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This article studies the stability of solutions of equilibrium equationsarising in so-called resource dependent branching processes. We argue thatthese new models, building on the model already presented by Bruss (1984 a),refined and elaborated in Bruss and Duerinckx (2015) and now extended to allowimmigration, are suitable to cope with specific properties of humanpopulations. Our main interest is here to understand under which conditionsimmigration may lead to an equilibrium. At the same time, we would like toadvertize resource dependent branching processes as possibly the best models tostudy such questions.  The equilibrium equations for the new models we obtain are clear andinformative for several important stability questions. The goal of the study ofthe specific examples we provide is to see where the impact of immigration ismost visible, and in how far increased efforts of integration can cope withdangers of instability. Moreover we discuss the advantages and a weaker pointof our model, and also include a brief look at continuous-state,continuous-time branching processes as an alternative.

Numerical Aspects of Computing Possible Equilibria for Resource Dependent Branching Processes with Immigration