For a generalized continuous-state branching process with non-vanishing diffusion part, finite expectation and a directed (“left-to-right”) interaction, we construct the height process of its forest of genealogical trees. The connection between this height process and the population size process is given by an extension of the second Ray–Knight theorem. This paper generalizes earlier work of the two last authors which was restricted to the case of continuous branching mechanisms. Our approach is different from that of Berestycki et al. (Probab Theory Relat Fields 172:725–788, 2018). There the diffusion part of the population process was allowed to vanish, but the class of interactions was more restricted.

对于具有非消失扩散部分、有限期望和有向（“从左到右”）相互作用的广义连续状态分支过程，我们构建了其系谱树森林的高度过程。这个高度过程和种群大小过程之间的联系是由第二个 Ray-Knight 定理的扩展给出的。本文概括了最后两位作者的早期工作，这些工作仅限于连续分支机制的情况。我们的方法与 Berestycki 等人的方法不同。(Probab Theory Relat Fields 172:725–788, 2018)。在那里，人口过程的扩散部分被允许消失，但相互作用的类别受到更多限制。