1. Introduction
Plant growth is a fundamental ecological process that is affected by
physiology, community dynamics, and ecosystem properties (Paine et al.,
2012). For a forest ecosystem, the large-tree growth trend determines
the carbon budget of forests, especially old forests. Tree growth has
been thought to follow a ‘rise-and-fall’ unimodal pattern (i.e., the
tree biomass increment per unit time first increases and then decreases
with tree size), thus presenting a sigmoidal trajectory of biomass over
the lifetime of a tree (e.g., Ryan and Yoder, 1997). Most of the data
from chronosequence-based studies supports a decline in biomass
accumulation at the community scale (e.g., Acker et al., 2002; Ryan et
al., 1997). However, some studies of very old trees suggested an
increase in the growth increment with tree size or age (e.g., Sillett et
al., 2010; Johnson et al., 2009), which directly contradict the unimodal
or sigmoidal growth model. Although there is obvious inconsistency in
both aggregate and individual growth trends (Sheil et al., 2017), the
root cause of the conflict remains unknown. Overall, technical or/and
theoretical limitations have limited a more comprehensive understanding
of the growth behavior of large trees (Sheil et al., 2017).
Plant biomass accumulation represents the balance of photosynthetic
gains and respiratory losses. Increased total respiratory expenditure is
the main cause of productivity decline, which is generally considered to
conform to von Bertalanffy paradigm (Von Bertalanffy, 1957; West et al.,
2001; Shi et al., 2013). Gompertz and/or logistic equations based on the
this theoretical framework (see below) reasonably explain the growth of
most small plants (e.g., crops) (e.g., Shi et al., 2013; Karadavut et
al., 2008). These results support the rationality of the unimodal
pattern, and impels us to consider some significant differences between
trees and other small plants. Compared with small plants, large trees
have larger-scale physiological and ecological activities, resulting in
stronger and more flexible self-regulation ability. For instance, for an
average stand, tree height growth, as a game-theory problem (Falster et
al., 2003), depends on the presence of the height strategies of other
trees. Compared with large trees, the shorter life history of small
plants means there are fewer opportunities to be affected by external
factors (e.g., disturbances). Thus, small plants are more likely to
maintain their inherent growth strategies, thus presenting a growth
pattern that is consistent with the theory. More flexible growth
strategies, in contrast, may delay achievement of
photosynthetic-respiration balance.
Plant functional traits are measurable morphological and physiological
attributes that significantly affect whole-plant performance (Enquist et
al., 2007). Classical life history theory indicates that at least four
independent trait-defined axes (leaf-height-seed-stem) (Baraloto et al.
2010b) can shape the core strategies plants use to acquire and invest
resources (Falster et al., 2018). For example, wood density is related
to biomass allocation and photosynthetic carbon gain (Santiago et al.,
2004) and stem economics and adult stature largely explained
interspecific differences in growth strategies for rain forest tree
species (Héraul et al., 2011). To maximize the efficiency of using
system resources, increased size may shift the benefits and costs of
some trait-based trade-offs, resulting in a size-dependent change in the
net effect of a particular trait on growth (Falster et al., 2011). A
recent meta-analysis supported this idea, showing that trait-growth
correlations change with plant size (Gibert et al., 2016). Moreover,
functional balance allows an individual to adjust its growth strategy to
effectively respond to its immediate environment within the envelope of
possibilities defined by allometry (Chen et al., 2013). For example,
trees may make substantial plastic adjustment in morphology and anatomy
of newly developing leaves, xylem, and fine roots to respond to
environment stress (West 2019). If an increase in the investment of
valuable traits, plant resource use efficiency may increase as a result.
Meanwhile, for trees with obvious changes in size, the relationship
between these traits and plant size will change significantly. Due to
the indeterminate and modular growth of plants (Weiner 2004), we
speculated that the growth trajectory of large trees may include two or
more unimodal curves with different scales (i.e., cascading growth). On
the whole, the downward trend of the former unimodal trajectory may be
obscured by the larger upward trend of the latter trajectory. In
essence, cascading growth is result from plant exhibit a range of
phenotypes depending upon its environment (acclimation) (i.e.,
phenotypic plasticity).
The measurement of tree biomass remains a difficult challenge.
Researchers have used multiple indicators (e.g., diameter and tree
height) or a specific empirical equation to estimate tree biomass.
However, the range of a measured indicator limits the applicability of
empirical equations (Sileshi 2014). Variation in architecture and form,
ontogeny, bark thickness, wood density, damage, and rot all contribute
to variation within and among species (Sheil et al., 2017). Thus, it is
appropriate to estimate the biomass of trees with fitness and
competitive advantage (termed ideal trees) using calibrated equations.
These ideal trees grow in relatively ideal environments, so they can
invest more resources in growth and approach the ideal growth pattern.
The functional traits of these trees must be optimal to promote growth.
Obviously, if the growth trajectories of ideal trees are unimodal, then
other non-unimodal growth trajectories may represent the incomplete
expression of a unimodal pattern. This may be related to the relatively
weak influence of functional traits on growth. The ideal growth pattern
should be considered separately rather than included in the average
results.
We tried to determine whether the observed continuous growth uptrend can
be attributed to cascading growth. We hypothesized that: 1) the ideal
growth pattern of trees is unimodal (H1); 2) tree growth trajectories
may follow unimodal curves with cascade characteristics, and the scale
of new curves should increase with tree size (H2), and 3) cascading
growth is due to the beneficial change of functional traits relative to
tree growth (H3). Based on extended classical growth equations, these
hypotheses were specifically tested by analyzing the growth dynamics of
different subalpine Abies fabri forests in western China.