Title

When Would You Tap That? Rubber Tree (Hevea Brasiliansis) Modeling

Authors

Ethan Williams

Document Type

Presentation

Journal/Book Title/Conference

USU Student Showcase

Publication Date

4-2014

Abstract

A model was developed for the growth of rubber trees by Dr. Chandrasekhar in his doctoral research study. He used data from a study performed in India which measured the girths of 82 rubber trees, 34 of them over 6 1/3 years and the rest over an 8 year time period. For a variety of animals there are two well-known models relating the growth in organism mass to growth in its girth or length. West's model says growth should be limited by the number of branches in the organisms fluid network, where-as von Bertalanffy's models says that growth should be limited by the surface area. Nobody knows which, if either, is true for trees, but Chandrasek's data allows us to find out! The parameters were determined by maximizing likelihood, or minimizing negative log likelihood (NLL), where SSE is the Sum Squared Error between model and observations and _2 is the variance. Models are compared according to Akaike Information Criterion corrected (AICc), where k is the number of parameters and the number of observations. The less SSE, the less unlikely the model's results, and the more information is captured by the model. Thus the smaller the AICc score the better the fit. The AICc scores clearly indicate that the Free West model is the overall best model for rubber trees in all cases. This indicates that the limiting factor on rubber tree growth is nutrient supply through the network of branches (_=3/4), but that trees transition from distributing their mass two dimensionally (_ = 1.95 ~ 2 for younger trees) to distributing their mass three dimensionally (_ = 2.92 ~ 3 for older trees). This is likely because younger trees in a stand compete for light first (i.e. occupy a two dimensional area in the canopy to get sun) and then fill out their volume of leaves later

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