Are leaf functional traits 'invariant' with plant size and what is 'invariance' anyway?

Studies of size-related plant traits have established a suite of mathematical functions describing whole plant investment and allocation. In parallel, studies of plant 'economic spectra' have measured the scaling and variance composition of traits related to the major dimensions of both structure and function. Here, we explore the intersection of these two broad areas by exploring the notion that many leaf economic traits are invariant with species differences in adult plant size. Invariant traits are those that do not change with plant size and are invoked as a key simplifying assumption of prominent models that purport to explain the scaling of plant size and metabolism. Unfortunately, leaf trait invariance is neither well defined nor understood and has never been critically evaluated. Using a global plant trait data set, we evaluated whether nine key traits can be considered as effectively invariant as a function of the maximum height of plant species, within and across plant growth forms and within and across broad taxonomic groups. We also examine the influence of habitat, biome and global spatial scales on the size-relative variance in plant functional traits. We suggest that while invariance is an intuitive concept, an objective statistical definition is elusive. Expanding on ideas drawn from the study of life-history invariants, we propose five criteria to identify traits that are effectively invariant, depending on the research question. We show that all studied 'leaf economic spectrum' (LES) traits approach invariance within and between herbaceous and woody plant groups, angiosperms and gymnosperms, and within most biome and habitat types. Individual leaf area, however, shows a modest increase with plant size, and there are significant shifts in the average LES trait values at a given plant maximum height, among the plant growth forms and taxonomic groups. Our results demonstrate that generally, LES traits show little interspecific variation with maximum plant height, which provides some support for attempts to model plants with 'average' leaf properties. Our work also highlights the need for a better understanding of the drivers of leaf size variation within and across individuals, functional groups, clades, biomes and habitats.