  Photometric observations of the spectroscopically confirmed $z\approx 9.1$
galaxy MACS1149-JD1 have indicated the presence of a prominent Balmer break in
its spectral energy distribution, which may be interpreted as due to very large
fluctuations in its past star formation activity. In this paper, we investigate
to what extent contemporary simulations of high-redshift galaxies produce star
formation rate variations sufficiently large to reproduce the observed Balmer
break of MACS1149-JD1. We find that several independent galaxy simulations are
unable to account for Balmer breaks of the inferred size, suggesting that
MACS1149-JD1 either must be a very rare type of object or that our simulations
are missing some key ingredient. We present predictions of spectroscopic Balmer
break strength distributions for $z\approx 7-9$ galaxies that may be tested
through observations with the upcoming James Webb Space Telescope and also
discuss the impact that various assumptions on dust reddening, Lyman continuum
leakage and deviations from a standard stellar initial mass function would have
on the results.
