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.

本研究通过可视化遗传编程系统的搜索轨迹作为基于图形的模型，探究基因型和表型空间中的搜索轨迹，特别是通过中性突变，帮助我们更好地理解进化的进展和算法行为。同时，通过量化表型特征，包括其基因型丰度和科尔莫戈洛夫复杂性，我们将这些量化指标与搜索轨迹可视化相连接，并发现更复杂的表型由较少的基因型代表，更难以被发现，而较简单的表型则被更多的基因型代表，更容易被发现，并经常被用作进化的垫脚石。