Dynamic modeling of branches and knot formation in loblolly pine (Pinus taeda L.) trees


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Virginia Tech


A stochastic framework to simulate the process of initiation, diameter growth, death and self-pruning of branches in loblolly pine (Pinus taeda L.) trees was developed. A data set was obtained from a destructive sampling of whorl sections from 34 trees growing under different initial spacing. Data from dissected branches were used to develop a model for representing knot shape, which assumed that the live portion of a knot can be modeled by a one-parameter equation and the dead portion by assuming a cylindrical shape. For the developed knot model analytical expressions were derived for estimating the volume of knots (live/dead portions) for three types of branch conditions on simulated trees: (i) live branches, (ii) non-occluded dead branches, and (iii) occluded dead branches. This model was intended to recover information on knots shape and volume during the simulation process of branch dynamics.

Three different components were modeled and hierarchically connected: whorl, branches and knots. For each new growing season, whorls and branches are assigned stochastically along and around the stem. Thereafter, branch diameter growth is predicted as function of relative location within the live crown and stem growth. Using a taper equation, the spatial location (X,Y,Z) of both live and dead portion of simulated knots is maintained in order to create a 3D representation of the internal stem structure. At the end of the projection period information on (i) vertical trend of branch diameter and location along and around the stem, (ii) volume of knots, and (iii) spatial location, size and type (live and dead) of knots can be obtained.

The proposed branch model was linked to the individual-tree growth and yield model PTAEDA3.1 to evaluate the effect of initial spacing and thinning intensity on branch growth in sawtimber trees. The use of the dynamic branch model permitted generation of additional information on sawlog quality under different management regimes. The arithmetic mean diameter of the largest four branches, one from each radial quadrant of the log (i.e. Branch Index, BI) and the number of whorls per log were considered as indicators of sawlog quality.

The developed framework makes it possible to include additional wood properties in the simulation system, allowing linkage with industrial conversion processes (e.g. sawing simulation). This integrated modeling system should promote further research to obtain necessary data on crown and branch dynamics to validate the overall performance of the proposed branch model and to improve its components.



individual-tree growth models, Loblolly pine, branch growth, knot shape