Historic, archived document Do not assume content reflects current scientific knowledge, policies, or practices. '.vi . ■ i V',, H... Occasional Paper 182 /' ^ '’■*■ iiPR^R'' may 1 T '962 c„„«« se««i 1961 V > ^ ifs.^ ^ *%!. ti . ^ J® V , ^ -x' -'fe V” «> v'* 5^ 4> Rc^ O ..V R>?*-=^ <> V <%> OiV 'v'' oT® V* ^ \' ^ v'-" .■>.'■ <<' ■C>' .-.V V’l''* .S' .:^' s'" •S’ S’ .S''' •S •S/' ^•v'" ,^' ^■>.'- ■.■^y V/.' y\y y\y ■•'“y y y y => o y ^■<.v y y y v'*' y y y ^ y y Y / Y Y> y y y y .4" ^ ^ <»^V^ A. ' % \ X. ' *« tJ^ R* ^ ^ Ri^y \ tJ'S' “R \ R^ n- \ SOUTHERN FOREST EXPERIMENT STATION PHILIP A. BRIEGLEB, DIRECTOR Forest Service, U. S. Department of Agriculture An exploratory study with shortleaf pine (Pinus echinata Mill.) in north Arkansas indi- cates that variations in basal area growth may be strongly correlated with measurable ele- ments of stand structure. This possibility was studied to reduce the time needed to assess the desirability of alternative forest cutting prac- tices, to make possible growth predictions based on data normally collected by forest inventories, to provide timber markers with guides to future tree behavior, and, ultimately, to permit linear programming aimed at pre- dicting the structure best calculated to achieve a specified objective given various cost-price assumptions and an initial structure. PLAN OF STUDY Twenty-seven one-acre plots installed in 1956 provided a controlled range in sawtimber stocking, tree diameter, and space occupied by pines of sawtimber size. Other variables included age in several forms, data pertaining to the density and size of various stand com- ponents ( such as growing stock, ingrowth reservoir, etc. ) competition, and other factors ( table 1 ) . Table 1. — Independent variables available for regression analysis Xj Number of residual pines per acre, larger than 3.5 inches d.b.h. X2 do. , larger than 7.5 inches X3 do. , from 6.6 to 7.5 inches X4 Sum of residual diameters (inches per acre), pines 0.6 to 3.5 inches X5 do. , pines larger than 3.5 inches X(; do. , pines 3.6 to 6.5 inches X7 do. , pines 3.6 to 7.5 inches X3 Sum of residual basal areas (square feet per acre) , all species, 0.6 to 3.5 inches X9 do. , pines 3.6 to 7.5 inches Xio do. , pines larger than 3.5 inches Xi^ do. , pines larger than 7.5 inches X12 Squared sum of basal areas of residual pines larger than 7.5 inches Xi3 Mean age of pine dominants Xji Reciprocal of mean age of pine dominants Xi5 Mean age of pines larger than 7.5 inches X^j Coefficient of variation about mean age, pines larger than 7.5 inches Xi7 Mean diameter of residual pines larger than 3.5 inches Xj^y Coefficient of variation about mean diameter, pines larger than 7.5 inches X,,) Coefficient of variation of basal-area spatial distribution (7-diopter point samples) Xof) Percent of live crown length, residual pines larger than 7.5 inches X21 Index to recent cutting: residual pines larger than 3.5 inches after recent cutting divided by total basal area (all species 0.6 inch and larger) present prior to recent cutting X02 Index to recent cutting: 100 times the reciprocal of 1 plus the ratio of basal area of resi- dual pines and hardwoods to basal area of cut pines and hardwoods ( in each case only pines larger than 7.5 inches and hardwoods larger than 6.5 inches are included) X2:; Basal area removed in recent cutting X24 Mean height of pine dominants divided by mean age in years Xo.j Site index ( mean height of dominants at age 50 years ) Xoo 10-year radial growth of pine dominants, in inches 1 Gross basal-area growth of sawtimber and cordwood, including mortality, was determined by stand remeasurement after two growing seasons. ANALYSIS The Southern Forest Experiment Station’s IBM 704 Regression Program was employed in the analysis. Regression program outputs, each yielding regression coefficients and the variation accounted for by 511 regressions (one for every possible linear combination of the 9 or fewer independent variables ) , were ob- tained for two-year basal-area growth of the following: (a) Pine cordwood and sawtimber com- ponent (survivors plus ingrowth), 3.6 inches d.b.h., threshold diameter. ( b ) Pine sawtimber component ( surviv- ors plus ingrowth), 7.6 inches d.b.h., threshold diameter. (c) Pine sawtimber component (surviv- ors only). Several exploratory selections of indepen- dent variables were made, and separate regres- sion outputs were obtained for each selection. Dependent and independent variables select- ed for each output are shown in table 2. Table 2. — Squared multiple correlation coefficients (R’) for several regression anaUises Dependent variable; two-year basal-area growth Independent variables R* for 9 Independent variables in in square feet per acre selected for analyses variables “best” regression Pine cordwood and sawtimber. survivors plus ingrowth ( first output ) Pine cordwood and sawtimber, survivors plus ingrowth (second output ) Pine sawtimber, survivors plus ingrowth (first output) Pine sawtimber, survivors plus ingrowth ( second output ) Pine sawtimber, survivors only Xs X« Xo Xxx Xx3 XxT Xxo X20 X2X .647 Xs Xx3 X,x .564 Xx Xx Xs Xio Xx3 Xxx Xx9 Xox X2X .635 Xx Xx3 .475 Xs Xt Xs Xii Xi3 Xxs Xx9 X23 X25 .836 X2 Xx3 .795 Xo Xs Xe Xxx Xjo Xxs Xx6 X22 X2S .824 Xo Xxs .721 Xo X, Xs Xxx Xx3 Xxs Xxo X23 X25 .893 Xxx Xx3 .837 RESULTS As table 2 indicates, the 9-variable regres- sions accounted for 65 percent of the variation in cordwood basal-area growth, 84 percent of the variation in sawtimber basal-area growth including ingrowth, and 89 percent of the vari- ation in sawtimber basal-area growth exclud- ing ingrowth. The most worthwhile regres- sions with fewer than 9 independent variables were easily screened from the remainder of the IBM 704 outputs. Residual mean squares from the 9-variable regressions were used as rough error terms to screen the difference in variation accounted for by the “best” 1-vari- able regression, the “best” 2-variable regres- sion, etc., up to the full 9-variable regression. Value of F()5 for degrees of freedom 1 and 17 (27 sets of observed values, less 10 degrees for data-derived constants) is 4.45, and any dif- ference in sums of squares attributable to re- gression that was 4.45 times as large as the residual mean square seemed unlikely to be chance-caused. Sums of squares attributable to regression were given directly as a part of the IBM 704 program outputs. 2 The “best” regressions for predicting two- year basal area growth in square feet per acre were : Pine cordwood and sawtimber, survivors plus ingrowth ( first output ) = 0.272066 Xg — 0.220255 Xi3 + 8.79020 X21 + 9.65455 Pine cordwood and sawtimber, survivors plus ingrowth (second output ) = 0.0112359 Xi - - 0.176182 Xi3 -f 11.9865 Pine sawtimber, survivors plus ingrowth (first output) = 0.0297886 X^ - - 0.190111 Xi3 -f 13.4249 Pine sawtimber, survivors plus ingrowth ( second output ) = 0.030790 X2 — 0.200788 Xi5 + 13.3904 Pine sawtimber, survivors only = 0.0587584 X^ - - 0.137340 Xi3 -f 7.81012 The importance of age in predicting growth on the study plots was unexpected. Average ages of dominant trees on a given plot ranged from 39 to 67 years Since a restricted age range of 39 to 48 years was present on 19 of the 27 plots, a separate regression output in- volving pine sawtimber ( survivors plus in- growth) was obtained for this group. Value of R’ ( the squared coefficient of multiple correla- tion) for the 9-variable regression was .8026 for the restricted range in age, compared with R" of .8362 for the corresponding regression involving all 27 plots. This difference supports the inference that age is important in account- ing for growth differences on these plots even when oldest trees are excluded. The “best” regression for the 19 plots with a narrow range in ages also included mean age of dominant pines (X]3) and number of pines 7.6 inches d.b.h. and larger (X2). The 19-plot R' involv- ing Xj3 and X2 was .707, as compared with an R of .736 for the 27-plot regression involving the same two independent variables. Unless age or some function of age was in- cluded with the independent variables, none of the regressions was significant at the .01 level. Several of the sawtimber growth regres- sions that lacked age, however, were significant at the .05 level, and might be of interest when it is impracticable to determine age. These were: 2-year basal-area growth in pine sawtimber, survivors plus ingrowth 2-year basal-area growth in pine sawtimber, survivors only = .101121 X. — .00127480 X12 -h 4.74338 X20 — 1.74492 = 0.0607037 Xo — .00186244 X-, + .0596870 Xii + 2.76410 DISCUSSION Examination of the amount of variation that each independent variable accounted for, in- dividually and in combination with others, shows that basal-area growth variations be- tween stands can be satisfactorily attributed to measurable elements of stand structure. Further research is needed to determine whether other easily measured important inde- pendent variables can be discovered. In addi- tion, it may be fruitful to investigate whether the accuracy of estimates can be improved by changing the functions of the variables used. 3 i > I I » I' .( ( This study indicates that the following types of independent variables are more or less corre- lated with basal-area growth of shortleaf pine in the Arkansas Ozarks : Some function of stand age. Variables describing distribution in size and space of growing stock component including N, D, D^, coefficient of varia- tion of diameter, and coefficient of vari- ation of basal-area spatial distribution. Similar variables describing potential in- growth components. Similar variables describing competitive components ( undesirable stems and de- sirable stems not contributing to sur- vivor growth or ingrowth). Variables describing severity of recent drastic reduction in tree population (due to cutting, TSI, windthrow, etc.). Past growth. Some specific findings in regard to choice of variables were as follows: 1. Age of dominant trees was a more useful variable than the reciprocal of age. For sawtimber growth, it was better than the mean age of sawtimber-size trees. The coefficient of variation of mean age im- proved the regression, but not significant- ly. Possibly, age of dominants may be best for use in predicting the growth of even-aged stands, and mean age of the growing stock components and the co- efficient of variation of mean age may be best for uneven-aged stands (i.e., where larger coefficients of variation of age pre- vail ) . 2. Site index did not appear important in the presence of age, but did appear im- portant in the absence of age. It is un- fortunate that through accident there was a fairly strong nonsense correlation ( nega- tive) between site and age. 3. A curvilinear function of basal area appeared somewhat better in general than the simple linear form for explaining growth differences. 4. Number of trees per acre, or the sum of tree diameters, can under some circum- stances be more important than basal area, and hence should be included as an expres- sion of density. These terms seem to be particularly important for introducing the effect of ingrowth and competition, where the range of sizes is not great. 5. Probably because the stands were essentially even-aged, the coefficient of variation of diameter did not show up as an important element. 6. The regression outputs indicate that ingrowth tends to increase directly with coefficient of variation of growing space. When ingrowth is not included in growth estimates, growth of survivors appears to be inversely proportional to the same vari- able. 7. Competition was not important in the present study, because hardwoods larger than 3 inches d.b.h. had been killed on all plots before the measured growth period. 8. Effects of recent cuttings may be quite important in predicting growth, but the effect should lessen with the length of time since cutting. 9. Past radial growth may be a useful variable, but exploratory work is needed to ascertain whether some non-linear func- tion of it might not be preferable, as well as to learn whether growth of dominants will suffice or whether the term should be broad enough to include past ingrowth. In designing studies for predicting growth by regression analysis, it seems best to express growth in terms of basal area, since this meas- ure will not be affected much by site variation, unless extreme. When predictions are in terms of volume growth, tree height is introduced as a variable that will fluctuate with site index, making the regression analyses more complex. Ultimately, when site-prediction regressions based on soil variables have been worked out, volume predictions based on both site and stand structure may be developed, but progress will be more rapid initially if each is studied separ- ately. 4