Fig 1.
Diagram illustrating the workflow for model calibration.
The figures correspond to a simple Generalized Lotka-Volterra model with 2 species in a competition scenario, specifically representing an in-vivo competitive mixture experiment with influenza strains in ferrets [27]. Further details about each phase of the workflow can be found in Methods.
Table 1.
The first row shows abbreviated model names. nx denotes the number of state variables, and the number of parameters. GLV denotes generalized Lotka-Volterra. For the GLV2 model, two subcases were analyzed: competition and coexistence. Further details are provided in S1 Text (Section 7).
Table 2.
FO: Fully Observed, PO: Partially Observed, GI: Globally Identifiable, NGI: Non-Globally Identifiable (i.e. only a subset of parameters are identifiable). Last column indicates which methods were successful. Key: 1 = GenSSI2, 2 = SIAN, 3 = Structural Identifiability. Full details, including the partially observed schemes considered, can be found in S1 Text (Sections 7.5.2, 7.6.2, 7.7.2, 7.8.2, 7.9.2 and 7.10.2).
Fig 2.
Case study GLV3: multistart optimization using the nl2sol local solver.
Top figure shows a histogram of the 35 optima obtained in 200 runs, highlighting the presence of overfitting (OF), underfitting (local optimum, LO), and good fit (GF) solutions. The x-axis shows the of the ratio between the objective function achieved and that of the nominal vector of parameters. Figures below present the nominal system behavior and show examples for the OF, GF, and LO cases, respectively.
Fig 3.
Left figure: An overfitted solution OF that agrees very well with the data but shows oscillatory behavior (and eventually blow-up) after t = 2.0. Center figure: cross-validation of the same OF for different initial conditions, showing very poor predictive value. Right figure: cross-validation of a good fit (GF), showing that due to practical identifiability issues, the agreement with the data is not very good, although ultimately predicts well steady state values at final time.
Fig 4.
Case study MGLV: Sign agreement between estimated and nominal values of the interaction coefficient .
The figures correspond to successful calibrations to data with 0, 5 and 10% noise. Details provided in S1 Text (Section 7.10.4).