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

The relationship between photosynthetic carbon assimilation (Amax) and leaf nitrogen content (Nleaf) can be expressed on either a leaf area basis (Aarea vs Narea) or a leaf mass basis (Amass vs Nmass). 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 Amax-Nleaf relationship is independent of the units of expression. In contrast, other authors have claimed that the area-based Amax-Nleaf relationship is fundamentally different from the mass-based relationship because of interactions between Amax, Nleaf, 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 Amax-Nleaf 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 Amax-Nleaf 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.