  Our recent work lays out a general framework for inferring information about
the parameters and associated dynamics of a differential equation model from a
discrete set of data points collected from the system being modeled. Rigorous
mathematical results have justified this approach and have identified some
common features that arise for certain classes of integrable models. In this
work we present a thorough numerical investigation that shows that several of
these core features extend to a paradigmatic linear-in-parameters model, the
Lotka-Volterra (LV) system, which we consider in the conservative case as well
as under the addition of terms that perturb the system away from this regime. A
central construct for this analysis is a concise representation of parameter
features in the data space that we call the $P_n$-diagram, which is
particularly useful for visualization of results for low-dimensional (small
$n$) systems. Our work also exposes some new properties related to
non-uniqueness that arise for these LV systems, with non-uniqueness manifesting
as a multi-layered structure in the associated $P_2$-diagrams.
