- Email: [email protected]
Self-thinning and size variation in a sugi (Cryptomeria japonica D. Don) plantation
Forest Ecology and Management 174 (2003) 413–421
Self-thinning and size variation in a sugi (Cryptomeria japonica D. Don) plantation Kazuharu Ogawaa,*, Akio Hagiharab a
Laboratory of Forest Ecology and Physiology, Graduate School of Bioagricultural Sciences, Nagoya University, Nagoya 464-8601, Japan b Laboratory of Ecology and Systematics, Faculty of Science, University of the Ryukyus, Okinawa 903-0213, Japan Received 18 October 2001; accepted 1 February 2002
Abstract Density and stem volume in a sugi (Cryptomeria japonica D. Don) plantation were monitored for 15 years from 1983 to 1997. The tree density decreased year after year from 5002 to 3108 ha1. The time-trajectory of mean stem volume and density provided evidence in favor of the 3/2 power law of self-thinning. The skewness of the frequency distribution of stem volume showed positive values, which means that the distribution is more or less L-shaped, and the skewness decreased with time, which indicates that smaller trees died as the stand grew. This trend is consistent with the asymmetric or one-sided competition hypothesis that self-thinning is driven by competition for light. Dead trees tended to distribute randomly with the stand growth. The relationship between standard deviation of stem volume and mean stem volume was formulated by a power function, whose exponent was significantly less than unity. This shows that coefficient of variation, ranging from 61.7 to 82.5%, decreased with increasing mean stem volume. That is, the relative size variation becomes small with stand growth. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Competition; Cryptomeria japonica D. Don; Size variation; Spatial distribution; Stem volume; The 3/2 power law of selfthinning
1. Introduction As trees in a stand grow larger they occupy more and more space, and sooner or later the gaps between trees are filled and they begin to interfere with each other’s access to resources like light, water and nutrients (Silvertown and Doust, 1993). Such interference or competition within the stand induces size variation and also density-dependent mortality or self-thinning. Much interest has been focused on size variation *
Corresponding author. Tel.: þ81-52-789-4071; fax: þ81-52-789-5014. E-mail address: [email protected] (K. Ogawa).
within tree populations (e.g., Benjamin and Hardwick, 1986; Begon et al., 1996) and self-thinning (e.g., Westoby, 1984; Weller, 1987), but very little is known about the relationship between the two. Changes in the frequency distribution of tree sizes that accompany the process of self-thinning include important implications for the structure and dynamics of tree populations. In the present study, we monitored a sugi (Cryptomeria japonica D. Don) population for 15 years to evaluate the self-thinning process, change in size variation and intraspecific competition. We analyzed the data to test the applicability of the 3/2 power law of self-thinning (Yoda et al., 1963), and to clarify
0378-1127/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 1 1 2 7 ( 0 2 ) 0 0 0 6 2 - 2
414
K. Ogawa, A. Hagihara / Forest Ecology and Management 174 (2003) 413–421
changes in the frequency distribution of stem volume and coefficient of variation. Since trees interact with their neighbors, it is more appropriate to study interference in a tree population by the measurement of explicit spatial relationships than measuring the population density (Silvertown and Doust, 1993). Therefore, subdividing the plot, we also identified the spatial distribution of occurrence of dead trees during the self-thinning process.
2. Materials and methods 2.1. Site description This study was made on a 21-year-old (as of 1983) sugi (C. japonica D. Don) stand in the Nagoya University Experimental Forest at Inabu, located about 55 km east of Nagoya, Aichi Prefecture, central Japan. This plantation was situated at an altitude of 960 m on an east-facing 238 slope. A plot of 15 m 20 m in area was established and was divided into 12 quadrats, each 5 m 5 m in area, in 1983. The seedlings were planted geometrically at initial planting density of 6000 ha1, and thinning was not made artificially after planting.
Fig. 1. Allometric relationships between stem volume, V, and stem girth at breast height, G. The regression lines are given by Eq. (1). *, 1983; ~, 1990; &, 1997.
2.2. Census and estimation of stem volume A yearly census was carried out on all the trees in the plot, in which stem girth at the breast height (1.3 m above the ground) was measured in October from 1983 to 1997. Six to fourteen different-sized sample trees were selected for non-destructively assessing the stem volume every year. Measurements were made of tree height, stem girths at 0.0, 0.3 and 1.3 m, and at 1.0 m interval thereafter. From the measurements, stem volume was calculated on the basis of Smalian’s formula (e.g., Avery and Burkhart, 1994). The stem volume of trees in the plot was estimated on the basis of the yearly allometric relation of stem volume, V (dm3), and stem girth at breast height, G (cm) (Fig. 1), V ¼ gGh
(1)
where g and h are coefficients (Ogawa and Kira, 1977; Hagihara et al., 1993). The values of g and h were,
respectively, in the range of 0.00273–0.0390 dm3 cmh, and 2.13–2.79 throughout the experimental period. 2.3. Size distribution of trees To compare the types of frequency distribution at different stages of stand growth, the histograms of tree size were made with the abscissa as the fixed width of stem volume irrespective of actual range, following the standardized method proposed by Koyama and Kira (1956). Skewness was used to measure the asymmetry of the frequency distribution of stem volume. The skewness, Sk, is defined as P 1=n ni¼1 ðVi vÞ3 (2) Sk ¼ s3 where Vi is the stem volume of the ith individual, v the mean of observed values, n the number of individuals and s the standard deviation. The Sk is zero for a
K. Ogawa, A. Hagihara / Forest Ecology and Management 174 (2003) 413–421
415
symmetric distribution, a positive value for a distribution with more individuals of small size and a negative value for a distribution with more individuals of large size. Trees which were arranged from the largest to the smallest ones were then numbered in order from the largest. Spearman’s coefficient of rank correlation of orders for the same trees between successive 2-year periods was calculated for 14 successive 2-year combinations.
present survey), and m and s2 are, respectively, the mean number of dead individuals per quadrat and the variance. The ratio m=m is served as a relative measure of aggregation (Lloyd, 1967; Iwao, 1968). The m=m is unity when dead trees is randomly distributed. If dead trees are contagiously distributed, the m=m is larger than unity and if evenly distributed the m=m is smaller than unity.
2.4. Spatial distribution of dead trees
3. Results
The patterns of the spatial distribution of dead trees were analyzed by the mm regression method (Iwao, 1968). The sample estimate of mean crowding (the mean number of other individuals per quadrat per individual), m, was plotted against the sample mean number per quadrat, m, over the measurement period. Here the mean crowding (Lloyd, 1967) is defined by the formula: Pq s2 j¼1 xj ðxj 1Þ Pq m¼ (3) ¼mþ 1 m j¼1 xj
3.1. Time trend of stand density
where xj is the number of dead individuals in the jth quadrat, q the total number of quadrates (q ¼ 12 in the
Fig. 2 depicts the time trend of stand density. The tree density was 5002 ha1 at the beginning of experiment in 1983. It decreased year after year, and became 3108 ha1 at the end of experiment in 1997. 3.2. Time-trajectory of mean stem volume and density The relationship between mean stem volume, v (dm3), and density, r (ha1), on logarithmic coordinates is shown in Fig. 3. The time-trajectory of v and r
Fig. 2. Time trend of stand density.
416
K. Ogawa, A. Hagihara / Forest Ecology and Management 174 (2003) 413–421
gradually approaches and eventually moves along the following self-thinning line at the final stage of stand development: (5) v ¼ Kra where a represents the slope of the self-thinning line on log v log r diagram. 3.3. Size distribution
Fig. 3. Time-trajectory of mean stem volume, v, and stand density, r. The regression curve is given by Eq. (2), where the coefficient of determination is 0.982.
was formulated as: r b a v ¼ Kr 1 r0
ða 1 < b < aÞ
(4)
where K, r0, a and b are coefficients (Hagihara, 1996). The values of K, r0, a and b were calculated as 52 693 000 dm3 haa, 6923 ha1, 1.474 and 0.7224, respectively. The time-trajectory of v and r is characterized by the following three stages (Perry, 1994). During the early stages of stand development, competition among trees is not severe enough to cause mortality, and average stem volume increases with no corresponding decrease in stand density. In this stage, the timetrajectory parallels the y-axis (stage 1). Eventually, the stand grows crowded enough that an increase in the average stem volume cannot occur unless some trees die. At this stage, the time-trajectory begins to curve left, denoting a reduction in stand density (stage 2). Following its initial bend to the left, the time-trajectory asymptotically approaches and then follows quite closely along straight line, which means that a given increase in average stem volume is matched by a given decrease in stand density (stage 3). The v r trajectory given by Eq. (4) indicates that the v r trajectory
The time trend of the frequency distribution of stem volume in the stand is given in Fig. 4. The frequency distribution skewed over the whole measurement period, and the skewness of the frequency distribution showed positive values (Fig. 5). The mode tended to be in the lowest class or the left end of the histogram, which means that the frequency distribution is more or less L-shaped in 1983–1989 (Fig. 4). After that, the frequency in the lowest class decreased. Therefore, the skewness tended to decrease with time (P < 0:05, Fig. 5). The dead trees belonged to the lowest class of the histogram (Fig. 4), which indicates that smaller trees died as the stand grew. Spearman’s coefficient of rank correlation of trees from the largest size between successive 2-year periods is shown in Fig. 6. The coefficient usually was above 0.993, suggesting that the individual tree’s rank from the largest is usually stable, and the reversion of order rarely occurs. Kikuzawa (1993) also reported a similar result on tree order in a Betula ermanii Cham. stand. 3.4. Spatial distribution of dead trees
Fig. 7 shows the mm relations over the whole measurement period. The ratio m=m was higher than unity at the beginning of measurement. After that, the m=m approached to unity with time, ranging from 1.27 to 0.870. The analysis by the mm regression method indicates that the death of trees occurred aggregatively at the beginning of measurement and thereafter occurred randomly. 4. Discussion 4.1. Self-thinning line Yoda et al. (1963) originally proposed Eq. (5) of the relationship between mean tree weight or mean stem
K. Ogawa, A. Hagihara / Forest Ecology and Management 174 (2003) 413–421
417
Fig. 4. Transition of the frequency distribution of stem volume. Relative frequencies are shown in 10 equal intervals in the range of stem volume. Shaded portions denote individuals died by next year.
418
K. Ogawa, A. Hagihara / Forest Ecology and Management 174 (2003) 413–421
Fig. 5. Time trend of the skewness of stem volume.
volume v and stand density r in fully stocked pure stands during the self-thinning process. The self-thinning slope a in Eq. (5) is close to 3/2 regardless of species, age or site conditions. In the present analysis, the a value of 1.474, which is closely 3/2, can be regarded as evidence in favor of the 3/2 power law of self-thinning.
4.2. Size variation The relationship between standard deviation, s (dm3) and mean, v (dm3), of stem volume on logarithmic coordinates is depicted in Fig. 8. The standard deviation, s increased with increasing mean, v. This
Fig. 6. Time trend of Spearman’s coefficient of rank correlation between successive 2-year periods.
Fig. 7. Relationship between mean crowding of dead trees, m, and mean density of dead trees, m. The dotted line indicates m=m ¼ 1. The arrows show the progress of time.
Fig. 8. Relationship of the standard deviation of stem volume, s, to mean stem volume, v. The regression line is given by Eq. (6), where the coefficient of determination is 0.953.
420
K. Ogawa, A. Hagihara / Forest Ecology and Management 174 (2003) 413–421
relation can be described as the following power function: s ¼ 1:380v0:862
(6)
where the coefficient of determination is 0.953. The exponent value of 0.862 in Eq. (6) is significantly less than unity at the level of 5%. Since the standard deviation is a measure of absolute rather than relative variation, it is usually inappropriate for the evaluation of size variability (Weiner, 1988). Dividing both sides of Eq. (6) with v leads to the relationship between coefficient of variation, ðs=vÞ 100, which is a measure of relative variation, and mean, v, as follows: ðs=vÞ 100 ¼ 138:0v0:138
(7)
The coefficient of variation, ranging from 61.7 to 82.5%, decreased with increasing mean stem volume (Fig. 9). This fact in Eq. (7) indicates that the relative variation in size becomes small with the stand growth. In the present study, density-dependent mortality was usually confined to small trees (Fig. 4), skewing less and less the frequency distribution of stem volume
(Fig. 5). Kikuzawa (1988) reported that dead trees were usually found in smaller diameter classes in the frequency distribution of diameter in a B. ermanii Cham. stand. Ford (1975) and Xue and Hagihara (1999) suggested, respectively, that continued mortality in smaller trees eventually led the frequency distributions of girth in Picea sitchensis (Bongard) Carr. stands and tree height in Pinus densiflora Sieb. et Zucc. stands to become symmetrical over time. The mortality of small trees reflects the following stand development (Xue and Hagihara, 1999): after the canopy of a stand has closed, a contest phase involving one-sided competition of larger sized trees to smaller ones for light becomes the major competitive factor (Weiner and Whigham, 1988). As the canopy closes, smaller trees are shed out by neighboring larger trees, so that the smaller trees may eventually be thinned out. From the viewpoint of stand density management, the present results imply that thinning is not necessary after the canopy closure because of self-thinning. Dead trees distributed randomly with the stand development (Fig. 7). The randomness of dead trees is considered to be caused by the randomness of small seedlings at planting.
Fig. 9. Regression of the coefficient of variation of stem volume, ðs=vÞ 100, on mean stem volume, v. The regression line is given by Eq. (7).
K. Ogawa, A. Hagihara / Forest Ecology and Management 174 (2003) 413–421
According to Givnish (1986), most mortality in selfthinning stands appears to occur because respiration exceeds photosynthesis in suppressed individuals for lack of light. The present results of mortality of small trees provides support for the hypothesis proposed by Weiner and Whigham (1988) that the process of self-thinning is driven by competition for light, i.e., that smaller individuals die because they are shaded.
Acknowledgements We thank Emeritus Professor K. Hozumi of Nagoya University for valuable field assistance and encouragement, and Professor K. Kikuzawa of Kyoto University for critical reading of the manuscript and invaluable comments. We also thank the staff in Nagoya University Forest for their help during this study. This study was supported in part by a grant-inaid for scientific research (No. 12660133) from the Ministry of Education, Science, Sport and Culture, Japan. References Avery, T.E., Burkhart, H.E., 1994. Forest Measurements. McGrawHill, New York, 408 pp. Begon, M., Haper, J.L., Townsend, C.R., 1996. Ecology: Individuals, Populations and Communities. Blackwell, Oxford, 1068 pp. Benjamin, L.R., Hardwick, R.C., 1986. Sources of variation and measures of variability in even-aged stands of plants. Ann. Bot. 58, 757–778. Ford, E.D., 1975. Competition and stand structure in some evenaged plant monocultures. J. Ecol. 63, 311–333. Givnish, T.J., 1986. Biomechanical constraints on self-thinning in plant populations. J. Theoret. Biol. 119, 139–146.
421
Hagihara, A., 1996. Theoretical studies on the time-trajectory of mean plant weight and density in self-thinning populations, Bull. Nagoya Univ. For. 15, 51–67 (in Japanese with English summary). Hagihara, A., Yokota, T., Ogawa, K., 1993. Allometric relations in hinoki (Chamaecyparis obtusa (Sieb. et Zucc.) Endl.). Bull. Nagoya Univ. For. 12, 11–29. Iwao, S., 1968. A new regression method for analyzing the aggregation pattern of animal populations. Res. Popul. Ecol. 10, 1–20. Kikuzawa, K., 1988. Intraspecific competition in a natural stand of Betula ermanii. Ann. Bot. 61, 727–734. Kikuzawa, K., 1993. Self-thinning line and B-point line of the yield–density diagram in a young birch stand. For. Ecol. Manage. 58, 287–298. Koyama, H., Kira, T., 1956. Intraspecific competition among higher plants. VII. Frequency distribution of individual plant weight as affected by the interaction between plants. J. Inst. Polytech. Osaka City Univ., Ser. D 7, 73–94. Lloyd, M., 1967. Mean crowding. J. Anim. Ecol. 36, 1–30. Ogawa, H., Kira, T., 1977. Methods of estimating forest biomass. In: Shidei, T., Kira, T. (Eds.), Primary Production of Japanese Forests. University of Tokyo Press, Tokyo, pp. 15–25, 35–36. Perry, D.A., 1994. Forest Ecosystems. The Johns Hopkins University Press, Baltimore, 649 pp. Silvertown, J.W., Doust, J.L., 1993. Introduction to Plant Population Biology. Blackwell, Oxford, 210 pp. Weiner, J., 1988. Variation in the performance of individuals in plant populations. In: Davy, A.J., Hutchings, M.J., Watkinson, A.R. (Eds.), Plant Population Ecology. Blackwell, Oxford, pp. 59–81. Weiner, J., Whigham, D.F., 1988. Size variability and self-thinning in wild-rice (Zizania aquatica). Am. J. Bot. 75, 445–448. Weller, D.E., 1987. A reevaluation of the 3/2 power rule of plant self-thinning. Ecol. Monogr. 57, 23–43. Westoby, M., 1984. The self-thinning rule. Adv. Ecol. Res. 14, 167–225. Xue, L., Hagihara, A., 1999. Density effect, self-thinning and size distribution in Pinus densiflora Sieb et Zucc. Stand. Ecol. Res. 14, 49–58. Yoda, K., Kira, T., Ogawa, H., Hozumi, K., 1963. Self-thinning in overcrowded pure stands under cultivated and natural conditions. Intraspecific competition among higher plants XI. J. Biol. Osaka City Univ. 14, 107–129.
Self-thinning and size variation in a sugi (Cryptomeria japonica D. Don) plantation Kazuharu Ogawaa,*, Akio Hagiharab a
Laboratory of Forest Ecology and Physiology, Graduate School of Bioagricultural Sciences, Nagoya University, Nagoya 464-8601, Japan b Laboratory of Ecology and Systematics, Faculty of Science, University of the Ryukyus, Okinawa 903-0213, Japan Received 18 October 2001; accepted 1 February 2002
Abstract Density and stem volume in a sugi (Cryptomeria japonica D. Don) plantation were monitored for 15 years from 1983 to 1997. The tree density decreased year after year from 5002 to 3108 ha1. The time-trajectory of mean stem volume and density provided evidence in favor of the 3/2 power law of self-thinning. The skewness of the frequency distribution of stem volume showed positive values, which means that the distribution is more or less L-shaped, and the skewness decreased with time, which indicates that smaller trees died as the stand grew. This trend is consistent with the asymmetric or one-sided competition hypothesis that self-thinning is driven by competition for light. Dead trees tended to distribute randomly with the stand growth. The relationship between standard deviation of stem volume and mean stem volume was formulated by a power function, whose exponent was significantly less than unity. This shows that coefficient of variation, ranging from 61.7 to 82.5%, decreased with increasing mean stem volume. That is, the relative size variation becomes small with stand growth. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Competition; Cryptomeria japonica D. Don; Size variation; Spatial distribution; Stem volume; The 3/2 power law of selfthinning
1. Introduction As trees in a stand grow larger they occupy more and more space, and sooner or later the gaps between trees are filled and they begin to interfere with each other’s access to resources like light, water and nutrients (Silvertown and Doust, 1993). Such interference or competition within the stand induces size variation and also density-dependent mortality or self-thinning. Much interest has been focused on size variation *
Corresponding author. Tel.: þ81-52-789-4071; fax: þ81-52-789-5014. E-mail address: [email protected] (K. Ogawa).
within tree populations (e.g., Benjamin and Hardwick, 1986; Begon et al., 1996) and self-thinning (e.g., Westoby, 1984; Weller, 1987), but very little is known about the relationship between the two. Changes in the frequency distribution of tree sizes that accompany the process of self-thinning include important implications for the structure and dynamics of tree populations. In the present study, we monitored a sugi (Cryptomeria japonica D. Don) population for 15 years to evaluate the self-thinning process, change in size variation and intraspecific competition. We analyzed the data to test the applicability of the 3/2 power law of self-thinning (Yoda et al., 1963), and to clarify
0378-1127/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 1 1 2 7 ( 0 2 ) 0 0 0 6 2 - 2
414
K. Ogawa, A. Hagihara / Forest Ecology and Management 174 (2003) 413–421
changes in the frequency distribution of stem volume and coefficient of variation. Since trees interact with their neighbors, it is more appropriate to study interference in a tree population by the measurement of explicit spatial relationships than measuring the population density (Silvertown and Doust, 1993). Therefore, subdividing the plot, we also identified the spatial distribution of occurrence of dead trees during the self-thinning process.
2. Materials and methods 2.1. Site description This study was made on a 21-year-old (as of 1983) sugi (C. japonica D. Don) stand in the Nagoya University Experimental Forest at Inabu, located about 55 km east of Nagoya, Aichi Prefecture, central Japan. This plantation was situated at an altitude of 960 m on an east-facing 238 slope. A plot of 15 m 20 m in area was established and was divided into 12 quadrats, each 5 m 5 m in area, in 1983. The seedlings were planted geometrically at initial planting density of 6000 ha1, and thinning was not made artificially after planting.
Fig. 1. Allometric relationships between stem volume, V, and stem girth at breast height, G. The regression lines are given by Eq. (1). *, 1983; ~, 1990; &, 1997.
2.2. Census and estimation of stem volume A yearly census was carried out on all the trees in the plot, in which stem girth at the breast height (1.3 m above the ground) was measured in October from 1983 to 1997. Six to fourteen different-sized sample trees were selected for non-destructively assessing the stem volume every year. Measurements were made of tree height, stem girths at 0.0, 0.3 and 1.3 m, and at 1.0 m interval thereafter. From the measurements, stem volume was calculated on the basis of Smalian’s formula (e.g., Avery and Burkhart, 1994). The stem volume of trees in the plot was estimated on the basis of the yearly allometric relation of stem volume, V (dm3), and stem girth at breast height, G (cm) (Fig. 1), V ¼ gGh
(1)
where g and h are coefficients (Ogawa and Kira, 1977; Hagihara et al., 1993). The values of g and h were,
respectively, in the range of 0.00273–0.0390 dm3 cmh, and 2.13–2.79 throughout the experimental period. 2.3. Size distribution of trees To compare the types of frequency distribution at different stages of stand growth, the histograms of tree size were made with the abscissa as the fixed width of stem volume irrespective of actual range, following the standardized method proposed by Koyama and Kira (1956). Skewness was used to measure the asymmetry of the frequency distribution of stem volume. The skewness, Sk, is defined as P 1=n ni¼1 ðVi vÞ3 (2) Sk ¼ s3 where Vi is the stem volume of the ith individual, v the mean of observed values, n the number of individuals and s the standard deviation. The Sk is zero for a
K. Ogawa, A. Hagihara / Forest Ecology and Management 174 (2003) 413–421
415
symmetric distribution, a positive value for a distribution with more individuals of small size and a negative value for a distribution with more individuals of large size. Trees which were arranged from the largest to the smallest ones were then numbered in order from the largest. Spearman’s coefficient of rank correlation of orders for the same trees between successive 2-year periods was calculated for 14 successive 2-year combinations.
present survey), and m and s2 are, respectively, the mean number of dead individuals per quadrat and the variance. The ratio m=m is served as a relative measure of aggregation (Lloyd, 1967; Iwao, 1968). The m=m is unity when dead trees is randomly distributed. If dead trees are contagiously distributed, the m=m is larger than unity and if evenly distributed the m=m is smaller than unity.
2.4. Spatial distribution of dead trees
3. Results
The patterns of the spatial distribution of dead trees were analyzed by the mm regression method (Iwao, 1968). The sample estimate of mean crowding (the mean number of other individuals per quadrat per individual), m, was plotted against the sample mean number per quadrat, m, over the measurement period. Here the mean crowding (Lloyd, 1967) is defined by the formula: Pq s2 j¼1 xj ðxj 1Þ Pq m¼ (3) ¼mþ 1 m j¼1 xj
3.1. Time trend of stand density
where xj is the number of dead individuals in the jth quadrat, q the total number of quadrates (q ¼ 12 in the
Fig. 2 depicts the time trend of stand density. The tree density was 5002 ha1 at the beginning of experiment in 1983. It decreased year after year, and became 3108 ha1 at the end of experiment in 1997. 3.2. Time-trajectory of mean stem volume and density The relationship between mean stem volume, v (dm3), and density, r (ha1), on logarithmic coordinates is shown in Fig. 3. The time-trajectory of v and r
Fig. 2. Time trend of stand density.
416
K. Ogawa, A. Hagihara / Forest Ecology and Management 174 (2003) 413–421
gradually approaches and eventually moves along the following self-thinning line at the final stage of stand development: (5) v ¼ Kra where a represents the slope of the self-thinning line on log v log r diagram. 3.3. Size distribution
Fig. 3. Time-trajectory of mean stem volume, v, and stand density, r. The regression curve is given by Eq. (2), where the coefficient of determination is 0.982.
was formulated as: r b a v ¼ Kr 1 r0
ða 1 < b < aÞ
(4)
where K, r0, a and b are coefficients (Hagihara, 1996). The values of K, r0, a and b were calculated as 52 693 000 dm3 haa, 6923 ha1, 1.474 and 0.7224, respectively. The time-trajectory of v and r is characterized by the following three stages (Perry, 1994). During the early stages of stand development, competition among trees is not severe enough to cause mortality, and average stem volume increases with no corresponding decrease in stand density. In this stage, the timetrajectory parallels the y-axis (stage 1). Eventually, the stand grows crowded enough that an increase in the average stem volume cannot occur unless some trees die. At this stage, the time-trajectory begins to curve left, denoting a reduction in stand density (stage 2). Following its initial bend to the left, the time-trajectory asymptotically approaches and then follows quite closely along straight line, which means that a given increase in average stem volume is matched by a given decrease in stand density (stage 3). The v r trajectory given by Eq. (4) indicates that the v r trajectory
The time trend of the frequency distribution of stem volume in the stand is given in Fig. 4. The frequency distribution skewed over the whole measurement period, and the skewness of the frequency distribution showed positive values (Fig. 5). The mode tended to be in the lowest class or the left end of the histogram, which means that the frequency distribution is more or less L-shaped in 1983–1989 (Fig. 4). After that, the frequency in the lowest class decreased. Therefore, the skewness tended to decrease with time (P < 0:05, Fig. 5). The dead trees belonged to the lowest class of the histogram (Fig. 4), which indicates that smaller trees died as the stand grew. Spearman’s coefficient of rank correlation of trees from the largest size between successive 2-year periods is shown in Fig. 6. The coefficient usually was above 0.993, suggesting that the individual tree’s rank from the largest is usually stable, and the reversion of order rarely occurs. Kikuzawa (1993) also reported a similar result on tree order in a Betula ermanii Cham. stand. 3.4. Spatial distribution of dead trees
Fig. 7 shows the mm relations over the whole measurement period. The ratio m=m was higher than unity at the beginning of measurement. After that, the m=m approached to unity with time, ranging from 1.27 to 0.870. The analysis by the mm regression method indicates that the death of trees occurred aggregatively at the beginning of measurement and thereafter occurred randomly. 4. Discussion 4.1. Self-thinning line Yoda et al. (1963) originally proposed Eq. (5) of the relationship between mean tree weight or mean stem
K. Ogawa, A. Hagihara / Forest Ecology and Management 174 (2003) 413–421
417
Fig. 4. Transition of the frequency distribution of stem volume. Relative frequencies are shown in 10 equal intervals in the range of stem volume. Shaded portions denote individuals died by next year.
418
K. Ogawa, A. Hagihara / Forest Ecology and Management 174 (2003) 413–421
Fig. 5. Time trend of the skewness of stem volume.
volume v and stand density r in fully stocked pure stands during the self-thinning process. The self-thinning slope a in Eq. (5) is close to 3/2 regardless of species, age or site conditions. In the present analysis, the a value of 1.474, which is closely 3/2, can be regarded as evidence in favor of the 3/2 power law of self-thinning.
4.2. Size variation The relationship between standard deviation, s (dm3) and mean, v (dm3), of stem volume on logarithmic coordinates is depicted in Fig. 8. The standard deviation, s increased with increasing mean, v. This
Fig. 6. Time trend of Spearman’s coefficient of rank correlation between successive 2-year periods.
Fig. 7. Relationship between mean crowding of dead trees, m, and mean density of dead trees, m. The dotted line indicates m=m ¼ 1. The arrows show the progress of time.
Fig. 8. Relationship of the standard deviation of stem volume, s, to mean stem volume, v. The regression line is given by Eq. (6), where the coefficient of determination is 0.953.
420
K. Ogawa, A. Hagihara / Forest Ecology and Management 174 (2003) 413–421
relation can be described as the following power function: s ¼ 1:380v0:862
(6)
where the coefficient of determination is 0.953. The exponent value of 0.862 in Eq. (6) is significantly less than unity at the level of 5%. Since the standard deviation is a measure of absolute rather than relative variation, it is usually inappropriate for the evaluation of size variability (Weiner, 1988). Dividing both sides of Eq. (6) with v leads to the relationship between coefficient of variation, ðs=vÞ 100, which is a measure of relative variation, and mean, v, as follows: ðs=vÞ 100 ¼ 138:0v0:138
(7)
The coefficient of variation, ranging from 61.7 to 82.5%, decreased with increasing mean stem volume (Fig. 9). This fact in Eq. (7) indicates that the relative variation in size becomes small with the stand growth. In the present study, density-dependent mortality was usually confined to small trees (Fig. 4), skewing less and less the frequency distribution of stem volume
(Fig. 5). Kikuzawa (1988) reported that dead trees were usually found in smaller diameter classes in the frequency distribution of diameter in a B. ermanii Cham. stand. Ford (1975) and Xue and Hagihara (1999) suggested, respectively, that continued mortality in smaller trees eventually led the frequency distributions of girth in Picea sitchensis (Bongard) Carr. stands and tree height in Pinus densiflora Sieb. et Zucc. stands to become symmetrical over time. The mortality of small trees reflects the following stand development (Xue and Hagihara, 1999): after the canopy of a stand has closed, a contest phase involving one-sided competition of larger sized trees to smaller ones for light becomes the major competitive factor (Weiner and Whigham, 1988). As the canopy closes, smaller trees are shed out by neighboring larger trees, so that the smaller trees may eventually be thinned out. From the viewpoint of stand density management, the present results imply that thinning is not necessary after the canopy closure because of self-thinning. Dead trees distributed randomly with the stand development (Fig. 7). The randomness of dead trees is considered to be caused by the randomness of small seedlings at planting.
Fig. 9. Regression of the coefficient of variation of stem volume, ðs=vÞ 100, on mean stem volume, v. The regression line is given by Eq. (7).
K. Ogawa, A. Hagihara / Forest Ecology and Management 174 (2003) 413–421
According to Givnish (1986), most mortality in selfthinning stands appears to occur because respiration exceeds photosynthesis in suppressed individuals for lack of light. The present results of mortality of small trees provides support for the hypothesis proposed by Weiner and Whigham (1988) that the process of self-thinning is driven by competition for light, i.e., that smaller individuals die because they are shaded.
Acknowledgements We thank Emeritus Professor K. Hozumi of Nagoya University for valuable field assistance and encouragement, and Professor K. Kikuzawa of Kyoto University for critical reading of the manuscript and invaluable comments. We also thank the staff in Nagoya University Forest for their help during this study. This study was supported in part by a grant-inaid for scientific research (No. 12660133) from the Ministry of Education, Science, Sport and Culture, Japan. References Avery, T.E., Burkhart, H.E., 1994. Forest Measurements. McGrawHill, New York, 408 pp. Begon, M., Haper, J.L., Townsend, C.R., 1996. Ecology: Individuals, Populations and Communities. Blackwell, Oxford, 1068 pp. Benjamin, L.R., Hardwick, R.C., 1986. Sources of variation and measures of variability in even-aged stands of plants. Ann. Bot. 58, 757–778. Ford, E.D., 1975. Competition and stand structure in some evenaged plant monocultures. J. Ecol. 63, 311–333. Givnish, T.J., 1986. Biomechanical constraints on self-thinning in plant populations. J. Theoret. Biol. 119, 139–146.
421
Hagihara, A., 1996. Theoretical studies on the time-trajectory of mean plant weight and density in self-thinning populations, Bull. Nagoya Univ. For. 15, 51–67 (in Japanese with English summary). Hagihara, A., Yokota, T., Ogawa, K., 1993. Allometric relations in hinoki (Chamaecyparis obtusa (Sieb. et Zucc.) Endl.). Bull. Nagoya Univ. For. 12, 11–29. Iwao, S., 1968. A new regression method for analyzing the aggregation pattern of animal populations. Res. Popul. Ecol. 10, 1–20. Kikuzawa, K., 1988. Intraspecific competition in a natural stand of Betula ermanii. Ann. Bot. 61, 727–734. Kikuzawa, K., 1993. Self-thinning line and B-point line of the yield–density diagram in a young birch stand. For. Ecol. Manage. 58, 287–298. Koyama, H., Kira, T., 1956. Intraspecific competition among higher plants. VII. Frequency distribution of individual plant weight as affected by the interaction between plants. J. Inst. Polytech. Osaka City Univ., Ser. D 7, 73–94. Lloyd, M., 1967. Mean crowding. J. Anim. Ecol. 36, 1–30. Ogawa, H., Kira, T., 1977. Methods of estimating forest biomass. In: Shidei, T., Kira, T. (Eds.), Primary Production of Japanese Forests. University of Tokyo Press, Tokyo, pp. 15–25, 35–36. Perry, D.A., 1994. Forest Ecosystems. The Johns Hopkins University Press, Baltimore, 649 pp. Silvertown, J.W., Doust, J.L., 1993. Introduction to Plant Population Biology. Blackwell, Oxford, 210 pp. Weiner, J., 1988. Variation in the performance of individuals in plant populations. In: Davy, A.J., Hutchings, M.J., Watkinson, A.R. (Eds.), Plant Population Ecology. Blackwell, Oxford, pp. 59–81. Weiner, J., Whigham, D.F., 1988. Size variability and self-thinning in wild-rice (Zizania aquatica). Am. J. Bot. 75, 445–448. Weller, D.E., 1987. A reevaluation of the 3/2 power rule of plant self-thinning. Ecol. Monogr. 57, 23–43. Westoby, M., 1984. The self-thinning rule. Adv. Ecol. Res. 14, 167–225. Xue, L., Hagihara, A., 1999. Density effect, self-thinning and size distribution in Pinus densiflora Sieb et Zucc. Stand. Ecol. Res. 14, 49–58. Yoda, K., Kira, T., Ogawa, H., Hozumi, K., 1963. Self-thinning in overcrowded pure stands under cultivated and natural conditions. Intraspecific competition among higher plants XI. J. Biol. Osaka City Univ. 14, 107–129.