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Evolutionary Growth of Genomesfor the Development and Replication

of Multi-Cellular Organisms with Indirect Encodings

Stefano Nichele and Gunnar Tufte

ICES 2014 - Orlando (USA)December 9-12, 2014

Stefano Nichele, 2014

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Genomes of biological organisms are not fixed in size

They evolved and diverged into different species acquiring new genes and thus having different lengths

• LUA (Last Universal Ancestor) ~ 3.5 / 3.8 billion years ago• Gene duplication: redundant gene with less selection pressure• Larger genome: genetic novelty, potential for innovation• Complexification: incremental elaboration• ~ 38% Homo Sapiens genome due to gene duplication

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Artificial EvoDevo systems often have static size genomes

System designer choice:• Trial & error• Estimation / heuristics

Fixed maximum complexity (vs. open-ended in nature)

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Goal

• Evolutionary growth of genomes (with indirect encodings)– Initialize genomes with a single gene (low dimensionality)– Allow gene duplications (add new degrees of freedom)

• Evo-Devo System based on Cellular Automata– Abstract model of development– Morphogenesis – Replication

• Evolve compact and effective genomes– Compare genome size and success rate– Fully specified genome (complete CA transition tables) vs growing genome

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EvoDevo Mappings

• Direct• Redundant (neutrality)• Indirect (generative/developmental)

– Full specification of representation– von Neumann replicator: 295

• Fixed length (subset)• Variable length• Complexification

– NEAT (Stanley & Miikkulainen): good for evolving modular structures with direct encodings

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CA as EvoDevo systems

• CA can be considered as a developmental system, in which an organism can develop (e.g. grow) from a zygote to a multi-cellular organism (phenotype) according to specific local rules, represented by a genome (genotype).

• The behavior of the CA is represented by the emergent phenotype, which is subject to shape and size modification, along the developmental process.

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Traditional CA dev. model

Example CA with 4 cell states and 5 neighbors:Search space = 4^4^5 = 41024 = ~ 3.23 x 10616

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Previous work

• Evolutionary growth of genomes– CA transition tables– abstract measures of complexity: trajectory / attractor length

• Scalability– Search space, number of cell states, geomerty size (phenotypic resources)

Current:• Different target: phenotypic structures of different complexity• Different mapping: IBD (Instruction-Based Development)

– Not bounded (evolve from one instruction to program)

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Evolutionary Growth

• A genetic algorithm (details in paper) with 4 regulation mechanisms to control gene duplication:– Upper bound, total number of genes– Duplication rate– Optimization time (before new duplication can occur)– Elitism

• Weighted fitness:– 80% actual fitness– 20% innovation parameter

• Rewards larger genomes• New genes most likely fitness-neutral or negative

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CA – IBD (Bidlo and Skarvada 2008, Bidlo and Vasicek 2012)

U

L C R

D

Inst. Code

Op1 Op2

gene

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Benchmark structures

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Development problem

6 1 3 3 3 1 8 3 4 11 4 3 6 3 0 2 4 3 1 1 4 2 1 4 6 4 1 15 4 3 5 2 0 1 2 4 13 4 0 0 2 0

Operands: U = 0, R = 1, D = 2, L = 3, C = 4.Inst. Code

Op1 Op2

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Development - results

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Rep

licat

ion

prob

lem

time

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Replication - results

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Replication of ”French” Flag

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Success rate

Table-based EvolutionSuccess Rate %

Genotype Size (# genes)Max Avg Min StDev

GenerationsAvg. StDev.

A 58 32 32 32 0 1336 2294

B 69 32 32 32 0 2254 2501

C 19 1024 1024 1024 0 5002 3157

D 23 32 32 32 0 2668 2942

Instruction-based Growing EvolutionSuccess Rate %

Genotype Size (# genes)Max Avg Min StDev

GenerationsAvg. StDev.

A 98 31 14.34 5 8.4318 1257 1152

B 98 31 15.28 5 7.0973 3956 1690

C 46 46 19.65 6 9.2236 6424 1922

D 100 13 5.25 4 1.4097 285 108

Table-based EvolutionSuccess Rate %

Genotype Size (# genes)Max Avg Min StDev

GenerationsAvg. StDev.

A 85 32 32 32 0 775 1393

C 8 1024 1024 1024 0 4331 3576

D 1 32 32 32 0 8259 0

E 0 1024 1024 1024 0 - -

Instruction-based Growing EvolutionSuccess Rate %

Genotype Size (# genes)Max Avg Min StDev

GenerationsAvg. StDev.

A 100 7 2.93 2 1.1742 39.7 19.6

C 100 6 2.84 2 1.1166 39.6 22.3

D 100 8 3.06 2 1.2128 41.8 20.5

E 100 5 1.38 1 0.8012 9.4 10.7

Development (avg. 100 runs) Replication (avg. 100 runs)

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Conclusion

• Evolutionary growth of genome• Initialize with single gene, allow duplication and

speciation (regulation mechanisms)• Traditional CA mapping vs instruction based

development (unbounded)• Development and replication problems• Compact and effective genotype solutions (not

designed a priori)• Better success rate

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Future work

• Investigate a major challenge in EvoDevo:– Development of complex morphologies and structures

(potentially at levels of complexity found in nature)

• True complexification– Allow growth of available cell states (unbounded state space)

• Optimization of instructions and instruction set• More benchmarks and tasks (example: circuit design)

• Introduce self-modifying instructions– Allow diversification of programs

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Stefano Nichelewww.nichele.eu