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

Abstract

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 rootshoot 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

Resource Allocation in Annual Plants

“…Throughout the growing season, fractions of carbon u SC (t), u RC (t), and u F C (t) and fractions of nitrogen u SN (t), u RN (t), and u F N (t) are allocated to the shoots, roots, and fruits, respectively, at time t. The resources pass through a synthesizing unit (SU) in each organ, where they are converted into biomass. We use Kooijman's parallel complementary synthesizing unit (PCSU) function from Kooijman (2010), employing the same simplification seen in (Ledder et al 2020, Appendix A), given by g(A, B) =…”

“…It has also been suggested that allocation may be an emergent property of the many processes involved in plant growth rather than the result of a central allocation process (Feller et al 2015). For a more complete review of allocation theory, we refer the reader to Ledder et al (2020) or Poorter et al (2012).…”

Timescale separation and models of symbiosis: state space reduction, multiple attractors and initialization

“…The conceptual foundation within DEB theory for such models is the work by Kooijman ( 2001 ), which sketches links involving excretion fluxes from animal host and algal symbiont in corals and interactions between root and shoot in a plant. Subsequent models for the coral symbiosis and the interaction of roots and shoots in plants have been developed in Muller et al ( 2009 ), Cunning et al ( 2017 ), Ledder et al ( 2020 ) and Schouten et al ( 2020 ). These models can be applied to describe responses to environmental stress, e.g.…”

“…Mathematically, several of the cited models take the form of differential equations that involve a small number of state variables. For instance, the models in ( Cunning et al , 2017 ) and Ledder et al ( 2020 ) describe two ‘players’ who exchange metabolic products that are surplus to their own needs. This interaction is described with a set of algebraic equations that characterize the flows of elemental matter within an interaction network; see schematic Fig.…”

“…In those cases, unambiguous tracking of only slow variables is not possible without at minimum additional information about the state of the fast dynamic network. An example for such a situation is the earlier mentioned model for the growth of the root and the shoot of a plant by Ledder et al ( 2020 ). This model does not only need information on the biomass of the two organelles, but it also needs to track the current rates at which root and shoot share nitrogen and carbon, respectively.…”