Predicting diameter distributions: a test of the stationary Markov model

TitlePredicting diameter distributions: a test of the stationary Markov model
Publication TypeJournal Article
Year of Publication1986
AuthorsRoberts MRichard, Hruska AJ
JournalCanadian Journal of Forest Research

We tested the null hypothesis that diameter class transitions over a 40-year period (1940-1980) in an even-aged mixed Pinus resinosa Ait. - Pinus strobus L. stand represent a stationary Markov process. Transition probabilities were constructed from growth data on 202 trees >= 5.1 cm DBH in a 0.4-ha permanent plot. For each species, a diameter distribution in 1980 was predicted with the stationary Markov model using the 1940-1950 transition probability matrix. The predicted and observed 1980 distributions were significantly different for P. resinosa (x2 = 31.67, p <0.1), but not P. strobus (x2 = 7.86, not significant). In P. resinosa, growth rates of trees in the same diameter class at different points in time declined with increasing stand age. This violates the assumption of stationarity. Growth did not decline in most diameter classes in P. strobus. The model also assumes that differences in the competitive histories of trees of the same size do not affect transition probabilities. The average growth rates of trees in different crown classes within two diameter classes were significantly different for P. resinosa, but not for P. strobus. Both assumptions of the model were violated in the case of P. resinosa. The model was not rejected for P. strobus because it is a midtolerant species capable of relatively constant growth in the understory. However, this study included only the middle period of stand development when growth rates are relatively constant. These results indicate that more biologically realistic modelling approaches which incorporate growth declines with stand age and past competitive effects should be pursued.