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Stochastic population models based on branching processes have progressed from single-type models to multi-type models. Jagers gives a marvellously elegant, succinct and insightful synthesis of this progress. To stimulate further progress, I wish to draw attention to two (of the many) questions that remain open. First, how should a population's dynamics be described when the population has unobserved heterogeneity, that is, when it contains more types than an observer distinguishes? Second, how can one understand the long-run behavior of simple nonlinear models that accommodate genetic and demographic processes? Specifically, how can one determine when the asymptotic or stable composition of a multi-type population does or does not depend on the initial composition of the population?

[The Growth and Stabilization of Populations]: Comment: Partially Observed Markov Chains and Genetic Demography