  The scatter about the mass-metallicity relation (MZR) has a correlation with
the star formation rate (SFR) of galaxies. The lack of evidence of evolution in
correlated scatter at $z\lesssim2.5$ leads many to refer to the relationship
between mass, metallicity, and SFR as the Fundamental Metallicity Relation
(FMR). Yet, recent high-redshift (z>3) JWST observations have challenged the
fundamental (i.e., redshift-invariant) nature of the FMR. In this work, we show
that the cosmological simulations Illustris, IllustrisTNG, and EAGLE all
predict MZRs that exhibit scatter with a secondary dependence on SFR up to
$z=8$. We introduce the concept of a "strong" FMR, where the strength of
correlated scatter does not evolve with time, and a "weak" FMR, where there is
some time evolution. We find that each simulation analysed has a weak FMR --
there is non-negligible evolution in the strength of the correlation with SFR.
Furthermore, we show that the scatter is reduced an additional ~10-40% at
$z\gtrsim3$ when using a weak FMR, compared to assuming a strong FMR. These
results highlight the importance of avoiding coarse redshift binning when
assessing the FMR.
