Bounds on stomatal size can explain scaling with stomatal density in forest plants

A prevailing hypothesis posits that achieving higher maximum rates of leaf carbon gain and water loss is constrained by geometry and/or selection to limit the allocation of epidermal area to stomata (f_S). Under this 'stomatal-area minimization hypothesis', higher g_s,max is associated with greater numbers of smaller stomata because this trait combination increases g_s,max with minimal increase in f_S, leading to relative conservation of f_S semi-independent of g_s,max due to coordination in stomatal size, density, and pore depth. An alternative hypothesis is that the evolution of higher g_s,max can be enabled by a greater epidermal area allocated to stomata, leading to positive covariation between f_S and g_s,max; we call this the 'stomatal-area adaptation hypothesis'. Under this hypothesis, the interspecific scaling between g_s,max, stomatal density, and stomatal size is a by-product of selection on a moving optimal g_s,max. We integrated biophysical and evolutionary quantitative genetic modeling with phylogenetic comparative analyses of a global data set of stomatal density and size from 2408 vascular forest species. The models present specific assumptions of both hypotheses and deduce predictions that can be evaluated with our empirical analyses of forest plants. There are three main results. First, neither the stomatal-area minimization nor adaptation hypothesis is sufficient to be supported. Second, estimates of interspecific scaling from common regression methods cannot reliably distinguish between hypotheses when stomatal size is bounded. Third, we reconcile both hypotheses with the data by including an additional assumption that stomatal size is bounded by a wide range and under selection; we refer to this synthetic hypothesis as the 'stomatal adaptation + bounded size' hypothesis. This study advances our understanding of scaling between stomatal size and density by mathematically describing specific assumptions of competing hypotheses, demonstrating that existing hypotheses are inconsistent with observations, and reconciling these hypotheses with phylogenetic comparative analyses by postulating a synthetic model of selection on g_s,max, f_S, and stomatal size.