Comparative study between discrete and continuum models for the evolution of competing phenotype-structured cell populations in dynamical environments.
Comparative study between discrete and continuum models for the evolution of competing phenotype-structured cell populations in dynamical environments.
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DOI：
10.1103/physreve.102.042404
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发表时间：
2020-09
期刊：
影响因子：
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通讯作者：
Aleksandra Ardaševa;A. Anderson;R. Gatenby;H. Byrne;P. Maini;T. Lorenzi
中科院分区：
文献类型：
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作者：
Aleksandra Ardaševa;A. Anderson;R. Gatenby;H. Byrne;P. Maini;T. Lorenzi
确定性连续体模型被表述为非局部偏微分方程，用于由表型特征构成的种群的进化动力学，最近已被用来解决有关无性物种适应周期性波动的环境条件的开放性问题。这些模型通常是根据种群规模的现象学假设来定义的，无法捕捉由单个个体进化路径中的随机变异驱动的适应性现象。鉴于这些考虑，在本文中，我们开发了一个基于个体的随机模型，用于两个竞争表型结构细胞群的共同进化，这两个细胞群暴露于随时间变化的营养水平，并以不同的概率经历自发的、可遗传的表型变化。在这里，每个细胞的进化由一组规则描述，这些规则导致表型状态空间上的离散时间分支随机游走，并且营养水平由差分方程控制，其中汇项模拟细胞的营养消耗。我们正式表明，该模型的确定性连续体对应物包含细胞群密度函数的非局部偏微分方程组以及营养物浓度的常微分方程。我们比较基于个体的模型及其连续模拟，重点关注两个模型的预测不同的场景。获得的结果阐明了由于瓶颈效应导致两个种群密度函数的规律性较低和人口随机性更加明显，两个模型之间可能出现显着差异的条件。特别是，在表型变异概率较低的情况下会出现瓶颈效应，并且当两个群体的初始平均表型适应度较低和表型异质性初始水平较小时，瓶颈效应会更加明显。这些效应的出现以及两种建模方法之间的一致性也取决于两个群体的初始比例。作为一个说明性的例子，我们在远处器官转移定植早期阶段的数学模型背景下展示了这些结果的含义。
Deterministic continuum models formulated as nonlocal partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the adaptation of asexual species to periodically fluctuating environmental conditions. These models are usually defined on the basis of population-scale phenomenological assumptions and cannot capture adaptive phenomena that are driven by stochastic variability in the evolutionary paths of single individuals. In light of these considerations, in this paper we develop a stochastic individual-based model for the coevolution of two competing phenotype-structured cell populations that are exposed to time-varying nutrient levels and undergo spontaneous, heritable phenotypic changes with different probabilities. Here, the evolution of every cell is described by a set of rules that result in a discrete-time branching random walk on the space of phenotypic states, and nutrient levels are governed by a difference equation in which a sink term models nutrient consumption by the cells. We formally show that the deterministic continuum counterpart of this model comprises a system of nonlocal partial differential equations for the cell population density functions coupled with an ordinary differential equation for the nutrient concentration. We compare the individual-based model and its continuum analog, focusing on scenarios whereby the predictions of the two models differ. The results obtained clarify the conditions under which significant differences between the two models can emerge due to bottleneck effects that bring about both lower regularity of the density functions of the two populations and more pronounced demographic stochasticity. In particular, bottleneck effects emerge in the presence of lower probabilities of phenotypic variation and are more apparent when the two populations are characterized by lower fitness initial mean phenotypes and smaller initial levels of phenotypic heterogeneity. The emergence of these effects, and thus the agreement between the two modeling approaches, is also dependent on the initial proportions of the two populations. As an illustrative example, we demonstrate the implications of these results in the context of the mathematical modeling of the early stage of metastatic colonization of distant organs.