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Complex Genetic Evolution of Self-Replicating Loops Chris Salzberg1,2 Antony Antony3 Hiroki Sayama1 1 University of Electro-Communications, Japan 2 University of Tokyo, Japan 3 University of Amsterdam, the Netherlands [email protected] Summary We re-examined the evolutionary dynamics of self-replicating loops on CA, by using new tools for complete genetic identification and genealogy tracing We found in the loop populations: 1. 2. 3. Diversities in macro-scale morphologies and mutational biases Genetic adaptation Genetic diversification and continuing exploration 2 Background: CA-based Alife Universal constructor (Von Neumann 1966; Codd 1968; Takahashi et al. 1990; Pesavento 1995) Self-replicating loops (Langton 1984; Byl 1989; Reggia et al. 1993) Self-inspecting loops/worms (Ibanez et al. 1995; Morita et al. 1995, 1996) Self-replicating loops with additional capabilities of construction/computation (Tempesti 1995; Perrier et al. 1996; Chou et al. 1998) Spontaneous emergence and evolution of self-replicators (Lohn et al. 1995; Chou et al. 1997; Sayama 1998, 2000, 2003; Salzberg et al. 2003, 2004; Suzuki et al. 2003, 2004) 3 Supposedly Limited Evolutionary Dynamics in CA McMullin (2000): “[SR loop] does not embody anything like a general constructive automaton and therefore has little or no evolutionary potential.” Suzuki et al. (2003): “Though there are many other variations of CA models for self-replication, their evolvability does not differ very much.” 4 Question Did we truly understand what was going on in this seemingly simple dynamics of our CA-based evolutionary systems? We didn’t know we didn’t, until we have developed the formal framework and the sophisticated tools for detailed analysis and visualization for those systems. 5 Subject: Evoloop An evolvable SR loop by Sayama (1999) constructed on nine-state fiveneighbor fully deterministic CA Robust statetransition rules give rise to evolutionary behavior Mutation/selection mechanisms are totally emergent 6 New Tools for Detailed Analysis At every birth, the newborn loop’s genotype & phenotype and its genealogical information is detected and recorded in an event-driven fashion phenotype 8 8 genotype G G G G C G C G T T G CC CC G Each genotype-phenotype pair is indexed in the Species Database 7 Observation (1): Diversities in Macro-Scale Morphologies and Mutational Biases 8 Huge Genetic State-Space Permutation of genes (G, T) and core states (C) under constraints estimates the number of viable genotypes to be 2n-2 n-2 Size n # of species Size n # of species Size n # of species 4 15 9 11,440 14 9,657,700 5 56 10 43,758 15 37,442,160 6 210 11 167,960 16 145,422,675 7 792 12 646,646 17 565,722,720 8 3,003 13 2,496,144 18 2,203,961,430 9 Diversity in Growth Patterns (size-4) 10 Diversity in Growth Patterns (size-6) 11 Diversity in Mutational Biases (size-6) (new result not included in paper) 12 Observation (2): Genetic Adaptation 13 Two Measures of (Possible) Fitness Survival rate (sustainability in competition): — Characterized by an average of relative population ratios of a species after a given period of time in competition with another species Colony density index (growth speed): — Characterized by a quadratic coefficient of a parabola fitted to the population growth curve of each species in an infinite domain 14 Variety and Correlation (size-4) 15 Evolution in vivo (starting from size-8) 16 Evolution Optimizes “Fitness” Evolutionary transition actually observed in the previous slide 17 Observation (3): Genetic Diversification and Continuing Exploration 18 Non-Mutable Subsequences GGGGCGC GCCTCCTG G Certain subsequences are found non-mutable: G{C*}T{C*}TG A long non-mutable sub-sequence injected to ancestor causes a relatively large lower bound of viable sizes upon its descendants, a reduced size-based selection pressure, and a highly biased mutational tendency to larger species Such “GMO” loops show long-lasting evolutionary exploration processes 19 control with long non-mutable subsequences with subsequences + hostile environment (new result not included in paper) 20 Conclusions Huge diversity, non-trivial genetic adaptation and diversification unveiled in the evoloop system Hierarchical emergence demonstrated, where macro-scale evolutionary changes of populations arises from micro-scale interactions between elements much smaller than individual replicators, traversing multiple scales 21 References & Acks Salzberg, C. (2003) Emergent Evolutionary Dynamics of SelfReproducing Cellular Automata. M.Sc. Thesis. Universiteit van Amsterdam, the Netherlands. Salzberg, C., Antony, A. & Sayama, H. Visualizing evolutionary dynamics of self-replicators: A graph-based approach. Artificial Life, in press. Sayama, H. The SDSR loop / Evoloop Homepage. http://complex.hc.uec.ac.jp/sayama/sdsr/ Antony, A. & Salzberg, C. The Artis Project Homepage. http://artis.phenome.org/ This work is supported in part by the Hayao Nakayama Foundation for Science, Technology & Culture, and the International Information Science Foundation, Japan. 22