1 Emergent Evolutionary Dynamics of Self-Reproducing Cellular Automata Chris Salzberg

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan2 Credits Research for this project fulfills requirements for the Master of Science Degree - Computational Science Universiteit van Amsterdam Project work conducted jointly with Antony Antony (SCS) Supervised by Dr. Hiroki Sayama (University of Electro-Communications, Japan) Mentor: Prof. Dick van Albada

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan3 Lecture Plan I. Context & History II. Self-reproducing loops, the evoloop III. A closer look a) New method of analysis b) Genetic, phenotypic diversity IV. New discoveries a) Mutation-insensitive regions b) Emergent selection, cyclic genealogy c) The evoloop as quasi-species V. Conclusions

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan4 Context Artificial Life: Artificial Life:  Study of ”life-as-it-could-be” (Langton).  Emphasizes “bottom-up” approach: synthesize using e.g. cellular automata (CA) synthesize using e.g. cellular automata (CA) study collective behaviour emerging from local interactions (complex systems) study collective behaviour emerging from local interactions (complex systems) Artificial self-reproduction: Artificial self-reproduction:  “abstract from the natural self-reproduction problem its logical form” (von Neumann)

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan5 A brief history John von Neumann Conway’s Game of Life 1950s Langton’s SR Loop First international conference on Artificial Life 1989 Chou & Reggia (emergence of replicators) Sayama (SDSR Loop, Evoloop) 1996 Morita & Imai (shape-encoding worms) Suzuki & Ikegami (interaction-basedevolution) 2003 Imai, Hori, Morita (3D self-reproduction)

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan6 Self-reproduction in Biology Traditionally (pre-1950): Traditionally (pre-1950):  Self-reproduction associated with biological systems of carbon-based organisms.  Research limited by variety of natural self-replicators.  Problem of machine self-replication discussed purely in philosophical terms.

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan7 Theory of self-reproduction John von Neumann (1950s): John von Neumann (1950s):  First attempt to formalize self-reproduction: Theory of Self-Reproducing Automata Theory of Self-Reproducing Automata Universal Constructor (UC) Universal Constructor (UC)  Cellular Automata (CA) introduced (with S. Ulam). This seminal work later spawns the field of Artificial Life (late 1980s). This seminal work later spawns the field of Artificial Life (late 1980s).

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan8 The Universal Constructor Universal Constructor (1950s): Universal Constructor (1950s):  29 state 5-neighbour cellular automaton.  Capable of universal construction.  Predicts separation between genetic information and translators/transcribers prior to discovery of DNA/RNA.

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan9 Separation for evolution Separation is necessary for evolution: Separation is necessary for evolution:  Self-description enables exact duplication.  Modified self-description (by noise, etc.) introduces inexact duplication (mutation). P = r-b-r-y C = r-b-y-y

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan10 UC-based replication: Loops Loop structure used to represent a cyclic set of instructions. Loop structure used to represent a cyclic set of instructions.  Langton (SR Loop), Morita & Imai, Chou & Reggia, Sayama, Sipper, Suzuki & Ikegami Self-replication mechanism dependent on structural configuration of self-replicator. Self-replication mechanism dependent on structural configuration of self-replicator.

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan11 The self-reproducing loop Sheath: Outer shell housing gene sequence. Sheath: Outer shell housing gene sequence. Genes: 7s (straight growth) and 4s (turning). Genes: 7s (straight growth) and 4s (turning). Tube: core (1) states within sheath. Tube: core (1) states within sheath. Arm: extensible loop structure for replication. Arm: extensible loop structure for replication. sheath arm tube genes

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan12 The evolving SR loop (evoloop) A new self-reproducing loop by Sayama (1999), based on SR Loop (Langton, 1984): A new self-reproducing loop by Sayama (1999), based on SR Loop (Langton, 1984):  9-state cellular automaton.  5-state (von Neumann) neighbourhood. Modifications to earlier models (SR, SDSR) enable adaptivity leading to evolution. Modifications to earlier models (SR, SDSR) enable adaptivity leading to evolution. Mutation mechanisms are emergent. Mutation mechanisms are emergent.

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan13 Evolutionary dynamics Continuous reproduction leads to high-density loop populations Continuous reproduction leads to high-density loop populations Evolution ends with a homogeneous, single- species population Evolution ends with a homogeneous, single- species population Evolutionary dynamics seem predictable. Evolutionary dynamics seem predictable

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan14 Hidden complexity? Emergent evolutionary dynamics demand sophisticated analysis routines. Emergent evolutionary dynamics demand sophisticated analysis routines. Original methods use size-based identification only. Original methods use size-based identification only. Missing structural detail: Missing structural detail:  gene arrangement and spacing  genealogical ancestry Computational routines highly expensive. Computational routines highly expensive.

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan15 A closer look Loops composed of phenotype and genotype: Loops composed of phenotype and genotype:  Phenotype: inner and outer sheath of loop  Genotype: gene sequence within loop Define loop species by phenotype + genotype. Define loop species by phenotype + genotype. Sufficient information for loop reconstruction. Sufficient information for loop reconstruction. phenotype w l genotype

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan16 Parallels to biology The evoloop is a “messy” system: The evoloop is a “messy” system:  replication is performed explicitly  mutation operator is emergent  interactions (collisions) produce “remnants” of inert sheath states and anomalous dynamic structures Birth and death must be externally defined. Birth and death must be externally defined. remnants dynamicstructures

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan17 Birth detection Umbilical Cord Dissolver (6) phenotypew l genotype

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan18 Scan-layer tracking Loop Layer Scan Layer “footprint” to parent loop umbilical cord dissolver

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan19 Death detection Dissolver state Scan layer I.D.

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan20 Labeling scheme GTC growthturningcore GGGGCGCGTT GCCCCG GGGGCGCGTTGCCCCG

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan21 How many permutations? Constraints for exact (stable) self-replicators: Constraints for exact (stable) self-replicators:  2 T-genes, n G-genes, (n-2) C-genes.  T-genes must have no G-genes between them.  Second T-gene directly followed by G-gene. ‘TG’‘T’ n (n-2) free ‘C’s (n-1) free ‘G’s

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan22 Genetic state-space For a loop of size n, there are different gene permutations resulting in exact self- replicators (stable species). For a loop of size n, there are different gene permutations resulting in exact self- replicators (stable species). Do gene these permutations affect behaviour? Do gene these permutations affect behaviour? (2n-2)n-2 ( ) loop size # of species loop size # of species loop size # of species ,440149,657, , ,442, , ,422, , ,722,720 83,003132,496, ,203,961,43 0

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan23 Phenotypic diversity GCCCCGGGTTGGGGGCGTTGCGCCGGGGTTGCCCCG

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan24 Population dynamics GCCCCGGGTTGGGGGCGTTGCGCCGGGGTTGCCCCG size Gene sequence 6 GCCCCGGGTTGG 7 GCCGGGCGTTGCC G GCCGGGCGTTGCC G 6 GCCGGGTTGCCG GCCGGGTTGCCG 5 GGCGTTGCCG GGCGTTGCCG 4 GGTTGCCG GGTTGCCG 4 GGTTGCGC GGTTGCGC size Gene sequence 6 GGGCGTTGCGCC GGGCGTTGCGCC 4 GCGTTGCG GCGTTGCG 5 GCGCGTTGCG size Gene sequence 6 GGGGTTGCCCCG GGGGTTGCCCCG 5 GGGTTGCCCG GGGTTGCCCG 4 GGTTGCGC GGTTGCGC 5 GGCGTTGCGC GGCGTTGCGC 4 GGTTGCCG GGTTGCCG

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan25 Emergent mutation GCCCCGGGTTGG GCCCCGGGTTGGGCCCCGGGTTGGGCCCC… C GTTGGGCCCCGGGC GTTGGGCCCCGGGCGTTGGGCCCCG… GGGCGTTGGGCC GGGCGTTGGGCCGGGCGTTGGGCCGGGCG… CC GGCCGGGCGTTGCC GGCCGGGCGTTGCCGGCCGGGCGTTGCCG… GCCGGGCGTTGCCG (a) (b) (c) (d) (a) (b) (c) (d)

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan26 Fitness landscape Evolution to both smaller and larger loops occurs. Evolution to both smaller and larger loops occurs. Smaller loops dominate: Smaller loops dominate:  higher reproductive rate  structurally robust Fitness landscape balances size-based fitness with genealogical connectivity. Fitness landscape balances size-based fitness with genealogical connectivity.

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan27 Graph-based genealogy Loop Size

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan28 Mutation insensitive regions Certain gene subsequences are insensitive to mutations: Certain gene subsequences are insensitive to mutations: G{C}T{C}TG These subsequences force a minimum loop size. These subsequences force a minimum loop size. Evolution confined to non-overlapping subsets of genealogy state-space. Evolution confined to non-overlapping subsets of genealogy state-space. GGGGCGC GCCTCCTG G

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan29 New discoveries Long-term genetic diversity: Long-term genetic diversity:  System continues to evolve over millions of iterations.  Selection criteria not exclusively size-based for species with long subsequences. Complex evolutionary dynamics: Complex evolutionary dynamics:  Strong graph-based genealogy.  Genealogical connectivity plays more important role in selection.

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan30 Convergence to minimal loop Size Gene sequence 14 GGGGCGGGGGGG GTCCCCCCCCCCCTG G GGGGCGGGGGGG GTCCCCCCCCCCCTG G 15 GGGGGCGGGGGGG GTCCCCCCCCCCCTG CG GGGGGCGGGGGGG GTCCCCCCCCCCCTG CG 16 GGGGGGCGGGGGGG GTCCCCCCCCCCCTG CCG GGGGGGCGGGGGGG GTCCCCCCCCCCCTG CCG 17 GGGGGGGCGGGGGGG GTCCCCCCCCCCCTG CCCG GGGGGGGCGGGGGGG GTCCCCCCCCCCCTG CCCG 15 GGGGCGGGGGGGGC GTCCCCCCCCCCCTG G 14 GGGGGGGGCGGG GTCCCCCCCCCCCTG G GGGGGGGGCGGG GTCCCCCCCCCCCTG G 15 GGGGGGGGCGGGGC GTCCCCCCCCCCCTG G 13 GGGGGGGGGG GTCCCCCCCCCCCTG G GGGGGGGGGG GTCCCCCCCCCCCTG G

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan31 Cyclic genealogy Size Gene sequence 18 GGGGGGGGGGGGGGG GCCCTCCCCCCCCCCCCCTG G GGGGGGGGGGGGGGG GCCCTCCCCCCCCCCCCCTG G 19 GGGGGGGGGGGGGGGGC GCCCTCCCCCCCCCCCCCTG G GGGGGGGGGGGGGGGGC GCCCTCCCCCCCCCCCCCTG G 19 GGGGGGGGGGGGGGGG GCCCTCCCCCCCCCCCCCTG CG GGGGGGGGGGGGGGGG GCCCTCCCCCCCCCCCCCTG CG 20 GGGGGGGGGGGGGGGGGC GCCCTCCCCCCCCCCCCCTG CG GGGGGGGGGGGGGGGGGC GCCCTCCCCCCCCCCCCCTG CG 20 GGGGGGGGGGGGGGGGG GCCCTCCCCCCCCCCCCCTG CCG GGGGGGGGGGGGGGGGG GCCCTCCCCCCCCCCCCCTG CCG 20 GGGGGGGGGGGGGGGGCGC GCCCTCCCCCCCCCCCCCTG G 20 GGGGGGGGGGGGGGGGG GCCCTCCCCCCCCCCCCCTG CGC GGGGGGGGGGGGGGGGG GCCCTCCCCCCCCCCCCCTG CGC 19 GGGGGGGGGGGGGGGG GCCCTCCCCCCCCCCCCCTG GC GGGGGGGGGGGGGGGG GCCCTCCCCCCCCCCCCCTG GC 20 GGGGGGGGGGGGGGGGGC GCCCTCCCCCCCCCCCCCTG GC GGGGGGGGGGGGGGGGGC GCCCTCCCCCCCCCCCCCTG GC

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan32 Observations Fitness landscape: Fitness landscape:  fitness  reproduction rate  genealogical connectivity (cycles)  self-generated environments (remnants) ? Stable state is reached with dominant species + nearest relatives. Stable state is reached with dominant species + nearest relatives. Similar to “quasi-species” model of Eigen, McCaskill & Schuster (1988). Similar to “quasi-species” model of Eigen, McCaskill & Schuster (1988).

Section Computational Science, Universiteit van Amsterdam University of Electro-Communications, Japan33 Conclusions Simple models may hide their complexity: Simple models may hide their complexity:  graph-based genealogy  mutation-insensitive regions  emergent selection (self-generated env.) Sophisticated observation and interpretation techniques play critical role. Sophisticated observation and interpretation techniques play critical role. Complex evolutionary phenomena need not require a complex model. Complex evolutionary phenomena need not require a complex model.