Evolutionarily stable growth of a sapling which waits for future gap formation under closed canopy

A model was developed to examine the ESS sapling growth waiting for future gap formation under closed canopy. Assumptions are: a sapling has two parts, a trunk and a photosynthetic part, and allocates annual photosynthates to these two parts; and a sapling with a larger photosynthetic part has a larger production rate, but a sapling with a larger trunk is more successful in competition after gap formation. The ESS growth schedule of a sapling typically consists of three phases: (1) the sapling first allocates all annual photosynthates to the photosynthetic part, then (2) it allocates annual photosynthates both to its trunk and to photosynthetic part, and both parts grow simultaneously, and finally (3) it also allocates annual photosynthates to both parts, but the size of the photosynthetic part stays constant due to annual loss, and only the trunk size increases. A sapling should allocate photosynthates more to the trunk if mortality or probability of gap formation is large. However, a sapling should allocate photosynthates more to the photosynthetic part if large trunks are strongly advantageous in competition after gap formation.