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A mathematical model is identifiable if its parameters can be recovered fromdata. Here, we focus on a particular class of model, linear compartmentalmodels, which are used to represent the transfer of substances in a system. Weanalyze what happens to identifiability when operations are performed on amodel, specifically, adding or deleting a leak or an edge. We first considerthe conjecture of Gross et al. that states that removing a leak from anidentifiable model yields a model that is again identifiable. We prove aspecial case of this conjecture, and also show that the conjecture isequivalent to asserting that leak terms do not divide the so-calledsingular-locus equation. As for edge terms that do divide this equation, weconjecture that removing any one of these edges makes the model becomeunidentifiable,and then prove a case of this somewhat surprising conjecture.

Identifiability of Linear Compartmental Models: The Impact of Removing Leaks and Edges