There isn't a way to validate [Lotka-Volterra-type predator-prey](https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations) models other than that they cycle in a fashion approximating that of observations. A more realistic model may take into account seasonal and climate variations that control populations directly. The following is a recent paper by a wildlife ecologist that has long been working on the thesis that seasonal/tidal cycles play a role (one paper that he wrote on the topic dates to 1977).
> Archibald, H. L. [Relating the 4-year lemming ( Lemmus spp. and Dicrostonyx spp.) population cycle to a 3.8-year lunar cycle and ENSO](https://tspace.library.utoronto.ca/bitstream/1807/97104/1/cjz-2018-0266.pdf). Can. J. Zool. 97, 1054–1063 (2019).
These are his main figures:
This directly agrees with the ENSO model driven by the fortnightly tropical cycle (13.66 days) described in this thread (see the middle right pane in the figure below):
The tidal forcing square wave aligns with the cyclic peak lemming populations. The 3.8 year cycle derives directly from 1/(27-365.242/13.6608) = 3.794 years.
There's also a derivation of Lotka-Volterra in the Azimuth Wiki -- https://www.azimuthproject.org/azimuth/show/Lotka-Volterra+equation
Which model is a better example of Green Math?
EDIT: This is in no way a validation either way but here is another view of the tidal forcing used in the climate index model in comparison to the peak years in lemming population. The dotted lines are a guide to the eye