Abstract
Planting density is a primary consideration in silviculture; however, planting arrangement is often ignored. Most, if not all, forest plantations are arranged in rectangular or square lattices (i.e., grids). Using a simple mathematical model, we investigate the potential influence of planting arrangement on planting density, biomass yield, and rotation period by assuming that efficiently arranging trees is similar to packing congruent circles on a plane. The hexagonal lattice achieves the densest circle packing on a plane; therefore, a hexagonal or triangular lattice arrangement of stems provides the highest planting density for a given spacing. Using packing density to quantify arrangement efficiency, tree crowns in a hexagonal lattice fill approximately 90.7% of available area at initial canopy contact, while tree crowns in a square lattice fill approximately 78.5% of available area at initial canopy contact. The hexagonal lattice permits about a 15% higher density than the square lattice, which allows canopy closure to occur earlier without any change in individual tree growth. Short rotation woody crop (SRWC) systems are excellent candidates under the model’s assumptions of level stand with even-age monoculture. If belowground resources are non-limiting, a hexagonal lattice arrangement shortens rotation period and thus optimizes the biomass yield per land area over time. Higher productivity over time is central to sustainable and efficient use of limited area for bioenergy and biomass products.
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Acknowledgements
We thank fellow researchers M.J. Dix and T. Lee for helpful comments on this manuscript. SWO was supported by University of Georgia Warnell School of Forestry and Savannah River Ecology Lab. DPA was supported by Agriculture and Food Research Initiative Competitive Grant no. 2013-67009-21405 from the USDA National Institute of Food and Agriculture during preparation of this manuscript. This material is based upon work supported by the Department of Energy under Award Number DE-EM0004391 to the University of Georgia Research Foundation.
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ESM 1
Stems (points) arranged in a square lattice spaced x by x (GIF 5 kb)
ESM 2
Stems (points) arranged in a rectangular lattice spaced x by y (GIF 4 kb)
ESM 3
Stems (points) arranged in a triangular lattice spaced by L with projected crowns forming a hexagonal lattice (GIF 18 kb).
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Oswald, S.W., Aubrey, D.P. Increasing Biomass Production on Limited Land Area Through an Optimal Planting Arrangement. Bioenerg. Res. 11, 13–21 (2018). https://doi.org/10.1007/s12155-017-9873-0
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DOI: https://doi.org/10.1007/s12155-017-9873-0