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The correlation between the mass of supermassive black holes (SMBHs;$\mathcal{M}_{\rm BH}$) and their host galaxies ($\mathcal{M}_\star$) in thereionization epoch provides valuable constraints on their early growth.High-redshift quasars typically have a $\mathcal{M}_{\rmBH}$/$\mathcal{M}_\star$ ratio significantly elevated in comparison to thelocal value. However, the degree to which this apparent offset is driven byobservational biases is unclear for the most distant quasars. To address thisissue, we model the sample selection and measurement biases for a compilationof 20 quasars at $z\sim6$ with host properties based on ALMA observations. Wefind that the observed distribution of quasars in the $\mathcal{M}_{\rm BH} -\mathcal{M}_\star$ plane can be reproduced by assuming that the underlying SMBHpopulation at $z\sim6$ follows the relationship in the local universe. However,a positive or even a negative evolution in $\mathcal{M}_{\rmBH}$/$\mathcal{M}_\star$ can also explain the data, depending on whether theintrinsic scatter evolves and the strength of various systematic uncertainties.To break these degeneracies, an improvement in the accuracy of massmeasurements and an expansion of the current sample to lower $\mathcal{M}_{\rmBH}$ limits are needed. Furthermore, assuming a radiative efficiency of 0.1 andquasar duty cycles estimated from the active SMBH fraction, significantoutliers in $\mathcal{M}_{\rm BH}$/$\mathcal{M}_\star$ tend to move toward thelocal relation given their instantaneous BH growth rate and star formationrate. This may provide evidence for a self-regulated SMBH-galaxy coevolutionscenario that is in place at $z\sim6$, with AGN feedback being a possibledriver.

On the Connection between Supermassive Black Hole and Galaxy Growth in the Reionization Epoch