA/genes• Genotype/phenotype

• Utility/profit• Selection (gains/losses)• Cultural transmission• Darwinian/Lamarckian• Rules of behavior/memes• Economic environment

In October 1838, that is, fifteen months after I had begun my systematic inquiry, I happened to read for amusement Malthus on Population, and being well prepared to appreciate the struggle for existence which everywhere goes on, from long-continued observation of the habits of animals and plants, it at once struck me that under these circumstances favourable variations would tend to be preserved, and unfavourable ones to be destroyed. The results of this would be the formation of a new species. Here, then, I had at last got a theory by which to work. Darwin, Autobiography

Some Underutilized Models?

• Sandpiles/self-organized criticality: Per Bak• (Re)production: Langton loops• Punctuated equilibrium: Bak-Sneppen• Parasitism: Tierra/Ray• Endogenous structure and function via

organizations: Buss and Fontana• Endogenous production processes: Padgett• Broken sticks: exponential to power laws

Structure of Self-Reproduction(Self-Replication, Self-Assembly)

• Stanislaw Ulam (graph theorist at Los Alamos, 1940s): cellular spaces

• John von Neumann (1950s): self-reproduction and universal computation (28 states)

• EF Codd (1968): 28 -> 8 states• Arthur Burks (1950-1990s): extensions• Chris Langton (1984)

– Langton loops (2D, 8 state, 5 neighbor, 29 rule, 86 cell loop)

– Birth of ‘artificial life’

Langton’s Loops

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Is It Alive?

• Are these non-carbon (silicon) life forms?

• When we shut down the computer are we ‘killing’ a life form?

• Silicon life analogous to silicon intelligence

• Chomsky: Just semantics since– we say birds fly and airplanes fly– but boats don’t swim although fish and people do

Abstract Model of Evolution

• Interacting ‘species’ on a graph/network– ‘Fitness’ of each species depends on its ‘neighbors’ (e.g., food

chains, symbionts)

– Entire biological world is ‘coupled’ in this way

• Perpetual mutation– Low fitness, low mutation barriers

– High fitness, high mutation barriers

• Once a species evolves it alters the fitness of its neighbors

Bak-Sneppen Model

• Place ‘species’ on a circle– Each has 2 neighbors

• At time zero, give each a random ‘fitness’• Update:

– Select the species with least fitness and give it a new random ‘fitness’

– Alter the fitness of each neighbor by giving each a new random fitness

Bak-Sneppen Dynamics

• No interactions: Each species evolves to arbitrary large fitness

• With interactions:– There emerges a critical fitness, fc, with species usually

between fc and the maximum fitness– fc depends on topology, mutation rate, and so on– Species with fitness below fc are the ones most likely to

mutate, and they take neighboring species with them– Avalanches of sub- fc mutations on all size scales– Power laws of avalanche size: N(s) = s-

– Dynamics look like ‘punctuated equilibria’

Tierra (Ray [1990s])

• Instead of trying to simulate evolution…

• …use computer for actual evolution

• Assembly language includes commands to copy, move, increment and decrement bits

• An organism in Tierra:– sequence of assembly language instructions– used to live and reproduce

Tierra ‘Genetics’

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Tierra ‘Genetics’ 2



Tierra ‘Genetics’ 3: Parasite



Tierra ‘Genetics’ 4: Hyperparasite



Tierra Visualization



Tierra Visualization 2: Parasites



Tierra Visualization 3: Immunity



Tierra Visualization 4:Parasites to Extinction



Possible Uses of Tierra-like Models

Experimentally examine economic and evolutionary processes:– Competitive between firms– Density-dependent population dynamics– Role of ‘parasites’ in altering economic

diversity– Evolutionary arms races/red queen effects– Role of chance in evolutionary success

What Is Life?

• Ancient writers, philosophers, physiologists, physicists (e.g., Schrodinger)

• Manfred Eigen: ability to self-reproduce• Stuart Kauffman: ability of biochemical

system to perform thermodynamic work cycle (e.g., Krebs cycle) + reproduction

• Walter Fontana/Leo Buss:– reproduction + self-maintenance– organizational novelty

Biochemical Pathways(Chart of Intermediary Metabolism)

Biochemical Pathways

Yeast Metabolism

First Abstraction: Hypercycles(Eigen and Schuster)

Ij: macromolecules (e.g., RNA)Ek: catalysts (e.g., enzymes)

Second Abstraction:Artificial Chemistry

• Observation: Self-reproducting systems are possible using the chemical system on Earth (in our Universe?)

• Hypothesis: Self-reproduction is a property of a system of interacting objects (automata)

• Design question: Can we come up with a system of interacting automata, simpler than real chemistry, that permits self-reproduction?

• Ubiquity question: Are such systems likely to be rare or common?

Calculus (Church 1932)

• Syntactical system for writing expressions that denote functions

• Objects are strings constructed according to certain rules of grammar; different grammars, different strings

• Objects can be shown to be either the same or different through reduction (rewrite and substitution) rules into normal form, e.g., 2 + 2 = 3 + 1

• expressions translatable into combinatorics

Fontana and Buss on Self-Reproducing Organizations

1. Start with random strings

2. React them:1. Combine (collide) them

2. Reduce the resultant to normal form

3. Update ‘reactor’ status

4. Repeat from 2

• Can be formalized by the replicator eqns

Level 0: Reproduction

• After a long time a fixed set of objects exists, i.e., production of novelty ceases

• Each of these objects is involved with copying either itself or some other object

• When novel objects are placed in the system they are consumed by the system

• A small stable ecology of objects is present

Level 1: Self-Maintenance

• Limit copying• Self-maintenance means that each object present is

produced by some set of interactions• Such organizations have the self-repair property• There thus exist seeding sets sufficient for

maintenance of the organization• There also exist cores of the organization that are

the minimum seeding sets

Level 2:Organizations of Organizations

• Once independent organizations exist they can be ‘glued’ together:– By simple combination– By ‘glue’ objects

• Functionality of level 2 organizations more than merely that of the components (superposition does not hold)

Ubiquity?

• Essentially all grammars/reduction rules lead to such organizations

• To what extent does this abstraction represent the real world?

Broken Stick Distributions

• Take a linear object of length 1• Break it at a random point, into 2 pieces• Pick up a piece with probability either

– 1/n

– in proportion to its length

• Repeat for a long, long time• The distribution of lengths of the pieces is either:

– a Pareto distribution

– an exponential distribution

Perhaps Relevant To…

Source:Yakovenko

agents. biology and complexity rob axtell external faculty member santa fe institute

Documents

new species

neighboring species

critical fitness

silicon life analogous

new random fitnessalter

mutation rate

silicon intelligencechomsky

extensionschris langton