Understanding the evolution of complexity is an important topic in a wide variety of academic fields. Implications of better understanding complexity include increased knowledge of major evolutionary transitions and the properties of living and technological systems. Genotype-phenotype (G-P) maps are fundamental to evolution, and biologically-oriented G-P maps have been shown to have interesting and often-universal properties that enable evolution by following phenotype-preserving walks in genotype space. Here we use a digital logic gate circuit G-P map where genotypes are represented by circuits and phenotypes by the functions that the circuits compute. We compare two mathematical definitions of circuit and phenotype complexity and show how these definitions relate to other well-known properties of evolution such as redundancy, robustness, and evolvability. Using both Cartesian and Linear genetic programming implementations, we demonstrate that the logic gate circuit shares many universal properties of biologically derived G-P maps, with the exception of the relationship between one method of computing phenotypic evolvability, robustness, and complexity. Due to the inherent structure of the G-P map, including the predominance of rare phenotypes, large interconnected neutral networks, and the high mutational load of low robustness, complex phenotypes are difficult to discover using evolution. We suggest, based on this evidence, that evolving complexity is hard and we discuss computational strategies for genetic-programming-based evolution to successfully find genotypes that map to complex phenotypes in the search space.
翻译:理解复杂性的进化是一系列广泛的学术领域的一个重要议题。 更好地了解复杂性的影响包括增加对重大进化转型和生命及技术系统特性的了解。 Genotype- phenotype(G-P) 地图是进化的基础,而生物导向的G- P 地图则显示具有有趣的和往往普遍的特性,通过在基因型空间中遵循苯类型保护行走而使进化成为可能。 我们在这里使用数字逻辑门路 G-P 地图,其中基因类型代表着电路和图型的进化。 我们比较了电路和书型复杂功能的两个数学定义,并展示了这些定义与演化的其他众所周知的特性,例如冗余性、稳健性和可变性。 我们用卡通和线性基因编程程序的实施,我们用逻辑门路路连接了生物衍生G-P 地图的许多通用特性,而一种计算精度型变异性、坚固性和复杂性等功能之间的关系除外。 我们比较了电路和书型复杂性结构的两种数学定义是如何与变异性图的内在结构,因此,我们使用G- pretraphen 型的精度的变化模型的变化图的精度与高型的变化模型的变化变化图的精度是高的, 的变化模型的变化的变化的变化的变化图状图状图状图状图状图状图状图状图状图状图状图,, 的内, 的内,我们的变的变化到的变的变的变的变化到到的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变和变的变的变的变的变的变的变的变的变的变的变的变的变的变和变的变和变和变的变的变的变和变的变的变的变的变的变的变的变和变的变的变的变的变为的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的