References

Acker, S, A., Halpern, B, C., Harmon, E, M., Dyrness, T , C., (2002). Trends in bole biomass accumulation, net primary production and tree mortality in Pseudotsuga menziesii forests of contrasting age. Tree Physiology, 22, 213-217.
Ashraf, M., Ahmad, A., Mcneilly, T., (2001). Growth and Photosynthetic Characteristics in Pearl Millet under Water Stress and Different Potassium Supply. Photosynthetica, 39(3), 389-394.
Bamber, K, R., (1976). Heartwood, its function and formation. Wood Science and Technology, 10(1), 1-8.
Baraloto, C., Goldberg, E, D., Bonal, D., (2005). Performance trade-offs among tropical tree seedlings in contrasting microhabitats. Ecology, 86, 2461–2472.
Carbone, S, M., Czimczik, I, C., Keenan, F, T., Murakami, F, P., Pederson, N., Schaberg, G, P., Xu, X, M., Richardson, D, A., (2013). Age, allocation and availability of nonstructural carbon in mature red maple trees. New Phytologist, 200(4), 1145-1155.
Chen, G, S., Yang, Y, S., Robinson, D., (2013). Allocation of gross primary production in forest ecosystems: allometric constraints and environmental responses. New Phytologist, 200(4), 1176-1186.
Enquist, B. J., Kerkhoff, A. J., Stark, S. C., Swenson, N. G., Mccarthy, M. C., & Price, C. A. (2007). A general integrative model for scaling plant growth, carbon flux, and functional trait spectra.Nature, 449(7159), 218-222.
Falster, S, D., Brannstrom, A., Dieckmann, U., Westoby. M., (2011). Influence of four major plant traits on average height, leaf-area cover, net primary productivity, and biomass density in single-species forests:theoretical investigation. Journal of Ecology, 99 (1), 148–164.
Falster, S, D., Duursma, A, R., Fitzjohn, G, R., (2018). How functional traits influence plant growth and shade tolerance across the life cycle. Proceedings of the National Academy of Sciences, 115(29), E6789-E6798.
Falster, S, D., Westoby, M., (2003). Plant height and evolutionary games. Trends in Ecology & Evolution, 18(7), 337-343.
Gibert, A., Gray, F, E., Westoby, M., Ian J Wright., Daniel S Falster., (2016). On the link between functional traits and growth rate: meta-analysis shows effects change with plant size, as predicted. Journal of Ecology, 104(5), 1488-1503.
Hérault, B., Bachelot, B., Poorter, L., Rossi, V., Bongers, F., Chave, J., Paine, T, C, E., Fabien Wagner., Baraloto, C., (2011). Functional traits shape ontogenetic growth trajectories of rain forest tree species. Journal of Ecology, 99(6):1431-1440.
Johnson, E, S., Abrams, D, M., (2009). Age class, longevity and growth rate relationships: protracted growth increases in old trees in the eastern United States. Tree Physiology, 29(11), 1317-1328.
Johnson, I, R., (1990). Plant respiration in relation to growth, maintenance, ion uptake and nitrogen assimilation. Plant, Cell and Environment. 13, 319-328.
Karadavut, U., kayiş, S, A., Okur, O., (2008). A growth curve application to compare plant heights and dry weights of some wheat varieties. American-Eurasian Journal of Agricultural & Environmental Sciences, 3(6), 888-892.
King, A, D., Davies, J, S., Tan, S., Noor, N. S.., (2006). The role of wood density and stem support costs in the growth and mortality of tropical trees. Journal of Ecology, 94(3), 670-680.
Kull, O., Tulva, I., (2000). Modelling canopy growth and steady-state leaf area index in an aspen stand. Annals of Forest Science, 57(5), 611-621.
Lehnebach, R., Morel, H., Bossu, J., Moguedec, L ,G., Amusant, N., Beauchene, J., Nicolini, E., (2017). Heartwood/sapwood profile and the tradeoff between trunk and crown increment in a natural forest: the case study of a tropical tree (Dicorynia guianensis Amsh., Fabaceae). Trees-structure and Function, 31(1), 199-214.
Mcdowell, G, N., Barnard, R, H., Bond, J, B., Hinckley, M, T., Hubbard, M, R., Ishii, H., Kostner, B., Magnani, F., Marshall, D, J., Meinzer, C, F., Phillips, N., Ryan, G, M., Whitehead, D., (2002). The relationship between tree height and leaf area: sapwood area ratio. Oecologia, 132(1), 12-20.
Mencuccini, M., Martinezvilalta, J., Vanderklein, D., Hamid, A, H., Korakaki, E., Lee, S., Michiels, B., (2005). Size-mediated ageing reduces vigour in trees. Ecology Letters, 8(11), 1183-1190.
Michaletz, T, S., Cheng, D, L., Kerkhoff, J, A., Enquist, J, B., (2014). Convergence of terrestrial plant production across global climate gradients. Nature, 512(7512), 39-43.
Mollier, A., Pellerin, S., (1999). Maize root system growth and development as influenced by phosphorus deficiency. Journal of Experimental Botany, 50(333), 487-497.
Paine C E,., Marthews, R, T., Vogt, R, D., Purves, W, D., Rees, M., Hector, A., Turnbull, A, L., (2012). How to fit nonlinear plant growth models and calculate growth rates: an update for ecologists. Methods in Ecology and Evolution, 3(2), 245-256.
Poorter, L., Wright, J, S., Paz, H., Ackerly, D, D., Condit, R., Ibarramanriquez, G., Harms, E, K., Licona, C, J., Martinezramos, M., Mazer, J, S., Mullerlandau, C, H., Penaclaros, M., Webb, O, C., Wright, J, L., (2008). Are functional traits good predictors of demographic rates? Evidence from five Neotropical forests. Ecology, 89(7), 1908-1920.
Phillips, N.G., Buckley, T.N., Tissue, D.T., 2008. Capacity of old trees to respond to environmental change. Journal of integrative plant biology. 50 (11), 1355-1364.
Reich, B, P., Walters, M. B., (1994). Photosynthesis-nitrogen relations in Amazonian tree species. II: Variation in nitrogen vis-a-vis specific leaf area influences mass- and area-based expressions. Oecologia, 97(1), 73-81.
Reich, P. B., Tjoelker, M.G., Machado, J.L., Oleksyn, J., 2006. Universal scaling of respiratory metabolism, size and nitrogen in plants. Nature, 439, 457-461.
Ryan MG, Phillips, N, Bond, BJ., (2006). The hydraulic limitation hypothesis revisited. Plant Cell Environment, 29, 367–381.
Ryan, G, M., Binkley, D., H Fownes, H, J., (1997). Age-related decline in forest productivity: Pattern and process. Advances in Ecological Research, 213-262
Ryan, G, M., Waring, H, R., (1992). Maintenance Respiration and Stand Development in a Subalpine Lodgepole Pine Forest. Ecology, 73(6), 2100-2108.
Santiago, S, L., Goldstein, G., Meinzer, C, F., Fisher, B, J., Machado, K., Woodruff, R, D., Jones, H, T., (2004). Leaf photosynthetic traits scale with hydraulic conductivity and wood density in Panamanian forest canopy trees. Oecologia, 140 (4), 543–550.
Sheil, D., Eastaugh, S, C., Vlam, M., Zuidema, A, P., Groenendijk, P., Der Sleen, P, V., Jay, A., Vanclay, J, K.., (2017). Does biomass growth increase in the largest trees? Flaws, fallacies and alternative analyses. Functional Ecology, 31(3), 568-581.
Shi, P, J., Men, X, Y., Sandhu, S, H., Chakraborty, A., Li, B., Ouyang, F., Sun, Y, C., Ge, F., (2013). The ‘general’ ontogenetic growth model is inapplicable to crop growth. Ecological Modelling, 266, 1-9.
Shu, S, M., Zhu, W, Z., Wang, W, Z., Jia, M., Zhang, Y, Y., Sheng, Z, L., (2019). Effects of tree size heterogeneity on carbon sink in old forests. Forest Ecology and Management, 637-648.
Sileshi, W, G., (2014). A critical review of forest biomass estimation models, common mistakes and corrective measures. Forest Ecology and Management, 329, 237-254.
Sillett, C, S., Pelt, V, R., Koch, W, G., Ambrose, R, A., Carroll, L, A., Antoine, E, M., Mifsud, M, B., (2010). Increasing wood production through old age in tall trees. Forest Ecology and Management, 259(5), 976-994.
Takashima, T., Hikosaka, K., Hirose, T., (2004). Photosynthesis or persistence: nitrogen allocation in leaves of evergreen and deciduous Quercus species. Plant Cell and Environment, 27(8), 1047-1054.
Tatuo, K., Shidei, T.., (1967). Primary production and turnover of organic matter in different forest ecosystems of the western pacific. Japanese Journal of Ecology, 17(2), 70-87.
Thornley, J.H.M., 2011. Plant growth and respiration re-visited: maintenance respiration defined–it is an emergent property of, not a separate process within, the system–and why the respiration: photosynthesis ratio is conservative. Annals of botany. 108, 1365-1380.
Van Iersel, M, W., 2003. Carbon use efficiency depends on growth respiration, maintenance respiration, and relative growth rate. A case study with lettuce. Plant Cell and Environment. 26, 1441-1449.
Von Bertalanffy, L., (1957). Quantitative laws in metabolism and growth. The Quarterly Eeview of Biology, 32(3), 217-231.
Wang, W., Jia, M., Wang, G., Zhu, W., McDowell, N.G., 2017. Rapid warming forces contrasting growth trends of subalpine fir (Abies fabri) at higher-and lower-elevations in the eastern Tibetan Plateau. Forest Ecology and Management. 402, 135-144.
Wang, Z. Q.A theoretical framework for whole-plant carbon assimilation efficiency based on metabolic scaling theory: a test case using Picea seedling. Tree Physiol. 35, 599–607 (2015).
Weiher, E., Der Werf, A. V., Thompson, K., Roderick, M. L., Garnier, E., Eriksson, O., (1999) Challenging Theophrastus: a common core list of plant traits for functional ecology. Journal of Vegetation Science, 10, 609-620.
Weiner, J., (2004). Allocation, plasticity and allometry in plants. Perspectives in Plant Ecology, Evolution and Systematics, 6(4), 207-215.
West, B, G., Brown, H, J., Enquist, J, B., (1997). A general model for the origin of allometric scaling laws in biology. Science, 276(5309), 122-126.
West, P. W., (2019). Dorespiratory costs explain the decline with age of forest growth rate. Journal of Forestry Research, 1-20.
Westoby, M., (1998). A leaf-height-seed (LHS) plant ecology strategy scheme. Plant and Soil, 199(2), 213-227.
Wilson, J, P., Thompson, K., Hodgson, J., (1999). Specific leaf area and leaf dry matter content as alternative predictors of plant strategies. New Phytologist, 143(1), 155-162.
Wright, S. J., Kitajima, K., Kraft, N. J., Reich, P. B., Wright, I. J., Bunker, D. E., Condit, R., Dalling, W, J., Davies, J, S., Diaz, S, Engelbrecht, B, M, J., Harms, E, K., Hubbell, P, S., Marks, O, C., Ruizjaen, C, M., Salvador, M, C., Zanne, E, A., (2010). Functional traits and the growth-mortality trade-off in tropical trees. Ecology, 91(12), 3664-3674.
Xie, J, B., Tang, L, S., Wang, Z, Y., Xu, G, Q, Li, Y., (2012). Distinguishing the biomass allocation variance resulting from ontogenetic drift or acclimation to soil texture. PLOS ONE, 7(7).
Zhou, P., Zhu, W.Z., Luo, J., 2013. Above-ground biomass and carbon storage of typical foerest types in Gongga Mountain. Acta Bot.Boreal.-Occident.Sin. 33(1),162-168. (in Chinese)
Lorimer, C.G., Dahir, S.E., Nordheim, E.V., 2001. Tree mortality rates and longevity in mature and old-growth hemlock-hardwood forests. J. Ecol. 89 (6), 960-971.
Foster, J.R., D’Amato, A.W., Bradford, J.B., 2014. Looking for age-related growth decline in natural forests: unexpected biomass patterns from tree rings and simulated mortality. Oecologia 175 (1), 363-374.
Coomes, D.A., Holdaway, R.J., Kobe, R.K., Lines, E.R., Allen, R.B., 2015. A general integrative framework for modelling woody biomass production and carbon sequestration rates in forests. J. Ecol. 100 (1), 42-64.
Pillet, M., Joetzjer, E., Belmin, C., Chave, J., Ciais, P., Dourdain, A., Evans, M., Hérault, B., Luyssaert, S., Poulter, B. 2017. Disentangling competitive vs. climatic drivers of tropical forest mortality. J. Ecol. 106 (3), 1165-1179.
Figure legends
Figure. 1. Conceptual diagram illustrating two types of unimodal curves and cascading growth. a and b: red and green arrows represent the effects of parameters cM (orM max) andTmr /gr (or λ) on unimodal curves; - and + represent the negative and positive correlation between parameters and the curve characteristics (height, kurtosis and length). c and d: the growth trajectories that trees may follow, i.e., cascading growth. Here, we only illustrate the concept of cascading growth. The green line in Figs. c and d represents the unimodal pattern that growth should follow. Dotted lines represent not fully realized trajectories. Blue or red lines represent two new and larger unimodal curves. The solid portions of lines may be in series with the green solid lines, which means growth will follow the new trajectories, resulting in a continuous increase in growth trend (α and β ). The dotted lines in the graph represent growth trajectories that do not occur. The lines with an arrow indicate growth trends. Another indistinguishable cascading trajectory (γ ) caused by a continuous increase ofcM and decrease ofTmr /gr .
Figure. 2. Tree ring maximum increment along DBH gradient for subalpine Abies fabri forest sites at different altitudes on Gongga Mountain. Circles represent the DBH maximum increment for each decade. Hollow circles represent the growth dynamics with certain regularity. Solid circles represent limited scattered data, and are not included in the fitting. The yellow line indicates 95% confidence interval.
Figure. 3. The aboveground biomass increments along tree size gradients for subalpine Abies fabri forest sites at different altitudes on Gongga Mountain. Green and white dots represent maximum and average aboveground biomass increments, respectively. The scatter points on the left side of the vertical solid line conform to the Gompertz equation, on the right side conform to the logistic equation or are not fitted. Roman numerals I, II, and III represent the size intervals corresponding to rising, falling and other trends of growth. The yellow line indicates 95% confidence interval.
Figure. 4. Growth trajectory of Abies fabri individuals at elevation of 3,100m. Hollow circles represent growth dynamics with obvious regularity. The change trend of solid circles is different from that of hollow circles, so is not included in the analyses.
Figure. 5. Elements and dry matter content in leaves of trees under different growth trends. Ⅰ, Ⅱ and Ⅲ indicate different size intervals, corresponding to those in Figure 3. Different lowercase letters indicate significant difference at P<0.05 level
Figure. 6. Stem economics and leaf dry matter contentunder different growth trends. Here, xd, wm, bt, and dc represent xylem density, wood moisture, bark thickness, and leaf dry matter content, respectively. Different lowercase letters indicate significant difference at the P<0.05 level. Ⅰ, Ⅱ and Ⅲ indicate different size intervals, corresponding to those in Figure 3.
Figure. 7. Relationships between morphological traits and tree size. The black rectangles or circles in Fig. 7b represent SWA/HWA and canopy/size, respectively, for individual trees with recent growth trajectories that exhibit a unimodal pattern (i.e., Fig. 4). The intersections of the fitting functions and horizontal dashed lines represent the sizes of ideal trees and the corresponding functional traits.
Figure. 8. Effects of morphological traits on equation parameters. The black dots and hollow circles represent ideal trees (i.e., green dots to the right of the vertical solid line in Figs. 3a, b and c) and individual trees (i.e., black symbols in Fig. 4b), respectively. The yellow line indicates the 95% confidence interval.