The talk focuses on positive equilibrium (i.e. time-independent) solutions to mathematical models for the dynamics of populations structured by age and spatial position. This leads to the study of quasilinear parabolic equations with nonlocal and possibly nonlinear initial conditions. We shall see in an abstract functional analytic framework how bifurcation techniques may be combined with optimal parabolic regularity theory to establish the existence of positive solutions. As an application of these results we give a description of the geometry of coexistence states in a two-parameter predator-prey model.