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Axiomatic Plant Ecology: Reflections Toward a Unified Theory for Plant Productivity

  • Chapter
Canopy Photosynthesis: From Basics to Applications

Part of the book series: Advances in Photosynthesis and Respiration ((AIPH,volume 42))

Summary

Starting from an axiom that sunlight is the fundamental energy source for green plants, we derived some theorems in plant ecology. We began by reviewing the Monsi-Saeki model, which was the first to relate the structure of canopy and productivity. Optimum leaf area (and thus leaf biomass) were predicted from the Monsi-Saeki model, which also introduced the concept of constant final yield per unit land area. A relationship between total biomass (y) and plant number (n) per unit land area was derived by combining the principles of constant final yield and logistic plant growth, which is based upon the diminishing return of total individual photosynthesis due to self-shading, An analogous equation was obtained in the analysis of cumulative plant biomass (Y) against cumulative plant number (N) within a stand. Mass-number relationships among stands (y-n) and within a stand (Y-N) were revealed to be the same under one-sided competition for light. The self-thinning line is the point where individual plant’s growth becomes zero on the translocation of a Y-N relationship through time. Self-thinning is expected to occur due to the death of the smallest plants shaded by larger plants. The Monsi-Saeki modeling framework was reoriented considering leaf longevity, which is the optimal timing to replace individual leaves to maximize carbon gain of the plant. Under canopy ergodic hypothesis, which supposes space-time equivalence in the performance of leaves, leaf longevity can be used to circumvent the difficulties in the scaling from leaf to canopy. Gross primary production then can be estimated using functional leaf longevity together with the mean labor time of a leaf, two measures of the time during the leaf span when it can be photosynthetically active. Finally, if leaf longevity is used in a species-specific normalization constant, plant productivity can be described as an allometric function of plant mass. In that case, the relative growth rate of plants can be shown to have an inverse relationship to leaf longevity.

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Abbreviations

A :

Specific parameter of the Y to N relationship that represents the reciprocal of maximum total biomass in a stand

α :

Stand compactness

a 1 ~ a 5 :

Regression coefficients

B :

Specific parameter of the Y to N relationship that represents the reciprocal of maximum plant mass in a stand

b 1 ~ b 3 :

Regression coefficients

\( {\beta}_1\sim {\beta}_3 \) :

Degree of one- (and two) sided competition

B L :

Leaf biomass of a stand per unit land area

C :

Construction cost of unit leaf area

χ :

Number of leaves that the solar flux encounters before reaching certain depth of a canopy

CV:

Coefficient of variation

δ :

Power exponent of allometry between H max and w max

d :

Dry matter density of a stand

F :

Cumulative leaf area from the top per unit land area

f :

Favorable period for photosynthesis

F opt :

Optimum leaf area of a stand which gives the maximum surplus production

G :

Cumulative gain by a single leaf per unit leaf area

g :

Marginal gain or G per time

GPP:

Gross primary production

H max :

Height of the hypothetical largest plant in a stand

I o :

Irradiance at the top of a canopy

I :

Irradiance at a certain depth of a canopy

K :

light extinction coefficient

K 1  ~ K 6 :

Regression coefficient

L :

Leaf longevity

L f :

Functional leaf longevity

LAI :

Leaf area index

λ:

Intrinsic growth rate of average plant mass

LMA:

Leaf mass per leaf area

m :

Mean labor time in a day for photosynthesis

N :

Number of plants in a unit land area from the largest to a certain sized one.

N 0 :

Number of plants in a unit land area in the course of self-thin ning

n :

Number of plants per unit land area

N B :

N axis of base point of Y-N curve

P :

Instantaneous gross photosynthetic rate of a canopy per unit land area

p :

Instantaneous gross photosynthetic rate of a leaf per unit leaf area

p′ :

Net photosynthetic rate of a leaf per unit leaf area

p day :

Daily photosynthetic rate per unit leaf area

p max :

Mean maximum photosynthetic rate of a leaf

PPFD:

Photosynthetic photon flux density

P s :

Instantaneous surplus production of a stand per unit land area

P year :

Annual photosynthetic rate of a stand per unit land area

r :

Instantaneous respiration rate of a leaf per unit leaf area

RGR :

Relative growth rate

S :

Land area which the plant canopy occupies

s :

Leaf area of a single leaf which comprises the canopy

t :

Time

t opt :

Optimal leaf longevity

t pot :

Time at which daily photosynthetic rate is zero

w :

Individual plant mass

\( \overline{w} \) :

Average plant mass

w L :

Leaf biomass of an individual plant

\( {\overline{w}}_o \) :

Initial average plant mass

\( {\overline{w}}_{max} \) :

Maximum asymptotic average plant mass which average plant reaches with time

w max :

Hypothetical maximum plant mass in a stand when number of plant (N) reaches zero which can be obtained as the reciprocal of parameter B of Y to N relationship

WBE:

West Brown and Enquist’s scaling theory

Y :

Biomass of plants from the largest to a certain sized one in a unit land area

Y B :

Y axis of base point of Y-N curve

y final :

Total biomass of plants per unit land area after canopy closure when the effect of planting density on total biomass is diminished

\( {Y}_{\infty } \) :

Asymptotic total biomass of plants per unit land area when maximum number of plants are packed into the space which is obtained as the reciprocal of parameter A of Y to N relationship

y :

Total biomass of plants per unit land area

Y 0 :

Total biomass of plants per unit land area in the course of self-thin ning

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Acknowledgements

We thank Martijn Slot, Kouki Hikosaka and Yasuo Konno for their review and comments on the manuscript. This analysis was initiated when MJL held an appointment as a visiting professor at Ishikawa Prefectural University funded by the Foundation of Science-Technology Center in Central Japan (Nagoya Fund). The work was also supported by MESSC of Japan #20370014 for KK.

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Authors and Affiliations

  1. Ishikawa Prefectural University, Nonoichi, Japan

    Kihachiro Kikuzawa

  2. Onoecho 14-16, Zushioku, Yamashina, Kyoto, 607-8453, Japan

    Kihachiro Kikuzawa

  3. Department of Biology, McGill University, 1205 Avenue Dr. Penfield, Montréal, QC, H3A 1B1, Canada

    Martin J. Lechowicz

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Correspondence to Kihachiro Kikuzawa .

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Editors and Affiliations

  1. Graduate School of Life Sciences, Tohoku University, Sendai, Japan

    Kouki Hikosaka

  2. Environmental Sciences, Estonian University of Life Sciences Institute of Agricultural and, Tartu, Estonia

    Ülo Niinemets

  3. Crop and Weed Ecology, Centre for Crop Systems Analysis, Wageningen University, Wageningen, Gelderland, The Netherlands

    Niels P.R. Anten

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Kikuzawa, K., Lechowicz, M.J. (2016). Axiomatic Plant Ecology: Reflections Toward a Unified Theory for Plant Productivity. In: Hikosaka, K., Niinemets, Ü., Anten, N. (eds) Canopy Photosynthesis: From Basics to Applications. Advances in Photosynthesis and Respiration, vol 42. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-7291-4_15

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