A mathematical model is identifiable if its parameters can be recovered from data. Here we investigate, for linear compartmental models, whether (local, generic) identifiability is preserved when parts of the model – specifically, inputs, outputs, leaks, and edges – are moved, added, or deleted. Our results are as follows. First, for certain catenary, cycle, and mammillary models, moving or deleting the leak preserves identifiability. Next, for cycle models with up to one leak, moving inputs or outputs preserves identifiability. Thus, every cycle model with up to one leak (and at least one input and at least one output) is identifiable. Next, we give conditions under which adding leaks renders a cycle model unidentifiable. Finally, for certain cycle models with no leaks, adding specific edges again preserves identifiability. Our proofs, which are algebraic and combinatorial in nature, rely on results on elementary symmetric polynomials and the theory of input-output equations for linear compartmental models.

如果可以从数据中恢复其参数，则可以识别数学模型。在这里，我们针对线性分区模型调查，当模型的某些部分——特别是输入、输出、泄漏和边缘——被移动、添加或删除时，是否保留了（局部的、通用的）可识别性。我们的结果如下。首先，对于某些悬链线、循环和乳头模型，移动或删除泄漏保留了可识别性。接下来，对于最多有一次泄漏的循环模型，移动输入或输出可以保持可识别性。因此，具有最多一个泄漏（以及至少一个输入和至少一个输出）的每个循环模型都是可识别的。接下来，我们给出添加泄漏导致循环模型无法识别的条件。最后，对于某些没有泄漏的循环模型，再次添加特定边可以保持可识别性。我们的证明，