论文标题
恒星图上Moran过程的固定概率的连续近似
Continuous approximations for the fixation probability of the Moran processes on star graphs
论文作者
论文摘要
我们考虑了Kaveh等人（2015年）引入的一般版本的死亡（BD）和死亡 - 出生（DB）过程，其中两个恒定的适应性，一种是出生，另一个用于死亡，描述了人口的选择机制。在本文中，我们考虑了更一般的频率依赖性适应性功能（允许任何平滑功能），而不是恒定的健身。对于以星形为单位的大量人群，我们为固定概率提供了近似值，该固定概率是某些ODE（或ODES系统）的解决方案。对于DB情况，我们证明我们的近似值有1/N的误差，其中n是人口的大小。这些近似值是以Chalub和Souza（2016）相同的精神获得的，尽管具有完全不同的技术。一般的BD和DB过程包含特殊情况，即Bd-*和db-*（其中*可以是b或d）在Hadjichrysanthou等人（2011）中描述的过程 - 此类包括文献中使用的许多更新规则的示例。
We consider a generalized version of the birth-death (BD) and death-birth (DB) processes introduced by Kaveh et al (2015), in which two constant fitnesses, one for birth and the other for death, describe the selection mechanism of the population. Rather than constant fitnesses, in this paper we consider more general frequency-dependent fitness functions (allowing any smooth functions) under the weak-selection regime. For a large population structured as a star graph, we provide approximations for the fixation probability which are solutions of certain ODEs (or systems of ODEs). For the DB case, we prove that our approximation has an error of order 1/N, where N is the size of the population. These approximations are obtained in the same spirit of Chalub and Souza (2016) albeit with quite different techniques. The general BD and DB processes contain, as special cases, the BD-* and DB-* (where * can be either B or D) processes described in Hadjichrysanthou et al (2011) -- this class includes many examples of update rules used in the literature.
