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

Comparisons between empirical and theoretical allometric modelsfor estimating tree biomass and the statistical caveats attachedto empirical stem volume equations are presented in this paper.First, the elastic and stress similarity models, derived fromfirst biomechanical principles, as well as predictions obtainedfrom geometric similitude, were validated against allometricequations that relate dry above-ground tree biomass M to stemdiameter D. In addition, a recent geometric model which predictsthat M D^8/3 was also validated against a pooled dataset whichconsisted of 764 M-D pairs compiled from empirical studies conductedthroughout the globe and for several tree species. Moreover,59 empirical equations which relate M to D were selected froma European database to validate the aforementioned theoreticalmodels. The analysis indicated that the biomechanical and thegeometric models failed to describe the shape in M-D allometryfor 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 empiricalmodels based on the six-parameter formula V = a + bD + cD² +dD³ + eH + fD²H were used in order to pinpoint the dependencybetween the parameters. It is illustrated that parameters a,b and c are highly related to each other, and parameter e isalso related to parameter f. It is concluded that the interrelationshipbetween D and stem height (H) could be one of the reasons forthis dependency and scepticism should be placed in the reliabilityof V estimates derived from these models.