Zhang Pei-ai, Nie Pu-yan, Hu Dai-qiang, Zou Fei-yan
Department of Mathematics, Jinan University, Guangzhou 510632, PR China.
Biosystems. 2007 Nov-Dec;90(3):897-902. doi: 10.1016/j.biosystems.2007.05.008. Epub 2007 Jun 8.
Evolutionary graphs (EGs), in which evolutionary dynamic is arranged on a graph, were initially proposed by Lieberman et al. [Lieberman, E., Hauert, C., Nowak, M.A., 2005. Evolutionary dynamics on graphs. Nature 433, 312-316] in the biological field and many biological phenomena are successfully explained. EGs on two levels (or bi-level EGs), based on some biological phenomena, are considered in this paper. The bi-level EGs are compared with the one-rooted EGs in two cases. One has the identical numbers of the followers, the other with the same numbers of total individuals. Then, some properties of the bi-level EGs are obtained. It is showed that bi-level EGs are more stable, and the bi-level EGs with just two leaders are the most stable, if they have identical followers respectively. The bi-level EGs theory can successfully explain the phenomena of symbiosis in biology.
进化图（EGs）是将进化动态安排在图上，最初由利伯曼等人[利伯曼，E.，豪尔特，C.，诺瓦克，M.A.，2005年。图上的进化动态。《自然》433，312 - 316]在生物学领域提出，并成功解释了许多生物现象。本文基于一些生物现象考虑了两级（或双层EGs）进化图。在两种情况下将双层EGs与单根EGs进行了比较。一种情况是追随者数量相同，另一种情况是个体总数相同。然后，得到了双层EGs的一些性质。结果表明，双层EGs更稳定，并且如果它们分别具有相同数量的追随者，那么恰好有两个领导者的双层EGs是最稳定的。双层EGs理论可以成功解释生物学中的共生现象。
