, Volume 33, Issue 1, pp 121–138 | Cite as

Tree allometry variation in response to intra- and inter-specific competitions

  • Miren del RíoEmail author
  • Andrés Bravo-Oviedo
  • Ricardo Ruiz-Peinado
  • Sonia Condés
Original Article


Key message

Crown, height and stem allometry vary with stand density and species composition, the plasticity in response to inter- and intra-specific competitions being related to species shade tolerances.


Determining the way in which variability in tree allometry is modulated by intra- and inter-specific competitions in different species and stand compositions is of particular interest for forest modelling and practice. In this study, we explore this variability by developing models for tree crown diameter, total height and diameter at a height of 4 m, which include intra- and inter-specific competition terms. More than 19,000 Scots pine, silver fir, sessile oak and European beech trees from 4711 sample plots belonging to the Spanish National Forest Inventory were included in the study, covering both monospecific and two species mixed stands in Northern Spain. Trees growing under conditions of high competition displayed narrower crowns, greater heights and less taper for a given tree diameter, the plasticity in crown and height in response to intra-specific competition being related to species shade tolerance. The inter-specific competition effect on crown diameter and height was related to the difference in shade tolerance between the two species of the mixture, while stem taper did not exhibit this pattern. These results suggest that trees in mixed stands indeed show a modified allometry, which might be related to complementary resource acquisition strategies. The large variability observed in tree allometry indicates the need to consider both intra- and inter-specific competitions in allometric models.


Species interactions Competition reduction Crown plasticity Height–diameter relationship Stem tapering 



The authors acknowledge Roberto Vallejo, in charge of the Spanish National Forest Inventory, for the provision of the NFI data. They also thank the Spanish Ministry of Economy and Competitiveness for funding the research project “Mixed Forest complexity and sustainability: dynamic, silviculture and adaptive management tools” (AGL2014-51964-C2-2-R).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

468_2018_1763_MOESM1_ESM.docx (631 kb)
Supplementary material 1 (DOCX 630 KB)
468_2018_1763_MOESM2_ESM.docx (39 kb)
Supplementary material 2 (DOCX 39 KB)


  1. Baldwin VC Jr, Peterson KD, Clark A III, Ferguson RB, Strub MR, Bower DR (2000) The effects of spacing and thinning on stand and tree characteristics of 38-year-old Loblolly Pine. For Ecol Manag 137:91–102CrossRefGoogle Scholar
  2. Barbeito I, Dassot M, Bayer D, Collet C, Drössler L, Löf M, del Río M, Ruiz-Peinado R, Forrester DI, Bravo-Oviedo A, Pretzsch H (2017) Terrestrial laser scanning reveals differences in crown structure of Fagus sylvatica in mixed vs. pure European forests. For Ecol Manag 405:381–390CrossRefGoogle Scholar
  3. Bayer D, Seifert S, Pretzsch H (2013) Structural crown properties of Norway spruce (Picea abies [L.] Karst.) and European beech (Fagus sylvatica [L.]) in mixed versus pure stands revealed by terrestrial laser scanning. Trees 27(4):1035–1047CrossRefGoogle Scholar
  4. Beauchamp JJ, Olson JS (1973) Corrections for bias in regression estimates after logarithmic transformation. Ecology 54:1403–1407CrossRefGoogle Scholar
  5. Benneter A, Forrester DI, Bouriaud O, Dormann CF, Bauhus J (2018) Tree species diversity does not compromise stem quality in major European forest types. For Ecol Manag 422:323–337CrossRefGoogle Scholar
  6. Bielak K, Dudzińska M, Pretzsch H (2014) Mixed stands of Scots pine (Pinus sylvestris L.) and Norway spruce [Picea abies (L.) Karst] can be more productive than monocultures. evidence from over 100 years of observation of long-term experiments. For Syst 23(3):573–589Google Scholar
  7. Bravo-Oviedo A, del Río M, Calama R, Valentine HT (2014) New approaches to modelling cross-sectional area to height allometry in four Mediterranean pine species. Forestry 87:399–406CrossRefGoogle Scholar
  8. Bravo-Oviedo A, Condés S, del Río M, Pretzsch H, Ducey MJ (2018) Maximum stand density strongly depends on species-specific wood stability, shade and drought tolerance. Forestry 91:459–469CrossRefGoogle Scholar
  9. Brüchert F, Gardiner B (2006) The effect of wind exposure on the tree aerial architecture and biomechanics of Sitka spruce (Picea sitchensis, Pinaceae). Am J Bot 93:1512–1521CrossRefGoogle Scholar
  10. Cameron AD, Watson BA (1999) Effect of nursing mixtures on the stem form, crown size, branching habit and wood properties of Sitka spruce (Picea sitchensis (Bong.) Carr.). For Ecol Manage 122:113–124CrossRefGoogle Scholar
  11. Condés S, del Río M (2015) Climate modifies tree interactions in terms of basal area growth and mortality in monospecific and mixed Fagus sylvatica and Pinus sylvestris forests. Eur J Forest Res 134:1095–1108CrossRefGoogle Scholar
  12. Dean TJ, Baldwin VC (1996) The relationship between Reineke’s stand-density index and physical stem mechanics. For Ecol Manag 81(1–3):25–34CrossRefGoogle Scholar
  13. del Río M, Montero G, Bravo F (2001) Analysis of diameter-density relationships and self-thinning in non-thinned even-aged Scots pine stands. For Ecol Manag 142(1–3):79–87Google Scholar
  14. del Río M, Condés S, Pretzsch H (2014) Analyzing size-symmetric vs. size-asymmetric and intra-vs. inter-specific competition in beech (Fagus sylvatica L.) mixed stands. For Ecol Manag 325:90–98CrossRefGoogle Scholar
  15. del Río M, Pretzsch H, Alberdi I, Bielak K, Bravo F, Brunner A, Condés S, Ducey MJ, Fonseca T, von Lüpke N, Pach M, Peric S, Perot T, Souidi Z, Spathelf P, Sterba H, Tijardovic M, Tomé M, Vallet P, Bravo-Oviedo A (2016) Characterization of the structure, dynamics, and productivity of mixed-species stands: review and perspectives. Eur J Forest Res 135:23–49CrossRefGoogle Scholar
  16. Dieler J, Pretzsch H (2013) Morphological plasticity of European beech (Fagus sylvatica L.) in pure and mixed-species stands. For Ecol Manag 295:97–108CrossRefGoogle Scholar
  17. Dietze MC, Wolosin MS, Clark JS (2008) Capturing diversity and interspecific variability in allometries: a hierarchical approach. For Ecol Manag 256:1939–1948CrossRefGoogle Scholar
  18. Ducey MJ (2012) Evergreenness and wood density predict height-diameter scaling in trees of the northeastern United States. For Ecol Manage 279:21–26CrossRefGoogle Scholar
  19. Ducey MJ, Knapp RA (2010) A stand density index for complex mixed species forests in the northeastern United States. For Ecol Manag 260(9):1613–1622. CrossRefGoogle Scholar
  20. Ducey MJ, Woodall CW, Bravo-Oviedo A (2017) Climate and species functional traits influence maximum live tree stocking in the Lake States, USA. For Ecol Manag 386:51–61CrossRefGoogle Scholar
  21. Duursma RA, Mäkelä A, Reid DEB, Jokela EJ, Porté AJ, Roberts SD (2010) Self-shading affects allometric scaling in trees. Funct Ecol 24:723–730CrossRefGoogle Scholar
  22. Enquist BJ, Niklas KJ (2002) Global allocation rules for patterns of biomass partitioning in seed plants. Science 295:1517–1520CrossRefGoogle Scholar
  23. Enquist BJ, Allen AP, Brown JH, Gillooly JF, Kerkhoff AJ, Niklas KJ, Price CA, West GB (2007) Biological scaling: does the exception prove the rule? Nature 445:E9–E10CrossRefGoogle Scholar
  24. Forrester DI (2014) The spatial and temporal dynamics of species interactions in mixed-species forests: from pattern to process. For Ecol Manag 312:282–292CrossRefGoogle Scholar
  25. Forrester DI (2017) Ecological and physiological processes in mixed versus monospecific stands. In: Pretzsch H, Forrester DI, Bauhus J (eds) Mixed-species forests. Ecology and management. Springer, Berlin, pp 73–115CrossRefGoogle Scholar
  26. Forrester DI, Pretzsch H (2015) On the strength of evidence when comparing ecosystem functions of mixtures with monocultures, Tamm review. For Ecol Manag 356:41–53CrossRefGoogle Scholar
  27. Forrester DI, Benneter A, Bouriaud O, Bauhus J (2017a) Diversity and competition influence tree allometric relationships—developing functions for mixed-species forests. J Ecol 105:761–774CrossRefGoogle Scholar
  28. Forrester DI, Tachauer IHH, Annighoefer P, Barbeito I, Pretzsch H, Ruiz-Peinado R, Stark H, Vacchiano G, Zlatanov T, Chakraborty T, Saha S, Sileshi GW (2017b) Generalized biomass and leaf area allometric equations for European tree species incorporating stand structure, tree age and climate. For Ecol Manag 396:160–175CrossRefGoogle Scholar
  29. Forrester DI, Ammer C, Annighöfer PJ, Barbeito I, Bielak K, Bravo-Oviedo A, Coll L, del Río M, Drössler L, Heym M, Hurt V, Löf M, den Ouden J, Pach M, Pereira MG, Plaga BNE, Ponette Q, Skrzyszewski J, Sterba H, Svoboda M, Zlatanov TM, Pretzsch H (2018) Effects of crown architecture and stand structure on light absorption in mixed and monospecific Fagus sylvatica and Pinus sylvestris forests along a productivity and climate gradient through Europe. J Ecol 106(2):746–760CrossRefGoogle Scholar
  30. Franceschini T, Schneider R (2014) Influence of shade tolerance and development stage on the allometry of ten temperate tree species. Oecologia 176:739–749CrossRefGoogle Scholar
  31. Harja D, Vincent G, Mulia R, van Noordwijk M (2012) Tree shape plasticity in relation to crown exposure. Trees Struct Funct 26(4):1275–1285CrossRefGoogle Scholar
  32. Hemery GE, Savill PS, Pryor SN (2005) Applications of the crown diameter-stem diameter relationship for different species of broadleaved trees. For Ecol Manag 215(1–3):285–294CrossRefGoogle Scholar
  33. Ikonen VP, Kellomäki S, Väisänen H, Peltola H (2006) Modelling the distribution of diameter growth along the stem in Scots pine. Trees Struct Funct 20(3):391–392CrossRefGoogle Scholar
  34. Jucker T, Bouriaud O, Coomes DA (2015) Crown plasticity enables trees to optimize canopy packing in mixed-species forests. Funct Ecol 29:1078–1086CrossRefGoogle Scholar
  35. Karlsson K (2000) Stem form and taper changes after thinning and Nitrogen fertilization in Picea abies and Pinus sylvestris stands. Scand J For Res 15:621–632CrossRefGoogle Scholar
  36. Larocque GR, Luckai N, Adhikary SN, Groot A, Bell FW, Sharma M (2013) Competition theory-science and application in mixed forest stands: review of experimental and modelling methods and suggestions for future research. Environ Rev 21:71–84CrossRefGoogle Scholar
  37. Larson PR (1963) Stem form development of forest trees. For Sci Monogr 4:a0001–a00042Google Scholar
  38. Lines ER, Zavala MA, Purves DW, Coomes DA (2012) Predictable changes in aboveground allometry of trees along gradients of temperature, aridity and competition. Glob Ecol Biogeogr 21:1017–1028CrossRefGoogle Scholar
  39. Maj A (2011) lmmfit: goodness-of-fit-measures for linear mixed models with one-level-grouping. R package version 1.0.
  40. Mäkelä A, Valentine HT (2006) Crown ratio influences allometric scaling in trees. Ecology 87:2967–2972CrossRefGoogle Scholar
  41. Mäkelä A, Vanninen P (1998) Impacts of size and competition on tree form and distribution of aboveground biomass in Scots pine. Can J For Res 28:216–227CrossRefGoogle Scholar
  42. Martin-Ducup O, Robert S, Fournier RA (2016) Response of sugar maple (Acer saccharum, Marsh.) tree crown structure to competition in pure versus mixed stands. For Ecol Manag 374:20–32CrossRefGoogle Scholar
  43. Niinemets Ü, Valladares F (2006) Tolerance to shade, drought, and waterlogging of temperate northern hemisphere trees and shrubs. Ecol Monogr 76:521–547CrossRefGoogle Scholar
  44. Niklas KJ (2004) Plant allometry: is there a grand unifying theory? Biol Rev Camb Philos Soc 79:871–889CrossRefGoogle Scholar
  45. Pinheiro J, Bates D, DebRoy S, Sarkar D, R Core Team (2017) nlme: linear and nonlinear mixed effects models. R package version 3.1-131Google Scholar
  46. Poorter H, Jagodzinski AM, Ruiz-Peinado R, Kuyah S, Luo Y, Oleksyn J, Usoltsev VA, Buckley TN, Reich PB, Sack L (2015) How does biomass distribution change with size and differ among species? An analysis for 1200 plant species from five continents. New Phytol 208:736–749CrossRefGoogle Scholar
  47. Pretzsch H (2014) Canopy space filling and tree crown morphology in mixed-species stands compared with monocultures. For Ecol Manag 327:251–264CrossRefGoogle Scholar
  48. Pretzsch H (2017) Individual tree structure and growth in mixed compared with monospecific stands. In: Pretzsch H, Forrester DI, Bauhus J (eds) Mixed-species forests. Ecology and management. Springer, Berlin, pp 271–336CrossRefGoogle Scholar
  49. Pretzsch H, Biber P (2005) A re-evaluation of Reineke’s rule and stand density index. Forest Science 51:304–320Google Scholar
  50. Pretzsch H, Biber P (2010) Size-symmetric versus size-asymmetric competition and growth partitioning among trees in forest stands along an ecological gradient in central Europe. Can J For Res 40:370–384CrossRefGoogle Scholar
  51. Pretzsch H, Dieler J (2012) Evidence of variant intra- and interspecific scaling of tree crown structure and relevance for allometric theory. Oecologia 169(3):637–649CrossRefGoogle Scholar
  52. Pretzsch H, Forrester DI (2017) Stand dynamics of mixed-species stands compared with monocultures. In: Pretzsch H, Forrester DI, Bauhus J (eds) Mixed-species forests. Ecology and management. Springer, Berlin, pp 117–209CrossRefGoogle Scholar
  53. Pretzsch H, Rais A (2016) Wood quality in complex forests versus even-aged monocultures: review and perspectives. Wood Sci Technol 50(4):845–880CrossRefGoogle Scholar
  54. Pretzsch H, Daubert E, Biber P (2013) Species-specific and ontogeny-related stem allometry of European forest trees: evidence from extensive stem analyses. For Sci 59:290–302Google Scholar
  55. Pretzsch H, Forrester D, Rötzer T (2015) Representation of species mixing in forest growth models. A review and perspective. Ecol Model 313:276–292CrossRefGoogle Scholar
  56. Pretzsch H, del Río M, Schütze G, Ammer C, Annighöfer P, Avdagic A, Barbeito I, Bielak K, Brazaitis G, Coll L, Drössler L, Fabrika M, Forrester DI, Kurylyak V, Löf M, Lombardi F, Matovic B, Mohren F, Motta R, den Ouden J, Pach M, Ponette Q, Schweig J, Skrzyszewski J, Sramek V, Sterba H, Svoboda M, Verheyen K, Zlatanov T, Bravo-Oviedo A (2016) Mixing of Scots pine (Pinus sylvestris L.) and European beech (Fagus sylvatica L.) enhances structural heterogeneity, and the effect increases with water availability. For Ecol Manag 373:149–166CrossRefGoogle Scholar
  57. Reineke LH (1933) Perfecting a stand-density index for even-aged forests. J Agric Res 46:627–638Google Scholar
  58. Rivas-Martínez SC (2007) Mapa de series, geoseries y geopermaseries de vegetación de España (Memoria del mapa de vegetación potencial de España). Parte I Itinera Geobotánica 17:5–436Google Scholar
  59. Ruiz-Peinado R, Heym M, Drössler L, Corona P, Condés S, Bravo F, Pretzsch H, Bravo-Oviedo A, del Río M (2018) Data platforms for mixed forests research: contributions from the EuMIXFOR network. In: Bravo-Oviedo A, Pretzsch H, del Río M (eds) Dynamics, silviculture and management of mixed forests. Springer, Berlin (in press)Google Scholar
  60. Steele PH (1984) Factors determining lumber recovery in sawmilling. Gen Tech Rep FPL-39. US Department of Agriculture, Forest Service, Forest Products Laboratory, Madison, p 8CrossRefGoogle Scholar
  61. Tasissa G, Burkhart H (1997) Modeling thinning effects on ring width distribution in loblolly pine (Pinus taeda). Can J For Res 27:1291–1301CrossRefGoogle Scholar
  62. Thorpe HC, Astrup R, Trowbridge A, Coates KD (2010) Competition and tree crowns: a neighborhood analysis of three boreal tree species. For Ecol Manag 259:1586–1596CrossRefGoogle Scholar
  63. Valladares F, Sánchez-Gómez D, Zavala MA (2006) Quantitative estimation of phenotypic plasticity: bridging the gap between the evolutionary concept and its ecological applications. J Ecol 94:1103–1116CrossRefGoogle Scholar
  64. Wang Y, Titus SJ, Lemay VM (1998) Relationship between tree slenderness coefficients and tree or stand characteristics for major species in boreal mixed forest. Can J For Res 28:1171–1183CrossRefGoogle Scholar
  65. West GB, Brown JH, Enquist BJ (1999) A general model for the structure and allometry of plant vascular systems. Nature 400:664–667CrossRefGoogle Scholar
  66. Williams LJ, Paquette A, Cavender-Bares J, Messier C, Reich PB (2017) Spatial complementarity in tree crowns explains overyielding in species mixtures. Nat Ecol Evol 1:63CrossRefGoogle Scholar
  67. Woodall CW, Miles PD, Vissage JS (2005) Determining maximum stand density index in mixed species stands for strategic-scale stocking assessments. For Ecol Manag 216(1–3):367–377CrossRefGoogle Scholar
  68. Wykoff WR (1990) A basal area increment model for individual conifers in the northern Rocky Mountains. For Sci 36:1077–1104Google Scholar
  69. Zanne AE, Lopez-Gonzalez G, Coomes DA, Ilic J, Jansen S, Lewis SL, Miller RB, Swenson NG, Wiemann MC, Chave J (2009) Global wood density database. Dryad. Identifier: Accessed 5 Feb 2018
  70. Zhang SY (2003) Wood quality: its definition, impact and implications for value-added timber management and end-uses. In: CTIA/IUFRO International wood quality workshop—timber management toward wood quality and end-product value. Quebec city, pp 117–139Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Forest Research CentreINIAMadridSpain
  2. 2.iuFOR, Sustainable Forest Management Research Institute University of Valladolid & INIAPalenciaSpain
  3. 3.Department of Biogeography and Global Change, National Museum of Natural SciencesSpanish National Research Council (MNCN,CSIC)MadridSpain
  4. 4.Department of Natural Systems and Resources, School of ForestryUniversidad Politécnica de MadridMadridSpain

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