We revisit a classical McKendrick--von Foerster age structured linear first order PDE (1926) population model from a probabilistic perspective. Specifically, we construct a recursive generation by generation particle system using Poisson processes with time dependent and age dependent intensity functions to model births and deaths. This stochastic framework captures the dynamics of individuals across generations and allows for natural interpretations of survival and reproduction also for small populations and is not that difficult to simulate.  The deterministic McKendrick--von Foerster equation then emerges as a scaled limit of the proposed Poissonian model.