Graduate School of Information Science, Nara Institute of Science and Technology, Ikoma, Nara 630-0192, Japan.
Graduate School of System Informatics, Kobe University, Nada, Kobe, Hyogo 657-8501, Japan.
Phys Rev E. 2017 May;95(5-1):052404. doi: 10.1103/PhysRevE.95.052404. Epub 2017 May 10.
Many biological populations, such as bacterial colonies, have developed through evolution a protection mechanism, called bet hedging, to increase their probability of survival under stressful environmental fluctuation. In this context, the concept of preadaptation refers to a common type of bet-hedging protection strategy in which a relatively small number of individuals in a population stochastically switch their phenotypes to a dormant metabolic state in which they increase their probability of survival against potential environmental shocks. Hence, if an environmental shock took place at some point in time, preadapted organisms would be better adapted to survive and proliferate once the shock is over. In many biological populations, the mechanisms of preadaptation and proliferation present delays whose influence in the fitness of the population are not well understood. In this paper, we propose a rigorous mathematical framework to analyze the role of delays in both preadaptation and proliferation mechanisms in the survival of biological populations, with an emphasis on bacterial colonies. Our theoretical framework allows us to analytically quantify the average growth rate of a bet-hedging bacterial colony with stochastically delayed reactions with arbitrary precision. We verify the accuracy of the proposed method by numerical simulations and conclude that the growth rate of a bet-hedging population shows a nontrivial dependency on their preadaptation and proliferation delays. Contrary to the current belief, our results show that faster reactions do not, in general, increase the overall fitness of a biological population.
许多生物群体，如细菌菌落，通过进化发展出一种保护机制，称为赌注避险，以增加它们在压力环境波动下的生存概率。在这种情况下，预适应的概念是指一种常见的赌注避险保护策略，其中群体中的少数个体随机地将表型转变为休眠代谢状态，从而增加它们对潜在环境冲击的生存概率。因此，如果在某个时间点发生了环境冲击，预先适应的生物在冲击结束后会更好地适应生存和繁殖。在许多生物群体中，预适应和增殖的机制存在延迟，其对群体适应性的影响尚不清楚。在本文中，我们提出了一个严格的数学框架，以分析延迟在生物群体生存中的预适应和增殖机制中的作用，重点是细菌菌落。我们的理论框架允许我们以任意精度分析定量具有随机延迟反应的赌注避险细菌菌落的平均增长率。我们通过数值模拟验证了所提出方法的准确性，并得出结论，赌注避险群体的增长率与其预适应和增殖延迟存在非平凡的依赖关系。与当前的观点相反，我们的结果表明，一般来说，更快的反应不会增加生物群体的整体适应性。
