Appendix S2: Analysis of switch between scenarios 7 & 8 of SYMPHONY model.
The objective of this supplementary analysis is to determine the conditions under which plant
switches from C to N limitation and vice versa. The minimum function of plant
photosynthesis (φph in Eq. 5 in main text of manuscript) determines the relative availabilities
of C (CO2+light) and N (mineral N) and thereby the switch between the two limitations. This
minimum function must be rewritten for each scenario by replacing variables by their
mathematical expressions at steady state. For scenario 7, the following equation determines
whether the system remains in scenario 7 or switches to scenario 8:
∗
𝜑𝑝ℎ
= 𝑀𝑖𝑛 {𝑘𝐶𝑎 ,
with
∗
𝑁 =
𝑒𝑁 ∗
𝛽
𝑘𝐶𝑎
+ 𝑟𝑝 (
𝑚𝑝 +𝑒𝑝 +𝑟𝑝
)}
𝛼(𝐴−𝑠)𝑚𝑝
𝑘𝐶𝑎
)(
−𝛽𝑒𝑝 )
𝑚𝑝 +𝑟𝑝 +𝑒𝑝
𝑠+𝑟−𝐴
𝛼𝑟𝑖𝐴
𝑙+(𝛼𝑠−𝛽(𝑠+𝑟))(𝑠+𝑟−𝐴)
(1)
𝜑𝑖 +(
(2)
For scenario 8, the following equation determines whether the system remains in scenario 8 or
switches to scenario 7:
∗
𝜑𝑝ℎ
= 𝑀𝑖𝑛 {𝑘𝐶𝑎 ,
with
𝑁∗ =
𝑒𝑁 ∗
𝛽
(1 + 𝑚
𝑟𝑝
𝑝 +𝑒𝑝
)}
𝜑𝑖
𝛼(𝐴−𝑠)𝑚𝑝
𝛼𝑟𝑖𝐴
𝑒
)(𝑒𝑝 −
)
𝑙+(𝛼𝑠−𝛽(𝑠+𝑟))(𝑠+𝑟−𝐴)+(
𝑚𝑝 +𝑒𝑝
𝛽(𝑠+𝑟−𝐴)
(3)
(4)
For a given CO2 concentration (Ca), the switch between the two scenarios depends on
the size of mineral N pool (N*) and thereby on parameters controlling ecosystem N balance (N
input, plant N exports and N leaching) (Table 3 in main manuscript). When φi increases,
mineral N also increases and plants tend to become C-limited (scenario 7). In contrast, when
N leaching (l) increases, mineral N decreases and plants tend to become N-limited (scenario
8). The effect of ep on N* is not trivial but we calculated the partial derivate of N* with respect
to ep. The negative value of partial derivative (results not shown) indicates that N* decreases
with export rate. Thus, frequent plant N export may favor plant N limitation (scenario 8).
Note that plants switch to C limitation (scenario 7) when the ecosystem is closed from the
point of view of N fluxes (φi-lN*-βepCp*=0) (results not shown). In a closed ecosystem, the
bank functioning of soil is able to satisfy plant N requirements, explaining plant C limitation.