Evaluation of Markov chains for projecting diameter distributions

Fifteen years of the University of Tennessee's Continuous Forest Inventory data were used to determine if Markov chains could be used to make accurate predictions of future diameter distributions for pulpwood size trees in natural hardwood stands. Distributions projected five and ten years were compared to actual data by means of the Kolmogorov - Smirnoff Test for Goodness of Fit. Projections were made for all hardwood species on each of three forest tracts and for several individual species that were abundant. Markov chain theory is based on the assumption that transition probabilities remain constant through time. To determine if this assumption was met when projecting forest stands, two initial probability matrices were constructed from data at five year intervals. If transition probabilities had not changed, differences between the two matrices would have been minimal. The two matrices were constructed and compared for all hardwoods on each tract and for the individual species. Markov chains and matrix algebra were employed to predict the average number of periods expected to pass before trees in each diameter class reach sawtimber size. Also, the number of periods spent in each diameter class before reaching sawtimber size was predicted. The results of the analysis of projected and actual diameter distributions indicated that Markov chains could be used as a reliable technique to determine future stand conditions. The only significant differences found between actual and projected data were because of the underestimation of the number of trees in upper diameter classes or, more often, the underestimation of mortality. In each of these cases actual mortality was unusually high as a result of an initial high proportion of intolerant trees in the stand which possibly succombed to suppression or competition; unprojected harvest or timber stand improvement; or catastrophic mortality caused by fire, insects or disease. Comparison of the probability matrices constructed at five year intervals indicated that, for each of the forest tracts studied, overall growth rates were not steady. Differences were not large, though, showing that short term projections were reliable. If longer time periods were projected, it would be expected that the differences between actual and projected data would increase. The other Markov chain calculations, average time to reach sawtimber size and average time spent in each diameter class, provided useful information about the growth and productivity of each tract. These predictions may be used in planning and timing various management activities.