Reconciling the apparent difference between mass- and area-based expressions of the photosynthesis-nitrogen...

The relationship between photosynthetic carbon assimilation (A _max) and leaf nitrogen content (N _leaf) can be expressed on either a leaf area basis (A _area vs N _area) or a leaf mass basis (A _mass vs N _mass). Dimensional analysis shows that the units for the slope of this relationship are the same for both expressions (μmol [CO₂] g^-1 [N] s^-1). Thus the slope measures the change in CO₂ assimilation per gram of nitrogen, independent of leaf mass or leaf area. Although they have the same units, large differences between the area and mass-based slopes have been observed over a broad range of taxonomically diverse species. Some authors have claimed that regardless of these differences, the fundamental nature of the A _max-N _leaf relationship is independent of the units of expression. In contrast, other authors have claimed that the area-based A _max-N _leaf relationship is fundamentally different from the mass-based relationship because of interactions between A _max, N _leaf, and leaf mass per area (LMA, g [leaf] m^-2 [leaf]). In this study we consider the mathematical relationships involved in the transformation from mass- to area-based expressions (and vice versa), and the implications this transformation has for the slope of the A _max-N _leaf relationship. We then show that the slope of the relationship is independent of the units of expression when the effect of LMA is controlled statistically using a multiple regression. The validity of this hypothesis is demonstrated using 13 taxonomically and functionally diverse C₃ species. This analysis shows that the slope of the A _max-N _leaf relationship is similar for the mass- and area-based expressions and that significant errors in the estimate of the slope can arise when the effect of LMA is not controlled.