Ibáñez-Marcelo Esther, Alarcón Tomás
Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, 08193 Bellaterra, Barcelona, Spain; Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, 08028 Barcelona, Spain.
Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, 08193 Bellaterra, Barcelona, Spain; Departament de Matemàtiques, Universitat Atonòma de Barcelona, 08193 Bellaterra, Barcelona, Spain.
J Theor Biol. 2014 Sep 7;356:144-62. doi: 10.1016/j.jtbi.2014.04.014. Epub 2014 Apr 30.
In this paper we formulate a topological definition of the concepts of robustness and evolvability. We start our investigation by formulating a multiscale model of the evolutionary dynamics of a population of cells. Our cells are characterised by a genotype-phenotype map: their chances of survival under selective pressure are determined by their phenotypes, whereas the latter are determined their genotypes. According to our multiscale dynamics, the population dynamics generates the evolution of a genotype-phenotype network. Our representation of the genotype-phenotype network is similar to previously described ones, but has a novel element, namely, our network contains two types of nodes: genotype and phenotype nodes. This network representation allows us to characterise robustness and evolvability in terms of its topological properties: phenotypic robustness by means of the clustering coefficient of the phenotype nodes, and evolvability as the emergence of giant connected component which allows navigation between phenotypes. This topological definition of evolvability allows us to characterise the so-called robustness of evolvability, which is defined in terms of the robustness against attack (i.e. edge removal) of the giant connected component. An investigation of the factors that affect the robustness of evolvability shows that phenotypic robustness and the cryptic genetic variation are key to the integrity of the ability to innovate. These results fit within the framework of a number of models which point out that robustness favours rather than hindering evolvability. We further show that the corresponding phenotype network, defined as the one-component projection of the whole genotype-phenotype network, exhibits the small-world phenomenon, which implies that in this type of evolutionary system the rate of adaptability is enhanced.
在本文中，我们阐述了稳健性和可进化性概念的拓扑定义。我们通过构建一个细胞群体进化动力学的多尺度模型来展开研究。我们的细胞由基因型 - 表型图谱表征：它们在选择压力下的存活机会由其表型决定，而表型又由基因型决定。根据我们的多尺度动力学，群体动力学产生基因型 - 表型网络的进化。我们对基因型 - 表型网络的表示与先前描述的类似，但有一个新颖的元素，即我们的网络包含两种类型的节点：基因型节点和表型节点。这种网络表示使我们能够根据其拓扑性质来表征稳健性和可进化性：通过表型节点的聚类系数来表征表型稳健性，将可进化性表征为允许在表型之间导航的巨大连通分量的出现。这种可进化性的拓扑定义使我们能够表征所谓的可进化性稳健性，它是根据巨大连通分量对攻击（即边移除）的稳健性来定义的。对影响可进化性稳健性的因素的研究表明，表型稳健性和隐性遗传变异是创新能力完整性的关键。这些结果符合许多模型的框架，这些模型指出稳健性有利于而非阻碍可进化性。我们进一步表明，定义为整个基因型 - 表型网络的单组分投影的相应表型网络表现出小世界现象，这意味着在这种类型的进化系统中适应性速率会提高。
