Age Structure Models of Balsam Fir and Eastern Hemlock

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Abstract
A quantitative approach to the dynamics of plant populations throughout a long life-span is explored, including estimation of vital population statistics and examination of these parameters through time. The objective was to examine mathematical models describing population depletions in A. balsamea and T. canadensis and to use the models to interpret mortality rates and other aspects of the biology of these tree species. The models investigated were the negative exponential, the power function and a negative exponential sine wave. The negative exponential implies a constant mortality rate, and has been used in previous studies to describe age-structure of seedlings and herbs. The power function is one of a family of distributions that could be fitted to populations with a survival pattern following a positively skewed distribution, implying a changing mortality rate. The negative exponential model does not adequately describe age depletions in long-lived species; the power function is an adequate model if wave-like departures from the straight line fits are overlooked. All of the balsam fir and hemlock populations showed an oscillation around the straight line form of the first 2 distributions. A sine wave model was developed to determine whether the population distributions could be described more adequately and whether a characteristic wave length occurred for each species. The sine wave model appears to be the best. An explanation of the cycle in terms of gradual changes in survivorship due to changes in stand structure is suggested.

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