  Galaxies forming in low-mass halos are thought to be primarily responsible
for reionizing the Universe during the first billion years after the Big Bang.
Yet, these halos are extremely inefficient at forming stars in the nearby
Universe. In this work, we address this apparent tension, and ask whether a
physically motivated model of galaxy formation that reproduces the observed
abundance of faint galaxies in the nearby Universe is also consistent with
available observational constraints on the reionization history. By interfacing
the Santa Cruz semi-analytic model for galaxy formation with an analytic
reionization model, we constructed a computationally efficient pipeline that
connects `ground-level' galaxy formation physics to `top-level'
cosmological-scale observables. Based on photometric properties of the galaxy
populations predicted up to $z=15$, we compute the reionization history of
intergalactic hydrogen. We quantify the three degenerate quantities that
influence the total ionizing photon budget, including the abundance of
galaxies, the intrinsic production rate of ionizing photons, and the LyC escape
fraction. We explore covariances between these quantities using a Markov chain
Monte Carlo method. We find that our locally calibrated model is consistent
with all currently available constraints on the reionization history, under
reasonable assumptions about the LyC escape fraction. We quantify the fraction
of ionizing photons contributed by galaxies of different luminosities and find
that the galaxies expected to be detected in JWST NIRCam wide and deep surveys
are responsible for producing $\sim 40$-$80\%$ of ionizing photons throughout
the EoR. All results presented in this work are available at
https://www.simonsfoundation.org/semi-analytic-forecasts-for-jwst/.
