Ashcroft Peter, Smith Cassandra E R, Garrod Matthew, Galla Tobias
ETH Zürich, Institut für Integrative Biologie, 8092 Zürich, Switzerland.
Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK.
J Theor Biol. 2017 May 7;420:232-240. doi: 10.1016/j.jtbi.2017.03.014. Epub 2017 Mar 18.
Understanding if and how mutants reach fixation in populations is an important question in evolutionary biology. We study the impact of population growth has on the success of mutants. To systematically understand the effects of growth we decouple competition from reproduction; competition follows a birth-death process and is governed by an evolutionary game, while growth is determined by an externally controlled branching rate. In stochastic simulations we find non-monotonic behaviour of the fixation probability of mutants as the speed of growth is varied; the right amount of growth can lead to a higher success rate. These results are observed in both coordination and coexistence game scenarios, and we find that the 'one-third law' for coordination games can break down in the presence of growth. We also propose a simplified description in terms of stochastic differential equations to approximate the individual-based model.
了解突变体是否以及如何在种群中达到固定是进化生物学中的一个重要问题。我们研究种群增长对突变体成功的影响。为了系统地理解增长的影响，我们将竞争与繁殖分离；竞争遵循生死过程，并由一个进化博弈支配，而增长则由外部控制的分支率决定。在随机模拟中，我们发现随着增长速度的变化，突变体固定概率呈现非单调行为；适量的增长可以导致更高的成功率。这些结果在协调和共存博弈场景中都能观察到，并且我们发现协调博弈的“三分之一定律”在有增长的情况下可能会失效。我们还提出了一个基于随机微分方程的简化描述来近似个体模型。
