## Transition time to P limitation on the weathering timescale.

The main determinant of the transition time, if it occurs on the weathering timescale, is the weathering rate. Equation 19 is plotted as a function of the weathering rate, with the rest of the parameters as in Table 1 (solid diagonal line), high dust deposition and parent material P (*α* = 0.05 kg P ha^{−1} y^{−1}, *γ* = 1 kg P ha^{−1}; dashed diagonal line) and low dust deposition and parent material (*α* = 0.001 kg P ha^{−1} y^{−1}, *γ* = 0.2 kg P ha^{−1}; dotted diagonal line). The weathering rate and transition time in Table 1 and Fig. 2 are plotted as an open circle. All parameter sets plotted here yield a transition to P limitation, although many possible parameters sets do not (see Figs. 4, 5). Weathering rates from the Hawai’i (solid vertical line) and Franz Josef (dotted vertical line) chronosequences from [51] are also plotted. Note that both axes are logarithmic.