Leaf mass per area is independent of vein length per area: avoiding pitfalls when modelling phenotypic integration (reply to Blonder et al. 2014)

It has been recently proposed that leaf vein length per area (VLA) is the major determinant of leaf mass per area (LMA), and would thereby determine other traits of the leaf economic spectrum (LES), such as photosynthetic rate per mass (A (mass)), nitrogen concentration per mass (N (mass)) and leaf lifespan (LL). In a previous paper we argued that this ‘vein origin’ hypothesis was supported only by a mathematical model with predestined outcomes, and that we found no support for the ‘vein origin’ hypothesis in our analyses of compiled data. In contrast to the ‘vein origin’ hypothesis, empirical evidence indicated that VLA and LMA are independent mechanistically, and VLA (among other vein traits) contributes to a higher photosynthetic rate per area (A (area)), which scales up to driving a higher A (mass), all independently of LMA, N (mass) and LL. In their reply to our paper, Blonder et al. (2014) raised questions about our analysis of their model, but did not address our main point, that the data did not support their hypothesis. In this paper we provide further analysis of an extended data set, which again robustly demonstrates the mechanistic independence of LMA from VLA, and thus does not support the ‘vein origin’ hypothesis. We also address the four specific points raised by Blonder et al. (2014) regarding our analyses. We additionally show how this debate provides critical guidance for improved modelling of LES traits and other networks of phenotypic traits that determine plant performance under contrasting environments.