A general method for calculating the optimal leaf

Authors: Motohide Seki Tomohiko Yoshida Takenori Takada

Publish Date: 2014/09/23

Volume: 71, Issue: 3, Pages: 669-690

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Abstract

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 1381250–1263 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 nonwinter 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 economyWe 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 TT 25340115 TTIn conclusion the optimal integer leaf longevity for trees subject to the immediate replacement rule varphi mathrmI is lfloor tddagger rfloor if 33 holds and lceil tddagger rceil otherwise which can be also expressed as 14In conclusion the optimal leaf longevity for deciduous trees subject to varphi mathrmC is f / Qdagger where Qdagger =lfloor qdagger rfloor if 40 holds and Qdagger =lceil qdagger rceil otherwise as shown in 24

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