Spatially correlated forest stand structures: A simulation approach using copulas

Spatial structure of forest stands is one of the main drivers of forest growth and yield, and is an important indicator of wildlife habitat, aesthetics, and other non-timber forest uses. Because spatial structure is costly to measure, a number of approaches for simulating spatial structures have been proposed. In this paper, we propose a simple approach that is capable of generating multispecies stand structures. Based on the method of copulas (Genest and MacKay, 1986, Am. Stat. 40:280–283), we utilize a normal copula to simulate spatially correlated stand structures. Species composition, diameter, height, and crown ratio distributions of each species, and their correlation with underlying spatial patterns are all controlled by user inputs. Example data sets are used to demonstrate how to estimate required parameters and compare simulated spatial structures with observed spatial structures. Except at the smallest scales (<10 m in the longleaf pine dataset and <2 m in the mixed Acadian Forest dataset), the simulated stand structures adequately captured the observed spatial patterns. Based on these comparisons, we conclude that the system is capable of simulating a range of forest stand spatial structures.

Research highlights▶ A spatially correlated stand structure system is developed based on the method of copulas and is implemented in the R statistic package. ▶ Standard Normal copulas are utilized to transform random normal variables into correlated variables. ▶ Example datasets and methods to estimate the required marginal distributions and correlation coefficients are presented. ▶ The system is capable of simulating a variety of forest stand structures from relatively simple single species structures to complex multispecies structures.