Local control of resource allocation is sufficient to model optimal dynamics in syntrophic systems

Syntrophic systems are common in nature and include forms of obligate mutualisms in which each participating organism or component of an organism obtains from the other an essential nutrient or metabolic product that it cannot provide for itself. Models of how these complementary resources are allocated between partners often assume optimal behavior, but whether mechanisms enabling global control exist in syntrophic systems, and what form they might take, is unknown. Recognizing that growth of plant organs that supply complementary resources, like roots and shoots, can occur autonomously, we present a theory of plant growth in which root-shoot allocation is determined by purely local rules. Each organ uses as much as it can of its locally produced or acquired resource (inorganic nitrogen or photosynthate) and shares only the surplus. Subject to stoichiometric conditions that likely hold for most plants, purely local rules produce the same optimal allocation as would global control across a wide range of environmental scenarios, with sharing the surplus being the specific mechanism stabilizing syntrophic dynamics. Our local control model contributes a novel approach to plant growth modeling because it assumes a simple mechanism of root:shoot allocation that can be considered a higher-level physiological rule, from which the optimal growth outcome emerges from the system's dynamics, rather than being built into the model. Moreover, our model is general, in that the mechanism of sharing the surplus can readily be adapted to many obligate syntrophic relationships.