Spatial regulation of resource allocation in response to nutritional availability

•We modeled the spatial regulation of resource allocation.•We focused on root system architecture in response to nutrient availability.•We showed that local control is sufficient to adaptation to low-level nutrition.•In contrast, systemic control is required for adaptation to high-level nutrition.•Systemic control could be evolved when an excess amount of nutrition is present. It is critical for a living organism to appropriately allocate resources among its organs, or within a specific organ, because available resources are generally limited. For example, in response to the nutritional environment of their soil, plants regulate resource allocation in their roots in order to plastically change their root system architecture (RSA) for efficiently absorbing nutrients. However, it is still not understood why and how RSA is adaptively controlled. Therefore, we modeled and investigated the spatial regulation of resource allocation, focusing on RSA in response to nutrient availability, and provided analytical solutions to the optimal strategy in the case of simple fitness functions. We first showed that our model could explain the experimental evidence where root growth is maximized at the optimal nutrient concentration under the homogeneous condition. Next, we extended our model to incorporate the spatial heterogeneity of nutrient availability. This extended model revealed that growth suppression by systemic control is required for adapting to high nutrient conditions, whereas growth promotion by local control is sufficient for adaptation to low-nutrient environments. This evidence predicts that systemic control can be evolved in the presence of excessive amounts of nutrition, consistent with the ‘N-supply’ systemic signal that is observed experimentally. Furthermore, our model can also explain various experimental results using nitrogen nutrition. Our model provides a theoretical basis for understanding the spatial regulation of adaptive resource allocation in response to nutritional environment.