Canopy ergodicity: can a single leaf represent an entire plant canopy?

While leaves typically emerge near shoot apices around the outer surface of a plant canopy, their relative position moves deeper into the canopy as additional leaves emerge. The photosynthetic capacity (A (max)) of a given leaf can be expected to decline over time as its relative position (P (r)) in the canopy becomes progressively deeper; this can be observed as a spatial gradient with the A (max) of leaves declining distally from the shoot apex. As a consequence, we propose that the photosynthetic capacity averaged over a single leaf's lifespan is equivalent to the average photosynthetic capacity of the entire plant canopy at a given time; in other words, there is an ergodic time to space averaging in the organization and development of plant canopies. We tested this canopy ergodic hypothesis in two woody (Alnus sieboldiana and Mallotus japonica) and two herbaceous (Polygonum sachalinensis and Helianthus tuberosus) species by following the photosynthetic capacity in 100 individual leaves from the time of their emergence until their death. We compared the average photosynthetic capacity of individual leaves through time (time-average) to the average photosynthetic capacity of all the leaves along a shoot at the time of emergence of the focal leaf (space-average). We found that A (max) and P (r) were positively correlated and that the time-averages of three plant species (Alnus, Mallotus, and Helianthus) were not significantly different from the corresponding space-averages, although the averages differed among individual plants. Polygonum, however, did show significant differences between time and space averages. Ergodicity appears to apply to the leaf-canopy relationship, at least approximately-the average photosynthetic capacity of a single leaf through time (time-average) can represent the average photosynthetic capacity of the entire canopy.