Presentation Information
[POS-31]Dynamic optimization of resource allocation represents the tragedy of the commons in plants under competition for limited resources
*Kim Bo-Moon1, Atsushi Yamauchi1 (1. Center for ecological research, Kyoto university (Japan))
Keywords:
Dynamic optimization,Pontryagin’s maximum principle,Plant competition,Tragedy of the commons in plant
In game theory, the interactions of multiple players utilizing shared public resources have been studied through the public goods game. This framework demonstrates that individuals achieve lower rewards in non-cooperative behavior than in cooperative ones, a phenomenon known as the tragedy of the commons (TOC). Plants also exhibit TOC empirically with root overproliferation and decline of seed production when competing for limited belowground resources, such as soil nutrients.
To explore the mechanisms behind TOC in plants, we analyzed the resource allocation schedule of an annual plant with two components: aboveground (shoot) and belowground (root) structures. Plant fitness was measured based on shoot biomass at the end of the growing season. The plant assimilates resources through nutrient absorption from the soil, allocating those between shoots and roots. The rate of nutrient absorption is assumed be proportional to the nutrient concentration in the soil and the plant’s shoot and root biomasses. We investigated the optimal resource allocation schedule by using Pontryagin’s maximum principle in the presence and absence of neighboring plants. By comparing those results, we reveal the mechanism causing TOC in the plant.
In both solitary and competitive scenarios, we found that plants can adopt a singular solution with simultaneous resource allocation to both root and shoot growth or a bang-bang control with a perfect switch of allocation between root and shoot. In the schedule with the singular control, plants initially allocate resources exclusively to shoots or roots and subsequently allocate to both evenly. Afterward, plants allocate all resources to shoots. In the case of the bang-bang control, the schedule immediately switches from exclusive allocation to roots to exclusive allocation to shoots.
The analysis shows that the presence of competitors extends the simultaneous allocation period in the singular condition and delays the switching time of allocation in the bang-bang control. This is associated with a reduction in final shoot size (i.e., fitness) and an increase in final root size. The present study shows that plants can exhibit TOC in response to the presence of competitors, in which a prolongation of the period allocating to roots is a key mechanism of TOC.
To explore the mechanisms behind TOC in plants, we analyzed the resource allocation schedule of an annual plant with two components: aboveground (shoot) and belowground (root) structures. Plant fitness was measured based on shoot biomass at the end of the growing season. The plant assimilates resources through nutrient absorption from the soil, allocating those between shoots and roots. The rate of nutrient absorption is assumed be proportional to the nutrient concentration in the soil and the plant’s shoot and root biomasses. We investigated the optimal resource allocation schedule by using Pontryagin’s maximum principle in the presence and absence of neighboring plants. By comparing those results, we reveal the mechanism causing TOC in the plant.
In both solitary and competitive scenarios, we found that plants can adopt a singular solution with simultaneous resource allocation to both root and shoot growth or a bang-bang control with a perfect switch of allocation between root and shoot. In the schedule with the singular control, plants initially allocate resources exclusively to shoots or roots and subsequently allocate to both evenly. Afterward, plants allocate all resources to shoots. In the case of the bang-bang control, the schedule immediately switches from exclusive allocation to roots to exclusive allocation to shoots.
The analysis shows that the presence of competitors extends the simultaneous allocation period in the singular condition and delays the switching time of allocation in the bang-bang control. This is associated with a reduction in final shoot size (i.e., fitness) and an increase in final root size. The present study shows that plants can exhibit TOC in response to the presence of competitors, in which a prolongation of the period allocating to roots is a key mechanism of TOC.