Increasing Biomass Production on Limited Land Area Through an Optimal Planting Arrangement

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.