Dynamic simulation of the multilayer crown net photosynthetic rate and determination of the functional crown for larch (Larix olgensis) trees


Pruning can encourage the early formation of knot-free wood with high economic value. However, few studies have assessed the costs and benefits of production in order to determine the optimal pruning design. The concept of a functional crown provides reasonable guidance for pruning, but there is no objective method of determining the functional crown. Semimonthly measurements of leaf traits and photosynthetic characteristics and the corresponding environmental conditions were conducted for young Larix olgensis plantations throughout the entire growing season. The dynamic crown net photosynthetic rate (An) was simulated by comprehensively considering the leaf mass per area, photosynthetically active radiation, air temperature (Tair), vapor pressure deficit and leaf position within the crown (relative depth into the crown, RDINC). The precision (P) was estimated to be 95.5%, indicating that our model performed well in predicting the dynamic crown An for young Larix olgensis plantations. The net primary productivity (NPP) of each whorl of the tree crown was calculated by numerically integrating the instantaneous An. The net carbon contribution from branches to the tree was obtained by subtracting the annual carbon increment from the NPP. The results showed that some live branches in the lower crown contributed negatively to the trunk, indicating that pruning should not focus only on dead branches. Thus, the lower boundary of the functional crown (LBFC) provides a valuable guideline for pruning treatments. Considering that the LBFC will shift upward as the tree grows, we suggest that advanced pruning techniques be applied to reduce costs and minimize labor.

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Data availability

The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.



Annual carbon increment (g)

A n :

Net photosynthetic rate (μmol m−2 s−1)


Allocated proportions of ACI (%)

k :

Extinction coefficient


Branch chord length (cm)


Branch diameter (cm)


Diameters inside the bark of the branch (cm)


Diameters outside the bark of the branch (cm)


Branch length (cm)

Bm d :

Dry mass of the sample branches (g)

Bm f :

Fresh mass of the sample branches (g)

BMf :

Fresh mass of all branches (g)

Brc :

Carbon content of the branch (%)


Total volume of the branch (cm3)


Length of the live crown (cm)


Cumulative leaf area (m2)


Whorl-specific cumulative leaf area index


Crown projected area (m2)


Guadratic mean diameter (cm)


Depth into the crown (cm)


Date of the year

Fm d :

Dry mass of the sample leaves (g)

Fm f :

Fresh mass of the sample leaves (g)

FMf :

Fresh mass of all roots (g)

Frc :

Carbon content of the leaf


Global site factor


Tree height (m)


Photosynthetically active radiation (μmol m−2 s−1)


Photosynthetic light response


Leaf area (m2)


Lower boundary of the functional crown


Leaf mass per area (g/m2)


Moisture content (%)


Mean error


Nitrogen content (g/kg)


Net carbon contribution (g)


Net primary productivity (g)

P :

Precision estimation (%)


Total volume of the trunk (cm3)

R 2 :

Coefficient of determination

R ac :

Relative to the carbon increment of the whole crown


Relative depth into the crown


Ratio of leaf mass to branch mass (g)

Rm d :

Dry mass of the sample roots (g)

Rm f :

Fresh mass of the sample roots (g)

RMf :

Fresh mass of all roots (g)


Root mean square error

Rrc :

Carbon content of the root (%)

T leaf :

Leaf temperature (℃)

Tm d :

Dry mass of the sample trunks (g)

Tm f :

Fresh mass of the sample trunks (g)


Total mass of the branch (g)

TMf :

Fresh mass of the total trunk (g)

Trc :

Carbon content of the trunk (%)


Diameter inside the bark of the disk (cm)


Diameter outside the bark of the disk (cm)


Vapor pressure deficit (kPa)


Annual carbon increment of the branch (g)

ΔBv :

Annual volumetric increment of the branch (cm3)


Annual carbon increment of the leaf (g)


Annual carbon increment of the root (g)


Annual carbon increment of the trunk (g)

ΔTv :

Annual volumetric increment of the trunk (cm3)

ψ :

Solar elevation angle


Branch azimuth


Branch angle


  1. Amthor JS (1994) Scaling CO2-photosynthesis relationships from the leaf to the canopy. Photosynth Res 39:321–350. https://doi.org/10.1007/BF00014590

    CAS  Article  PubMed  Google Scholar 

  2. Atkinson LJ, Campbell CD, Zaragoza-Castells J, Hurry V, Atkin OK (2010) Impact of growth temperature on scaling relationships linking photosynthetic metabolism to leaf functional traits. Funct Ecol 24:1181–1191. https://doi.org/10.1111/j.1365-2435.2010.01758.x

    Article  Google Scholar 

  3. Aubin I, Beaudet M, Messier C (2000) Light extinction coefficients specific to the understory vegetation of the southern boreal forest, Quebec. Can J For Res 30:168–177. https://doi.org/10.1139/cjfr-30-1-168

    Article  Google Scholar 

  4. Balandier P, Lacointe A, Roux XL, Sinoquet H, Cruiziat P, Dizès SL (2000) SIMWAL: a structural-functional model simulating single walnut tree growth in response to climate rand pruning. Ann For Sci 57:571–585. https://doi.org/10.1051/forest:2000143

    Article  Google Scholar 

  5. Bedker PJ, O'Brien JG, Mielke ME (1995) How to prune trees. USDA Forest Service, Northeastern Area State and Private Forestry. http://www.recovery.ct.gov/deep/lib/deep/forestry/icestorm/htprune.pdf

  6. Calama R, Puértolas J, Madrigal G, Pardos M (2013) Modeling the environmental response of leaf net photosynthesis in Pinus pinea L. natural regeneration. Ecol Model 251:9–21. https://doi.org/10.1016/j.ecolmodel.2012.11.029

    Article  Google Scholar 

  7. Campbell GS (1986) Extinction coefficients for radiation in plant canopies calculated using an ellipsoidal inclination angle distribution. Agric For Meteorol 36:317–321. https://doi.org/10.1016/0168-1923(86)90010-9

    Article  Google Scholar 

  8. Cavaleri MA, Oberbauer SF, Clark DB, Clark DA, Ryan MG (2010) Height is more important than light in determining leaf morphology in a tropical forest. Ecology 91:1730–1739. https://doi.org/10.1890/09-1326.1

    Article  PubMed  Google Scholar 

  9. Chaturvedi RK, Raghubanshi AS, Singh JS (2011) Leaf attributes and tree growth in a tropical dry forest. J Veg Sci 22:917–931

    Article  Google Scholar 

  10. Chen JM, Leblanc SG (1997) A four-scale bidirectional reflectance model based on canopy architecture. IEEE Trans Geosci Remote 35:1316–1337. https://doi.org/10.1109/36.628798

    Article  Google Scholar 

  11. Chen JM, Black TA (2010) Defining leaf area index for non-flat leaves. Plant Cell Environ 15:421–429. https://doi.org/10.1111/j.1365-3040.1992.tb00992.x

    Article  Google Scholar 

  12. Clark DA, Brown S, Kicklighter DW, Chambers JQ, Thomlinson JR, Ni J (2001) Measuring net primary production in forests: concepts and field methods. Ecol Appl 11:356–370. https://doi.org/10.2307/3060894

    Article  Google Scholar 

  13. Clark DB, Mercado LM, Sitch S, Jones C, Gedney N, Best MJ, Pryor M, Rooney GG, Essery RLH, Blyth E (2011) The joint UK land environment simulator, (JULES) model description: part 2—carbon fluxes and vegetation dynamics. Geosci Model Dev 4:701–722. https://doi.org/10.5194/gmd-4-701-2011

    Article  Google Scholar 

  14. Djomo AN, Knohl A, Gravenhorst G (2011) Estimations of total ecosystem carbon pools distribution and carbon biomass current annual increment of a moist tropical forest. For Ecol Manag 261:1448–1459. https://doi.org/10.1016/j.foreco.2011.01.031

    Article  Google Scholar 

  15. Domisch T (2001) Effects of soil temperature on biomass and carbohydrate allocation in scots pine (Pinus sylvestris) seedlings at the beginning of the growing season. Tree Physiol 21:465–472. https://doi.org/10.1093/treephys/21.7.465

    CAS  Article  PubMed  Google Scholar 

  16. Emmingham W, Fitzgerald S (1995) Pruning to enhance tree and stand value. Extension Serv. Pub. EC 1457. https://catalog.extension.oregonstate.edu

  17. Falster DS, Brännström Å, Dieckmann U, Westoby M (2011) The influence of four major plant traits on average height, leaf-area cover, net primary productivity, and biomass density in single-species forests: a theoretical investigation. J Ecol 99:148–164. https://doi.org/10.1111/j.1365-2745.2010.01735.x

    Article  Google Scholar 

  18. Farquhar GD, Von CS, Berry JA (1980) A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta 149:78–90. https://doi.org/10.1007/BF00386231

    CAS  Article  PubMed  Google Scholar 

  19. Ford R, Ford ED (1990) Structure and basic equations of a simulator for branch growth in the Pinaceae. J Theor Biol 146:1–13. https://doi.org/10.1016/s0022-5193(05)80041-4

    Article  Google Scholar 

  20. Hanley DP, Oliver CD, Maguire DA, Briggs DG, Fight RD (1995) Forest pruning and wood quality. Seattle, Washington

    Google Scholar 

  21. Jin S, Zhou X, Fan J (2003) Modeling daily photosynthesis of nine major tree species in northeast China. For Ecol Manag 184:125–140. https://doi.org/10.1016/s0378-1127(03)00205-6

    Article  Google Scholar 

  22. Kerr G, Morgan G (2006) Does formative pruning improve the form of broadleaved trees? Can J For Res 36:132–141. https://doi.org/10.1139/X05-213

    Article  Google Scholar 

  23. Kohler P, Huth A (1998) The effects of tree species grouping in tropical rainforest modeling: simulations with the individual-based model Formind. Ecol Model 109:301–321. https://doi.org/10.1016/S0304-3800(98)00066-0

    Article  Google Scholar 

  24. Kramer PJ, Kozlowski TT (1979) Physiology of woody plants, 2nd edn. Manhattan, New York

    Google Scholar 

  25. Kupka I (2007) Growth reaction of young wild cherry (Prunus avium L.) trees to pruning. J For Sci 53:555–560. https://doi.org/10.17221/2165-JFS

  26. Lachapelle PP, Shipley B (2012) Interspecific prediction of photosynthetic light response curves using specific leaf mass and leaf nitrogen content: effects of differences in soil fertility and growth irradiance. Ann Bot 109:1149–1157. https://doi.org/10.1093/aob/mcs032

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  27. Lam F, Barrett JD, Nakajima S (2005) Influence of knot area ratio on the bending strength of Canadian Douglas fir timber used in Japanese post and beam housing. J Wood Sci 51:18–25. https://doi.org/10.1007/s10086-003-0619-6

    Article  Google Scholar 

  28. Leuning R, Kelliher FM, Pury DGG, Schulze ED (1995) Leaf nitrogen, photosynthesis, conductance and transpiration: scaling from leaves to canopies. Plant Cell Environ 18:1183–1200. https://doi.org/10.1111/j.1365-3040.1995.tb00628.x

    Article  Google Scholar 

  29. Li FR, Wang ZF, Wang BS (1996) Studies on the effective crown development of Larix olgensis (I)—determination of the functional crown. J N For Univ 24: 1–8 (in Chinese). https://doi.org/10.13759/j.cnki.dlxb.1996.01.004.

  30. Liu Q, Li FR (2018) Spatial and seasonal variations of standardized photosynthetic parameters under different environmental conditions for young planted Larix olgensis Henry trees. Forests 9:522. https://doi.org/10.3390/f9090522

    Article  Google Scholar 

  31. Liu Q, Dong LH, Li FR (2018) Modeling net CO2 assimilation (AN) within the crown of young planted Larix olgensis trees. Can J For Res 48:1085–1098. https://doi.org/10.1139/cjfr-2018-0151

    CAS  Article  Google Scholar 

  32. Liu Q, Li FR, Xie LF (2016) Optimal model of photosynthesis-light response curve in canopy of planted Larix olgensis tree. Chin. J. Appl. Ecol. 27: 2420–2428 (in Chinese). https://doi.org/10.13287/j.1001-9332.201608.023.

  33. Liu Q, Xie LF, Li FR (2019) Dynamic simulation of the crown net photosynthetic rate for young Larix olgensis Henry trees. Forests 10:321. https://doi.org/10.3390/f10040321

    Article  Google Scholar 

  34. Lockhart BR, Gardiner ES, Hodges JD, Ezell AW (2008) Carbon allocation and morphology of cherrybark oak seedlings and sprouts under three light regimes. Ann Forest Sci 65:801. https://doi.org/10.1051/forest:2008064

    CAS  Article  Google Scholar 

  35. Marchi E, Neri F, Fioravanti M, Picchio R, Goli G, Giulio GD (2013) Effects of cutting patterns of shears on occlusion processes in pruning of high-quality wood plantations. Croat J For Eng 34:295–304

    Google Scholar 

  36. Mayoral C, Calama R, Sánchez-González M, Pardos M (2015) Modelling the influence of light, water and temperature on photosynthesis in young trees of mixed Mediterranean forests. New Forest 46:485–506. https://doi.org/10.1007/s11056-015-9471-y

    Article  Google Scholar 

  37. Marino G, Aqil M, Shipley B (2010) The leaf economics spectrum and the prediction of photosynthetic light–response curves. Funct Ecol 24:263–272. https://doi.org/10.1111/j.1365-2435.2009.01630.x

    Article  Google Scholar 

  38. Meloche CG, Diggle PK (2003) The pattern of carbon allocation supporting growth of preformed shoot primordia in Acomastylis rossii (Rosaceae). Am J Bot 90:1313–1320. https://doi.org/10.3732/ajb.90.9.1313

    CAS  Article  PubMed  Google Scholar 

  39. Mengistu T, Sterck FJ, Fetene M, Tadesse W, Bongers F (2001) Leaf gas exchange in the frankincense tree (Boswellia papyrifera) of African dry woodlands. Tree Physiol 31:740–750. https://doi.org/10.1093/treephys/tpr067

    Article  Google Scholar 

  40. Monsi M, Saeki T (2005) On the factor light in plant communities and its importance for matter production. Ann Bot 95:549–567. https://doi.org/10.1093/aob/mci052

    Article  PubMed  PubMed Central  Google Scholar 

  41. Niklas KJ, Enquist BJ (2002) Canonical rules for plant organ biomass partitioning and annual allocation. Am J Bot 89:812–819. https://doi.org/10.3732/ajb.89.5.812

    Article  PubMed  Google Scholar 

  42. O’Hara KL (2007) Pruning wounds and occlusion: a long-standing conundrum in forestry. J Forest 105:131–138

    Google Scholar 

  43. Oliver CD, Larson BC (1996) Forest stand dynamics, 1st edn. Wiley, New York

    Google Scholar 

  44. Ow LF, Ghosh S, Sim EK (2013) Mechanical injury and occlusion: an urban, tropical perspective. Urban For Urban Gree 12:255–261. https://doi.org/10.1016/j.ufug.2013.02.004

    Article  Google Scholar 

  45. Pearcy R, Valladares F, Wright SJ, Lasso E (2004) A functional analysis of the crown architecture of tropical forest Psychotria species: Do species vary in light capture efficiency and consequently in carbon gain and growth? Oecologia 139:163–177. https://doi.org/10.1007/s00442-004-1496-4

    Article  PubMed  Google Scholar 

  46. Petruncio MD (1994) Effects of pruning on growth of western hemlock (Tsuga heterophylla) and Sitka spruce (Picea sitchensis) in Southeast Alaska. Ph.D. dissertation, College of Forest Resources, University of Washington, Seattle

  47. Poorter H, Niklas KJ, Reich PB, Oleksyn J, Poot P, Mommer L (2012) Biomass allocation to leaves, stems and roots: meta-analyses of interspecific variation and environmental control. New Phytol 193:30–50. https://doi.org/10.1111/j.1469-8137.2011.03952.x

    CAS  Article  PubMed  Google Scholar 

  48. Prentice IC, Leemans R (1990) Pattern and process and the dynamics of forest structure: a simulation approach. J Ecol 78:340–355. https://doi.org/10.2307/2261116

    Article  Google Scholar 

  49. Pierce LL, Running SW (1988) Rapid estimation of coniferous forest leaf area Index using a portable integrating radiometer. Ecology 69:1762–1767. https://doi.org/10.2307/1941154

    Article  Google Scholar 

  50. Quan XK, Wang CK (2018) Acclimation and adaptation of leaf photosynthesis, respiration and phenology to climate change: a 30-year Larix gmelinii common-garden experiment. Forest Ecol Manag 411:166–175. https://doi.org/10.1016/j.foreco.2018.01.024

    Article  Google Scholar 

  51. Rachmilevitch S, Huang B, Lambers H (2010) Assimilation and allocation of carbon and nitrogen of thermal and nonthermal Agrostis species in response to high soil temperature. New Phytol 170:479–490. https://doi.org/10.1111/j.1469-8137.2006.01684.x

    CAS  Article  Google Scholar 

  52. Reiter IM, Häberle KH, Nunn AJ, Heerdt C, Reitmayer H, Grote R, Matyssek R (2005) Competitive strategies in adult beech and spruce: space-related foliar carbon investment versus carbon gain. Oecologia 146:337–349. https://doi.org/10.1007/s00442-005-0146-9

    CAS  Article  PubMed  Google Scholar 

  53. Risser JPG (1974) Biomass, annual net primary production, and dynamics of six mineral elements in a post Oak-Blackjack Oak Forest. Ecology 55:1246–1258. https://doi.org/10.2307/1935453

    Article  Google Scholar 

  54. Sato H, Itoh A, Kohyama T (2007) SEIB–DGVM: A new dynamic global vegetation model using a spatially explicit individual-based approach. Ecol Model 200:279–307. https://doi.org/10.1016/j.ecolmodel.2006.09.006

    Article  Google Scholar 

  55. Sitch S, Smith B, Prentice IC, Arneth A, Bondeau A, Cramer W, Kaplan JO, Levis S, Lucht W, Sykes MT, Thonicke K, Venevsky S (2003) Evaluation of ecosystem dynamics, plant geography and terrestrial carbon cycling in the LPJ dynamic global vegetation model. Global Change Biol 9:161–185. https://doi.org/10.1046/j.1365-2486.2003.00569.x

    Article  Google Scholar 

  56. Springmanna S, Rogersb R, Spiecker H (2011) Impact of artificial pruning on growth and secondary shoot development of wild cherry (Prunus avium L.). Forest Ecol Manag 261:764–769. https://doi.org/10.1016/j.foreco.2010.12.007

    Article  Google Scholar 

  57. Sprugel DG, Hinckley TM, Schaap W (1991) The theory and practice of branch autonomy. Ann Rev Ecol Ecol S 22:309–334. https://doi.org/10.1146/annurev.es.22.110191.001521

    Article  Google Scholar 

  58. Sumida A, Miyaura T, Torii H (2013) Relationships of tree height and diameter at breast height revisited: analyses of stem growth using 20-year data of an even-aged Chamaecyparis obtuse stand. Tree Physiol 33:106–118. https://doi.org/10.1093/treephys/tps127

    Article  PubMed  PubMed Central  Google Scholar 

  59. Sun YB, Liu Q, Li FR (2019) Dynamic simulation of light distribution in the live crown of Larix olgensis trees. J Beijing Forest Uni 41:77−87 (in Chinese). https://doi.org/10.12171/j.1000-1522.20190324

  60. Vose JM, Swank WT (1990) Assessing seasonal leaf area dynamics and vertical leaf area distribution in eastern white pine (Pinus strobus L.) with a portable light meter. Tree Physiol 7:125–134. https://doi.org/10.1093/treephys/7.1-2-3-4.125

    Article  PubMed  Google Scholar 

  61. Vose JM, Clinton BD, Sullivan NH, Bolstad PV (1995) Vertical leaf area distribution, light transmittance, and application of the Beer-Lambert Law in four mature hardwood stands in the southern Appalachians. Can J For Res 25:1036–1043. https://doi.org/10.1139/x95-113

    Article  Google Scholar 

  62. Wang YP, Jarvis PG (1990) Influence of crown structural properties on PAR absorption, photosynthesis, and transpiration in Sitka spruce: application of a model (MAESTRO). Tree Physiol 7:297–316. https://doi.org/10.1093/treephys/7.1-2-3-4.297

    Article  PubMed  Google Scholar 

  63. Wang YP, Leuning R (1998) A two-leaf model for canopy conductance, photosynthesis and partitioning of available energy I: model description and comparison with a multi-layered model. Agric Forest Meteorol 91:89–111. https://doi.org/10.1016/S0168-1923(98)00061-6

    Article  Google Scholar 

  64. Wang X, Taub D (2010) Interactive effects of elevated carbon dioxide and environmental stresses on root mass fraction in plants: a meta-analytical synthesis using pairwise techniques. Oecologia 163:1–11. https://doi.org/10.1007/s00442-010-1572-x

    Article  PubMed  Google Scholar 

  65. Wang P, Sun R, Hu J, Zhu Q, Zhou Y, Li L, Chen JM (2007) Measurements and simulation of forest leaf area index and net primary productivity in Northern China. J Environ Manage 85:607–615. https://doi.org/10.1016/j.jenvman.2006.08.017

    CAS  Article  PubMed  Google Scholar 

  66. Wyka TP, Żytkowiak R, Oleksyn J (2016) Seasonal dynamics of nitrogen level and gas exchange in different cohorts of Scots pine needles: a conflict between nitrogen mobilization and photosynthesis? Eur J For Res 135:483–493. https://doi.org/10.1007/s10342-016-0947-x

    CAS  Article  Google Scholar 

  67. Xu P (2002) Estimating the influence of knots on the local longitudinal stiffness in radiata pine structural timber. Wood Sci Technol 36:501–509. https://doi.org/10.1007/s00226-002-0156-2

    CAS  Article  Google Scholar 

  68. Xu JZ, Yu YM, Peng SZ, Yang SH, Liao LX (2014) A modified nonrectangular hyperbola equation for photosynthetic light-response curves of leaves with different nitrogen status. Photosynthetica 52:117–123. https://doi.org/10.1007/s11099-014-0011-3

    CAS  Article  Google Scholar 

  69. Yan X, Shugart H (2010) FAREAST: a forest gap model to simulate dynamics and patterns of eastern Eurasian forests. J Biogeogr 32:1641–1658. https://doi.org/10.1111/j.1365-2699.2005.01293.x

    Article  Google Scholar 

  70. Zhang XQ, Xu DY (2003) Eco-physiological modelmodelling of canopy photosynthesis and growth of a Chinese fir plantation. Forest Ecol Manag 173:201–211. https://doi.org/10.1016/s0378-1127(02)00015-4

    Article  Google Scholar 

  71. Zhu GL, Ju WM, Fan WY, Zhou YL, Li XF, Li MZ (2010) Forest canopy leaf area index in Maoershan Mountain: Ground measurement and remote sensing retrieval. Chin J Appl Ecol 21:2117–2124 (in Chinese). https://doi.org/10.3724/SP.J.1142.2010.40521

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This research was financially supported by the National Key R&D Program of China (Project: 2017YFD0600402), Provincial Funding for the National Key R&D Program of China in Heilongjiang Province (Project: GX18B041), the Fundamental Research Funds for the Central Universities (No. 2572020DR03), the Talent Special Scientific Research Fund of Hebei Agricultural University (YJ201942), and the Heilongjiang Touyan Innovation Team Program (Technology Development Team for High-efficiency Silviculture of Forest Resources).

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LD and FL conceived of the ideas and designed the methodology; QL and LX collected and analyzed the data; QL wrote the original draft; LD and FL reviewed and edited the manuscript. All authors contributed critically to the drafts and gave final approval for publication.

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Correspondence to Lihu Dong or Fengri Li.

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Liu, Q., Xie, L., Dong, L. et al. Dynamic simulation of the multilayer crown net photosynthetic rate and determination of the functional crown for larch (Larix olgensis) trees. New Forests (2021). https://doi.org/10.1007/s11056-021-09839-0

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  • Allocation of photosynthetic production
  • Functional crown
  • Cumulative contribution rate
  • Pruning treatments