Tero Kokkila , Annikki Mäkelä, Eero Nikinmaa

A method for generating stand structures using Gibbs marked point process

Kokkila T., Mäkelä A., Nikinmaa E. (2002). A method for generating stand structures using Gibbs marked point process. Silva Fennica vol. 36 no. 1 article id 562. https://doi.org/10.14214/sf.562

Abstract

Stand growth modelling based on single tree responses to their surroundings requires a description of the spatial structure of a stand. While such detailed information is rarely available from field measurements, a method to create it from more general stand variables is needed. A marked Gibbs point potential theory combined with Markov chain Monte Carlo (MCMC) random process was used to create a spatial configuration for any given number of trees. The trees are considered as charges rejecting each other and building ‘potential energy’. As an analogue of the potential energy in physical systems, the potential of a stand is defined in terms of size-dependent tree-to-tree interactions that can be thought of as related to resource depletion and competition. The idea that bigger trees induce larger potentials brings 3-dimensional effects into the system. Any feasible spatial structure is a state of the system, and the related potential can be calculated. The probability that a certain state occurs is assumed to be a decreasing function of its potential. Because more regular structures have lower potentials, by adjusting the steepness of the probability distribution the spatial structure can be allowed to have a lot of randomness (naturally regenerated stands) or forced to be very regular (planted stands). The MCMC algorithm is a numerical method of finding stand configurations that correspond to the expected level of the potential, given the size distribution of trees and the shape of the probability density function. The method also allows us to take into account spatial variation in the terrain. Some spots can be defined to have lower basic potential than others (ditch, planting furrow, etc.) in order to create areas of higher than average stocking density. A preliminary test of the method was conducted on two measured stands. The results suggest that the method could provide an efficient and flexible means of mimicking variable stand structures.

Keywords
spatial distribution; stand simulation; Gibbs point process; Markov chain Monte Carlo

Received 16 November 2000 Accepted 21 March 2002 Published 31 December 2002

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