On testing structural identifiability by a simple scaling method: relying on scaling symmetries can be misleading

A recent paper (Castro M, de Boer RJ, "Testing structural identifiability by a simple scaling method", PLOS Computational Biology, 2020, 16(11):e1008248) introduces the Scaling Invariance Method (SIM) for analysing structural local identifiability and observability. These two properties define mathematically the possibility of determining the values of the parameters (identifiability) and states (observability) of a dynamic model by observing its output. In this note we warn that SIM considers scaling symmetries as the only possible cause of non-identifiability and non-observability. We show that other types of symmetries can cause the same problems without being detected by SIM, and that in those cases the method may yield a wrong result. Finally, we demonstrate how to analyse structural local identifiability and observability with symbolic computation tools that do not exhibit those issues.