Transcript Axtell_CEEL16_Agents,_Biology_and_Complexity

Agents.
Biology
and
Complexity
Rob Axtell
External Faculty Member
Santa Fe Institute
Biology  Economics
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
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Fitness
Selection (lethal)
Reproduction
Darwinian
DNA/genes
Genotype/phenotype
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Utility/profit
Selection (gains/losses)
Cultural transmission
Darwinian/Lamarckian
Rules of behavior/memes
Economic environment
Some Underutilized Models?
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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
black - 0
blue - 1
red -2
yellow - 3
green - 4
cyan - 5
magenta - 6
white -7
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-t
– 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
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Tierra ‘Genetics’ 3: Parasite
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Tierra ‘Genetics’ 4: Hyperparasite
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Tierra Visualization
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Tierra Visualization 2: Parasites
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Tierra Visualization 3: Immunity
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Tierra Visualization 4:
Parasites to Extinction
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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
Biochemical Pathways
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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?
l 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
• l expressions translatable into combinatorics
Fontana and Buss on SelfReproducing 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