关于亚种进化的一个模型
On a model of evolution of subspecies
摘要：
Ben-Ari和Schinazi（2016）引入了一个随机模型来研究“具有高突变率的病毒样进化群体”。该模型是一个出生和死亡模型，其中出生时的个体要么是$[0,1]$中具有随机适应度参数的突变体，要么是具有均匀概率的现有适应度参数之一;而死亡事件会删除最不适合站点的整个种群。我们改变这一点，以纳入"适者生存“的概念，通过要求一个非突变个体，在出生时，具有根据优先连接机制的适应性，即，它具有适应度$f$，其概率与适应度群体的大小成比例$f$。死亡也只是在最不适合的地方移走一个人。这种优先连接规则导致渐近的幂律行为，与Ben-Ari和Schinazi（2016）获得的指数行为不同。
英文摘要：
Ben-Ari and Schinazi (2016) introduced a stochastic model to study `virus-like evolving population with high mutation rate'. This model is a birth and death model with an individual at birth being either a mutant with a random fitness parameter in $[0,1]$ or having one of the existing fitness parameters with uniform probability; whereas a death event removes the entire population of the least fit site. We change this to incorporate the notion of `survival of the fittest', by requiring that a non-mutant individual, at birth, has a fitness according to a preferential attachment mechanism, i.e., it has a fitness $f$ with a probability proportional to the size of the population of fitness $f$. Also death just removes one individual at the least fit site. This preferential attachment rule leads to a power law behaviour in the asymptotics, unlike the exponential behaviour obtained by Ben-Ari and Schinazi (2016).
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