Effectiveness of the Canopy Closure Curve to Inform Management of Two-Storied Stands

Abstract

In this study we examined the validity of the canopy closure curve as a reference in relation to light conditions and demonstrated the applicability of the curve to different thinning types. An even-aged sugi (Cryptomeria japonica) plantation of 91 years was thinned heavily and transformed to a two-storied stand by underplanting with sugi and hinoki cypress (Chamaecyparis obtusa) seedlings. Three initial sample plots were selected in the stand before thinning. After the conversion, five permanent sample plots were established and both overstory and understory trees were measured up to the age of 118 and 28 years, respectively. The canopy closure curve was estimated from measurements collected in the initial sample plots and crown density (i.e. the ratio of overstory productivity to the maximum stand productivity) was calculated based on the canopy closure curve as a reference. To validate the curve, we derived three time points from the measurements collected in the permanent sample plots: one when the trajectory of stem density and stand volume of the overstory trees intersected the canopy closure curve, one when the relationships between the volume of individual overstory trees and their growth changed, and one point when the growth of understory trees dropped. The first of these time points coincided with the second and third time points. This means that dominant overstory trees suppressed smaller overstory trees and overstory trees constrained the growth of understory trees because of light reduction when the canopy closed. The canopy closure curve was found to be a valid way to assess light controlling the growth of understory trees. Furthermore, we generated virtual thinning data from the measurements taken in the initial sample plots for different thinning types. We obtained the canopy closure curve for these. We plotted the trajectory of stem density and stand volume in relation to the thinning as well as the canopy closure curve to demonstrate the applicability of the canopy closure curve. The thinning simulation showed sufficient effect to demonstrate that there was no need for additional accretion cutting.

INTRODUCTION

In Japan, to deliver environmental benefits, there have been attempts to transform conifer plantations to two-storied stands by artificial or natural regeneration after heavy thinning in 1980s. Recently, the transformation to mixed conifer-broadleaved stands has drawn a lot of attention. In Europe, interest in continuous cover forestry (CCF) was revived in 1980s as a result of environmental problems, and an emphasis is placed on the direct transformation of even-aged plantation forests to mixed uneven-aged forests (Pommerening and Murphy, 2004). Mason et al. (2022) undertook a questionnaire survey and found that a lack of experience of undertaking such transformations is one of the major obstacles that limit wider use of CCF. One of the problems with a multi-storied forest management system is that inappropriate management decreases light intensity, which causes a decrease in the growth of understory trees and possible mortality, leading to the destruction of stand structure (Oka, 1991). Control of light conditions is important to establish and manage multi-storied plantation forests, and indicators of light conditions have been used to predict the growth of understory trees in two-storied stands.

Because light conditions vary inside a stand and light intensity is difficult to measure for all individual trees using light sensors or hemispherical photography (see Fujiyama et al., 2020), stand characteristics have been used as indicators of light condition. To model the growth of understory trees, relative light intensity is first estimated from a stand characteristic, then their growth is predicted using this figure. Variables related to stem volume, such as yield index and basal area, can be used as indicators of relative light intensity to some extent, as can variables related to crown structure (Fujimori, 1989). For example, Ando (1983) and Kaminaka et al. (1983) used yield index to estimate relative light intensity after thinning in sugi (Cryptomeria japonica D.Don) and hinoki cypress (Chamaecyparis obtusa (Sieb. et Zucc.) Endl.) plantations, whilst Kiyono (1990) used mean land area per tree and mean crown length to estimate relative light intensity in hinoki cypress plantations and to develop charts for estimating relative light intensity. Yield index has also been used by Ando and Takeuchi (1990) to predict the growth of two-storied stands of sugi and hinoki cypress.

Instead of estimating light conditions directly, stand characteristics can be used to derive an indicator, then the growth of understory trees predicted using this. Yamamoto (1993, 1995) used the relative spacing of overstory trees to predict the growth of understory trees in two-storied stands containing a mixture of Japanese larch (Larix kaempferi Carr.) and Sakhalin fir (Abies sachalinensis (Fr. Schm.) Masters). Tatsuhara and Suzuki (1995) determined 'stand productivity' from stem density and stand volume and incorporated 'crown density' (i.e. the ratio of overstory productivity to the maximum stand productivity) as an indicator of the shading of the understory by the overstory. They then used the stand productivity to predict the growth of understory trees in two-storied sugi stands.

The 'canopy closure curve' acts as a reference for the measured crown density. The curve theoretically represents the stem density and stand volume when the canopy closes again after thinning and can change depending upon stand conditions just before and after thinning; it is drawn parallel to the full density curve on a stand density control diagram (Tatsuhara, 1993; 2001). The stand density control diagram was developed, assuming typical low thinning; the yield index in the diagram was calculated using the full density curve as a reference. The yield index is calculated simply from the stem density and stand volume of a stand, although it is limited for use as an indicator of the light conditions experienced by understory trees because it depends on individual species only and a typical thinning method is assumed. Conversion thinning from an even-aged stand into a two-storied stand is usually heavier than typical thinning and this type of thinning may be different from low thinning.

In this paper, we examine the validity of the canopy closure curve as a reference in relation to light conditions and demonstrate the applicability of the curve to different thinning approaches. For these, we use long-term measurements from a two-storied stand transformed from an even-aged sugi stand by heavy thinning. To validate the curve, we derived three time points: one when the trajectory of stem density and stand volume of the overstory trees intersected the canopy closure curve, one when the relationships between the volume of individual overstory trees and their growth changed, and one when the growth of understory trees dropped as a result of suppression by the overstory trees. We compare the first of these time points with the second and third time points. To demonstrate the applicability of the canopy closure curve, we generated virtual thinning data, simulated different thinning types, and plotted the trajectory of stem density and stand volume in relation to the thinning as well as the canopy closure curve.

MATERIALS AND METHODS

Study Site

The study was conducted in Subcompartment C5, Compartment 2 of The University of Tokyo Chiba Forest (hereafter called Chiba Forest), located in the southern part of Boso Peninsula, in Chiba Prefecture, Japan (35°10´N; 140°6´E). Almost the entire subcompartment was planted with sugi in 1902. A 0.073-ha permanent experimental plot named Anno No.2 was established within the even-aged sugi stand in May, 1916 and has been measured every five years (Takeuchi and Hasegawa, 1975). The even-aged sugi stand was thinned at 91 years of age during the period January to March, 1992. Part of the stand was thinned heavily at that time to transform to a two-storied stand. The thinning ratios of the overstory trees in terms of the number of trees and volume were 50% and 30%, respectively. The relative light intensity just after thinning was 28.2%. The stand was underplanted with sugi and hinoki cypress seedlings in October, 1992. The seedlings were planted in lines, parallel to the direction of the slope and two consecutive lines of sugi seedlings and one line of hinoki cypress seedlings were alternated with lower planting stem density than in an even-aged stand. The stand is situated at an elevation of 190–217 m above sea level on an east-facing slope. Anno No.2 was outside the two-storied stand and have been kept an even-aged stand. Measurements taken in Anno No.2 were also used to compare the growth of underplanted trees on a two-storied stand with that of unshaded trees on an even-aged stand because it has the same site quality as the study site.

Field Investigation

In December, 1991, prior to the thinning operation, three plots were sampled on lower, intermediate, and upper parts of the slope in the stand to be transformed into a two-storied stand to calculate thinning intensity. The three initial sample plots are referred to as Plots 1, 2, and 3, respectively, in this paper. We measured diameter at breast height (DBH) and height of both trees to be retained and to be thinned. These data were used to obtain a parameter for the canopy closure curve, which requires information on stand structure just before and after thinning in the case of the actual thinning and simulated thinnings.

In December, 1996, after conversion into a two-storied stand, five permanent sample plots were established parallel to the direction of the slope in the stand; these are referred to as Plots A to E (Fig. 1). The DBH and height of all the overstory trees were measured five times: at 95, 98, 102 (the age was regarded as 102 years because the plots were measured at 103 years before the growth period), 111, and 118 years of age. The volume of the overstory trees, including trees before the thinning, was calculated using cubic curves to account for stem taper and with parameters calculated from the data obtained by Tange et al. (1987) for Chiba Forest. For all understory trees, DBH and height were measured nine times: at 5, 7, 8, 10, 12, 14, 16, 21, and 28 years of age. These data were used for main analyses of the growth of overstory and understory trees in the two-storied stands.

Fig. 1.

The layout of the permanent sample plots at the study site.

Note: The lowermost part of Plot D was excluded because it contained some different overstory species, including hardwoods.

Validating the Canopy Closure Curve

Obtaining a parameter for the canopy closure curve

The stem density and stand volume of each of Plots 1–3 were calculated from the measurements. The stem density and stand volume of Plots A to E were calculated from the measurements and then the total stem density and stand volume for all the plots combined were obtained. Because the five permanent sample plots were established in 1996, the stem density and stand volume in 1991 were unknown. Thus, the stem density in 1991 was assumed to be the same as that in 1996. The stand volume was assumed to have increased by 10 m³ ha^-1 year^-1 for the five years immediately after thinning in 1991 because the periodic annual increments (PAIs) of stand volume just after thinning were around 10 m³ ha^-1 year^-1 in Anno No.2. To create a virtual stand with the same stem density and stand volume as the study site in 1991, the area ratio to mix was calculated, using Plots 1–3. The area ratio between the three initial plots was set at 1 for Plot 2 and at x and y for Plots 1 and 3, respectively, and simultaneous equations relating to the stem density and stand volume were solved to obtain the values of x and y.

Tatsuhara (1993) suggested that the following equation linking stand volume V (m³ ha^-1) and number of trees N (trees ha^-1) is true when the canopy closes.   

$\text{log}V+\frac{1-\beta }{\beta }\text{log}N=-\frac{\text{log}\alpha }{\beta }$(1)

. It is referred to as the 'canopy closure curve'. Parameter β is a constant that is dependent on species. Parameter α is a constant that is dependent on species before the first canopy closure, and depends on thinnings thereafter; it is obtained from the stand structures before and after thinning by Eq. (2):   

$\text{α}=\frac{v_{max}{}^{0.15}\sum v_A^{0.85}}{V_A^{\beta }{N}_A^{1-\beta }{V}_B}$(2)

, where V_B is the stand volume (m³ ha^-1) before thinning, v_max is the volume (m³) of the largest tree in a stand, and V_A, N_A, and v_A are the stand volume (m³ ha^-1), stem density (trees ha^-1), and the volume (m³) of each tree after thinning, respectively. We calculate parameter α with Eq. (2) from the virtual stand created from the three initial sample plots. We determined the canopy closure curve expressed by Eq. (1), setting parameter β at 0.521, which was obtained for sugi by Tatsuhara (1993). We calculated the stem density and stand volume for overstory trees every time they were measured and plotted them on a log-log scale with the canopy closure curve. 'Crown density' C is expressed as the ratio of overstory productivity P_o (m³ ha^-1 year^-1) to the maximum stand productivity A (m³ ha^-1 year^-1) (Tatsuhara and Suzuki, 1995) as follows:    C=P_o/A=αV^βN^1-β.    (3)    The equation above is transformed as follows:   

$\text{log}V+\frac{1-\beta }{\beta }\text{log}N=\frac{\log C-\text{log}\alpha }{\beta }$(4)

. The curves with C of 0.9, 0.8, 0.7, 0.6, 0.5, and 0.4 were also drawn on the graph. They are 'equivalent crown density curves', and are plotted parallel to the canopy closure curve on a log-log scale.

Obtaining a growth model parameter for overstory trees

Tatsuhara (1992a) derived the following volume growth equation:    dv/dt = kvⁿ – bv^2/3,    (5)    where k is a variable which is constant for trees in the same stand at the same time and b is a constant that varies according to species and region. Parameter n is around 1 for closed stands and varies between 0.7 and 1 for open stands (Tatsuhara, 1992b; 1993). This means that the relationships between the volume of individual trees and their growth change when the canopy closes and that the value of parameter n indicates whether the canopy is open or closed. The first term on the right-hand side of Eq. (5) is referred to as 'productivity' (Tatsuhara, 1992b). We calculated the productivity p (m³ year^-1) from two consecutive measurements of each of the overstory trees in the permanent sample plots, setting parameter b at 0.0305, which was obtained for sugi by Tatsuhara (1992), as follows:   

$p=\frac{v_2-v_1}{\Delta t}+b\frac{v_2^{2/3}-v_1^{2/3}}{2}$(6)

, where Δt is the interval (year) between two consecutive measurement, v₁ and v₂ are volumes (m³) of each overstory tree at the beginning and at the end of the measurement period, respectively. Then we obtained parameter n for each pair of consecutive measurements. The measurements in December, 1996 were excluded from this analysis because tree numbers were not the same as in the next investigation.

Growth of understory trees

We counted the number of understory trees in the permanent sample plots and calculated their mean DBH and height and their PAIs. A lot of understory trees were damaged by snow and deer browsing during the experiment. The trees fatally damaged by stem breakage, uprooting, or deer browsing were excluded from this analysis. That is, these trees were not counted as live trees, even though they were still alive during part of the investigation. Trees whose tops had been damaged but continued to grow were included in this analysis. That is, these trees were counted as live trees, and their DBHs and heights were included in the average calculation once they exceeded the size before the damage.

We compared the DBH and height mean values and PAIs of sugi in the experimental plots to those in Anno No. 2 to compare the growth of the understory trees to that of trees grown without shading. The measurements in Anno No. 2 before the age of 40 years, that is, 14, 19, 23, 28, 33, and 39 years were used. Anno No. 2 was thinned at the age of 19 years (Takeuchi and Hasegawa, 1975).

Applying the Canopy Closure Curve to Different Thinning Types

We simulated different thinning types and derived the canopy closure curves for them. At the study site, low thinning was implemented to transform an even-aged stand to a two-storied stand. Thus, different thinning types, that is, mechanical thinning and crown thinning were simulated in the virtual stand. In the simulation of the mechanical thinning, random numbers were generated for each tree between 0 and 1 with MS Excel and the half of the trees with the lowest allocated numbers were selected for thinning. In the simulation of the crown thinning, trees that were actually thinned were retained and the remaining trees were thinned. After the selection of trees to be thinned, the values of parameter α from Eq. (2) were calculated and the canopy closure curves were obtained using Eq. (1). The crown densities were calculated from stem density and stand volume after thinning using Eq. (3). We compared the canopy closure curve and the crown density after thinning for low thinning, mechanical thinning, and crown thinning.

RESULTS

Validating the Canopy Closure Curve

Overstory trees

The stem density and stand volume of the three initial sample plots and the overstory trees in the five permanent sample plots are shown in Tables 1 and 2. Simultaneous equations relating to the stem density and stand volume were as follows:    (238x+392+634y) / (x+1+y) = 376,    (7)       (755x+565+488y) / (x+1+y) = 594.    (8)   

Table 1. Condition of the three initial sample plots before and after thinning

Plot	Area (ha)	Site location on the slope	Stem density (trees ha-1)			Stand volume (m3 ha-1)
			Before thinning	After thinning		Before thinning	After thinning
1	0.122	Low	508	238		1,041	755
2	0.120	Intermediate	742	392		832	565
3	0.101	Upper	1,307	634		723	488

Table 2. Initial condition of the five experimental plots

Plot	Area (ha)	Overstory trees at establishment of the plots			Understory trees at planting
		Stem density (trees ha-1)	Stand volume (m3 ha-1)		Stem density (trees ha-1)	Species composition (%)
						Sugi	Hinoki cypress
A	0.1379	486	589		2,212	68	32
B	0.1398	365	650		2,082	71	29
C	0.1020	343	656		2,255	65	35
D*	0.0803	324	708		2,017	62	38
E	0.1044	316	645		2,146	65	35
Total	0.5644	376	644		2,147	67	33

* The lowermost part of Plot D was excluded because it contained some different overstory species, including hardwoods.

Solving Eqs. (7) and (8), the values of the two variables obtained were x=0.219 and y=0.055. The stem density and stand volume of the study site just before thinning were estimated using an area ratio between the three initial plots of 0.219:1:0.055. The parameter α was 0.001745. Eq. (1) was expressed as follows:    logV + 0.919logN = 5.311.    (9)   

Thus the trajectory of stem density and stand volume was drawn continuously from the virtual stand to the total value for the five permanent sample plots (Fig. 2). The stand transitioned from low stem density/stand volume with a crown density of 0.82 immediately after thinning, increasing until values approached the canopy closure curve. The crown density at 106 years, when the understory trees were 16 years old, was estimated to be 0.95 from the values at 102 years and 111 years. The value for crown density became 1.0 at 111 years when the understory trees were 21 years old, meaning that the trajectory of stem density and stand volume reached the curve at 111 years and crossed over the curve at 118 years.

Fig. 2.

The actual trajectory of stem density and stand volume with respect to the overstory trees.

The trajectory between thinnings was estimated from the measurements collected in the three initial plots and the trajectory after thinning was determined using measurements from all the permanent sample plots. The numbers besides the dots indicate the stand ages.

Parameter n in Eq. (5) for the overstory trees was around 0.85 for the first two measurement periods, 98–102 years and 102–111 years, and increased to over 0.9 in the last measurement period, 111–118 years (Table 3). The time when the overstory trees intersected the canopy closure curve coincided with the time when parameter n approached 1.

Table 3. Stand conditions and the values of parameters for the overstory trees

Age (year)	98		102		111		118
Stem density (trees ha-1)	370		369		363		363
Stand volume (m3 ha-1)	702		755		885		1,013
Mean volume (m3 tree-1)	1.90		2.05		2.44		2.79
Crown density	0.88		0.92		0.99		1.00
Parameter k		0.0456		0.0472		0.0449
Parameter n		0.8442		0.8372		0.9174

Understory trees

The stem density of the understory trees had reached about two-thirds of their planting stem density at 28 years (Fig. 3). Hinoki cypress always exhibited larger mean values than sugi both for DBH and for height, and hinoki cypress had larger PAI than sugi in many cases both for DBH and for height (Fig. 4). PAI peaked at an age younger than 10 years both for DBH and height for both sugi and hinoki cypress and after that it tended to decrease (Fig. 4). PAI of DBH dropped sharply in the penultimate measurement period, 16–21 years, and continued to decrease in the last measurement period, 21–28 years (Fig. 4a). For height, PAI dropped in the last measurement period, 21–28 years, after leveling off in the two to three previous measurement periods (Fig. 4b).

Fig. 3.

The change in the stem density of understory trees in all the permanent sample plots over time.

Fig. 4.

Means and PAIs of (a) DBH and (b) height of understory trees in all the permanent sample plots.

Comparing the increments of sugi to those of the same species in Anno No.2, the stem density of the latter was high and was estimated to be about 4,000 trees ha^-1 (Fig. 5). At 14 years, when Anno No.2 was established, the mean DBH of the sugi understory trees at the study site was 39% of that in Anno No.2. Thereafter, the PAI of DBH in Anno No.2 was around 0.2 cm and that of the sugi understory trees at the study site during the last two measurement periods dropped to 0.15 cm and 0.08 cm (Fig. 6a). At 14 years, the mean height of the sugi understory trees at the study site was 52% of those in Anno No.2. Thereafter, the PAI of height in Anno No.2 was around 0.2 m and that of the sugi understory trees at the study site during the last measurement period dropped to 0.13 m (Fig. 6b).

Fig. 5.

Comparison between the stem density in all the permanent sample plots and that in Anno No.2.

Fig. 6.

Comparison of means and PAI of (a) DBH and (b) height between understory sugi trees in all the permanent sample plots and the unshaded trees in Anno No.2.

Applying the Canopy Closure Curve to Different Thinning Types

In the thinning simulation, the crown densities immediately after mechanical thinning and crown thinning were 0.63 and 0.42, respectively. The crown density after mechanical thinning was lower than that in the actual thinning, as was the value for crown thinning in relation to mechanical thinning (Fig. 7). The parameter α obtained was 0.001545 for mechanical thinning and 0.001481 for crown thinning. The canopy closure curve after mechanical thinning was in the upper right on the graph of stem density and stand volume compared to that for the actual thinning, and the canopy closure curve after crown thinning was in the upper right on the graph of stem density and stand volume compared to that for the mechanical thinning (Fig. 7).

Fig. 7.

The simulated trajectory of stem density and stand volume with respect to the overstory trees in the case of (a) mechanical thinning and (b) crown thinning.

DISCUSSION

We analyzed the measurements of overstory and understory trees in a two-storied stand. We found that the time point during the period 111–118 years of age at which the trajectory of stem density and stand volume of the overstory trees intersected the canopy closure curve (Fig. 2) coincided with the time when parameter n for the overstory trees approached 1 (Table 3) and the time when the PAI of the mean height of understory trees dropped sharply, when they were aged 21–28 years (Fig. 4). It follows from this that the relevant point on the canopy closure curve corresponded to the time when the canopy had just closed and constrained the growth of understory trees. Thus, the canopy closure curve can be used as a reference in relation to light control of underplanted trees. It can also be used as a criterion to judge when to undertake thinning. When the trajectory of the stem density and stand volume crosses through the curve, the stand should soon be thinned. However, this point would be too late for thinning if there are understory trees, and thinning should be implemented before the curve is intersected.

Kawahara (1983) suggested that sugi is more sensitive to shading than hinoki cypress and DBH is more responsive to this than height. In addition, the light compensation point of photosynthesis for hinoki cypress is about half that for sugi, and hinoki cypress proved to be more tolerant of shading than sugi (Osono et al., 2021). At our study site, hinoki cypress understory trees have grown more than sugi understory trees (Fig. 4). Note that sugi understory trees were not suppressed by hinoki cypress understory trees in the study site. Comparisons of DBH and height of sugi understory trees at 14 years of age at the study site against unshaded trees in Anno No.2 revealed that the relative value of DBH of understory trees compared to unshaded trees was smaller than that of height (Fig. 6). PAIs of DBH dropped sharply in the penultimate measurement period, 16–21 years, although PAIs of height clearly reduced in the last measurement period, 21–28 years (Fig. 6). These results correspond to those reported by Kawahara (1983). It is difficult to compare the understory trees at the study site with Anno No.2 because in Anno No.2, the first canopy closure occurred earlier and DBH growth was lower as a result of the high planting stem density (Fig. 5). We compared the measurements of the two stands at 14 years of age because of the limited effect of stem density on the measurements in the earlier growth stage. Relative values of DBH and height were 39% and 52%, respectively, and these correspond to the relative light intensities of 17% and 16%, respectively according to Kawahara's (1983) equations describing relative values of diameter at the ground and height and relative light intensities. This result would be reasonable if we consider the relative light intensity of 28.2% just after thinning.

Twenty years after thinning, the stand volume of overstory trees recovered to the value just prior to thinning, and the canopy of the overstory trees was considered to have closed at that time (Fig. 2). PAIs of DBH for the understory trees, especially of sugi, approached zero in the last measurement period, 21–28 years, after having dropped sharply in the penultimate measurement period, 16–21 years (Fig. 4a). PAIs of height also dropped in the last measurement period, 21–28 years (Fig. 4b). Thus future DBH growth of understory trees will be very restricted and the future height growth is expected to be small. Therefore, the overstory trees should have been thinned around 106 years (16 years for understory trees), or 111 years (21 years for understory trees) at the latest, to allow the understory trees to grow. It suggests that a crown density of 0.95 can be used to indicate the time when accretion cutting operation should be undertaken.

To avoid the need for additional thinning, more intensive thinning should have been implemented to the overstory trees before conversion into a two-storied stand. Thinning more trees has been employed to increase canopy openness in experiments to develop two-storied stands by Suzuki et al. (1996). However, even with the same thinning ratio in terms of the number of trees, mechanical thinning and crown thinning led to greater canopy openness, and the stem density and stand volume attained lower values early on than the values recorded for the actual thinning (Fig. 7). Moreover, the value of parameter α decreased and the value of the right side of Eq. (1) increased, moving closer to the canopy closure curve later on, with higher values of stem density and stand volume on the log-log scale. Furthermore, the productivity of residual trees decreased, resulting in slow increases in stand density. More time is needed before the next canopy closure.

The same effect can be achieved by raising the thinning ratio in terms of the number of trees managed by low thinning. However, the thinning simulation showed sufficient effect to prevent the need for additional accretion cutting. The method is applicable to different thinning types other than low thinning.

CONCLUSIONS

In this paper we have shown that the canopy closure curve of overstory trees is relevant to light control of the growth of understory trees according to the relationships between the growth of overstory trees and the change in growth of understory trees. The canopy closure curve is a useful reference for light control because it can be derived easily from the thinning condition of the stand upon which it depends. Crown density based on the canopy closure curve as a reference can also be a useful indicator of light condition. The results reveal the need for additional thinning at the study sites, and suggest that a crown density of 0.95 indicates the need for an accretion cutting to keep the PAI of DBH. Because limited thinning was implemented at the study site, mechanical thinning and crown thinning were simulated as the conversion thinning. This showed the possibility of avoiding the need for a second thinning. The canopy closure curve could also act as a reference in relation to stand density control, although further investigations are necessary to determine the specific value indicating the need for thinning.

FUNDING

This study was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Numbers JP08406012, JP10760093, JP24580215, and JP15K07469.

ACKNOWLEDGEMENTS

We would like to thank staff at Chiba Forest, members of 'Abies' which is a volunteer group working for Chiba Forest, students at the Laboratory of Forest Management, Graduate School of Agricultural and Life Sciences, The University of Tokyo, and students at the Laboratory of Forest Mensuration, Faculty of Agriculture, Niigata University for their assistance in measuring trees on the study site.

LITERATURE CITED

• Ando, T. (1983) Relative light intensity in sugi (Cryptomeria japonica) stands after thinning. Bull. For. & For. Prod. Res. Inst. 323 : 58–59 (in Japanese)
• Ando, T. and Takeuchi, I. (1990) Sugi, hinoki nidanrin no mitsudo kanri shishin no sakusei to seicho yosoku hoho no kento [Prescribing density management and examining growth prediction method for two-storied stands of Cryptomeria japonica and Chamaecyparis obtusa]. Kaiho 331 : 1–11 (in Japanese)
• Fujimori, T. (1989) Fukusorin no seitai to toriatsukai [Ecology and management of multi-storied stands]. Ringyokagakugijutsushinkojo, Tokyo, 96 pp (in Japanese)
• Fujiyama, M., Igarashi, S. and Ichie, T. (2020) Effects of environmental conditions on the survival and growth of seedlings and small- and medium-sized trees of Japanese cedar (Yanase-sugi) in Senbonyama Gene Preservation Forest. J. Jpn. For. Soc. 102 : 239-243 (in Japanese with English abstract)
• Kaminaka, S., Ogata, N. and Ando, T. (1983) Relative light intensity in hinoki (Chamaecyparis obtusa) stand after thinning. Bull. For. & For. Prod. Res. Inst. 323 : 55–57 (in Japanese)
• Kiyono, Y. (1990) Dynamics and control of understories in Chamaecyparis obtusa plantations. Bull. For. & For. Prod. Res. Inst. 359 : 1–122 (in Japanese with English abstract)
• Kawahara, T. (1983) Comparison between the growth of seedlings under the artificial shading and that of seedlings underplanted in the forest. Bull. For. & For. Prod. Res. Inst. 323 :133–134 (in Japanese)
• Mason, W.L., Diaci, J., Carvalho, J. and Valkonen, S. (2022) Continuous cover forestry in Europe: usage and the knowledge gaps and challenges to wider adoption. Forestry 95 : 1–12
• Oka, S. (1991) Gemba kara mita fukusorin no mondaiten nitsuite [About problems with multi-storied forests viewed by a forester]. Shinrin Kagaku 1 : 72 (in Japanese)
• Osone, Y., Hashimoto, S. and Kenzo, T. (2021). Verification of our empirical understanding of the physiology and ecology of two contrasting plantation species using a trait database. Plos One, 16 (11): e0254599. https://doi.org/
• Pommerening, A. and Murphy, S.T. (2004) A review of the history, definitions and methods of continuous cover forestry with special attention to afforestation and restocking. Forestry 77 : 27–44
• Suzuki, M., Tatsuhara, S. and Nagumo, H. (1996) Growth of understory trees in two-storied sugi (Cryptomeria japonica) stands: Effect of thinned overstory shading on growth of understory trees. J. Jpn. For. Soc. 78 : 50–56 (in Japanese with English abstract)
• Takeuchi, K. and Hasegawa, S. (1975) Records on the growth of stands in the Tokyo University Forest in Chiba. Misc. Inform. Univ. of Tokyo For. 19 : 69–175 (in Japanese)
• Tange, K., Yamanaka, I. and Suzuki, M. (1987) Growth and biomass of an old manmade Cryptomeria japonica stand. Misc. Inform. Tokyo Univ. For. 25 : 243–259 (in Japanese with English abstract)
• Tatsuhara, S. (1992a) An integrated description of stand growth and tree growth in pure even-aged closed stands. J. Jpn. For. Soc. 74 : 28–36 (in Japanese with English abstract)
• Tatsuhara, S. (1992b) An integrated description of stand growth and tree growth in pure even-aged young stands. J. Jpn. For. Soc. 74 : 364–372 (in Japanese with English abstract)
• Tatsuhara, S. (1993) The relationship between volume growth and canopy closure in pure even-aged stands. J. Jpn. For. Soc. 75 : 120–128 (in Japanese with English abstract)
• Tatsuhara, S. (2001) Modelling growth for two-storied stands: incorporating an effect of shading on the tree growth into growth and yield models. J. For. Res. 6 : 231–239
• Tatsuhara, S. and Suzuki, M. (1995) Modelling volume growth for two-storied sugi (Cryptomeria japonica) stands. J. Jpn. For. Soc. 77 : 9–19
• Yamamoto, H. (1993) Studies on growth prediction of two-storied artificial stands (II) Growth model of mixed planting two-storied stands of Japanese larch and Saghalien fir. J. Jpn. For. Soc. 75 : 65–69 (in Japanese)
• Yamamoto, H. (1995) Studies on growth predictions of two-storied artificial stands (III) A system yield table of two-storied stands for Japanese larch and Saghalien fir. J. Jpn. For. Soc. 77 : 197–204 (in Japanese with English abstract)