Abstract
Background: Hybrid mensurational and physiological models seek to combine precision, process explanation, simplicity in parameter definition, and ability to estimate wood products. The aim of this study was to assess the suitability and the advantages of the hybrid mensurational-physiological approach where time has been substituted for light sums in growth equations, to replace traditional time-based models in forecasting systems for Eucalyptus grandis W.Hill and Pinus taeda L.
 Methods: Using 974 permanent sample plots from plantations in Uruguay, we adjusted growth equations to project dominant height, net basal area, maximum diameter breast height, and standard deviation of diameters as a function of accumulated light restricted by modifiers that account for principal physiological limitations on photosynthesis. We analysed: i) the inclusion of terrain aspect and slope information for computing radiation; ii) the use of modifiers for temperature, vapour pressure deficit and water balance; iii) bias and precision of hybrid models with respect to time-based equations.
 Results: Growth equations showed a good fit for both species when modelled as a function of light sums modified by vapor pressure deficit, air temperature, and water balance. Accounting for slope orientation when computing light sums did not increase precision. Compared to time-based formulations, hybrid models presented a root mean squared error reduction of 10.7% and 4.5% on average for Eucalyptus grandis and for Pinus taeda, respectively, and the relationship between growth and resource availability was consistent with eco-physiological principles for both species.
 Conclusions: The hybrid methodology can be applied as a basis of forecasting systems for the species studies with significant advantages over time-based models, such as: (i) an increase in precision; (ii) an increase in spatial and time resolution; and (iii) the possibility of simulating the effect of changes in air temperature and water availability on tree growth.
Highlights
Hybrid growth and yield models have been developed to include the best features of mensurational and physiological approaches while attempting to avoid the shortcomings of complicated physiological models.The features that are typically enhanced are: precision, process explanation, ability to estimate wood products, and simplicity in parameter definition
The hybrid methodology can be applied as a basis of forecasting systems for the species studies with significant advantages over time-based models, such as: (i) an increase in precision; (ii) an increase in spatial and time resolution; and (iii) the possibility of simulating the effect of changes in air temperature and water availability on tree growth
Results of applying potentially useable light sum equations (PULSE) seem promising with respect to precision and outputs for predicting height and especially basal area, there is still much to explore with respect to the potential performance of this approach, especially seeking its full application as a basis of forecasting systems
Summary
Hybrid growth and yield models have been developed to include the best features of mensurational and physiological approaches while attempting to avoid the shortcomings of complicated physiological models (e.g. limitations from a forest management perspective).The features that are typically enhanced are: precision, process explanation, ability to estimate wood products, and simplicity in parameter definition. A hybrid mensurational-physiological approach using equations based on potentially useable light sums (PULSE) was proposed by Mason et al (2007). It combines light use efficiency with mensurational approaches to describe growth using difference sigmoidal models. Hybrid mensurational and physiological models seek to combine precision, process explanation, simplicity in parameter definition, and ability to estimate wood products. The aim of this study was to assess the suitability and the advantages of the hybrid mensurational-physiological approach where time has been substituted for light sums in growth equations, to replace traditional time-based models in forecasting systems for Eucalyptus grandis W.Hill and Pinus taeda L
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