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Mathematical consideration of the pipe model theory in woody plant species

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Abstract

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Using the pipe model theory, a quantitative relationship between leaves and non-green plant organs has been defined that depends on tree size.

Abstract

In the pipe model theory, the cumulative mass of leaves and the density of non-photosynthetic organs at depth (z) from the crown surface of a woody plant are defined as F(z) and C(z), respectively. In this study, the F(z)–C(z) relationship was approximated by a non-rectangular hyperbola for Abies veitchii, Chamaecyparis obtusa, Cryptomeria japonica and Larix leptolepis. The initial slope of the non-rectangular hyperbola, corresponding to the specific pipe length, varied among individual trees. The relationship between the initial slope and the square of the stem diameter at the crown base, which can be expressed as a power function with positive exponents, was species dependent. Based on the size dependence of the initial slope, the value of the allometric exponent describing the relationship between leaf mass and the square of the stem diameter at the crown base was theoretically shown to exceed unity. Empirically, the value of the allometric exponent usually exceeds two. However, in the allometric model developed here, the allometric exponent between the leaf mass and the square of the stem diameter at the crown base did not differ significantly from unity, indicating that the leaf mass was directly proportional to the stem cross-sectional area at the crown base.

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Author contribution statement

The author (KO) designed research, collected the data, analyzed them, and wrote the paper.

Acknowledgments

I thank David Warton and Daniel Falster for their helpful advice on the use of the freely available software program SMATR.

Conflict of interest

The author (KO) declares that he has no conflict of interest.

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Authors and Affiliations

  1. Laboratory of Forest Ecology and Physiology, Graduate School of Bioagricultural Sciences, Nagoya University, Nagoya, 464-8601, Japan

    Kazuharu Ogawa

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  1. Kazuharu Ogawa
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Correspondence to Kazuharu Ogawa.

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Communicated by E. Priesack.

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Ogawa, K. Mathematical consideration of the pipe model theory in woody plant species. Trees 29, 695–704 (2015). https://doi.org/10.1007/s00468-014-1147-2

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  • DOI: https://doi.org/10.1007/s00468-014-1147-2

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