Abstract
The leaves of many trees emit volatile organic compounds (abbreviated as BVOCs), which protect them from various damages, such as herbivory, pathogens, and heat stress. For example, isoprene is highly volatile and is known to enhance the resistance to heat stress. In this study, we analyze the optimal seasonal schedule for producing isoprene in leaves to mitigate damage. We assume that photosynthetic rate, heat stress, and the stress-suppressing effect of isoprene may vary throughout the season. We seek the seasonal schedule of isoprene production that maximizes the total net photosynthesis using Pontryagin's maximum principle. The isoprene production rate is determined by the changing balance between the cost and benefit of enhanced leaf protection over time. If heat stress peaks in midsummer, isoprene production can reach its highest levels during the summer. However, if a large portion of leaves is lost due to heat stress in a short period, the optimal schedule involves peaking isoprene production after the peak of heat stress. Both high photosynthetic rate and high isoprene volatility in midsummer make the peak of isoprene production in spring. These results can be clearly understood by distinguishing immediate impacts and the impacts of future expectations.