Lorentzian model of roots for understory yellow birch and sugar maple saplings

Total 66 small (<50 m2), 24 medium (101-200 m2) and 36 large (201-500 m2) canopy gaps at the three sites of yellow birch (Betula alleghaniensis Britton) and sugar maple (Acer saccharum Marsh) forests were established in southern Québec, Canada. Half of the gaps were covered by 8×8 m2 shading cloths to mimic a closed canopy. From these gaps, 46 understory yellow birch and 46 sugar maple saplings with different tree ages and sizes were sampled. Single- and multi-variable linear and nonlinear models of root biomass and traits (root surface area, volume, length and endings) were developed and examined. Lorentzian model as a multi-variable nonlinear model was firstly applied to the simulations using both base diameter and height, and performed the best fit to total root biomass in both species with the highest correlation coefficients (R2=0.96 and 0.98) and smallest root mean squared deviations (RMSD=7.85 and 7.02) among all the examined models. The model also accurately simulated small fine root (⩽2.0 mm in diameter), coarse fine root (>2.0-5.0 mm) and coarse root (>5.0 mm) biomass (R2=0.87-0.99; RMSD=2.24-6.41), and the root traits (R2=0.71-0.99; RMSD=0.19-19.38). The study showed yellow birch roots were longer, larger, had more endings (tips) and grew faster than sugar maple roots. The root traits were largely distributed to small fine roots, sharply decreased from small fine roots to coarse fine roots, the fewest in coarse roots except for root volume. When trees were large, coarse root biomass increased more rapidly than fine root biomass, but vise versa when the trees were small.