# Acclimation of leaf nitrogen and canopy NPP to light

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after

Dewar R.C., 1996. The correlation between plant growth and intercepted radiation: an interpretation in terms of optimal plant nitrogen content. Annals of Botany 78, 125-136.

. See also Dewar (1996).

Following Hirose and Werger (1987), leaf nitrogen is assumed to be distributed inside the canopy so as to maximize gross canopy photosynthesis. This assumption considerably simplifies the spatial integration of assimilation over the canopy (Kull \& Jarvis 1995).

The simplification arises because, at each level within the crown, the optimal value of ni(and therefore the light-saturated value of Ai) is found to be proportional to local irradiance. This result enables the canopy integration to be done analytically (Charles-Edwards 1982;Dewar 1996). When this procedure is applied to Equation 11, daily gross crown photosynthesis ${\displaystyle }$ can be expressed as:

${\displaystyle =h\cdot {\frac {\alpha \cdot {\overline {I_{c}}}\cdot {\overline {c_{i}}}\cdot k_{1}\cdot n_{c}}{\alpha \cdot {\overline {I_{c}}}+{\overline {c_{i}}}\cdot k_{1}\cdot n_{c}}}}$ (A1)

where ${\displaystyle {\overline {I_{c}}}}$ is the mean instantaneous irradiance intercepted by the crown (=${\displaystyle }$).

Crown nitrogen content nc} can also be defined as a function of the nitrogen content of plant unshaded leaves (${\displaystyle n_{l}^{0}}$) as:

${\displaystyle n_{c}=n_{l}^{0}\cdot {\frac {\overline {I_{c}}}{\overline {I_{l}^{0}}}}=n_{l}^{0}\cdot {\frac {\overline {I_{c}}}{k\cdot {\overline {I_{0}}}}}}$ (A2)

where ${\displaystyle {\overline {I_{0}}}}$ and ${\displaystyle {\overline {I_{l}^{0}}}}$ are mean instantaneous irradiance reaching the top of the canopy and experienced by an unshaded leaf, respectively, and k} is a light extinction coefficient (of value 0.5 for random leaf angle distribution).

The relationship between maintenance respiration and tissue nitrogen content is known to be approximatively linear (Ryan 1991). Whole-plant maintenance respiration is therefore given by:

${\displaystyle =r\cdot n_{p}}$ (A3)

where np} is total plant nitrogen content and r} is the daily rate of maintenance respiration per unit nitrogen. For simplicity, a common r value is assumed here for all plant parts.

Total plant nitrogen content can be expressed in terms of crown content as:

${\displaystyle n_{p}=\left(1+\lambda _{sw}+\lambda _{r}\right)\cdot n_{c}}$ (A4)

The parameters ${\displaystyle \lambda _{sw}}$ and ${\displaystyle \lambda _{r}}$, which represent the ratio of nitrogen content of sapwood and fine roots, respectively, to the nitrogen content of the crown, will be a precise function of plant allometry (to be further elaborated).

Daily plant growth respiration is proportional to daily NPP}(Thornley \& Johnson 1990):

${\displaystyle =0.25\cdot }$ (A5)

where the factor 0.25 accounts for the biosynthetic efficiency of conversion of sugars to structural dry matter (Johnson 1990). Plant daily net primary production is then given by:

${\displaystyle =0.8\cdot \left(-\right)}$ (A6)

where the factor 0.8 again accounts for biosynthetic efficiency.

In the above model, daily gross canopy photosynthesis ${\displaystyle }$ is a saturating function of canopy nitrogen content (Equation 25), whilst plant maintenance respiration ${\displaystyle }$ increases linearly with nc} (Equation A3). Hence, for a given plant leaf area index, there is an optimal crown (and leaf) nitrogen content (${\displaystyle n_{c}^{opt}}$ ) at which plant net primary production has a maximum value (${\displaystyle }$ ) which is proportional to ${\displaystyle n_{c}^{opt}}$.

The value of ${\displaystyle n_{c}^{opt}}$ for a given crown light interception can be obtained analytically from Equations A1, A3 and A6, with the result:

${\displaystyle n_{c}^{opt}={\overline {I_{c}}}\cdot {\frac {\alpha }{{\overline {c_{i}}}\cdot k_{1}}}\cdot \left({\frac {1}{\lambda }}-1\right)}$ (A7)

where ${\displaystyle \lambda }$ is a dimensionless parameter combination:

${\displaystyle \lambda ={\sqrt {\frac {r\cdot \left(1+\lambda _{sw}+\lambda _{r}\right)}{h\cdot {\overline {c_{i}}}\cdot k_{1}}}}}$ (A8)

which characterizes the relative nitrogen sensitivities of maintenance respiration (numerator) and light-saturated crown photosynthesis (denominator).

Optimal leaf nitrogen content under unshaded conditions (as presented in Equation 13) can be hence derived by combining Equations A2 and A7.

In summary, two optimisation steps have been applied in sequence to obtain optimal crown nitrogen content. In step 1 (Equation A1), the distribution of nitrogen within the crown was optimized for a given total crown content nc, so as to maximize crown gross photosynthesis. This is equivalent to maximizing <NPPc> at fixed nc}. In step 2 (Equation A7), crown nitrogen content nc} was then optimized. The net result is the same as if we had performed an unconstrained optimisation of nitrogen content within the crown.