A continuous-state branching process is the mathematical model for the random evolution of a large population. The genealogical structure the population is represented by a Levy forest, which is uniquely characterized by its height process. The later was constructed by Le Gall and Le Jan (1998) and Duquesne and Le Gall (2002) as a functional of a spectrally positive Levy process. A flow of continuous-state branching processes was constructed in Dawson and Li (2012) as strong solutions to a stochastic equation driven by space-time noises. By a simple variation of the stochastic equation, a more general population model can be constructed by introducing a competition structure through a function called the competition mechanism. For a diffusion model with logistic computation, the genealogical structures were characterized by Le et al. (2013) and Pardoux and Wakolbinger (2011) in terms of a stochastic equation of the corresponding height process. The genealogical forest of the general model with competition was constructed in the recent work of Berestycki et al. (2017+) by pruning the Levy forest according to an intensity identified as a fixed point of certain transformation on the space of all adapted intensities determined by the competition mechanism. In this talk, we present a construction of the corresponding height process in terms of a stochastic integral equation based on a Poisson point measure. This generalizes the results of Le et al. (2013) and Pardoux and Wakolbinger (2011) to general branching mechanisms. The advantage of this construction is that it unifies the treatments for models with or without competition. However, up to now the stochastic equation is established only for the model with a nontrivial diffusion component. This talk is based on a joint work with E. Pardoux (Aix-Marseille) and A. Wakolbinger (Frankfurt).