Application of small-world mutation topologies to an Artificial Life system

The mutation networks observed in biological systems have the properties of small-world networks. These properties of short average path length and high transitivity confer a favourable exploration of mutation space. Any evolvable string-based ALife system (for example stringmol, typogenetics, Tierra, or Avida) uses a substitution network either implicitly or explicitly. Current ALife simulations use either regular or random mutations schemes. We have previously discussed the requirement for small-world substitution networks for ALife simulations. In this paper, we explore the effects of rewiring the stringmol mutation lattice on the evolution of a self-replicating molecule. Introduction Mutation is an essential component of any evolvable system, allowing it to explore its fitness landscape and therefore to evolve. The evolutionary dynamics of a system are thus critically dependent upon its mutation strategy. Amino acid substitution matrices (Dayhoff et al., 1978; Henikoff and Henikoff, 1992) give an indication of the likelihood of observing an amino acid substitution in homologous proteins. Ideally, a substitution matrix should allow any token to mutate to any other token relatively easily (thus allowing a rapid exploration of the fitness landscape); whilst simultaneously favouring mutations to tokens of similar function (thus minimising the chance of deleterious mutations). Networks that exhibit these properties of short average path length and high clustering coefficient were described by Watts and Strogatz (Watts and Strogatz, 1998). We have previously demonstrated that biological mutation networks exhibit these small-world properties (Droop and Hickinbotham, 2011). Although biological mutation networks exhibit smallworld properties, ALife simulation mutation schemes do not. The typogenetics (Gwak and Wee, 2007) and Avida (Johnson and Wilke, 2004) systems use essentially random mutation schemes. By contrast, the stringmol (Hickinbotham et al., 2010a,b) and Tierra (Ray, 1991) systems use regular mutation networks. Figure 1 shows the mutation lattices used by the stringmol and Tierra systems. ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● A: stringmol B: Tierra opcode bitflip ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●