Optimal size of storage for recovery after unpredictable disturbances

Terrestrial plants often live in environments in which above-ground photosynthetic organs (production parts) are suddenly removed by unpredictable disturbances, such as fire, frost, desiccation, pathogen attack, breakage by wind and trampling, or herbivory by insects and mammals. We study the optimal growth schedule for a plant having a below-ground storage organ that is used for recovery (or regrowth) of photosynthetic organs after disturbances. We assume the following: (1) the daily production rate increases with the production part size, but saturates for large size due to shading and local resource depletion, (2) disturbances occur randomly and remove all the aerial parts, (3) plants are finally killed by fatal disturbances that also occur randomly and (4) the plant chooses the pattern of growth, reproduction, storage and recovery after disturbances by reallocation of stored material to maximize the total lifetime reproductive success. The model is analysed by stochastic dynamic programming. The results are as follows: (1) the ratio of storage size to production part size (S/F ratio) is large if the longevity is large and if the disturbance rate is large but a little smaller than the productivity coefficient, (2) the S/F ratio is larger for mature plants than for small immature plants, (3) after disturbances, the above-ground production part recovers relatively quickly, but reproductive activity is depressed until storage size recovers and (4) the variations over time and between habitats differing in disturbance frequency are larger for storage size and for reproductive activity than for production part size. These tendencies are more pronounced for a linear production function (with initial linear increase followed by a sudden stop), but less so for a hyperbolic production function (with a gradually decreasing slope). We also discuss the growth and regrowth behaviour of plants adapted to a disturbance frequency growing under one different disturbance frequency.