Stem cells are required for tissue maintenance and homeostasis during an organism's lifetime. When dividing, stem cells can either self-renew into stem cells, or their progeny can become progenitor cells that can then differentiate into more specialized cells. Feedback from the differentiated cell population onto regulation of division controls tissue growth and maintains tissue homeostasis. Here I consider how to differentiate between multiple cell lineage models with potential nonlinear feedback terms. I consider the influence of several commonly made assumptions in stem cell models including: (1) whether or not more differentiated progeny can divide, (2) whether or not stem cell death is included, (3) the impact of symmetric and asymmetric stem cell divisions. Including differentiated cell division in the simplified model can lead to emergence of a spurious steady state that may not be biologically realistic, and the parameter region for existence of nontrivial equilibrium, which corresponds to tissue at homeostasis, shrinks rapidly as more feedbacks are added to the model. I consider two potential ways to modify a stem cell lineage model to get rid of this unrealistic steady state: getting rid of differentiated cell division altogether or modifying their division to depend on stem cells. Next, I consider a model for neural stem cells (NSCs) that can be in an actively dividing state or in a quiescent state. The balance between stem cell quiescence and cycling activity determines the rate of neurogenesis. With age, more NSCs enter the quiescent state, while the total number of NSCs decreases. I consider which model variant could best explain the observed decline of neural stem cells seen in experimental data from mice.