Limit Cycle Model of Messinian Salinity Crisis Incorrect and Irreproducible

During the Messinian Salinity Crisis (5.97-5.33 Ma), evaporite deposition throughout the Mediterranean basin records a
series of dramatic environmental changes as flow through the Strait of Gibraltar was restricted. In the first stage of
evaporite deposition, cycles of gypsum appear in shallow basins on the margins of the Mediterranean. The complex
environmental history giving rise to these cycles has been investigated for decades but remains somewhat mysterious.
Notably, whether the evaporites are connected to significant changes in Mediterranean sea level is an open question.
In one proposed model, competition between tectonic uplift and erosion at the Strait of Gibraltar gives rise to self-sustaining
sea-level oscillations, or limit cycles, which trigger evaporite deposition. I show that limit cycles
are not a robust result of the proposed model and discuss how any oscillations produced by this model depend on
an unrealistic formulation of a key model equation. A more realistic formulation would render sea-level limit cycles improbable,
if not impossible, in the proposed model.