Fundamental to almost all vegetation function models are descriptions of plant carbon uptake and water use. A lot of (experimental and theoretical) effort has been made to understand plant stomatal behavior under constant leaf area, even though whole-plant carbon gain and water consumption are simultaneously determined by stomatal conductance and leaf area. The role of leaf phenology on plant water/carbon tradeoff has received much less attention likely because, unlike stomatal conductance, there exist carbon costs associated with maintaining the current leaf area and constructing new leaves. A high leaf construction cost also suggests that plants should not shed too many leaves whenever the environment becomes less favorable. This is because plants will need these leaves when the environment becomes favorable again in future.
In this theoretical study, we search for plants’ optimal control over gas exchange under stochastic rainfall using dynamic programming algorithm. More specifically, we aim to optimize plant leaf area and stomatal conductance simultaneously over time. This study analyzes how leaf phenology and stomatal regulation should be coordinated to maximize plant net carbon gain in a water limited environment, and can provide a more complete understanding of plant water and carbon economy.
Results/Conclusions
Our results show that leaf area should be kept within a certain range of values to maximize plants’ long-term total net carbon gain under stochastic rainfall in a water-limited environment. Plants should shed leaves when the soil becomes too dry. This is because, under dry conditions, a high value of leaf area can boost photosynthesis, but it incurs an even higher leaf maintenance carbon cost. Plants should grow more leaves when there is plenty of water. Under intermediate conditions, there is no need to shed leaves, but plants cannot afford the construction cost to grow new leaves either. This range of the optimal leaf area shrinks as the soil becomes drier and/or the leaf construction cost and/or leaf maintenance cost become higher. These results represent the first time that leaf phenological strategies have been quantitatively derived from optimization principles.