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  are also plotted. Note that both axes are logarithmic.