Optimal Growth Schedule of a Perennial Plant

Abstract

The optimal growth schedule of a deciduous perennial plant is studied theoretically. We make three basic assumptions. First, the daily net photosynthetic rate of a plant increases but saturates with the size of the production part (vegetative organs working for photosynthesis). Second, the production part is discarded at the end of a growing season, but it may be rebuilt at the beginning of the next season using stored material. And finally, the plant maximizes the lifetime reproductive investment by choosing both the growth schedule within each season and the resource allocation between reproduction for the year and storage for the next season. The model is analyzed by the combination of maximum principle and dynamic programming. Our analysis showed three basic results. First, the annual life cycle is optimal under low storage efficiency, low habitat reliability, low growth rate, and a short growing season. Second, under any other conditions, perennial growth is optimal. During years in which the final amount of resources is smaller than a critical value S*, the plant remains immature and saves all of the resources for the next season. If it becomes larger than S*, the plant invests the excess in reproductive activities and repeats the same growth schedule thereafter (steady state). Finally, reproductive effort (the ratio of reproductive investment to total annual production) of a mature plant is high for an annual, is lowest for a perennial just above the threshold for the perennial growth pattern, increases as the length of the season increases, and in a very productive habitat may even exceed the level for an annual. The ratio of the plant size established by stored material to the maximum plant size decreases with the length of the growing season, which quantitatively fits the available data. In light of the model, reported growth patterns and leaf phenology of many deciduous plants indicate that the nonlinearity of photosynthetic rate as a function of the size of the production part is important. For a case with nonlinear photosynthesis but without an upper limit to the leaf expansion rate, a plant's optimal phenology, if normalized by size, can be parameterized by two quantities: productivity (maximum relative growth rate multiplied by a season's length) and stability (annual survival multiplied by storage efficiency). The timing of the cessation of leaf production within a season by a small immature plant is determined by productivity (occurring later in a more productive habitat). Leaf production ends earlier in the season as the plant grows. The optimal time for ending leaf production in a mature plant, in contrast, is controlled mainly by stability (it ceases earlier at a more stable site) and is almost independent of productivity.