  The phenomenon of multiple stellar populations is exacerbated in massive
globular clusters, with the fraction of first-population (1P) stars a
decreasing function of the cluster present-day mass. We decipher this relation
in far greater detail than has been done so far. We assume (i) a fixed stellar
mass threshold for the formation of second-population (2P) stars, (ii) a
power-law scaling $F_{1P} \propto m_{ecl}^{-1}$ between the mass $m_{ecl}$ of
newly-formed clusters and their 1P-star fraction $F_{1P}$, and (iii) a constant
$F_{1P}$ over time. The $F_{1P}(m_{ecl})$ relation is then evolved up to an age
of 12Gyr for tidal field strengths representative of the entire Galactic halo.
The 12Gyr-old model tracks cover extremely well the present-day distribution of
Galactic globular clusters in (mass,$F_{1P}$) space. The distribution is
curtailed on its top-right side by the scarcity of clusters at large
Galactocentric distances, and on its bottom-left side by the initial scarcity
of very high-mass clusters, and dynamical friction. Given their distinct
dissolution rates, "inner" and "outer" model clusters are offset from each
other, as observed. The locus of Magellanic Clouds clusters in (mass,$F_{1P}$)
space is as expected for intermediate-age clusters evolving in a gentle tidal
field. Given the assumed constancy of $F_{1P}$, we conclude that 2P-stars do
not necessarily form centrally-concentrated. We infer a minimum mass of $4
\cdot 10^5~M_{\odot}$ for multiple-populations clusters at secular evolution
onset. This high-mass threshold severely limits the amount of 2P-stars lost
from evolving clusters, thereby fitting the low 2P-star fraction of the
Galactic halo field.
