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

机译:基于连续增长规则衡量开发系统的健壮性

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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.
机译:理解复杂结构如何以健壮的方式从局部相互作用中脱颖而出,对于弄清生物和人工系统发展过程的基础机制至关重要。这项研究使用简单的,进化的开发系统研究基因组复杂性对鲁棒性的影响,在该系统中,依次应用细胞自动机(CA)规则以生成细胞的一维模式。该系统采用具有128个不同的最近邻居更新规则的一维二维状态CA。每个发育运行都由单个细胞启动。根据“基因组”中包含的指令,允许每个单元在每个时间步骤采用的单元更新规则在不同时间顺序更改。为了生成用于此分析的一组生产性开发程序,使用了一种遗传算法来选择在固定数量的时间步长后其细胞状态与一组预定目标模式匹配的个体。对于不同大小的基因组重复此操作。通过在模式开发过程中系统地应用单细胞状态扰动,比较了进化和随机化CA模式的鲁棒性。该分析表明,在这些进化的系统中,基因组的大小通过使用相对无偏的一组规则释放系统来释放模式以生成模式,从而对健壮性产生积极影响,这些规则具有非常不同的个体属性。相反,较小的基因组经常被迫依赖复杂的模式规则以生成复杂的模式,从而放大损伤并因此降低其健壮性。另外,模式大小(单元数)被发现是该系统中测得的鲁棒性的主要因素。这是因为由发育扰动引起的累积损害不会随图案大小而变化。结果,增加图案尺寸可减少扰动后的损坏百分比,并提高整体鲁棒性。总之,我们已经表明,模式鲁棒性是单个规则传播和治愈由这种简单CA系统中的环境扰动引起的缺陷的能力的累加效应,并且可能通过增加模式大小和基因组大小而增加。这些结果对我们对生物和人工系统的鲁棒性的理解具有影响。

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