Department of Mathematical Sciences, Chalmers University of Technology, 41296 Gothenburg, Sweden
Department of Mathematical Sciences, University of Gothenburg, 40530 Gothenburg, Sweden.
J R Soc Interface. 2017 Sep;14(134). doi: 10.1098/rsif.2017.0342.
Cancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumour cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the time scales, in particular, in coevolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell-type-specific rates have to be accounted for explicitly.
癌症的进化和发展是由细胞间的相互作用和达尔文选择塑造的。进化博弈论包含了这两个原则，并被提议作为理解肿瘤细胞群体动态的框架。进化动力学的基石是复制子方程，它描述了不同细胞类型相对丰度的变化，并能够预测进化平衡点。通常，复制子方程侧重于相对适应性的差异。我们在这里表明，在所有情况下，这个框架可能都不充分，因为它忽略了种群增长的重要方面。标准的复制子动力学可能会错过达到平衡所需时间的关键差异，因为这个时间也取决于生长但有限的种群中的细胞周转率。随着系统达到稳定流形，达到平衡所需的时间取决于细胞的死亡和出生率。这些速率特别是在生长因子产生者和免费搭乘者的共进化动力学中塑造了时间尺度。只有当出生率和死亡率的大小相当时，复制子动力学才可能是一个合适的框架。否则，在预测达到平衡所需的时间时，不能忽略种群增长的影响，并且必须明确考虑细胞类型特异性的速率。
