Evaluation of different approaches to individual tree growth and survival modelling using data collected at irregular intervals – a case study for Pinus patula in Kenya

Abstract

Background: The minimum set of sub-models for simulating stand dynamics on an individual-tree basis consists of tree-level models for diameter increment and survival. Ingrowth model is a necessary third component in uneven-aged management. The development of this type of model set needs data from permanent plots, in which all trees have been numbered and measured at regular intervals for diameter and survival. New trees passing the ingrowth limit should also be numbered and measured. Unfortunately, few datasets meet all these requirements. The trees may not have numbers or the length of the measurement interval varies. Ingrowth trees may not have been measured, or the number tags may have disappeared causing errors in tree identification. Methods: This article discussed and demonstrated the use of an optimization-based approach to individual-tree growth modelling, which makes it possible to utilize data sets having one or several of the above deficiencies. The idea is to estimate all parameters of the sub-models of a growth simulator simultaneously in such a way that, when simulation begins from the diameter distribution at the first measurement occasion, it yields a similar ending diameter distribution as measured in the second measurement occasion. The method was applied to Pinus patula permanent sample plot data from Kenya. In this dataset, trees were correctly numbered and identified but measurement interval varied from 1 to 13 years. Two simple regression approaches were used and compared to the optimization-based model recovery approach. Results: The optimization-based approach resulted in far more accurate simulations of stand basal area and number of surviving trees than the equations fitted through regression analysis. Conclusions: The optimization-based modelling approach can be recommended for growth modelling when the modelling data have been collected at irregular measurement intervals.

GENERAL HEIGHT-DIAMETER EQUATION WITH BIOLOGICAL ATTRIBUTES FOR Pinus taeda L. STANDS

“…In an individual-tree growth model, a tree height growth equation or a static height-diameter equation should be added as an additional component in order to predict total and merchantable volume growth (TOMÉ, 1988;LEDUC;GOELZ, 2009;CRECENTE-CAMPO et al, 2010). The use of hypsometric relation was adopted as a sub-model in the individual-tree growth models by several authors, as Harrison et al (1986), Tomé (1988), Palahí et al (2008), Paulo and Tomé (2009), Alegria and Tomé (2013), Juma et al (2014) and Miranda (2016). The lack of successive height measurements of the same tree is commonly forcing the use of compatible height projection equation and height-diameter prediction equation in the individual-tree growth models (TOMÉ, 1988;TOMÉ, 2002).…”

Development and evaluation of an individual tree growth and yield model for the mixed species forest of the Adirondacks Region of New York, USA

“…Although this assumption of linear growth is likely too simplified for highly irregular and longer remeasurement intervals (>10 years), the iterative approach used in this analysis does produce model behavior similar to a more sophisticated optimization approach and is more effective than using the remeasurement interval as a covariate (e.g. Juma et al 2014).…”

Site Specific Stem Volume Models for Pinus patula and Pinus oocarpa

“…Plausible advocacy for use of localised modelling has been reported in several studies [8][9][10][11] particularly where precision and revenues are priorities. This modelling approach yields accurate and reliable volume estimates for sustainable decision support in the forest management [2,12]. However, the quality of a model estimate is only as good as the quality of data variables from which the model is developed.…”

“…The commonly planted timber species in these plantations include Pinus patula, P. kesiya, P. elliottii, and P. oocarpa [1,2]. Volume is customarily used in these forest plantations as a standard measure on which timber pricing and yield are based.…”