莫兰模型中最古老的等位基因
The Oldest Allele in a Moran Model
AI总结：
研究无限多中性等位基因的莫兰模型，通过特定表示证明平稳时最古老等位基因对应的个体数为马尔可夫过程，还得到其扩散极限。
AI中文摘要：
我们研究了一种具有无限多个中性等位基因的莫兰模型，其中等位基因频率按等位基因的年龄递增顺序记录。利用这种表示，我们证明在平稳状态下，具有最古老等位基因类型的个体数量会作为一个马尔可夫过程演化，即使在最古老等位基因灭绝（并立即被此前第二古老的等位基因取代）的时间段内也是如此。我们还得到了最古老等位基因链的扩散极限。
英文摘要：
We study an infinitely many neutral alleles Moran model where the allelic frequencies are recorded in increasing order of the ages of the alleles. Using this representation, we show that in stationarity the number of individuals with the oldest allelic type evolves as a Markov process, even across times when the oldest allele goes extinct (and is immediately replaced by the formerly second oldest allele). We also find the diffusive limit of the oldest allele chain.
