Is whole-plant photosynthetic rate proportional to leaf area? A test of scalings and a logistic equation by leaf demography census.

Allometric scalings and a logistic equation assume that whole-plant photosynthetic rate under resource-unlimited conditions is proportional to leaf area. We tested this proportionality for the herb Helianthus tuberosus. During growth, we repeatedly measured the percentage of leaves with high, medium, and low photosynthetic capacity to estimate the whole-plant sum of photosynthetic capacity. We found that the whole-plant sum of the light-saturated photosynthetic rate of leaves is proportional to the whole-plant leaf area, disregarding the dynamics of the leaf population. We also found that the daily photosynthesis of each leaf appeared as a linear function of the light-saturated photosynthetic rate of that leaf, as predicted by the optimization theory. Using those results, we expressed whole-plant photosynthetic rate as a product of the light-saturated whole-plant photosynthetic rate and an efficiency index that reflects resource limitation as in the logistic equation. This efficiency decreased with increasing leaf area, reflecting light limitation. Therefore, realized whole-plant photosynthetic rate is not proportional to leaf area. These "diminishing returns" are well explained by a simple saturating curve, such as the logistic equation.