Relative branch size in branch clusters modelled through a Markovian process

The branches 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.