  The Messinian Salinity Crisis (5.97-5.33 Ma) may be one of the most
significant periods of sea-level change in recent geologic history. During this
period, 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 controversial. 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 -- limit cycles -- which trigger evaporite deposition. Here 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. First, I simplify the model equations and test whether
limit cycles are produced in 64 million unique combinations of model
parameters, finding oscillations in only 0.2 % of all simulations. Next, I
examine the formulation of a critical model equation representing stream
channel slope over the Strait of Gibraltar, concluding that a more realistic
formulation would render sea-level limit cycles improbable, if not impossible,
in the proposed model.
