  A mathematical model is identifiable if its parameters can be recovered from
data. Here, we focus on a particular class of model, linear compartmental
models, which are used to represent the transfer of substances in a system. We
analyze what happens to identifiability when operations are performed on a
model, specifically, adding or deleting a leak or an edge. We first consider
the conjecture of Gross et al. that states that removing a leak from an
identifiable model yields a model that is again identifiable. We prove a
special case of this conjecture, and also show that the conjecture is
equivalent to asserting that leak terms do not divide the so-called
singular-locus equation. As for edge terms that do divide this equation, we
conjecture that removing any one of these edges makes the model become
unidentifiable,and then prove a case of this somewhat surprising conjecture.
