Interacting particle systems undergoing repeated mutation and selection steps model genetic evolution, and also describe a broad class of sequential Monte Carlo methods. The genealogical tree embedded into the system is important in both applications. Under neutrality, when fitnesses of particles are independent from those of their parents, rescaled genealogies are known to converge to Kingman's coalescent. Recent work has established convergence under non-neutrality, but only for finite-dimensional distributions. We prove weak convergence of non-neutral genealogies on the space of c\`adl\`ag paths under standard assumptions, enabling analysis of the whole genealogical tree.

翻译：经历反复突变与选择步骤的相互作用粒子系统可模拟遗传进化，并描述了一类广泛的序贯蒙特卡洛方法。嵌入系统中的系谱树在这两类应用中均至关重要。在中性条件下，当粒子的适应度与其亲代适应度无关时，重标度系谱已知收敛于金氏并合过程。近期研究已建立了非中性条件下的收敛性，但仅限于有限维分布。我们在标准假设下证明了非中性系谱在càdlàg路径空间上的弱收敛，从而能够分析整个系谱树。