# Canadian Forest Service Publications

A new approach to modeling stand-level dynamics based on informed random walks: influence of bandwidth and sample size. 2013. McGarrigle, E.; Kershaw, J.A. Jr.; Ducey, M.J.; Lavigne, M.B. *Forestry* **86**: 377–389.

**Year:** 2013

**Issued by:**
Atlantic Forestry Centre

**Catalog ID:** 34843

**Language:** English

**Availability:** PDF (request by e-mail)

Available from the Journal's Web site. †

DOI: 10.1093/forestry/cpt008

† This site may require a fee

## Abstract

A new stand-level dynamics model based on observed stand growth trajectories is presented. This stand-level dynamics model uses the trajectories of observed plots through Reineke's quadratic mean diameter-density space to predict the change in quadratic mean diameter, ingrowth and mortality over time. The model uses the collection of observed trajectories as a probability distribution that is used to guide an informed random walk. An imputation model is used to select *k* nearest neighbors (bandwidth) which are then used to build joint kernel distributions. From these kernel distributions, *m* random samples (sample intensity) are averaged to predict the change in quadratic mean diameter, ingrowth and mortality. All levels of *k* tested (10, 20, 30) performed well as long as sampling intensity was above 1. Variability in predictions was reduced at sampling intensities above 1, but no significant differences were visible among sampling intensities 5 and above.

## Plain Language Summary

A novel approach to predicting mean tree growth, mortality and ingrowth is presented and key methodological details are assessed. The novel approach randomly selects ‘nearest neighbours’ to prescribe a ‘random walk’ through the two dimensional graphical space defined by stand density on the x-axis and quadratic mean diameter on the y-axis. Remeasured permanent sample plots from Nova Scotia and New Brunswick are used to develop and test this approach. Nearest neighbours are periodic remeasurements of permanent sample plots having similar quadratic mean diameter, stand density and species composition to those of the random walk starting point. The periodic annual increment in quadratic mean diameter, mortality and ingrowth are calculated for the samples of permanent sample plots and used to estimate the quadratic mean diameter and stand density at the end of the prediction period (usually 3 – 5 years). These procedures are repeated to estimate mean tree growth, mortality and ingrowth for the subsequent periods until stands are mature. The number of nearest neighbours randomly selected to establish joint distributions of the directional changes in quadratic mean diameter and stand density and the amount of change (length of the line segment describing the change), and the appropriate number of times to sample from these joint distributions in order to reliably predict change of quadratic mean diameter, ingrowth, and mortality were investigated. Selecting 10 nearest neighbours to establish joint distributions produced similar results to selecting more permanent sample plots. Also five random samples from the joint distributions were sufficient to obtain reliable predictions. This approach may provide a simpler, more reliable method than the more conventional, regression-based approaches to using permanent sample plots for the prediction of stand growth and yield.