Studies of Regeneration in Forest Stands Devastated by the Spruce Budworm. III. Problems of Sampling Precision and Seedling Distribution

The precision of estimates of Abies balsomea (L.) Mill. populations is adequately described by the rectangular hyperbola that relates standard error and sample size in elementary statistical theory. With sample size held constant, standard error is found to be a power function of density, of the form Y.X a = b . Inspection of standard error vs. sample size hyperbolas at selected population densities demonstrates that the sampling effort required to attain a given level of precision varies inversely with density. The roles of competitive and non-competitive influences upon seedling distributions are considered. A new method of applying the binomial to the assessment of contagion demonstrates that areas of both very high and very low seedling densities are contagiously distributed, while areas of intermediate density are more randomly dispersed. Studies of the influence of observational scale upon the apparent distribution of A. balsamea seedlings show this to be independent of quadrat size over the range from 0.25 to 2.25 milacres. The apparent distribution changes dramatically, however, with changes in the total area over which the quadrats are spread. Disagreement with the Poisson distribution, rather than agreement with the negative binomial or other variance-dependent distribution, is found to be the more reliable criterion of contagion. Unlike A. balsamea , Pinus strobus L. seedling distributions do show a change in apparent distribution with increasing quadrat size, and illustrate the convergence of the negative binomial to the Poisson distribution as mean and variance approach equality.