Measuring the robustness of a developmental system based on sequential growth rules

摘要

Understanding how complex structures emerge from localised interactions in a robust way is essential to unraveling the mechanisms that underlie developmental processes in both biological and artificial systems. This study investigates the effects of genome complexity on robustness using a simple, evolved developmental system in which cellular automata (CA) rules are applied in sequence in order to generate a 1D pattern of cells. The system employs a 1D two state CA with 128 distinct nearest neighbour update rules. Each developmental run is initiated with a single cell. The cell update rules adopted by every cell at each time-step are allowed to change sequentially at different times according to the instructions contained in a 'genome'. In order to generate a set of productive developmental programs for this analysis, a genetic algorithm was used to select for individuals whose cell states, after a fixed number of time steps, match a set of pre-defined target patterns. This was repeated for genomes of different sizes. The robustness of evolved and randomized CA patterns were compared by systematically applying single cell state perturbations during pattern development. This analysis revealed that in these evolved systems genome size has a positive effect on robustness by freeing the system to generate patterns using a relatively unbiased set of rules, which have very different individual properties. In contrast, smaller genomes are frequently forced to rely on complex patterning rules to generate complex patterns, which amplify damage and hence reduce their robustness. In addition, pattern size (the number of cells) was found to be a major factor in the measured robustness in this system. This is because the cumulative damage induced by developmental perturbations does not scale with pattern size. As a result, increasing pattern size reduces the percentage damage following perturbations and improves overall robustness. In conclusion, we have shown that pattern robustness is an additive effect of the ability of individual rules to propagate and heal defects resulting from environmental perturbation in this simple CA system, and is potentially increased by increasing pattern size and genome size. These results have implications for our understanding of robustness in biological and artificial systems.