Identifiability of linear compartmental tree models and a general formula for input-output equations

A foundational question in the theory of linear compartmental models is how to assess whether a model structurally identifiable – that is, parameter values can be inferred from noiseless data directly combinatorics model. Our main result completely answers this for (with one input and output) which underlying graph bidirectional tree; moreover, identifiability such verified visually. Models structure include two families often appearing biological applications: catenary mammillary models. analysis enabled by supporting results, are significant their own right. One gives first general formula coefficients input-output equations (certain used determine identifiability) allows output distinct compartments. In another result, we prove preserved when enlarged altered specific ways involving adding new compartment with bidirected edge an existing compartment.