  Gas-phase metallicity gradients in galaxies provide important clues to those
galaxies' formation histories. Using SDSS-IV MaNGA data, we previously
demonstrated that gas metallicity gradients vary systematically and
significantly across the galaxy mass--size plane: at stellar masses beyond
approximately $10^{10}$ $\mathrm{M_\odot}$, more extended galaxies display
steeper gradients (in units of $\mathrm{dex/R_e}$) at a given stellar mass.
Here, we set out to develop a physical interpretation of these findings by
examining the ability of local $\sim$kpc-scale relations to predict the
gradient behaviour along the mass--size plane. We find that local stellar mass
surface density, when combined with total stellar mass, is sufficient to
reproduce the overall mass--size trend in a qualitative sense. We further find
that we can improve the predictions by correcting for residual trends relating
to the recent star formation histories of star-forming regions. However, we
find as well that the most extended galaxies display steeper average gradients
than predicted, even after correcting for residual metallicity trends with
other local parameters. From these results, we argue that gas-phase metallicity
gradients can largely be understood in terms of known local relations, but we
also discuss some possible physical causes of discrepant gradients.
