Indices of forest compositional change based on linear regressions of species size class distributions

The approach taken here was to consider linear regressions of species size class distribution on arithmetic axes, to modify components of these regressions, and to plot such modified components against classical importance value (V₃) for all species in a stand, after both sets of values were normalized to 100% scales. The slope of the stand regression fitted to this plot was the desired index of compositional change. Two species regression components were used, the slope and the x-intercept, yielding two indices of compositional change – M_s and M_x, respectively.

To investigate the behavior of these indices, sixty-five forest tally data sets were gleaned from the ecological literature, and the computational procedures applied, using a pocket calculator. These data sets represented an extensive variety of forest types (species present), ages, geographical locations, and categories (old growth/ virgin, transitional, selectively cut, old fields/cleared areas). A hypothesis was posed concerning the magnitude of the stand regression slope (M_s or M_x) and regression correlation (R_s or R_x) and their changes during a forest sere. Several additional calculations were made, beyond those used in testing this hypothesis, in order to elucidate characteristics of the two indices and to compare and contrast their behavior. These included correlation between each stand slope (index) and its associated correlation ( R_MX, R_MS R_S), correlations between the two indices ( R_{MX MS}), calculations of average mean stand correlation (| r̿ |) and grand mean species correlation (| r̅ |_G), and correlation of the number of size classes and number of species with the mean stand correlation (R_{NSC | r̅ |}, R_{NX | r̅ |}).

The results indicated that the indices were both flexible and accurate, relative to the nature of the forest stand analyzed. The hypothesis concerning the magnitudes of the indices was verified. The argument for the use of linear regressions over other functions, given in the development of the indices, was strongly supported by correlations showing the accuracy with which the linear model fit the species size class distributions over all stands. A comparison of the indices with the differential weighting index of compositional change proposed by Goff (l968) yielded a somewhat perplexing result, a low correlation between the two indices presented here and Goff's index. Possible reasons were suggested. Several minor problems associated with the M_S and M_X indices were discussed and the advantages and disadvantages of each were summarized.

The conclusion drawn from this study was that indices of forest compositional change can be easily derived using size class data from one point in time, when based on arithmetic linear regressions of species size class distributions. The indices were concluded to be potentially useful in the analysis of forest trends.