Table 1:

Recommended best practices when performing TDSA.

1.	Understand the dynamical properties of the model, and choose a reward function that best reflects the objective—which can represent a management goal, or a feature of model predictions that you are trying to understand better by tracing its sensitivity to state or parameter perturbations. A time-discounted reward should be considered if perturbations do not damp out over time (see next point) so that the sensitivities are insensitive to the choice of time horizon.
2.	Verify that the adjoint equations and numerical solutions have been correctly derived and implemented, by comparing the adjoint variables with the sensitivities calculated from the effect of making small perturbations to each state variable at a few time points. Also, plot the changes in the trajectories after those perturbations to see whether the effects of the perturbations grow over time, stay constant, or damp out.
3.	In management settings, think about whether sensitivities (same-size perturbations) or demi-elasticities (perturbations that scale with the state variables) better reflect the cost-benefit tradeoffs of potential actions, especially if the state variables being perturbed vary over several orders of magnitude.
4.	Try to interpret the main qualitative features in the time-dependent sensitivities, and decide whether they are biologically meaningful or instead artifacts of questionable model assumptions — don’t just accept results “because the math says so”.
5.	If a mechanistic interpretation of sensitivities cannot be easily obtained, perform TDSA on variants of the models (e.g. different functional forms) to assess the robustness of the main results under different mathematical assumptions.