Identifiability of linear compartmental tree models

A foundational question in the theory of linear compartmental models is how to assess whether a model is identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics of the model. We completely answer this question for those models (with one input and one output) in which the underlying graph is a bidirectional tree. Such models include two families of models appearing often in biological applications: catenary and mammillary models. Our proofs are enabled by two supporting results, which are interesting in their own right. First, we give the first general formula for the coefficients of input-output equations (certain equations that can be used to determine identifiability). Second, we prove that identifiability is preserved when a model is enlarged in specific ways involving adding a new compartment with a bidirected edge to an existing compartment.Comment: 32 page