考虑一个通过可交换的繁殖动力学进化的单倍体种群，其中所有在时间$t$存活的个体都有一个最近的共同祖先（MRCA），他们生活在时间$A_t$。随着时间的推移，不仅人口会发生变化，而且其谱系也会发生变化：一些家庭将从人口中消失，最终将建立新的MRCA。对于一个时间平稳的情况下，并在无穷总体规模$N$与时间测量的$N$代，即在缩放的人口遗传学，导致费舍尔-赖特扩散和金曼的合并，我们研究的过程$\mathcal A = (A_t)$的跳跃形成的点过程的时间对$(E,B)$时，新的MRCA建立，当他们住。通过将这些粒子对表示为粒子的进入和离开时间，这些粒子的轨迹嵌入Donnelly和Kurtz（1999）的俯视图中，我们可以通过交换论证来证明泊松过程的时间$E$和时间$B$。此外，粒子表示有助于计算MRCA过程的各种特征，例如建立新MRCA时聚结的分布，以及今天过去的MRCA数量的分布。
英文摘要：
Consider a haploid population which has evolved through an exchangeable reproduction dynamics, and in which all individuals alive at time $t$ have a most recent common ancestor (MRCA) who lived at time $A_t$, say. As time goes on, not only the population but also its genealogy evolves: some families will get lost from the population and eventually a new MRCA will be established. For a time-stationary situation and in the limit of infinite population size $N$ with time measured in $N$ generations, i.e. in the scaling of population genetics which leads to Fisher-Wright diffusions and Kingman's coalescent, we study the process $\mathcal A = (A_t)$ whose jumps form the point process of time pairs $(E,B)$ when new MRCAs are established and when they lived. By representing these pairs as the entrance and exit time of particles whose trajectories are embedded in the look-down graph of Donnelly and Kurtz (1999) we can show by exchangeability arguments that the times $E$ as well as the times $B$ from a Poisson process. Furthermore, the particle representation helps to compute various features of the MRCA process, such as the distribution of the coalescent at the instant when a new MRCA is established, and the distribution of the number of MRCAs to come that live in today's past.
Inference with selection, varying population size and evolving population structure: Application of ABC to a forward-backward coalescent process with interactions
Center for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS, INSERM, PSL Research University（跨学科生物学研究中心，法兰西学院，法国国家科学研究中心，法国国家健康与医学研究院，PSL研究大学）；Laboratoire de Probabilités, Statistique et Modélisation (LPSM), Sorbonne Université, CNRS（概率、统计与建模实验室，索邦大学，法国国家科学研究中心）；Institut de Systématique, Évolution, Biodiversité (ISYEB), MNHN, CNRS, Sorbonne Université（系统分类学、进化与生物多样性研究所，法国国家自然历史博物馆，法国国家科学研究中心，索邦大学）
Genetic contribution of advantaged ancestors in the biparental Moran model -- finite selection
Université Paris-Saclay, AgroParisTech, INRAE, UMR MIA Paris-Saclay（巴黎萨克雷大学、农业巴黎技术学院、法国国家农业食品环境研究院）；Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay（巴黎萨克雷大学、法国国家科学研究中心）
Evolving genealogies in cultural evolution, the descendant process, and the number of cultural traits
School of Interdisciplinary Mathematical Sciences（交叉数理科学学院）；Research Center for Integrative Evolutionary Science, SOKENDAI (The Graduate University for Advanced Studies)（前沿科学研究中心，SOKENDAI（advanced studies大学））；Kochi University of Technology（高知工科大学）；Faculty of Technology, Bielefeld University（比勒费尔德大学技术学院）
