论文标题
马尔可夫分支过程的合并树，具有广义逻辑生长
The coalescent tree of a Markov branching process with generalised logistic growth
论文作者
论文摘要
我们考虑一类密度依赖的分支过程，该过程概括了指数，逻辑和gompertz的增长。人口始于一个人，最初成倍增长，然后随着人口规模朝着承载能力发展而变慢。在人口仍在高等的时期，对固定数量的个体进行了采样，并绘制了固定的个人。我们将抽样时间和同时承载到无穷大，我们证明了融合树与有限的树的融合，这在我们类模型中是普遍的。
We consider a class of density-dependent branching processes which generalises exponential, logistic and Gompertz growth. A population begins with a single individual, grows exponentially initially, and then growth may slow down as the population size moves towards a carrying capacity. At a time while the population is still growing superlinearly, a fixed number of individuals are sampled and their coalescent tree is drawn. Taking the sampling time and carrying capacity simultaneously to infinity, we prove convergence of the coalescent tree to a limiting tree which is in a sense universal over our class of models.
