Genotype-to-phenotype mappings translate genotypic variations such as mutations into phenotypic changes. Neutrality is the observation that some mutations do not lead to phenotypic changes. Studying the search trajectories in genotypic and phenotypic spaces, especially through neutral mutations, helps us to better understand the progression of evolution and its algorithmic behaviour. In this study, we visualise the search trajectories of a genetic programming system as graph-based models, where nodes are genotypes/phenotypes and edges represent their mutational transitions. We also quantitatively measure the characteristics of phenotypes including their genotypic abundance (the requirement for neutrality) and Kolmogorov complexity. We connect these quantified metrics with search trajectory visualisations, and find that more complex phenotypes are under-represented by fewer genotypes and are harder for evolution to discover. Less complex phenotypes, on the other hand, are over-represented by genotypes, are easier to find, and frequently serve as stepping-stones for evolution.

翻译：基因型到表型的映射将突变等基因型变异转化为表型变化。中性是指某些突变不会导致表型变化的现象。研究基因型和表型空间中的搜索轨迹，尤其是通过中性突变的轨迹，有助于我们更好地理解进化过程及其算法行为。在本研究中，我们将遗传编程系统的搜索轨迹可视化为基于图的模型，其中节点代表基因型/表型，边表示它们的突变转换。我们还定量测量了表型的特征，包括其基因型丰度（中性需求）和科尔莫戈罗夫复杂度。我们将这些量化指标与搜索轨迹可视化相结合，发现更复杂的表型由较少的基因型代表，因此更难被进化发现。相比之下，较不复杂的表型由更多的基因型代表，更容易被发现，并经常作为进化的跳板。