Variation in individual biomass decreases faster than mean biomass with increasing density of bamboo stands

Abstract

The total biomass of a stand is an indicator of stand productivity and is closely related to the density of plants. According to the self-thinning law, mean individual biomass follows a negative power law with plant density. If the variance of individual biomass is constant, we can expect increased stand productivity with increasing plant density. However, Taylor’s power law (TPL) that relates the variance and the mean of many biological measures (e.g. bilateral areal differences of a leaf, plant biomass at different times, developmental rates at different temperatures, population densities on different spatial or temporal scales), affects the estimate of stand productivity when it is defined as the total biomass of large plants in a stand. Because the variance of individual biomass decreases faster than mean individual biomass, differences in individual biomass decline with increasing density, leading to more homogeneous timbers of greater economic value. We tested whether TPL in plant biomass holds for different species and whether the variance of individual biomass changes faster than the mean with increasing stand density. The height, ground diameter and fresh weight of 50 bamboo species were measured in 50 stands ranging from 1 m by 1 m to 30 m by 30 m to ensure more than 150 bamboos in every stand. We separately examined TPL in height, ground diameter, and weight, and found that TPL holds for all three biological measures, with the relationship strongest for weight. Using analysis of covariance to compare the regression slopes of logarithmic mean and variance against the logarithm of density, we found that the variance in individual biomass declined faster than the mean with increasing density. This suggests that dense planting reduced mean individual biomass but homogenized individual biomass. Thus, there exists a trade-off between effective stand productivity and stand density for optimal forest management. Sparse planting leads to large variation in individual biomass, whereas dense planting reduces mean individual biomass. Consequently, stand density for a plantation should be set based on this trade-off with reference to market demands.

Keywords

Bamboo / Linear fitting / Self-thinning law / Taylor’s power law / Variance

References

[1] Anderson RM, Gordon DM, Crawley MJ, Hassell MP. Variability in the abundance of animal and plant species. Nature, 1982, 296: 245-248.

[2] Ballantyne F, Kerkhoff AJ. The observed range for temporal mean-variance scaling exponents can be explained by reproductive correlation. Oikos, 2007, 116: 174-180.

[3] Bamboo Phylogeny Group. An updated tribal and subtribal classification of the bamboos (Poaceae: Bambusoideae). Bamboo Sci Cult J Am Bamboo Soc, 2012, 24: 1-10.

[4] Cheng XF, Shi PJ, Hui C, Wang FS, Liu GH, Li BL. An optimal proportion of mixing broad-leaved forest for enhancing the effective productivity of moso bamboo. Ecol Evol, 2015, 5: 1576-1584.

[5] Cheng L, Hui C, Reddy GVP, Ding YL, Shi PJ. Internode morphometrics and allometry of Tonkin Cane Pseudosasa amabilis. Ecol Evol, 2017, 7: 9651-9660.

[6] Cohen JE, Xu M. Random sampling of skewed distributions implies Taylor’s power law of fluctuation scaling. Proc Natl Acad Sci USA, 2015, 112: 7749-7754.

[7] Cohen JE, Xu M, Schuster WS. Allometric scaling of population variance with mean body size is predicted from Taylor’s law and density-mass allometry. Proc Natl Acad Sci USA, 2012, 109: 15829-15834.

[8] Cohen JE, Lai J, Coomes DA, Allen RB. Taylor’s law and related allometric power laws in New Zealand mountain beech forests: the roles of space, time and environment. Oikos, 2016, 125: 1342-1357.

[9] Cohen JE, Rodríguez-Planes LI, Gaspe MS, Cecere MC, Cardinal MV, Gürtler RE. Chagas disease vector control and Taylor’s law. PLoS Negl Trop Dis, 2017 11 11 e0006092

[10] Cohen JE, Xu M, Schuster WSF. Stochastic multiplicative population growth predicts and interprets Taylor’s power law of fluctuation scaling. Proc R Soc B Biol Sci, 2017, 280: 20122955.

[11] Dai QL (2002) Studies on the high-yield techniques and biological characters of Pseudosasa amabilis. Master Dissertation of Fujian Agriculture and Forestry University, Fuzhou, Fujian Province, China (in Chinese with English Abstract)

[12] Eisler Z, Bartos I, Kertész J. Fluctuation scaling in complex systems: Taylor’s law and beyond. Adv Phys, 2008, 57: 89-142.

[13] Enquist BJ, Niklas KJ. Invariant scaling relations across tree-dominated communities. Nature, 2001, 410: 655-660.

[14] Franco F, Kelly CK. The interspecific mass-density relationship and plant geometry. Proc Natl Aca Sci USA, 1998, 95: 7830-7835.

[15] Franklin DC. Synchrony and asynchrony: observations and hypotheses for the flowering wave in a long-lived semelparous bamboo. J Biogeogr, 2004, 31: 773-786.

[16] Giometto A, Formentin M, Rinaldo A, Cohen JE, Maritan A. Sample and population exponents of generalized Taylor’s law. Proc Natl Acad Sci USA, 2015, 112: 7755-7760.

[17] Hanley QS, Khatun S, Yosef A, Dyer R-M. Fluctuation scaling, Taylor’s law, and crime. PLoS ONE, 2014 9 10 e109004

[18] Hanski I. Cross-correlation in population dynamics and the slope of spatial variance: mean regressions. Oikos, 1987, 50: 148-151.

[19] Horne JK, Schneider DC. Spatial variance in ecology. Oikos, 1995, 74: 18-26.

[20] Inoue A. Culm form analysis for bamboo, Phyllostachys pubescens. J For Res, 2013, 24(3): 525-530.

[21] Kaltz O, Escobar-Páramo P, Hochberg ME, Cohen JE. Bacterial microcosms obey Taylor’s law: effects of abiotic and biotic stress and genetics on mean and variance of population density. Ecol Process, 2012, 1: 5.

[22] Kilpatrick AM, Ives AR. Species interactions can explain Taylor’s power law for ecological time series. Nature, 2003, 422: 65-68.

[23] Li BL, H-i W, Zou GZ. Self-thinning rule: a causal interpretation from ecological field theory. Ecol Model, 2000, 132: 167-173.

[24] Lin SY, Shao LJ, Hui C, Sandhu HS, Fan TT, Zhang L, Li F, Ding YL, Shi PJ. The effect of temperature on the developmental rates of seedling emergence and leaf-unfolding in two dwarf bamboo species. Trees Struct Funct, 2018, 32: 751-763.

[25] Liu GH, Shi PJ, Xu Q, Dong XB, Wang FS, Wang GG, Hui C. Does the size–density relationship developed for bamboo species conform to the self-thinning rule?. For Ecol Manag, 2016, 361: 339-345.

[26] Pu XL, Du F. Anatomical studies on the culm and variation of Dendrocalamus sinicus. J Southwest For College, 2003, 23(1): 1-5. (in Chinese with English Abstract)

[27] Qin P, Gu Q, Wang SC, Cao JJ, Wang FS, Shi PJ. Point pattern analysis on the distributions of large individuals of four dwarf bamboos. J Nanjing For Univ, 2018, 42(4): 39-45. in Chinese with English Abstract)

[28] R Core Team. R: a language and environment for statistical computing, 2015, Vienna: R Foundation for Statistical Computing.

[29] Scurlock JMO, Dayton DC, Hames B. Bamboo: An overlooked biomass resource?. Biomass Bioenergy, 2000, 19: 229-244.

[30] Shi PJ, Xu Q, Sandhu HS, Johan G, Ding YL, Li HR, Dong XB. Comparison of dwarf bamboos (Indocalamus sp.) leaf parameters to determine relationship between spatial density of plants and total leaf area per plant. Ecol Evol, 2015, 5: 4578-4589.

[31] Shi PJ, Sandhu HS, Reddy GVP. Dispersal distance determines the exponent of the spatial Taylor’s power law. Ecol Model, 2016, 335: 48-53.

[32] Shi PJ, Fan ML, Ratkowsky D, Huang JG, Wu HI, Chen L, Fang SY, Zhang CX. Comparison of two ontogenetic growth equations for animals and plants. Ecol Model, 2017, 349: 1-10.

[33] Shi PJ, Ratkowsky D, Wang NT, Li Y, Zhao L, Reddy GV, Li BL. Comparison of five methods for parameter estimation under Taylor’s power law. Ecol Complex, 2017, 32: 121-130.

[34] Shi PJ, Zheng X, Ratkowsky DA, Li Y, Wang P, Cheng L. A simple method for measuring the bilateral symmetry of leaves. Symmetry, 2018, 10: 118.

[35] Taylor LR. Aggregation, variance and the mean. Nature, 1961, 189: 732-735.

[36] Taylor RAJ. The behavioural basis of redistribution. II. Simulations of the delta-model. J Anim Ecol, 1981, 50: 587-604.

[37] Tippett MK, Cohen JE. Tornado outbreak variability follows Taylor’s power law of fluctuation scaling and increases dramatically with severity. Nat Commun, 2016, 7: 10668.

[38] Vanclay JK, Sands PJ. Calibrating the self-thinning frontier. For Ecol Manag, 2009, 259: 81-85.

[39] Walgenbach JF. Distribution of parasitized and nonparasitized potato aphid (Homoptera: Aphididae) on staked tomato. Environ Entomol, 1994, 23: 795-804.

[40] Wang P, Lin SY, Fan TT, Zhang Y, Li F, Fan ML, Fang SY, Wang FS, Dong LN, Shi PJ. Relationship between the mean diameter of breast height (DBH) and the number per unit area of moso bamboo in Zijin Mountain. J Anhui Agric Sci, 2018, 46(7): 106-108. in Chinese with English Abstract)

[41] Wang P, Ratkowsky DA, Xiao X, Yu XJ, Su JL, Zhang LF, Shi PJ. Taylor’s power law for leaf bilateral symmetry. Forests, 2018, 9: 500.

[42] Wei Q, Jiao C, Guo L, Ding YL, Cao JJ, Feng JY, Dong XB, Mao LY, Sun HH, Yu F, Yang GY, Shi PJ, Ren GD, Fei ZJ. Exploring key cellular processes and candidate genes regulating the primary thickening growth of Moso underground shoots. N Phytol, 2017, 214: 81-96.

[43] Wei Q, Jiao C, Ding YL, Gao S, Guo L, Chen M, Hu P, Xia SJ, Ren GD, Fei ZJ. Cellular and molecular characterizations of a slow-growth variant provide insights into the fast growth of bamboo. Tree Physiol, 2018, 38: 641-654.

[44] Xiao X, Locey KJ, White EP. A process-independent explanation for the general form of Taylor’s law. Am Nat, 2015, 186: E51-E60.

[45] Yamamura K. Colony expansion model for describing the spatial distribution of populations. Popul Ecol, 2000, 42: 161-169.

[46] Yoda K. Self-thinning in overcrowded pure stands under cultivated and natural conditions (Intraspecific competition among higher plants XI). J Biol Osaka City Univ, 1963, 14: 107-129.

[47] Yuan JL, Yue JJ, Gu XP, Lin CS. Flowering of woody bamboo in tissue culture systems. Front Plant Sci, 2017, 8: 1589.