  We investigate the evolution of the ionisation parameter of star-forming
galaxies using a high-redshift ($z\sim 1.5$) sample from the FMOS-COSMOS survey
and matched low-redshift samples from the Sloan Digital Sky Survey. By
constructing samples of low-redshift galaxies for which the stellar mass
($\mathrm{M}_{*}$), star formation rate (SFR) and specific star formation rate
(sSFR) are matched to the high-redshift sample we remove the effects of an
evolution in these properties. We also account for the effect of metallicity by
jointly constraining the metallicity and ionisation parameter of each sample.
We find an evolution in the ionisation parameter for main-sequence,
star-forming galaxies and show that this evolution is driven by the evolution
of sSFR. By analysing the matched samples as well as a larger sample of
$z<0.3$, star-forming galaxies we show that high ionisation parameters are
directly linked to high sSFRs and are not simply the byproduct of an evolution
in metallicity. Our results are physically consistent with the definition of
the ionisation parameter, a measure of the hydrogen ionising photon flux
relative to the number density of hydrogen atoms.
