Tall shrub biomass estimates

Whole-shrub biomass-DRC (“one-component”) allometry constructed from Alnus and Salix shrubs with DRC >Dmin = 2.5 cm was applied to 1,430 individual tall shrubs measured among 17 circular plots (169 m2) in southcentral Alaska. Our protocol considers shrubs as “two-component” structures: stem internodes of length L with D >Dmax and terminal aerial shoots (tips) with Dmin ≤D ≤Dmax, where Dmax is a threshold diameter for treating stem internodes as conic frustra and Dmin defines the minimum shrub size. We identify Dmax subjectively as the diameter where biomass variability rapidly expands as identified in plots of back-transformed residuals vs. arithmetic values of D. In our examples, we consider only shrub individuals with DRC >2.5 cm = Dmin. Our example includes 134 Alnus and Salix individuals (2.9 ≤DRC ≤40.5 cm; 0.9 ≤M ≤374.1 kg) that we destructively sampled in southcentral Alaska to derive biomass-diameter allometry, shown to be similar between Alnus and Salix. Among these shrubs, 29 Alnus individuals were dissected and weighed as terminal aerial tips to investigate self-similarity. We dissected eight further individuals (3.4 ≤DRC ≤36.1 cm; 0.9 ≤M ≤374.1 kg) as internodes and terminal aerial tips, each individually weighed and measured. Aerial tip allometry: Inspection of the 134 shrubs indicated that variability in M increased substantially at DRC >7.5 cm (Fig. 2a), suggesting Dmax = 7.5 cm. Using 7.5 cm as the threshold diameter, we established allometric relationships between DRC ≤Dmax and M for n = 37 individual shrubs; between D ≤ Dmax and M for n = 95 terminal aerial tips from large (DRC >Dmax); and those two samples taken together (n = 132). We also calculated the percent overlap between the aerial tip allometric estimates and individual shrub allometric estimates. Allometry was established by regressing ln(M) on ln(D), then exponentiating the 95%PI upri and lwri bounds of ln(Mi) found with 2.5 ≤Di ≤7.5 cm at intervals of 0.01 cm to determine uncertainty. Stem internode allometry: Stem internodes with D >7.5 cm were modeled as regular conic frustra with diameters D1 and D2 and length L, where frustrum volume V = p L (D12 + D1 D2 + D22)/12. We cut, measured, and weighed in the field as wet field-mass 40 internodes from eight individual alder shrubs of two species (n = 20 internodes each from A. viridus and A. incana). Internodes varied as 2.7 ≤D ≤36.1 cm (mean = 9.6 cm), 16.5 ≤L ≤224.2 cm, and 0.2 ≤M ≤ 9.1 kg (mean = 8.2 kg). We compared these linear regression wet-density estimates (i.e., the regression coefficient estimates) to wet-density directly measured in two field-cut stem pieces (A. incana: 0.74 kg L-1 = 3.49 kg/4.73 L and A. viridis: 0.83 kg L-1 = 2.35 kg/2.84 L) with known weight and estimated volume as measured by submersion in water. Besides regression of untransformed variables, we also regressed ln(M) on ln(V); we inspected both regressions for heteroscedasticity. Calculating plot-level uncertainty: Given regressions for internodes, aerial tips, and for whole shrubs, we calculated point estimates of wet field-mass M together with upper and lower bounds of 95%PI for every shrub piece and individual measured in the field among 17 sample-plots (2,019 pieces of 1,430 individual shrubs). Because the sum of lognormal distributions have no closed-formed distribution, we employed the following Monte Carlo algorithm (n = 10,000) to estimate uncertainty for each plot using each sampling method (DRC single-component and tips + internodes two-component):