  Intertwined charge and magnetic fluctuations in high-$T_\text{c}$ copper
oxide superconductors (cuprates) are hypothesized to be a consequence of their
correlated electronic nature. Among other observables, this is apparent in the
doping dependence of incommensurate magnetic order, known as the Yamada
relation (YR). We analyze the Hubbard model to challenge the universality of YR
as a function of interaction strength $U$ through Kotliar-Ruckenstein
slave-boson (SB) mean-field theory and truncated unity functional
renormalization group (TUFRG). While TUFRG tends to lock in to a doping
dependence of the incommensurate magnetic ordering vector obtained for the
perturbative weak-coupling limit, SB not only exhibits an enhanced sensitivity
upon a variation of $U$ from weak to strong coupling, but also shows good
agreement with experimental data. It supports the placement of weakly
hole-doped cuprates in the intermediate-to-strong coupling regime.
