Division of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, United Kingdom.
Math Biosci. 2012 Nov;240(1):70-5. doi: 10.1016/j.mbs.2012.06.004. Epub 2012 Jun 28.
We propose a hybrid dynamical system approach to model the evolution of a pathogen that experiences different selective pressures according to a stochastic process. In every environment, the evolution of the pathogen is described by a version of the Fisher-Haldane-Wright equation while the switching between environments follows a Markov jump process. We investigate how the qualitative behavior of a simple single-host deterministic system changes when the stochastic switching process is added. In particular, we study the stability in probability of monomorphic equilibria. We prove that in a "constantly" fluctuating environment, the genotype with the highest mean fitness is asymptotically stable in probability while all others are unstable in probability. However, if the probability of host switching depends on the genotype composition of the population, polymorphism can be stably maintained.
我们提出了一种混合动力系统方法来模拟病原体的进化，该病原体根据随机过程经历不同的选择压力。在每个环境中，病原体的进化都由一个版本的费希尔-霍尔丹-莱特方程来描述，而环境之间的切换则遵循马尔可夫跳跃过程。我们研究了当添加随机切换过程时，简单单宿主确定性系统的定性行为如何变化。特别是，我们研究了单形平衡点的概率稳定性。我们证明，在一个“持续”波动的环境中，具有最高平均适应度的基因型在概率上是渐近稳定的，而所有其他基因型在概率上是不稳定的。然而，如果宿主转换的概率取决于种群的基因型组成，则可以稳定地维持多态性。
