  Mathematical models of the real world are simplified representations of
complex systems. A caveat to using mathematical models is that predicted causal
effects and conditional independences may not be robust under model extensions,
limiting applicability of such models. In this work, we consider conditions
under which qualitative model predictions are preserved when two models are
combined. Under mild assumptions, we show how to use the technique of causal
ordering to efficiently assess the robustness of qualitative model predictions.
We also characterize a large class of model extensions that preserve
qualitative model predictions. For dynamical systems at equilibrium, we
demonstrate how novel insights help to select appropriate model extensions and
to reason about the presence of feedback loops. We illustrate our ideas with a
viral infection model with immune responses.
