Large-tree growth follows a unimodal cascading pattern under the
combined effect of allometric scaling and growth plasticity
Shu-miao Shua,b†, Wen-zhi Wanga†,
Wan-ze Zhua* Yang-yi Zhaoc Min
Jiaa,b Xiao-xiang Zhaoa,b
a Institute of Mountain Hazard and Environment, Chinese Academy of
Sciences, Chengdu 610041, China;
b University of Chinese Academy of Sciences, Beijing 100000, China;
c Southwest Forestry University, Kunming 650000, China;
Corresponding authors. W.Z. Zhu
† These authors contributed equally to this work and should be regarded
as co-first authors.
Addresses: Institute of Mountain Hazards and Environment, Chinese
Academy of Sciences, Chengdu 610041, China, E-mail addresses:
wzzhu@imde.ac.cn (W.Z. Zhu)
Abstract :
The continuously increasing trend of large-tree growth challenges the
assertion of the unimodal pattern in classical growth theories. Here, we
considered the effect of phenotypic plasticity on growth and extended
classical growth equations (i.e.,
Gompertz and
logistic curves) to reconcile this
contradiction. Tree growth is indeterminate and modular, and we
speculated that a trajectory of tree growth should be viewed as a
combination of a series of different unimodal curves, termed cascading
growth. Mathematically, the increasing growth trend may be attributable
to the later emergence of larger-scale unimodal curves, which depend on
some beneficial change of functional traits relative to tree size. To
test this hypothesis, we determined tree growth in four plots across the
subalpine Abies fabri forest belt on Gongga Mountain in the
eastern Tibetan Plateau of China, and then analyzed the effects of some
important functional traits (i.e., leaf and stem economics and
morphological traits) on the growth curve. Our results indicate that the
ideal growth trajectory that is composed of the maximum growth increment
of different trees follow a unimodal curve with a cascade
characteristic. At individual levels, the emergence of a larger unimodal
curve is caused by an increase in the relative amount of canopy and a
decrease in the relative amount of sapwood. This study clarifies the
general growth rule of large trees, offers a concise way to link traits
and growth performance, and reveals the complexity and sustainability of
a old forest acting as a carbon sink to some extend.
Key words: Abies fabri ; large-tree growth; tree ring;
aboveground biomass; unimodal pattern; logistic and Gompertz curves;
cascading growth
Symbolic meaning
M : biomass
M a: aboveground biomass
b: metabolic exponent, usually equal to 0.75 for trees
T : the time of development of unit tissue, controlled by genes
and physiological activity, independent of size, such as cell, callus or
organ formation time
f (M ): discrete biomass increment (∝ total amount of new
tissue) during time T
F (M ): discrete biomass increment
cM : average f (M ) throughout the
growth process, related to the average resource acquisition and
respiration consumption during time T
M max and M amax: tree
maximum biomass and tree maximum aboveground biomass
mr : maintenance respiration coefficients, i.e.,
the rate of maintenance respiration rate per unit of tissue
gr : growth respiration coefficient, i.e., the
amount of respiration needed to produce a unit of tissue, usually
considered as a constant
λ+ 1: intrinsic growth rate
o : initial biomass