Evaluation of unconstrained and constrained mathematical functions to model girth growth of rubber trees (Hevea brasiliensis) using young age measurements

Abstract

No attempt has been made to date to model growth in girth of rubber tree (Hevea brasiliansis). We evaluated the few widely used growth functions to identify the most parsimonious and biologically reasonable model for describing the girth growth of young rubber trees based on an incomplete set of young age measurements. Monthly data for girth of immature trees (age 2 to 12 years) from two locations were subjected to modelling. Re-parameterized, unconstrained and constrained growth functions of Richards (RM), Gompertz (GM) and the monomolecular model (MM) were fitted to data. Duration of growth was the constraint introduced. In the first stage, we attempted a population average (PA) model to capture the trend in growth. The best PA model was fitted as a subject specific (SS) model. We used appropriate error variance-covariance structure to account for correlation due to repeated measurements over time. Unconstrained functions underestimated the asymptotic maximum that did not reflect the carrying capacity of the locations. Underestimations were attributed to the partial set of measurements made during the early growth phase of the trees. MM proved superior to RM and GM. In the random coefficient models, both Gf and G0 appeared to be influenced by tree level effects. Inclusion of diagonal definite positive matrix removed the correlation between random effects. The results were similar at both locations. In the overall assessment MM appeared as the candidate model for studying the girth-age relationships in Hevea trees. Based on the fitted model we conclude that, in Hevea trees, growth rate is maintained at maximum value at t0, then decreases until the final state at dG/dt ≥0, resulting in yield curve with no period of accelerating growth. One physiological explanation is that photosynthetic activity in Hevea trees decreases as girth increases and constructive metabolism is larger than destructive metabolism.