Reformulated self-thinning exponents as applied to black spruce

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Abstract
Five self-thinning exponents (ηi, i = 1,…,5) for the asymptotic total stem volume – density relationship within black spruce (Piceamariana (Mill.) B.S.P.) stands were estimated and compared: (i) the empirically observed value (η1); (ii) η2 = −[(2 + α)/2β] + 1, where α and β are species-specific allometric exponents for the relationship between stem height and stem diameter, and crown basal diameter and stem diameter, respectively; (iii) η3 = −(2.5/2β) + 1; (iv) η4 = −{l/[2(0.5 − 0.5δ)]} + 1, where δ is the allometric exponent for the relationship between mean stem height and mean stem volume; and (v) η5 = −[(ε + 1)/ζ] + 1, where ε and ζ are stem and crown form exponents, respectively. Employing data derived from 27 permanent and 21 temporary sample plots situated on medium sites throughout central Newfoundland, thinning, allometric, and form exponents were estimated. Resultant exponents were as follows: η1 = −0.618 estimated by principal component analysis; η2 = −1.633, where α = 0.682 and β = 0.509; η3 = −1.454; η4 = −0.470, where δ = 0.320; and η5 = −0.528, where ε = 2.144 and ζ = 2.058. Hence two numerically distinct sets of thinning exponents were obtained: A = {η1, η4, η5} and B = {η2, η3}. Set A corresponds to commonly observed or expected values, whereas set B exhibits substantial departure. It is proposed that the underlying allometric relationships employing stem diameter are partially responsible for these set differences.