Journal of Mathematical Biology

, Volume 71, Issue 3, pp 669–690 | Cite as

A general method for calculating the optimal leaf longevity from the viewpoint of carbon economy

  • Motohide SekiEmail author
  • Tomohiko Yoshida
  • Takenori Takada


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.


Leaf lifespan Optimal strategy Deciduous Evergreen  Multiple flushing 

Mathematics Subject Classification

92C80 (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.).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Motohide Seki
    • 1
    Email author
  • Tomohiko Yoshida
    • 2
  • Takenori Takada
    • 1
  1. 1.Faculty of Environmental Earth ScienceHokkaido UniversitySapporoJapan
  2. 2.Graduate School of Environmental ScienceHokkaido UniversitySapporoJapan

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