Skip to main content
SpringerLink
Log in

Evaluating the Development and Application of Stand Density Index for the Management of Complex and Adaptive Forests

  • Forest Management (M Watt, Section Editor)
  • Published:
Current Forestry Reports Aims and scope Submit manuscript

Abstract

Purpose of Review

The objective quantification of stand density (SD) is necessary for predicting forest dynamics over space and time. Despite the development of various synthetic representations of SD, consensus remains elusive regarding a primary integrated measure due to contrasting data sources, statistical modeling methods, and distinct regional variations in forest structure and composition. One of the most enduring and robust measures of SD is Reineke’s (1933; J. Ag Res. 46, 627-638) stand density index (SDI), which has long formed the basis for the prediction of stand development concerning self-thinning processes in single-species, even-aged stands and stand density management diagrams (SDMDs). Thus, this review tracks the development of different methodologies and necessary data for properly estimating SDI, including its application in complex forests and adaptive management contexts.

Recent Findings

Limitations of SDI in its earliest form have led to important modifications centered on refinement and expanding its application beyond even-aged, single-species stands to multi-cohort, mixed composition stands. Statistical advances for better determination of the maximum size-density boundary line have also been applied to SDI estimates using the ever-expanding availability of remeasured field data including large-scale, national forest inventories. Other innovations include the integration of regional climate information and species functional traits, e.g., wood specific gravity, drought, and shade tolerance.

Summary

In this synthesis, we describe the attributes of SDI that have promulgated its use as a leading measure of SD for nearly 90 years. Recent applications of robust statistical techniques such as hierarchical Bayesian methods and linear quantile mixed modeling have emerged as the best performing methods for establishing the maximum size-density boundary, especially those incorporating ancillary variables like climate.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Data Availability

The data used in this article is acquired from inventory data of FIA and is publicly available from https://www.fia.fs.fed.us/. Additional data is accessed from Figshare. Stand density index and relative density calculator for the United States is available at https://doi.org/10.6084/m9.figshare.24412246. Forest growth, removals, and mortality for FIA Time 1 and 2 across the United States available at https://doi.org/10.6084/m9.figshare.19690936.v1. Relative density estimates for United States available at https://doi.org/10.6084/m9.figshare.19630119.v1. Maximum stand density index for the United States is available at https://doi.org/10.6084/m9.figshare.19521970.v1.

References

Papers of particular interest, published recently, have been highlighted as: • Of importance •• Of major importance

  1. Vospernik S, Sterba H. Do competition-density rule and self-thinning rule agree? Ann For Sci. 2015;72:379–90.

    Article  Google Scholar 

  2. Urgoiti J, Messier C, Keeton WS, Belluau M, Paquette A. Functional diversity and identity influence the self-thinning process in young forest. J Ecol. 2023;00:1–13.

    Google Scholar 

  3. Burkhart HE. Comparison of maximum size-density relationships based on alternate stand attributes for predicting tree numbers and stand growth. For Ecol Manage. 2013;289:404–8.

    Article  Google Scholar 

  4. Weiskittel AR, Hann DW, Kershaw JA, Vanclay JK. Forest growth and yield modeling. 1st ed. Hoboken, NJ: John Wiley & Sons, Ltd; 2011.

    Book  Google Scholar 

  5. •• Gingrich SF. Measuring and evaluating stocking and stand density in upland hardwood forests in the central states. For Sci. 1967;38:38–53. The paper is important as it relates and integrates SDIMAX into the construction of size-density management chart (SDMC).

    Google Scholar 

  6. Krajicek JE, Brinkman KA, Gingrich SF. Crown competition-a measure of density. For Sci. 1961;7:35–42.

    Google Scholar 

  7. Dean TJ, Baldwin VC. The relationship between Reineke’s stand-density index and physical stem mechanics. For Ecol Manage. 1996;81:25–34.

    Article  Google Scholar 

  8. Ducey MJ. The ratio of additive and traditional stand density indices. West J Appl For. 2009;24:5–10.

    Article  Google Scholar 

  9. Weiskittel A, Gould P, Temesgen H. Sources of variation in the self-thinning boundary line for three species with varying levels of shade tolerance. For Sci. 2009;55:84–93.

    Google Scholar 

  10. Curtis RO. Effect of diameter limits and stand structure on relative density indices: a case study. West J Appl For. 2010;25:169–75.

    Article  Google Scholar 

  11. Ducey MJ, Knapp RA. A stand density index for complex mixed species forests in the northeastern United States. For Ecol Manage. 2010;260:1613–22.

    Article  Google Scholar 

  12. Heiderman RR, Kimsey MJ. A species-specific, site-sensitive maximum stand density index model for Pacific Northwest conifer forests. Can J For Res. 2021;51:1166–77.

    Article  CAS  Google Scholar 

  13. Dean TJ, D’Amato AW, Palik BJ, Battaglia MA, Harrington CA. A direct measure of stand density based on stand growth. For Sci. 2021;67:103–15.

    Google Scholar 

  14. Kern CC, Kenefic LS, Kuehne C, Weiskittel AR, Kaschmitter SJ, D’Amato AW, et al. Relative influence of stand and site factors on aboveground live-tree carbon sequestration and mortality in managed and unmanaged forests. For Ecol Manage. 2021;493:1–12.

    Article  Google Scholar 

  15. Weiskittel AR, Maguire DA, Monserud RA, Rose R, Turnblom EC. Intensive management influence on Douglas-fir stem form, branch characteristics, and simulated product recovery. New Zeal J For Sci. 2006;36:293–312.

    Google Scholar 

  16. Franklin O, Moltchanova E, Kraxner F, Seidl R, Böttcher H, Rokityiansky D, et al. Large-scale forest modeling: deducing stand density from inventory data. Int J For Res. 2012;2012:934974. https://doi.org/10.1155/2012/934974.

  17. Barrere J, Reineking B, Cordonnier T, Kulha N, Honkaniemi J, Peltoniemi M, et al. Functional traits and climate drive interspecific differences in induced tree mortality. Glob Chang Biol. 2023;00:1–16.

    CAS  Google Scholar 

  18. Curtis RO. A simple index of stand density of Douglas-fir (Pseudotsuga menziesii). For Sci. 1982;28:92–4.

    Google Scholar 

  19. Stout SL, Nyland RD. Role of species composition in relative density measurement in Allegheny hardwoods. Can J For Res. 1986;16:574–9.

    Article  Google Scholar 

  20. Zeide B. Comparison of self-thinning models: an exercise in reasoning. Trees - Struct Funct. 2010;24:1117–26.

    Article  Google Scholar 

  21. Lee D, Choi J. Evaluating maximum stand density and size–density relationships based on the Competition Density Rule in Korean pines and Japanese larch. For Ecol Manage. 2019;446:204–13.

    Article  Google Scholar 

  22. Lindenmayer DB, Hobbs RJ, Likens GE, Krebs CJ, Banks SC. Newly discovered landscape traps produce regime shifts in wet forests. Proc Natl Acad Sci U S A. 2011;108:15887–91.

    Article  CAS  Google Scholar 

  23. Tang S, Meng FR, Meng CH. The impact of initial stand density and site index on maximum stand density index and self-thinning index in a stand self-thinning model. For Ecol Manage. 1995;75:61–8.

    Article  Google Scholar 

  24. Williams RA. Use of stand density index as an alternative to stocking percent in upland hardwoods. North J Appl For. 2003;20:137–42.

    Article  Google Scholar 

  25. Stankova TV, Diéguez-Aranda U. Dynamic Structural Stand Density Management Diagrams for even-aged natural stands and plantations. For Ecol Manage. 2020;458:1–20.

    Article  Google Scholar 

  26. Forrester DI, Baker TG, Elms SR, Hobi ML, Ouyang S, Wiedemann JC, et al. Self-thinning tree mortality models that account for vertical stand structure, species mixing and climate. For Ecol Manage. 2021;487:1–17.

    Article  Google Scholar 

  27. Ducey MJ, Larson BC. Is there a correct stand density index? An alternate interpretation. West J Appl For. 2003;18:179–84.

    Article  Google Scholar 

  28. Brunner A, Forrester DI. Tree species mixture effects on stem growth vary with stand density – an analysis based on individual tree responses. For Ecol Manage. 2020;473:1–15.

    Article  Google Scholar 

  29. • Drew TJ, Flewelling JW. Stand density management: an alternative approach and its application to douglas-fir plantations. For Sci. 1979;25:518–32. The paper provides a method that relates stand density to volume and tree size in size density management charts and also defines key levels.

    Google Scholar 

  30. Jack SB, Long JN. Linkages between silviculture and ecology: an analysis of density management diagrams. For Ecol Manage. 1996;86:205–20.

    Article  Google Scholar 

  31. Shaw JD, Long JN. Consistent definition and application of Reineke’s Stand Density Index in silviculture and stand projection. In: Jain TB, Graham RT, Sandquist J, editors. Integrating managment carbon sequestration biomass utilization opportunities in a changing climate. Proc 2009 National Silviculture Workshop. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station; 2010. pp. 199–209.

  32. Harvey BJ, Holzman BA, Davis JD. Spatial variability in stand structure and density-dependent mortality in newly established post-fire stands of a California closed-cone pine forest. For Ecol Manage. 2011;262:2042–51.

    Article  Google Scholar 

  33. Bravo-Oviedo A, Pretzsch H, Ammer C, Andenmatten E, Barbati A, Barreiro S, et al. European mixed forests: definition and research perspectives. For Syst. 2014;23:518–33.

    Article  Google Scholar 

  34. Forrester DI. The spatial and temporal dynamics of species interactions in mixed-species forests: from pattern to process. For Ecol Manage. 2014;312:282–92.

    Article  Google Scholar 

  35. Burkhart HE, Tome M. Modelling forest trees and stands. Dordrecht: Springer; 2012.

    Book  Google Scholar 

  36. Enquist BJ, West GB, Charnov EL, Brown JH. Allometric scaling of production and life-history variation in vascular plants. Nature. 1999;401:907–11.

    Article  CAS  Google Scholar 

  37. West GB, Brown JH, Enquist BJ. A general model for the origin of allometric scaling laws in biology. Science (80). 1997;276:122–6.

    Article  CAS  Google Scholar 

  38. Hart HMJ. Stem density and thinning: pilot experiment to determine the best spacing and thinning methods of teak. Proefsta: Boschwesen, Batavia, Meded; 1926.

  39. •• Reineke LH. Perfecting a stand-density index for even-aged forests. J Agric Res. 1933;46:627–38. This is the seminal paper on SDI upon which the review is based on and provides initial estimates of SDI in even-aged stands.

    Google Scholar 

  40. Yoda K, Kira T, Ogawa H, Hozumi K. Self-thinning in over-crowded pure stands under cultivated and natural conditions (intraspecific competition among higher plants XI). J Biol Osaka City Univ. 1963;14:107–20.

    Google Scholar 

  41. Vanclay JK, Sands PJ. Calibrating the self-thinning frontier. For Ecol Manage. 2009;259:81–5.

    Article  Google Scholar 

  42. Long JN. A technique for the control of stocking in two-storied stands. West J Appl For. 1996;11:59–61.

    Article  Google Scholar 

  43. • Zhang L, Bi H, Gove JH, Heath LS. A comparison of alternative methods for estimating the self-thinning boundary line. Can J For Res. 2005;35:1507–14. This paper reviews different statistical methods used to estimate the self-thinning line especially selection of data points and most appropriate statistical method for coefficient estimation.

    Article  Google Scholar 

  44. • Shaw JD. Reineke’s stand density index: where are we and where do we go from here? In: Proc: Soc Am For 2005 Natl Conv. Ft. Worth: Society of American Foresters; 2006. pp. 1-13. This paper reviews the history, characteristics and silvicultural application of stand density index in even-aged, uneven-aged stands and multi-species stands. It is one of the few papers that reviewed the silvicultural applications and extension of SDI.

  45. • VanderSchaaf CL, Burkhart HE. Comparison of methods to estimate Reineke’s maximum size-density relationship species boundary line slope. For Sci. 2007;53:435–42. The paper compares the slopes of the size density relationship based on different statistical methods. It also acted as a primer on the review of statistical methods previously used.

    Google Scholar 

  46. Pretzsch H, Forrester DI. Stand dynamics of mixed-species stands compared with monocultures. In: Pretzsch H, Forrester DI, Bauhus J, editors. Mix For. Berlin: Springer-Verlag GmbH; 2017. p. 117–209.

    Google Scholar 

  47. Bravo F, Fabrika M, Ammer C, Barreiro S, Bielak K, Coll L, et al. Modelling approaches for mixed forests dynamics prognosis. Research gaps and opportunities. For Syst. 2019;28:1–18.

    Article  Google Scholar 

  48. Marchi M. Nonlinear versus linearised model on stand density model fitting and stand density index calculation: analysis of coefficients estimation via simulation. J For Res. 2019;30:1595–602.

    Article  Google Scholar 

  49. Curtis RO. Stand density measures: an interpretation. For Sci. 1970;16:403–14.

    Google Scholar 

  50. •• Long JN, Daniel TW. Assessment of growing stock in uneven-aged stands. West J Appl For. 1990;5:93–6. The paper employed the summation method and apportioned the growing stock between the diameter size classes for uneven-aged stands.

  51. Long JN. A practical approach to density management. For Chron. 1985;61:23–7.

    Article  Google Scholar 

  52. Sterba H. Estimating potential density from thinning experiments and inventory data. For Sci. 1987;33:1022–34.

    Google Scholar 

  53. Chisman HH, Schumacher FX. On the tree-area ratio and certain of its applications. J For. 1940;38:311–7.

    Google Scholar 

  54. • Woodall CW, Miles PD, Vissage JS. Determining maximum stand density index in mixed species stands for strategic-scale stocking assessments. For Ecol Manage. 2005;216:367–77. The paper details the use of functional traits such as specific gravity in estimating SDIMAX in mixed species further refining the application of SDI which was initially developed for even-aged stands. The study also made use of national inventory data to produce SDIMAX estimates of eight common trees of the United States.

    Article  Google Scholar 

  55. Zeide B. How to measure stand density. Trees - Struct Funct. 2005;19:1–14.

    Article  Google Scholar 

  56. Weiskittel AR, Kuehne C. Evaluating and modeling variation in site-level maximum carrying capacity of mixed-species forest stands in the Acadian region of Northeastern North America. For Chron. 2019;95:171–82.

    Article  Google Scholar 

  57. Ray DG. Quantitative silviculture of northern conifers. University of Maine; 2022. Available from: digitalcommons.library.umaine.edu/etd/3712. Accessed 21 Jan 2023.

  58. •• Andrews C, Weiskittel A, D’Amato AW, Simons-Legaard E. Variation in the maximum stand density index and its linkage to climate in mixed species forests of the North American Acadian Region. For Ecol Manage. 2018;417:90–102. One of first papers to apply linear quantile mixed model (LQMM) to mixed species forests. LQMM is later applied in a follow-up analysis to provide national SDImax estimates for the US.

    Article  Google Scholar 

  59. Pretzsch H, Biber P. Tree species mixing can increase maximum stand density. Can J For Res. 2016;46:1179–93.

    Article  Google Scholar 

  60. •• Ando T. Growth analysis on the natural stands of Japanese red pine (Pinus densiflora Sieb. et Zucc.). II. Analysis of stand density and growth. Bulletin Gov For Exp Stn. 1962;147:71. The paper first developed non-English version of DMD which was the basis upon which the English version was based on by Drew and Flewelling 1977.

    Google Scholar 

  61. • Drew TJ, Flewelling JW. Some recent Japanese theories of yield. Density relationships and their application to Monterey pine plantations. For Sci. 1977;23:517–34. The paper demonstrates the development English version of DMD to show the density yield relationships in pine plantations.

    Google Scholar 

  62. Smith NJ. A stand-density control diagram for western red cedar, Thuja plicata. For Ecol Manage. 1989;27:235–44.

    Article  Google Scholar 

  63. Oliver WW, Uzoh FCC. Maximum stand densities for ponderosa pine and red and white fir in Northern California. In: Proc 18th Annu For Veg Manag Conf. Sacramento, CA: Forest Vegetation Management Conference. Redding, California; 1997. pp. 57–65.

  64. Ducey MJ, Woodall CW, Bravo-Oviedo A. Climate and species functional traits influence maximum live tree stocking in the Lake States, USA. For Ecol Manage. 2017;386:51–61.

    Article  Google Scholar 

  65. Quiñonez-Barraza G, Ramírez-Maldonado H. Can an exponential function be applied to the asymptotic density-size relationship? Two new stand-density indices in mixed-species forests. Forests. 2018;10:1–19.

    Article  Google Scholar 

  66. Zhao D, Bullock BP, Montes CR, Wang M. Rethinking maximum stand basal area and maximum SDI from the aspect of stand dynamics. For Ecol Manage. 2020;475:1–10.

    Article  Google Scholar 

  67. Yang SI, Brandeis TJ. Estimating maximum stand density for mixed-hardwood forests among various physiographic zones in the eastern US. For Ecol Manage. 2022;521:1–9.

    Article  Google Scholar 

  68. Mrad A, Manzoni S, Oren R, Vico G, Lindh M, Katul G. Recovering the metabolic, self-thinning, and constant final yield rules in mono-specific stands. Front For Glob Chang. 2020;3:1–2.

    Article  Google Scholar 

  69. Ducey MJ, Knapp RA. Rapid assessment of relative density in mixed-species stands of the northeastern United States. Int J For Res. 2010;1:1–8.

    Google Scholar 

  70. •• Stage AR. A tree-by-tree measure of site utilization for grand fir related to stand density index. Ogden, Utah: Intermountain Forest and Range Experiment Station, Forest Service, United States Department of Agriculture; 1968. Made modifications to traditional SDI to develop additive stand density index for uneven-aged stands.

  71. Rivoire M, Le Moguedec G. A generalized self-thinning relationship for multi-species and mixed-size forests. Ann For Sci. 2012;69:207–19.

    Article  Google Scholar 

  72. Zeide B. The mean diameter for stand density index. Can J For Res. 1983;13:1023–4.

    Article  Google Scholar 

  73. North MP, Tompkins RE, Bernal AA, Collins BA, Stephens SL, York RA. Operational resilience in western US frequent-fire forests. For Ecol Manage. 2022;507:1–9.

    Article  Google Scholar 

  74. Woodall CW, D’Amato AW, Bradford JB, Finley AO. Effects of stand and inter-specific stocking on maximizing standing tree carbon stocks in the eastern United States. For Sci. 2011;57:365–78.

    Google Scholar 

  75. Ducey MJ, Valentine HT. Direct sampling for stand density index. West J Appl For. 2008;23:78–82.

    Article  Google Scholar 

  76. Woodall CW, Weiskittel AR. Relative density of United States forests has shifted to higher levels over last two decades with important implications for future dynamics. Sci Rep. 2021;11:1–12.

    Article  Google Scholar 

  77. Woodall CW, Fiedler CE, Milner KS. Stand density index in uneven-aged ponderosa pine stands. Can J For Res. 2003;33:96–100.

    Article  Google Scholar 

  78. Salas-Eljatib C, Weiskittel AR. Evaluation of modeling strategies for assessing self-thinning behavior and carrying capacity. Ecol Evol. 2018;8:10768–79.

    Article  Google Scholar 

  79. Bi H, Wan G, Turvey ND. Estimating the self-thinning boundary line as a density-dependent stochastic biomass frontier. Ecology. 2000;81:1477–83.

    Article  Google Scholar 

  80. Weller DE. Will the real self-thinning rule please stand up?--A reply to Osawa and Sugita. Ecology. 1990;71:1204–7.

    Article  Google Scholar 

  81. Zeide B. Self-thinning and stand density. For Sci. 1991;37:517–23.

    Google Scholar 

  82. Smith NJ, Hann DW. A new analytical model based on the− 3/2 power rule of self-thinning. Can J For Res. 1984;14:605–9.

    Article  Google Scholar 

  83. Charru M, Seynave I, Morneau F, Rivoire M, Bontemps JD. Significant differences and curvilinearity in the self-thinning relationships of 11 temperate tree species assessed from forest inventory data. Ann For Sci. 2012;69:195–205.

    Article  Google Scholar 

  84. Zeide B. The mean diameter for stand density index. Can J For Res. 1983;13:1023–2024.

    Article  Google Scholar 

  85. Niklas K. Plant allometry and the scaling of form process. Chicago: The University of Chicago Press; 1994.

    Google Scholar 

  86. Moore MM, Deiter DA. Stand density index as a predictor of forage production in northern Arizona pine forests. J Range Manag. 1992;45:267–71.

    Article  Google Scholar 

  87. Pretzsch H, Biber P. A re-evaluation of Reineke’s Rule and Stand Density Index. For Sci. 2005;51:304–20.

    Google Scholar 

  88. Lappi J, Bailey RL. A height prediction model with random stand and tree parameters: an alternative to traditional site index methods. For Sci. 1988;34:907–27.

    Google Scholar 

  89. Vanclay JK. Modelling forest growth and yield: applications to mixed tropical forests. Wallingford: CAB International; 1994.

    Google Scholar 

  90. Hann DW. Maximum size-density line and its trajectory line for tree species: observations and opinions. Corvallis, Oregon: Oregon State University; 2014.

  91. Li R, Stewart B, Weiskittel A. A Bayesian approach for modelling non-linear longitudinal/hierarchical data with random effects in forestry. Forestry. 2012;85:17–25.

    Article  Google Scholar 

  92. •• Zhang X, Zhang J, Duan A, Deng Y. A hierarchical Bayesian model to predict self-thinning line for Chinese fir in Southern China. PLoS One. 2015;10:1–11. Paper showcases the application of hierarchical Bayesian model (HBM) in estimating the self-thinning line. HBM is one of the robust method that can deal with nested data estimating uncertainty of parameter estimates.

    Google Scholar 

  93. Mohler CL, Marks PL, Sprugel DG. Stand structure and allometry of trees during self-thinning of pure stands. J Ecol. 1978;66:599.

    Article  Google Scholar 

  94. Lynch TB, Wittwer RF, Stevenson DJ. Estimation of Reineke and volume-based maximum size-density lines for shortleaf pine. In: Connor KF, editor. Proc 12th Bienn South Silvic Res Conf. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern Research Station; 2004. pp. 226.

  95. Kimsey MJ Jr, Shaw TM, Coleman MD. Site sensitive maximum stand density index models for mixed conifer stands across the Inland Northwest, USA. For Ecol Manage. 2019;433:396–404.

    Article  Google Scholar 

  96. Zhang X, Duan A, Zhang J. Tree biomass estimation of Chinese fir (Cunninghamia lanceolata) based on Bayesian method. PLoS One. 2013;8:1–7.

    CAS  Google Scholar 

  97. Riofrío J, Del Río M, Bravo F. Mixing effects on growth efficiency in mixed pine forests. Forestry. 2017;90:381–92.

    Google Scholar 

  98. Bailey RG. Bailey’s ecoregions and subregions of the United States, Puerto Rico, and the U.S. Virgin Islands. Fort Collins, CO: Forest Service Research Data Archive; 2016.

  99. Long JN, Shaw JD. A density management diagram for even-aged ponderosa pine stands. West J Appl For. 2005;20:205–15.

    Article  Google Scholar 

  100. Bi H, Turvey ND. A method of selecting data points for fitting the maximum biomass-density line for stands undergoing self-thinning. Aust J Ecol. 1997;22:356–9.

    Article  Google Scholar 

  101. Nicoulaud-Gouin V, Gonze MA, Hurtevent P, Calmon P. Bayesian inference of biomass growth characteristics for sugi (C. japonica) and hinoki (C. obtusa) forests in self-thinned and managed stands. For Ecosyst. 2021;8:1–18.

    Article  Google Scholar 

  102. Hamilton NRS, Matthew C, Lemaire G. In defence of the - 3/2 boundary rule: a re-evaluation of self-thinning concepts and status. Ann Bot. 1995;76:569–77.

  103. Zeide B. Analysis of the 3/2 power law of self-thinning. For Sci. 1987;33:517–37.

    Google Scholar 

  104. Bravo-Oviedo A, Condés S, Del Río M, Pretzsch H, Ducey MJ. Maximum stand density strongly depends on species-specific wood stability, shade and drought tolerance. Forestry. 2018;91:459–69.

    Article  Google Scholar 

  105. Poage NJ, Marshall DD, Mcclellan MH. Maximum stand density index of 40 western hemlock–Sitka spruce stands in southeast Alaska. West J Appl For. 2007;22:99–104.

  106. Donato DC, Campbell JL, Franklin JF. Multiple successional pathways and precocity in forest development : can some forests be born complex ? J Veg Sci. 2012;23:576–84.

    Article  Google Scholar 

  107. Condés S, Vallet P, Bielak K, Bravo-Oviedo A, Coll L, Ducey MJ, et al. Climate influences on the maximum size-density relationship in Scots pine (Pinus sylvestris L.) and European beech (Fagus sylvatica L.) stands. For Ecol Manage. 2017;385:295–307.

    Article  Google Scholar 

  108. Reynolds JH, Ford ED. Improving competition representation in theoretical models of self-thinning: a critical review. J Ecol. 2005;93:362–72.

    Article  Google Scholar 

  109. Shen C, Nelson AS. Natural conifer regeneration patterns in temperate forests across the Inland Northwest, USA. Ann For Sci. 2018;75:1–17.

  110. Pretzsch H. The effect of tree crown allometry on community dynamics in mixed-species stands versus monocultures. A review and perspectives for modeling and silvicultural regulation. Forests. 2019;10:1–33.

    Article  Google Scholar 

  111. Aubin I, Munson AD, Cardou F, Burton PJ, Isabel N, Pedlar JH, et al. Traits to stay, traits to move: a review of functional traits to assess sensitivity and adaptive capacity of temperate and boreal trees to climate change. Environ Rev. 2016;24:164–86.

    Article  Google Scholar 

  112. Malmsheimer RW, Heffernan P, Brink S, Crandall D, Deneke F, Galik CS, et al. Forest management solutions for mitigating climate change in the United States. J For. 2008;106:115–71.

    Google Scholar 

  113. Gara TW, Rahimzadeh-Bajgiran P, Darvishzadeh R. Forest leaf mass per area (LMA) through the eye of optical remote sensing : a review and future outlook. Remote Sens. 2021;13:1–25.

    Article  Google Scholar 

  114. Rudnicki M, Silins U, Lieffers VJ. Crown cover is correlated with relative density, tree slenderness, and tree height in lodgepole pine. For Sci. 2004;50:356–63.

    Google Scholar 

  115. Reynolds JH, Ford ED. Improving competition representation in theoretical models of self-thinning: a critical review. J Ecol. 2005;93:362–72.

    Article  Google Scholar 

  116. Withrow-Robinson B, Maguire D. Competition and density in woodland stands. OSU Ext. Serv. Corvallis, Oregon; 2018.

  117. D’Amato AW, Woodall CW, Weiskittel AR, Littlefield CE, Murray LT. Carbon conundrums: do United States’ current carbon market baselines represent an undesirable ecological threshold? Glob Chang Biol. 2022;28:3991–4.

    Article  Google Scholar 

  118. Allen MG II, Burkhart HE. Growth-density relationships in loblolly pine plantations. For Sci. 2018;65:1–15.

    Google Scholar 

  119. Crookston NL, Dixon GE. The forest vegetation simulator: a review of its structure, content, and applications. Comput Electron Agric. 2005;49:60–80.

    Article  Google Scholar 

  120. Pretzsch H, Grote R. Tree mortality: revisited under changed climatic and silvicultural conditions. In: Lüttge U, Canovas FM, Risueño M-C, Leuschner C, editors. Prog Bot. Berlin: Springer Berlin Heidelberg; 2023. p. 4–43.

  121. Woodall CW, Westfall JA. Relationships between the stocking levels of live trees and dead tree attributes in forests of the United States. For Ecol Manage. 2009;258:2602–8.

    Article  Google Scholar 

  122. Russell MB, Woodall CW, Fraver S, D’Amato AW, Domke GM, Skog KE. Residence times and decay rates of downed woody debris biomass/carbon in eastern US forests. Ecosystems. 2014;17:765–77.

  123. Palik BJ, D’Amato AW, Franklin JF, Johnson KN. Ecological silviculture: foundations and applications. Long Grove, Illiois: Waveland Press, Inc; 2021.

    Google Scholar 

  124. Lhotka JM, Loewenstein EF. An examination of species-specific growing space utilization. Can J For Res. 2008;38:470–9.

    Article  Google Scholar 

  125. Reyes-Hernandez V, Comeau PG, Bokalo M. Static and dynamic maximum size-density relationships for mixed trembling aspen and white spruce stands in western Canada. For Ecol Manage. 2013;289:300–11.

    Article  Google Scholar 

  126. Vacchiano G, Derose RJ, Shaw JD, Svoboda M, Motta R. A density management diagram for Norway spruce in the temperate European montane region. Eur J For Res. 2013;132:535–49.

    Article  Google Scholar 

  127. Newton PF. Stand density management diagrams: modelling approaches, variants, and exemplification of their potential utility in crop planning. Can J For Res. 2021;51:236–56.

    Article  Google Scholar 

  128. Nakajima T, Matsumoto M, Shiraishi N. Modeling diameter growth and self-thinning in planted sugi (Cryptomeria japonica) stands. Open For Sci J. 2011;4:49–56.

    Google Scholar 

  129. Pretzsch H, Del Río M. Density regulation of mixed and mono-specific forest stands as a continuum: a new concept based on species-specific coefficients for density equivalence and density modification. Forestry. 2020;93:1–15.

    Article  Google Scholar 

  130. Ritchie MW. standview. R package. 2024. Available from: https://github.com/mwritchie/standview. Accessed 1 Mar 2023.

  131. Jang W. Stand density management diagram. Vancouver, BC; 2021. Available from: https://bcgov-env.shinyapps.io/SDMD/. Accessed 10 Mar 2023.

  132. Ray D, Seymour R, Fraver S, Berrill J-P, Kenefic L, Rogers N, et al. Relative density as a standardizing metric for the development of size-density management charts. J For. 2023;121:443–56.

    Google Scholar 

  133. Newton PF. Stand density management diagrams: review of their development and utility in stand-level management planning. For Ecol Manage. 1997;98:251–65.

    Article  Google Scholar 

  134. Zeide B. Thinning growth: and a full turnaround. J For Sci. 2001;99:20–5.

    Google Scholar 

  135. Assmann E. The principles of forest yield study. Oxford: Pergamon Press; 1970.

    Google Scholar 

  136. Woodall CW, Perry CH, Miles PD. The relative density of forests in the United States. For Ecol Manage. 2006;226:368–72.

    Article  Google Scholar 

  137. Kubiske ME, Woodall CW, Kern CC. Increasing atmospheric CO2 concentration stand development in trembling aspen forests : are outdated density management guidelines in need of revision for all species? J For. 2019;117:38–45.

    Google Scholar 

  138. Tymińska-Czabańska L, Hawryło P, Janiec P, Socha J. Tree height, growth rate and stand density determined by ALS drive probability of Scots pine mortality. Ecol Indic. 2022;145:1–9.

    Article  Google Scholar 

  139. Dettmann GT, Macfarlane DW, Radtke PJ, Weiskittel AR, Affleck DLR, Poudel KP, et al. Testing a generalized leaf mass estimation method for diverse tree species and climates of the continental United States. Ecol Appl. 2022;32:1–21.

    Article  Google Scholar 

  140. DeRose RJ, Seymour RS. Patterns of leaf area index during stand development in even-aged balsam fir – red spruce stands. Can J For Res. 2010;40:629–37.

    Article  Google Scholar 

  141. Crookston NL, Rehfeldt GE, Dixon G, Weiskittel AR. Addressing climate change in the forest vegetation simulator to assess impacts on landscape forest dynamics. For Ecol Manage. 2010;260:1198–211.

    Article  Google Scholar 

  142. Carson MT, Zobel JM, Bronson DR, McGraw AM, Woodall CW, Kern CC. The case for stand management guidelines as dynamic as global change: aspen forest stockings of the western Great Lakes. For Ecol Manage. 2023;536:1–9.

    Article  Google Scholar 

  143. Frescino TS, Moisen GG, Patterson PL, Toney C, White GW. FIESTA: a forest inventory estimation and analysis R package. Ecography (Cop). 2023;0:1–9.

    Google Scholar 

Download references

Funding

Emmerson Chivhenge and Dr. Weiskittel received funding from National Science Foundation Center for Advanced Forestry Systems (Award #1915078) and United States Department of Agriculture (USDA) Sustainable Agricultural Systems (SAS) Award #2023-68012-38992.

Author information

Authors and Affiliations

  1. University of Maine, School of Forest Resources, Orono, ME, USA

    Emmerson Chivhenge

  2. University of Maine, Center for Research on Sustainable Forests, Orono, ME, USA

    Emmerson Chivhenge, David G. Ray & Aaron R. Weiskittel

  3. USDA Forest Service, Inventory, Monitoring, and Assessment Research, Research and Development, Washington, DC, USA

    Christopher W. Woodall

  4. University of Vermont, Rubenstein School of Environment and Natural Resources, Burlington, VT, USA

    Anthony W. D’Amato

Authors
  1. Emmerson Chivhenge
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David G. Ray
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aaron R. Weiskittel
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Christopher W. Woodall
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Anthony W. D’Amato
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Emmerson Chivhenge.

Ethics declarations

Competing interests

The authors declare no competing interests.

Human and Animal Rights and Informed Consent

This article does not contain any studies with human or animal subjects performed by any of the authors.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chivhenge, E., Ray, D.G., Weiskittel, A.R. et al. Evaluating the Development and Application of Stand Density Index for the Management of Complex and Adaptive Forests. Curr. For. Rep. 10, 133–152 (2024). https://doi.org/10.1007/s40725-024-00212-w

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40725-024-00212-w

Keywords

Search

Navigation