Comparison between empirical and theoretical biomass allometric models and statistical implications for stem volume predictions

Comparisons between empirical and theoretical allometric models for estimating tree biomass and the statistical caveats attached to empirical stem volume equations are presented in this paper. First, the elastic and stress similarity models, derived from first biomechanical principles, as well as predictions obtained from geometric similitude, were validated against allometric equations that relate dry above-ground tree biomass M to stem diameter D. In addition, a recent geometric model which predicts that M varies D8/3 was also validated against a pooled dataset which consisted of 764 M-D pairs compiled from empirical studies conducted throughout the globe and for several tree species. Moreover, 59 empirical equations which relate M to D were selected from a European database to validate the aforementioned theoretical models. The analysis indicated that the biomechanical and the geometric models failed to describe the shape in M-D allometry for the empirical datasets. Finally, the multicollinearity problem, which is directly related to the reliability of the predictions, was analysed for stem volume equations (V). In total, 23 empirical models based on the six-parameter formula V = a + bD + cD2 + dD3 + eH + fD2H were used in order to pinpoint the dependency between the parameters. It is illustrated that parameters a, b and c are highly related to each other, and parameter e is also related to parameter f. It is concluded that the interrelationship between D and stem height (H) could be one of the reasons for this dependency and scepticism should be placed in the reliability of V estimates derived from these models.