Results

3.1 Underlying growth pattern of trees

We revealed the growth trajectories of trees on the century scale, at the aggregate, and individual levels. With DBH as the gradient, the maximum tree ring increment of fir communities at different altitudes was determined and the results are presented in Fig. 2, which reflects the inherent or ideal growth law independent of the environment. The radial growth of ideal trees at altitude of 2,900m, 3,100m and 3,300m exhibit unimodal (Figs. 2b and c) or bimodal (Fig. 2a) characteristics. For a range of DBH less than 80 cm, the fir radial growth at all altitudes except at the treeline exhibit a unimodal curve extended by Gompertz pattern (Eq. 1b) (Tab. S2). We also directly observed a unimodal curve based on logistic pattern in the larger DBH interval (>80 cm) (Tab. S2). The growth also shows an initial increase and then a linear decreasing pattern, as shown in Fig. 2d. Trees at the altitude of the treeline are subjected to a harsher environment, and the observed linear growth pattern may indicate the incomplete expression of a unimodal pattern.
The aboveground biomass measurements also reveal the unimodal growth of ideal trees, as shown in Fig. 3. These unimodal curves are as obvious as those corresponding to radial growth. The unimodal parts are still well explained by Eqs. 3 and 2 (R2>0.7, P<0.01. Tab. S3). From a more complete growth curve, it can be seen that the growth trajectory of trees can transit from one smaller unimodal curve to a larger one, as shown in Fig. 3a. Not only that, the average increment dynamics may be unimodal or multimodal because of the covariant relationship with the ideal increment dynamics (Fig. S2). For the same reason, the biomass dynamic near the forest line (Fig. 3d) was similar to that of DBH (Fig. 2d). To a large extent, these results directly support H1.
The growth trajectories of selected trees were determined and are shown in Fig. 4. Clearly, these unimodal curves vary in size and do not fully cover the entire growth process, as some independent growth changes occur before and after the unimodal curve. In fact, there may be more than one unimodal curve, as shown in Fig. 4e. The maximum heights and lengths of the unimodal curves increase with tree size. For example, the lengths of unimodal trajectories of trees with biomass 1412 kg and 4855 kg are 510 kg and 2053 kg respectively, and the heights of those are 115 kg and 180 kg respectively (Figs. 4h and i). These trajectories driven by radial and tree height growth conform to the Gompertz curve. See Tab. S4 for fitting results.These results support H2.

3.2 Change of functional traits with growth

Due to the lack of significant difference in module traits (i.e., leaf and stem economics) of individual trees, here, we only presented the traits corresponding to different size intervals (Ⅰ, Ⅱ, and Ⅲ), as shown in Figs. 5 and 6. However, structural indicators (canopy/size and SWA/SHA) are not stable. Except for trees located at the treeline (Fig. 7d), the canopy/size and size of other trees at other elevations should conform to the logistic relationship. The SWA/SHA and sizes of all trees show an obvious inverse relationship (see Tab. S5 for fitting results). According to our hypothesis, increasing canopy/size and decreasing SWA/SHA would result in a greater growth increment and maximum biomass (Fig.1 and Tab. 1). Thus, these two traits may be related to cascading growth. In practice, in accordance with the actual biomass intervals in Figs. 3a and c where the Gompertz curves are located (i.e., left side of vertical solid line in Figs. 3a and c), the SWA/SHA and canopy/size of ideal trees can be estimated by the size of ideal trees (dotted line in Fig. 7) and the size-traits function. The calculated SWA/SHA and canopy/size are 0.28 and 0.75 (2,900m), 0.30 and 0.79 (3,100m) and 0.47 and 0.70 (3,300m).

3.3 Changes in canopy and sapwood relative to size are the main causes of cascading growth

With very stable leaf and stem economics, we next tested whether canopy /size and SWA/HWA can affect the formation of unimodal curve. According to Fig. 1 and Tab. 1, we tested canopy /size ∝ maximum growth rate (∝cM ), SWA/HWA ∝ mr and SWA/HWA∝ 1/maximum growth rate (∝ 1/cM ). In addition to individual trees at an elevation of 3,100m, these analyses also included ideal trees at different altitudes (black dots). All relationships are confirmed well (R2>0.56, p<0.01), as shown in Figs. 8a, b and c. Due toM maxcM /mr (Fig. S3), we expected a positive correlation between canopy /size ×HWA/SWA andM amax. WhenM amax is less than 2100kg, this correlation tends to be linear (R2= 0.93, p<0.01), as shown in Fig. 8d. Overall, this relationship is closer to power function (R2= 0.93, p<0.01). Obviously, the the height and length of the growth curve can be largely explained by the morphological traits, consistent with H3.