A general method for calculating the optimal leaf longevity from the viewpoint of carbon economy
- 259 Downloads
According to the viewpoint of the optimal strategy theory, a tree is expected to shed its leaves when they no longer contribute to maximisation of net carbon gain. Several theoretical models have been proposed in which a tree was assumed to strategically shed an old deteriorated leaf to develop a new leaf. We mathematically refined an index used in a previous theoretical model [Kikuzawa (Am Nat 138:1250–1263, 1991)] so that the index is exactly proportional to a tree’s lifelong net carbon gain. We also incorporated a tree’s strategy that determines the timing of leaf expansion, and examined three kinds of strategies. Specifically, we assumed that a new leaf is expanded (1) immediately after shedding of an old leaf, (2) only at the beginning of spring, or (3) immediately after shedding of an old leaf if the shedding occurs during a non-winter season and at the beginning of spring otherwise. We derived a measure of optimal leaf longevity maximising the value of an appropriate index reflecting total net carbon gain and show that use of this index yielded results that are qualitatively consistent with empirical records. The model predicted that expanding a new leaf at the beginning of spring than immediately after shedding usually yields higher carbon gain, and combined strategy of the immediate replacement and the spring flushing earned the highest gain. In addition, our numerical analyses suggested that multiple flushing seen in a few species of subtropical zones can be explained in terms of carbon economy.
KeywordsLeaf lifespan Optimal strategy Deciduous Evergreen Multiple flushing
Mathematics Subject Classification92C80 (Plant biology) 90B35 (Scheduling theory, deterministic)
We are grateful to S. Oikawa and K. Kikuzawa for their helpful comments. We also thank A. Ushijima–Akasaka, S. Aiba, K. Umeki, and T. S. Kohyama for acquainting us with suggestive empirical records. This study was supported by JSPS KAKENHI Grant Number 24247003 (T.T.), 25340115 (T.T.).
- Ackerly DD, Bazzaz FA (1995) Leaf dynamics, self-shading and carbon gain in seedlings of a tropical pioneer tree. Oecol 101:289–298Google Scholar
- Bentley BL (1979) Longevity of individual leaves in a tropical rainforest under-story. Ann Bot 43:119–121Google Scholar
- Coley PD (1980) Effects of leaf age and plant life history patterns on herbivory. Nature 284:545–546Google Scholar
- Givnish TJ (1978) On the adaptive significance of compound leaves, with particular reference tropical trees. In: Tomlinson PB, Zimmermann MH (eds) Tropical trees as living systems. Cambridge University Press, Cambridge, pp 351–380Google Scholar
- Gower ST, Reich PB, Son Y (1993) Canopy dynamics and aboveground production of five tree species with different leaf longevities. Tree Physiol 12:327–345Google Scholar
- Hikosaka K, Hirose T (2000) Photosynthetic nitrogen-use efficiency in evergreen broad-leaved woody species coexisting in a warm-temperate forest. Tree Physiol 20:1249–1254Google Scholar
- Hiremath AJ (2000) Photosynthetic nutrient-use efficiency in three fast-growing tropical trees with differing leaf longevities. Tree Physiol 20:937–944Google Scholar
- Reich PB, Walters MB, Ellsworth DS (1992) Leaf life-span in relation to leaf, plant, and stand characteristics among diverse ecosystems. Ecol Monogr 62:365–392Google Scholar
- Šesták Z, Tichá I, Čatský F, Solárová J, Pospišilová J, Hodáňová D (1985) Integration of photosynthetic characteristics during leaf development. In: Šesták Z (ed) Photosynthesis during leaf development. Dr. W. Junk Publishers, Dordrecht, pp 263–286Google Scholar
- Takada T, Kikuzawa K, Fujita N (2006) A mathematical analysis of leaf longevity of trees under seasonally varying temperatures, based on a cost-benefit model. Evol Ecol Res 8:605–615Google Scholar