Relative branch size in branch clusters modelled through a Markovian process

Information on tree canopy architecture is crucial in forestry practice because the quality and price of standing trees and final logs directly depend on it. Simultaneously, accurate empirical or functional–structural models require information based on field observations. Pinus radiata is a polycyclic species that follows an acrotony law when forming a new branch cluster, showing smaller branches in its base and larger ones at the top of a forming cluster. The objective of this study was to describe the acrotony of the branches in a branch cluster as a Markov chain. Markov chains represent stochastic processes in discrete time that undergo a transition from one state to another among a finite number of possible states. The probability of transition from state i to a state j depends only on the current state, i. For modelling acrotony, the relative vigour (expressed as relative branch diameter in relation to the largest one) of each branch was selected as the stochastic variable and the states corresponded to five possible relative size ranges. anches observed within a P. radiata cluster were ordered following their relative sizes (from largest to smallest), and Markovian transition matrixes were calculated for each branch cluster (whorls of 3–12 branches). The transition matrixes were defined as the probabilities of one branch being followed by an equal-sized or smaller branch when observing the cluster from the top down. The obtained Markov chain matrixes were used in a stochastic data simulation, which was validated with an independent dataset. The presented matrixes can be incorporated into traditional simulation models or functional–structural models. The validation results show that the proposed methodology accurately reflects the variability of the branch sizes in a cluster, and we suggest its application to other species that display a clustered organisation of branches.