Under-canopy lighting can increase whole-plant carbon gain only if the bottom leaves are light-limited (often near or below the compensation point) and still physiologically capable of photosynthesis. If lower leaves are already above the compensation point and other factors (CO2, temperature, stomata, leaf nitrogen) are limiting, extra light produces a smaller benefit.
Step 1: Estimate light reaching bottom leaves (canopy attenuation)
A common first approximation for canopy light transmission uses Beer–Lambert attenuation with cumulative leaf area above the leaf (leaf area index, LAI):
\[ I_{\text{bottom}} = I_0 e^{-k\cdot \text{LAI}}, \]where \(I_0\) is incident light at the top of the canopy (often measured as PPFD), and \(k\) is the light extinction coefficient (depends on leaf angle and clumping).
| Quantity | Symbol | Example value | Meaning |
|---|---|---|---|
| Top-of-canopy light (PPFD) | \(I_0\) | \(1200\ \mu\text{mol}\ \text{m}^{-2}\ \text{s}^{-1}\) | Full sun / high growth light |
| Leaf area index above bottom leaves | \(\text{LAI}\) | \(4.0\) | Dense canopy shading lower leaves |
| Extinction coefficient | \(k\) | \(0.6\) | Moderately planophile canopy |
Compute the transmitted light:
\[ I_{\text{bottom}} = 1200\,e^{-0.6\cdot 4} =1200\,e^{-2.4} \approx 1200\cdot 0.0907 \approx 109\ \mu\text{mol}\ \text{m}^{-2}\ \text{s}^{-1}. \]Step 2: Determine whether bottom leaves have positive net photosynthesis
A simple saturating light-response model for net photosynthesis (gross minus respiration) is:
\[ P_{\text{net}}(I)=\frac{P_{\max}\,I}{K+I}-R_d, \]where \(P_{\max}\) is light-saturated photosynthesis, \(K\) is the half-saturation constant, and \(R_d\) is dark respiration.
| Parameter | Symbol | Example value |
|---|---|---|
| Max photosynthetic rate | \(P_{\max}\) | \(18\ \mu\text{mol CO}_2\ \text{m}^{-2}\ \text{s}^{-1}\) |
| Half-saturation light level | \(K\) | \(300\ \mu\text{mol}\ \text{m}^{-2}\ \text{s}^{-1}\) |
| Dark respiration | \(R_d\) | \(1.5\ \mu\text{mol CO}_2\ \text{m}^{-2}\ \text{s}^{-1}\) |
Step 3: Find the light compensation point
The light compensation point \(I_c\) satisfies \(P_{\text{net}}(I_c)=0\):
\[ 0=\frac{P_{\max}\,I_c}{K+I_c}-R_d \quad\Rightarrow\quad P_{\max}I_c = R_d(K+I_c) \quad\Rightarrow\quad (P_{\max}-R_d)I_c = R_dK. \] \[ I_c=\frac{R_dK}{P_{\max}-R_d} =\frac{(1.5)(300)}{18-1.5} =\frac{450}{16.5} \approx 27.3\ \mu\text{mol}\ \text{m}^{-2}\ \text{s}^{-1}. \]Step 4: Evaluate net photosynthesis at the bottom leaves
Using \(I_{\text{bottom}}\approx 109\):
\[ P_{\text{net}}(109)=\frac{18\cdot 109}{300+109}-1.5 =\frac{1962}{409}-1.5 \approx 4.797-1.5 \approx 3.30\ \mu\text{mol CO}_2\ \text{m}^{-2}\ \text{s}^{-1}. \]Since \(I_{\text{bottom}} \approx 109\) is greater than \(I_c \approx 27.3\), the bottom leaves have positive net photosynthesis in this example. Additional light from below can still increase \(P_{\text{net}}\), but the marginal gain depends on how close the leaf is to saturation and whether other factors become limiting.
When under-canopy light helps (and when it does not)
- Most effective: bottom leaves are below or near \(I_c\); leaves are not severely senescent; CO2 supply and stomatal conductance allow additional carbon fixation; the added photons actually reach photosynthetic tissue.
- Less effective: bottom leaves already have moderate \(P_{\text{net}}\) and approach saturation; canopy architecture blocks light placement; strong limitations by CO2, temperature, or water stress dominate.
- Potential trade-offs: extra light can raise leaf temperature and transpiration demand, and older shade leaves often have lower \(P_{\max}\), reducing the benefit per photon.
Visualization: canopy shading and the light-response curve
Final determination for the example
The bottom leaves receive \(I_{\text{bottom}}\approx 109\ \mu\text{mol}\ \text{m}^{-2}\ \text{s}^{-1}\), which exceeds the compensation point \(I_c\approx 27.3\ \mu\text{mol}\ \text{m}^{-2}\ \text{s}^{-1}\), so net photosynthesis is positive. Providing light to bottom leaves can work, but the biological payoff is largest when the canopy is so shaded that lower leaves sit near or below \(I_c\) and light is the dominant limiting factor.