Eccentric trees, biased estimates: sampling design reduces error in basal area increment estimates under stem and pith eccentricity

Julie Messier, Christina AM Rossi

Accurate tree growth quantification is crucial in ecological research. Basal area increment (BAI) is often calculated from tree rings on increment cores, assuming the stems form perfect circles with centered piths. However, piths are often offset and rings not perfectly round, which leads to BAI estimation errors. Yet, we do not know how much estimation error results from these two types of eccentricities. Using geometric principles that hold across all tree sizes, we quantified the effects of
these eccentricities on BAI accuracy on 109 cross-sections from 25 temperate species ranging in stem out-of-roundness and pith offset. We compared BAI estimates calculated with four methods and with radii estimated from one to four cores against true BAIs taken from cross-sectional scans. We found that with one core, pith eccentricity accounts for 21% of the error in BAI estimation, and stem eccentricity 8%. Taking multiple cores significantly reduces these errors, with four cores fully accounting
for both eccentricities and two cores sampled at 180° significantly reducing this error. We recommend using multiple cores to minimize error, with two-opposite cores being the most cost-effective approach. We also provide methods for quantifying and reporting pith and stem eccentricity in the field, offering practical guidance for practitioners to calculate estimation errors based on their methods.