UNIVERSITY OF CALIFORNIA COLLEGE OF AGRICULTURE AGRICULTURAL EXPERIMENT STATION BERKELEY, CALIFORNIA EFFECT OF PARTIAL CUTTING IN THE VIRGIN STAND UPON THE GROWTH AND TAPER OF WESTERN YELLOW PINE FRANCIS X. SCHUMACHER BULLETIN 540 SEPTEMBER, 1932 UNIVERSITY OF CALIFORNIA PRINTING OFFICE BERKELEY, CALIFORNIA CONTENTS PAGE Introduction 3 The area and the stand 3 The virgin stand 4 The cut-over stand 4 The basic data 4 Results of the investigation 7 Comparison by volume board measure 7 Comparison by taper 8 Comparison by diameter growth along the stems 11 Detailed analysis of the data 13 Tree volumes 13 Tree tapers 17 The 1928 taper of the trees from the virgin stand 18 Comparison of the tree tapers from the virgin and cut-over stands in 1909 and 1928 23 The taper by tree class 24 Bark thickness at breast height 24 The taper tables 24 Diameter growth 27 Conclusion 32 Note : The Western Pine Association and the United States Forest Serv- ice have now adopted the name PONDEROSA PINE instead of western yellow pine. Digitized by the Internet Archive in 2012 with funding from University of California, Davis Libraries http://www.archive.org/details/effectofpartialc540schu EFFECT OF PARTIAL CUTTING IN THE VIRGIN STAND UPON THE GROWTH AND TAPER OF WESTERN YELLOW PINE 1 FRANCIS X. SCHUMACHER2, s INTRODUCTION In the early summer of 1910, a moderately heavy selective cutting was made on the government timber-sale area in the Stanislaus National Forest. During the summer of 1928 a second cutting was made on this same previously cut-over area, as well as a first cutting in the adjoining virgin timber. This afforded an opportunity to investigate (1) the form or taper of virgin timber by the method of stem analysis, and (2) changes in form and growth following the opening up of the virgin stand 18 years previously. This paper aims to set forth the results of the study for western yellow pine (Pinus ponderosa), the only species in sufficient numbers for reliable basic data. THE AREA AND THE STAND The area is on the watershed of the North Fork of the Tuolumne River in sections 29 and 32, township 4 north, range 18 east, Mt. Diablo meridian, at an average elevation of about 5,800 feet. The soil is fine, sandy loam of granitic origin. Normal precipitation is probably about 45 inches, though no records of much value have been kept nearby. The general aspect of the logged-off area is north-easterly with gentle to moderately steep slopes. The timber vegetation is of the western-yellow-pine — sugar-pine type with white fir and incense cedar. As the tallest trees were well over 200 feet high, the area is classed as Site Quality I. For convenience, the stand first cut in 1910 and later in 1928 will be designated as the cut-over stand, and the stand first cut in 1928 as the virgin stand. i Received for publication May 27, 1932. 2 Assistant Professor of Forestry and Assistant Forester in the Experiment Station; resigned November 16, 1930. s The writer is indebted to Director E. I. Kotok of the California Forest Experiment Station, United States Department of Agriculture, for information which led to the gathering of data for this investigation; and to Mr. Duncan Dun- ning for personal instruction of the field assistants in the identification of tree classes. University of California — Experiment Station THE VIRGIN STAND This was in the south half of section 29 and the northeast quarter of section 32. From the cruise of these three quarter-sections made by the United States Forest Service in 1926, the stand per acre averaged 59,000 feet board measure distributed among the species shown in table 1. TABLE 1 Virgin Stand by Species Species Board measure, in per cent by volume Western yellow pine Sugar pine White fir 22 53 20 Incense cedar 5 THE CUT-OVER STAND This was in the northwest quarter of section 32. Its original volume is not known, but as the 1928 cutting was taken mostly from a Forest Service 20-acre permanent sample plot, established in the summer of 1910, a fair estimate may be made of the stand per acre before and after the first cutting from the cruise figures for the plot given in table 2. TABLE 2 Stand per Acre of Forest Service Permanent Sample Plot, Before and After Cutting Trees 11.6 Inches in Diameter and Over Original stand, trees per acre Trees left Original volume, board measure Volume left Species Number Per cent Board measure Per cent Western yellow pine Sugar pine 15.40 2 85 2 00 5 30 25.55 10.85 1.65 70 2.20 15.40 70 5 57.9 35 41 5 60.2 29,130 11,780 5,070 5,800 51,780 14,070 4,670 230 670 19,640 48.3 39.7 White fir Incense cedar Total 4.5 11.5 37.9 THE BASIC DATA A partial stem analysis was made of each western yellow pine tree as felled and bucked in 1928, both virgin and cut-over, by measuring and plotting in the field on United States Forest Service Bul. 540] Partial Cutting in Western Yellow Pine form 558a the following data: (1) diameter at breast height outside bark; (2) diameter outside and inside bark in 1928, and diameter inside bark at the end of the 1909 growing season, at stump and at each log length of usually 16.3 feet; and (3) total height in 1928 and in 1909. TABLE 3 Summary of Basic Data Number of trees Tree class From virgin stand From cut-over stand 1 2 3 4 5 6 7 Total 40 43 74 49 40 30 17 293 20 3 25 25 14 8 17 112 Tree class by Dunning 's 4 classification was also recorded. Table 3 summarizes the data by tree class. In order to visualize the tree classes as encountered in a selection forest of western yellow pine, the description and typical form of each class, taken from Dunning 's paper, is here reproduced : Seven classes are proposed, as follows [see fig. 1] : Class 1: Age class, young or thrifty mature (up to 150 years) ; position, isolated or dominant (rarely codominant) ; crown length, 65 per cent or more of the total height; crown ividth, average or wider; form of top, pointed; vigor, good. Trees of this class are rarely over 30 inches in diameter even on good sites. The bark is dark brown and roughly fissured into ridges or small plates. The foliage is rich green in color and dense, owing to retention of the needles of three to five seasons or more, except at the base of the crown. The needles are often long and coarse, especially near the top. Terminal buds are large. The top is pointed, owing to the rapid elongation of the terminal. Thrifty open-grown young trees belonging to this class are, however, sometimes round topped because of excessive lateral growth of branches near the top. On the other hand, slow- growing trees sometimes have pointed tops, due to weak development of laterals. The annual whorls of branches and internodes are still distinct, except in the lower crown. Branches are horizontal or upward curving, except at the base of the crown where suppression is taking place. Numerous stubs of dead branches are likely to be present below the crown. 4 Dunning, Duncan. A tree classification for the selection forests of the Sierra Nevada. Jour. Agr. Research 36:755-771. 1928. 6 University of California — Experiment Station Class 2 : Age class, young or thrifty mature (up to 150 years) ; position, usually codominant (rarely isolated or dominant) ; crown length, less than 65 per cent of the total height; crown width, average or narrower; form of top, pointed; vigor, good or moderate. Such trees are usually less than 24 inches in diameter. They are commonly the inside codominant trees of groups. The crowns are smaller and less dense than in trees of the first type. Otherwise they are similar to those of class 1. Class 3: Age class, mature (150-300 years); position, isolated or dominant (rarely codominant) ; crown length, 65 per cent or more of total height; crown width, average or wider ; form of top, round ; vigor, moderate. 16 2 3 4 7 5 Fig. 1. — Tree classes of western yellow pine. (After Dunning.) These trees are ordinarily between 18 and 40 inches in diameter, depending on site quality. The bark is light brown or yellow, with moderately large smooth plates. The foliage is less dense than in class 1 trees. The top is round, because of slow height growth. The nodes are indistinct, because of incomplete whorls of branches. The branches are nearly all horizontal or drooping. Class 4: Age class, mature (150-300 years); position, usually codominant (rarely isolated or dominant) ; crown length, less than 65 per cent of the total height; crown width, average or narrower; form of top, round; vigor, moderate or poor. These are commonly the inside or codominant trees of this age class. Except for their small, poorly developed crowns and smaller size, they are similar to class 3 trees. Bul. 540] Partial Cutting in Western Yellow Pine 7 Class 5: Age class, overmature (over 300 years) ; position, isolated or dominant (raredy codominant) ; crown, of any size; form of top, flat; vigor, poor. These are usually the largest trees in the stand. The bark is light yellow in color, the plates often very wide, long and smooth, especially near the base. The bark may be thin, having weathered more rapidly than it has grown. The foliage is usually rather pale green and very thin. The needles are fairly short, appear- ing as tufts on the ends of the twigs. The needles of two or three seasons only may be retained, even near the top. The top is flat, the terminal rarely discernible. There is no appreciable elongation of the main axis. Scarcely any nodes are distinguishable. Nearly all the branches are drooping, gnarled, and crooked. Class 6: Age class, young or thrifty mature (up to 150 years) ; position, inter- mediate or suppressed; crown, of any size, usually small; form of top, round or pointed; vigor, moderate or poor. These are understory trees, rarely over 12 or 14 inches in diameter. The bark is dark and rough. The top is round or pointed, showing that some height growth is taking place. Whorls of branches are evident, though the internodes are short. Class 7: Age class, mature or overmature (over 150 years); position, interme- diate or suppressed; crown, of any size, usually small; form of top, flat; vigor, poor. These understory trees are rarely over 18 inches in diameter. The bark is light in color, thin, and smooth. The top is flat, the terminal rarely distinguish- able. The foliage is excessively thin. The few branches present are gnarled and drooping. After several hours of personal instruction by Mr. Dunning, com- bined with a, little practice, the four students who measured and recorded the data became very proficient in classifying the trees, sel- dom indeed disagreeing on the class of any individual tree. RESULTS OF THE INVESTIGATION The data from the cut-over stand were compared with those from the virgin stand, (1) by volume for trees of the same sizes, (2) by taper inside bark, and (3) by diameter growth along the stem between 1910 and 1928. Such comparisons should be legitimate because (1) site quality is broadly the same in both stands, Site I for western yellow pine, and (2) both stands originally contained about the same volume on the acre basis, between 50 and 60 thousand feet board measure. COMPARISON BY VOLUME BOARD MEASURE The removal of 40 per cent of the number of merchantable trees from a virgin selection stand of western yellow pine, even though they contain 60 per cent of the volume board measure, does not result in 8 University of California — Experiment Station mensurational changes in the remaining trees sufficiently definite, after 18 years, to warrant separate volume tables for the residual stand. This conclusion was reached after checking the actual volumes of the trees taken from the virgin and cut-over stands against the United States Forest Service general volume table for western yellow pine, Site I. Aggregate tree volumes expressed as percentage difference from the corresponding aggregate tabular volumes are as follows : For 285 trees from the virgin stand, + 6.3 per cent. For 110 trees from the cut-over stand, + 5.8 per cent. Detailed analyses of volume relations are given on pages 13 to 16. COMPAEISON BY TAPER Diameter inside bark at each tenth of stem height was correlated with the tenth of height at which the diameter measurement was taken, with diameter breast high inside bark, with height of tree, and with tree class. On the basis of this part of the investigation, taper tables for the species on Site I were constructed. Contrary to hypothesis, the form of the trees from the cut-over stand in 1928, after 18 years of growth under released conditions, does not differ significantly from the form of the trees grown under virgin conditions, that is, from the relative 1909 tapers of the trees from the cut-over stand and the relative 3909 and 1928 tapers of the trees from the virgin stand. Hence the inside bark tapers presented (table 4) are based upon the average of the four sets. Bark thickness at breast height of the cut-over stand was found to be about 8 per cent less than that of the virgin stand ; hence the inside bark diameters at breast height of table 4 are based upon bark thick- ness of the trees from the virgin stand only. Therefore the taper tables strictly apply only to virgin western yellow pine. Table 5 gives the corrections to be added to the values of table 4, to obtain taper by tree class. Methods of making detailed analysis of tree taper from the basic data are explained on page 17. Bul. 540] Partial Cutting in Western Yellow Pine TABLE 4 Per Cent Taper of Western Yellow Pine, Site Quality I, Average of All Tree Classes* Diameter breast high outside bark, in inches Diameter breast high inside bark, in inchest Per cent length from breast-height to tip 10 20 30 40 50 60 70 80 Diameter inside bark in per cent of diameter breast high inside bark Total height of tree, 40 feet 8 6.7 100.0 91.2 83.1 76.9 69.6 61.7 54.1 45.9 35.3 21.9 12 10.2 100.0 91.2 83.1 76.9 69.7 61.8 54.3 46.1 35.5 22 16 13 6 100.0 91.2 83.1 76.9 69.7 62.0 54.5 46.4 35.7 22.1 Total height of tree, 60 feet 8 6.7 100.0 91.4 83.8 77.9 70.7 62.8 55 46.2 35 3 21.9 12 10.2 100 91.4 83.8 77.9 70.8 62.9 55.2 46.4 35.5 22 16 13 6 100.0 91.4 83.8 77.9 70.8 63.1 55.4 46.7 35.7 22.1 20 17.1 100.0 91.4 83.8 77.9 70.9 63.2 55.6 46.9 35.9 22.2 Total height of tree, 80 feet 8 6.7 100.0 91.5 84.5 78.9 71.9 64.0 55.8 46 6 34.8 21.9 12 10.2 100.0 91.5 84.5 78.9 72.0 64 1 56.0 46.8 35 22.0 16 13.6 100.0 91.5 84.5 78.9 72.0 64.3 56.2 47.1 35.2 22.1 20 17.1 100.0 91.5 84.5 78.9 72 64.4 56.4 47.3 35.4 22.2 24 20 8 100.0 91.5 84.5 78.9 72.0 64.5 56.6 47.5 35.6 22.3 28 24 5 100.0 91.5 84 5 78.9 72.0 64.6 56.8 47.8 35.8 22.5 32 28 3 100.0 91.5 84.5 78.9 72 64.8 57.1 48.1 36.0 22 6 Total height of tree 100 feet 12 10.2 100.0 91.6 85.2 80.0 73.2 65.3 56.9 47.2 35.6 22.0 16 13.6 100.0 91.6 85.2 80.0 73.2 65.5 57.1 47.5 35.8 22.1 20 17.1 100.0 91.6 85.2 80.0 73.3 65.6 57.3 47.7 36.0 22.2 24 20 8 100.0 91.6 85.2 80.0 73.3 65.7 57.5 47.9 36.2 22.3 28 24.5 100.0 91.6 85.2 80.0 73.3 65.8 57.7 48.2 36.4 22.5 32 28.3 100.0 91.6 85.2 80.0 73.3 66.0 58.0 48.5 36.6 22.6 36 32.1 100.0 91.6 85.2 80.0 73.3 66.1 58.2 48.7 36.9 22.7 40 35.9 100.0 91.6 85.2 80.0 73.4 66.3 58.4 49 37.1 22.9 Total height of tree, 120 feet 12 10.2 100.0 91.7 85.9 81.0 74.4 66.5 57.7 47.6 35.7 22.0 16 136 100.0 91.7 85.9 81.0 74.4 66.7 57.9 47.9 35.9 22.1 20 17.1 100.0 91.7 85.9 81.0 74.5 66.8 58.1 48.1 36.1 22.2 24 20.8 100.0 91.7 85.9 81.0 74.5 66.9 58.3 48.3 36.3 22.3 28 24.5 100.0 91.7 85.9 81.0 74.5 67.0 58.5 48.6 36.5 22.5 32 28.3 100.0 91.7 85.9 81.0 74.5 67.2 58.8 48.9 36.7 22.6 36 32.1 100.0 91.7 85.9 81.0 74.5 67.3 59.0 49.1 37.0 22.7 40 35.9 100.0 91.7 85.9 81.0 74.6 67.5 59.2 49.4 37.2 22.9 44 39.7 100.0 91.7 85.9 81.0 74.6 67.6 59.4 49.6 37.4 23.0 Total height of tree 140 feet 16 13.6 100.0 918 86.6 82.1 75.6 67.9 58.8 48.3 35.9 22.1 20 17.1 100.0 91.8 86.6 82.1 75.7 68.0 59.0 48.5 36.1 22.2 24 20.8 100.0 91.8 86.6 82.1 75.7 68.1 59.2 48.7 36.3 22.3 28 24.5 100.0 91.8 86.6 82.1 75.7 68.2 59.4 49.0 36.5 22.5 * Taper figures are averages of 1909 and 1928 figures from both virgin and cut-over stands, t Based on bark thickness of trees from virgin stand only. 10 University of California — Experiment Station TABLE 4— ( Continued) Diameter breast high outside bark, in inches Diameter breast high inside bark, in inchest Per cent length from breast-height to tip 10 20 30 40 50 70 80 90 100 Diameter inside bark in per cent of diameter breast high inside bark Total height of tree, 140 feet (continued) 32 28 3 100.0 91.8 86.6 82.1 75.7 68.4 59.7 49.3 36.7 22.6 36 32.1 100.0 91 .8 86.6 82.1 75.7 68.5 59.9 49.5 37.0 22.7 40 35.9 100.0 91.8 86.6 82.1 75.8 68.7 60.1 49.8 37.2 22.9 44 39.7 100 91.8 86.6 82.1 75.8 68.8 60 3 50 37.4 23.0 48 43 5 100.0 91.8 86.6 82.1 75.8 68.9 60 5 50.3 37.6 23.1 52 47.3 100.0 91.8 86.6 82.1 75.9 69.1 60.7 50.5 37.8 23.2 Total height of tree , 160 feet 24 20 8 100.0 91.9 87.3 83.1 76.9 69.3 60.0 49.1 36.3 22 3 28 24.5 100.0 919 87.3 83.1 76.9 69.4 60.2 49.4 36.5 22.5 32 28.3 100.0 91.9 87.3 83.1 76.9 69.6 60.5 49.7 36.7 22.6 36 32.1 100.0 91.9 87.3 83.1 76.9 69.7 60.7 49.9 37.0 22.7 40 35.9 100.0 91.9 87.3 83.1 77.0 69.9 60.9 50 2 37.2 22.9 44 39.7 100.0 91.9 87.3 83.1 77.0 70.0 61.1 50.4 37.4 23.0 48 43.5 100.0 91.9 87.3 83.1 77.0 70.1 61.3 50.7 37.6 23.1 52 47.3 100.0 91.9 87.3 83.1 77.1 70 3 61.5 50.9 37.8 23.2 56 51.1 100.0 91.9 87.3 83.1 77.1 704 61.8 51.2 38.0 23.3 Total height of tree , 180 feet 32 28.3 100.0 92.0 87.9 84.1 78.0 70.7 61.4 50 37 22.6 36 32 1 100.0 92 87.9 84.1 78.0 70.8 61.6 50.2 37.1 22.7 40 35 9 100.0 92 87.9 84.1 78.1 71.0 61.8 50 5 37.3 22.9 44 39.7 100.0 92.0 87.9 84.1 78.1 71.1 62.0 50.7 37.5 23.0 48 43.5 100.0 92.0 87.9 84.1 78.1 71.2 62.2 51.0 37.7 23.1 52 47.3 100.0 92.0 87.9 84.1 78.2 71.4 62.4 51 2 37.9 23.2 56 51.1 100.0 92.0 87.9 84.1 78.2 71.5 62.7 51 5 38.1 23.3 60 54.9 100.0 92.0 87.9 84.1 78.3 71.7 62.9 51.7 38.4 23.4 64 58.6 100.0 92.0 87.9 84.1 78.3 71.8 63.1 52.0 38.6 23.6 68 62.4 100 92.0 87.9 84.1 78.3 71.9 63.3 52.2 38.8 23.7 72 66.2 100.0 92.0 87.9 84.1 78.4 72.1 63.6 52.4 39 23.8 Total height of tree, 200 feet 44 39.7 100.0 92.1 88.6 85.1 79.3 72.3 62.9 51.1 37.5 23.0 48 43.5 100.0 92.1 88.6 85.1 79.3 72.4 63.1 51.4 37.7 23.1 52 47.3 100.0 92.1 88.6 85.1 79.4 72.6 63.3 51.6 37.9 23.2 56 51.1 100.0 92.1 88.6 85.1 79.4 72.7 63.6 51.9 38.1 23.3 60 54.9 100.0 92.1 88.6 85.1 79.5 72.9 63.8 52.1 38.4 23.4 64 58.6 100.0 92.1 88.6 85.1 79.5 73.0 64.0 52.4 38.6 23.6 68 62.4 100.0 92.1 88.6 85.1 79.5 73.1 64.2 52.6 38.8 23.7 72 66.2 100.0 92.1 88.6 85.1 79.6 73.3 64.5 52.8 39 23.8 76 70 100.0 92.1 88.6 85.1 79.6 73.4 64.7 53.1 39.2 23.9 Total height of tree, 220 feet 56 51.1 100.0 92.2 89.4 86.2 806 73.9 64.4 52.2 38.2 23.3 60 54.9 100.0 92.2 89.4 86.2 80.7 74.1 64.6 52.4 38.5 23.4 64 58.6 1000 92.2 89.4 86.2 80.7 74.2 64.8 52.7 38.7 23.6 68 62.4 100.0 92.2 89.4 86.2 80.7 74.3 65.0 52.9 38.9 23.7 72 66.3 100.0 92.2 89.4 86.2 808 74.5 65.3 53.1 39.1 23.8 76 700 100.0 92.2 89.4 86.2 80.8 74.6 65.5 53.4 39.3 23.9 * Taper figures are averages of 1909 and 1928 figures from both virgin and cut-over stands. t Based on bark thickness of trees from virgin stand only. Bul. 540] Partial Cutting in Western Yellow Pine 11 TABLE 5 Deviation of Percentage Diameters (Taper) by Tree Class From the Average for All Classes Combined* Per cent length from breast-height to tip Tree class 10 20 30 40 50 60 70 80 90 100 Deviation of percentage diameters from the average for all classes combined 1 2 3 4 5 6 7 -0 5 -0.4 -0.8 +1.0 +10 +10 -0.9 -0.8 -1.1 +1.0 +14 +2.3 -1.2 -1.2 -0.7 +12 +11 +3.9 -1.2 -1.6 +0.2 +1.6 -0.5 +5.5 -0 5 -1.3 -2.0 +1.3 +2.5 -1.6 +7.5 - 2.0 - 1.3 - 2.5 + 2.8 + 3.9 - 2.1 +10.0 - 3.9 - 1.2 - 3 2 + 2.8 + 5.4 - 2.1 +11.9 - 3.8 - 0.9 - 3.5 + 16 + 6.2 - 1.5 +12.8 - 2.9 - 0.6 - 3.2 + 0.2 + 6.1 +12.4 To be added to the values of table 4 for taper curves by tree class. COMPAEISON BY DIAMETEE GKOWTH ALONG THE STEMS By definition, the following relation exists in the basic data: Du />, + A, 910-1928 i n which D 1909 is the diameter in inches at any point along the stem in 1909, Z> 1928 is the diameter at the same point in 1928, and A 1910 _ 1928 is the diameter growth at that point during the time interval. The analysis of the tapers discloses that for trees of the same tree class, total height, and diameter breast high, there is no significant difference in the relative values of either D 1909 or Z> 1928 — that is, in taper — between the trees from the virgin and cut-over stand. But D 1909 and D 1Q28 are large in comparison with A 19 i _ 1928 , and their very dimensions may entirely overshadow the relatively small though sig- nificant differences in A 1910 -i 928 following partial cutting in the virgin stand. On this account the diameter growth at ten equidistant points along the stem of the trees from the cut-over stand was compared with the the diameter growth at the same relative points along the stems of the trees from the virgin stand. Figure 2 portrays graphically the final results by tree class. The excess of periodic diameter growth of the cut-over stand over that of the virgin represents the acceleration of diameter growth for constant height growth, following a selection cutting 18 years before. Classes 1, 3, and 5 — the dominant trees in their respective age groups — show the greatest acceleration, whereas classes 2 and 4 — the codominants — show comparatively little. The acceleration in class 6 is least, but the growth before release is exceeded only by that of class 1. The ability of 12 University of California — Experiment Station ^n r Co>f-oyer()((> frees) UA— V ^3 4—4- l//rg/r? (40 treesJ f/ass / (of- oyer (3 frees) *F=X x (/&ss 2 \//r (?4frees) 1_J I I * 3 (of-oyer(25 frees) \ I I I i i r + ^ ■+-- I I I (/ass 4 1 I 1_ rr\ i Mro//? (49 frees) J I I I rs 3 (of-oyer ()4 frees) (/ass 3 J I L Mrcs/f? (40 frees) LlJ I L_ *' \( of- oyer (3 'frees) (/ass C f/ro/r? (30 frees) l_j i i «5 (of- oyer//? frees) Mi l (/ass >-4 4- V/r4/f7 (/7 frees) J I I I O /O ZO 30 40 SO GO 70 SO 30 SOO Per cerf of ' /eryt/? 110 ^ 285 or 3.5 ± 1.68 per cent. 14 University of California — Experiment Station Hence the difference between the volume ratios is about twice the standard error of the difference — just enough to raise doubt as to the homogeneity of the two stands ; this, in turn, suggests further analysis. ■t/5 to $ o s I *7 5 ""•"x. ^ 31 1*2 35 ^ f -21 & \"z \ » ?0 §^5 + /o \ to /O 20 30 40 50 GO 70 SO IO / 3t 3,4, '34 ■Z4 ; v \ / x / V I 1 \ 1 * ■>4.~ / / \33 35 yy. 2 4 28 = 0.158 ± 0.058, showing a very weak relation. For Bul. 540] Partial Cutting in Western Yellow Pine 15 +/s -h/o 5> + IS * \ I2» }--l > I ^*>-^ y 1 ' \ / + 5 V + 12 IO .4- 8 \ -5 \ '*\ ^' -tcr 5 to / 4 for relative wood growth at breast height. In bark thickness at breast height, as stated on page 24, the trees taken from the cut-over stand averaged about 8 per cent less, throughout the range of diameters encountered, than those from the virgin stand. Bul. 540] Partial Cutting in Western Yellow Pine 17 TREE TAPERS The 1909 and 1928 taper curve of each tree — plotted in the field on Forest Service form 558a at the time the stem analyses were taken in 1928 — was divided into ten sections of equal length from breast height to the tip ; and for purposes of better comparison between large and small trees, section heights were translated to percentage of total height above breast height, and section diameters inside bark to per- centage of diameter at breast height inside bark. The example of table 6 may serve to clarify the procedure used. Section heights of the 1909 stem of this sample tree are at 8.30-foot intervals, and for the 1928 stem at 10.75-foot intervals from breast height. TABLE 6 Translation 1 of Taper Measurements in Inches to Percentile Taper Measurements for Tree Number 66, * Class 1, Virgin Stand 1909 Taper 1928 Taper Section height in per cent of height above breast height Diameter inside bark, in inches Diameter inside bark, in per cent of diameter breast high inside bark Section height, in per cent of height above breast height Diameter inside bark, in inches Diameter inside bark, in per cent of diameter breast high inside bark 13.2 100 19.7 100 10 11.5 87 10 18.4 93 20 10.8 82 20 17.4 88 30 10.6 80 30 16 81 40 10.2 77 40 14 3 72 50 8.5 64 50 12 6 64 60 6.9 52 60 10.6 54 70 5.6 42 70 8.2 42 80 4.1 31 80 5.7 29 90 2.7 20 90 3.6 18 100 100 * In 1909 the diameter breast high inside bark was 13.2 inches, and the height above breast height 83 feet. In 1928 the diameter breast high inside bark was 19.7 inches, and the height above breast height 107.5 feet. With the data put up in this form the evident and positive relations which are associated with tree size only, are eliminated because upper diameters are in units which in themselves are independent of size ; for instance, the diameter in inches halfway up a 10-inch tree is obviously less than the diameter halfway up a 60-inch tree, even should the percentage diameters be the same. It follows that identical per- centage diameters at corresponding percentile heights mean identical form — a fact which may be completely hidden if absolute units are used. 18 University of California — Experiment Station Site quality is, broadly at least, common to all the data, while such variables as age, crown size, and vigor, which make up the basic factors of tree classification, are treated together, though only in an indirect way, through the detection of form differences of the several tree classes. The 1928 Taper of the Trees from the Virgin Stand. — Attention was first focused on the 1928 taper of the trees from the virgin stand ; indeed, the 1909 tapers of both the virgin and cut-over stands might have been combined with it and the three sets analyzed as one, there being no reason to suspect that in their average values they should be at all unlike. Still the latter two sets cannot be considered as having been as accurately measured in the field as the former. This follows from the usual method of taking stem analyses. At each cross section of every tree, a penciled line was drawn from pith to cambium along the average radius. By definition this is average radius to the cambium of 1928, though the radius along this line to the 1909 annual ring may or may not have been average for any one section in 1909. Hence while the means of the 1909 radii become reliable with sufficient number of trees, greater dispersion is to be expected on account of the discrepancies inherent in the method of taking individual 1909 measurements. The attempt to correlate percentage diameter inside bark with percentile height, diameter breast high inside bark, and total height above breast height, as a curvilinear relation in four variables in the usual way, was unsuccessful because of the failure to translate the functional form of the regression equation to an alignment chart of the additive type, i.e., a chart with parallel axes. Since the trees must have zero diameter at their tips, and 100 per cent diameter at breast height, it follows that the percentile height axis and the per- centage diameter axis must meet at base and tip, necessitating a curved axis for one. or both of these variables in order to meet the other at the two necessary points. If the tapers were independent of either diameter inside bark at breast height or total height above breast height, a chart with one curved axis might have been constructed without difficulty by intersection. It was finally decided to study the relations at each given percentile height separately. Then percentage diameter inside bark was cor- related with diameter breast high inside bark in inches, and total height above breast height in feet, at each tenth of height above breast height. Table 7 sets forth the results, Bul. 540] Partial Cutting in Western Yellow Pine 19 TABLE 7 Correlation and Regression Coefficients of Diameter, Inside Bark for Known Diameter Breast High Inside Bark and Total Height Above Breast Height, at Given Percentage Heights Above Breast Height Per cent Correlation coefficient,* Regression coefficients* height n.23 fel2.3 bl32 10 0.224 +0.021 +0 006 20 .447 + .002 + .034 30 .602 + .003 + .052 40 .601 + .001 + .059 50 .641 + 039 + .058 60 .538 + .077 + .034 70 .495 + .032 + .041 80 .245 + .074 + .002 90 0.123 +0.035 -0 020 * Subscript 1 refers to per cent diameter inside bark; subscript 2 refers to diameter breast high inside bark in inches; subscript 3 refers to total height above breast height in feet. An alignment chart was next constructed for each regression equa- tion and deviations of the percentage diameters were plotted over the net regression lines for diameter breast high with average height above breast height, and for height with average diameter. The calculated straight lines indicated the best fit to the data, but as they were not harmonized with percentage height the following values were plottted over percentile height and adjusted by free-hand curves : (1) The means of the percentage diameters (fig. 5A). (2) The slope of the net regression line (6 12 . 3 ) of percentage diam- eter on diameter breast high at the several percentile heights (fig. 55). (3) The slope of the net regression line (6 13 . 2 ) of percentage diam- eter on total height at the several percentile heights (fig. 5C). Figures 6 and 7 portray graphically the final assemblage of the percentage diameter with the adjusted regression lines, figure 6 showing the fit to the data for diameter with average height, and figure 7 for height with average diameter. As a check on the work thus far the corrections for diameter breast high inside bark and total height were added to the curved diameters of figure 5A. Comparison of actual with calculated percentage diam- eters revealed that the standard error of estimate increases from base to tip as brought out in table 8. 20 University of California — Experiment Station loo X \! A > eo X ■ \ \ \ Y \ Q) Art \ \ • x ^ JO \ \ ► \ \ i »- ?° \ ^ o \ 10 10 to o 2> (1) / h x _ t v 5 I-. ■ ^*^ / "s N *0 ol -=i c "o /o ?o 30 4o so~ co no eo oo /oo Per ccr?J- cpF Je/7^/7 •fhosr? jbreos-r--£}e/gh~f i'o ~^//=> Fig. 5. — Curves that harmonize the relation of taper to tree size. A, The average taper of all trees. B, The net regression slopes of percentage diameter on diameter breast high harmonized with percentile height, C, The net regression slopes of percentage diameter on height harmonized with percentile height. Bul. 540] Partial Cutting in Western Yellow Pine 21 A further check was. afforded in the calculation of the board-foot volumes from the estimated taper curves of the same number of trees by diameter breast high outside bark and total height classes as were used in the volume table check. This operation was carried out after bark thickness at breast height was correlated with diameter breast high outside bark and total height, 7 A taper curve was drawn for each °a /o 20 3>a 40 30 ■' """^"N.^.^ c ' — + i- ' i i -5 II . - -_— — • - - \ ^\ 1 C/C755 5 1 1 1 1 a • . ' -r -5 + ^ -' r |\ j - \ ■ - — "" -^ \ C/ass 7 i i /O ?0 30 40 SO CO lO 80 DO /OO Per cent of tenyth from breast fie/ght to t/p Fig. 8. — Deviation of the taper of each tree class from the average taper of all classes combined. 26 University of California — Experiment Station 8 ? I! s <9 * I • 7 G 6 f" '?..£ * 2 t 4 3 ? 32 ^+-- + '2 e> 35 •" / / / 4? 2G 4^ 4?/ 5 7 ♦'9 U < ? /< 5 ? O 3 O -<* 3 ^ £? <£ a "7 O e o 3 O IC o )> D/c7rr?e-/-&f~ foreosJ- h /a/7 our < s/c/ ' + - — * + SI * ' 4C 30 30 <40 " 50 £>& 70 SO jO > /'&'77G>/ / +„ 2 *"» N // 21 43 B -+-. --+-- ---»-■—, 1 ' + -- 30 - + ' 35 47 45 n --+ / 20 40 60 30 /OO 120 140 160 180 BOO 2ZO 240 Total height in -feet I c K -»^ -' .-*^< y y' 6 15 fc*^" 3 1 9 10 15 20 25 30 35 40 45 Heiqht growth 1910-/ 928 in -feet SO D h— = — — — - ■ — • h — J r to 20 30 40 50 60 70 60 90 100 Per cent o-f Jenqth above breast heioht in IS09 Fig. 11. — Diameter growth along the stem as associated with A, diameter breast high; B, height; C, height growth; and D, percentile height, . Trees from the virgin stand. Bul. 540] Partial Cutting in Western Yellow Pine 31 6 7-S 1 A •K "■»•-- a '•"T 13 6 19 J <9 to +. 10 20 30 UQ 50 60 70 ^ D/ 3 ?a Q» £ PO 4<9 50 SO /00 /■?(? /*<9 /60 /so 200 220 240 V. 6 £ 1 1 B s,- " + - /4 22 /5 To-tal height in -feet ^6 0^ ^ 2 / + c ' \ N J ; v x n ,+ «; — r" \ J/ ^ 25 25 "•*+' 4 2 V 2 ^ 4 6 8/0/2/4-/6 IB Heiyhi- growth /9/0-/928 in -feet ? 2 4 £ u ? {ft D ^""""""* H h _J r - H t- ■ " 10 20 30 40 50 60 70 80 90 100 Rpr cent of lenqth above, breast heiaht in 1909 Fig. 12. — Diameter growth along the stem as associated with A, diameter breast high; B, height; C, height growth; and D, percentile height. Trees from the cut-over stand. 32 University of California — Experiment Station succeeding estimates, three of which were required, were made sep- arately for the two sets of data. In figures 11 and 12 the deviations of the actual periodic growth figures are plotted over the net regression lines for the virgin and cut-over stands respectively. The outstanding features common to both sets of data are the following : 1. Average diameter growth along the stem and size of tree — that is, diameter of trunk and total height — are practically independent of one another (figs. 11 A and B, and 12A and B) . 2. Average diameter growth along the stem and height growth of tree are interdependent. An analogy may explain this: Given two similar isosceles triangles so placed that the midpoints of their bases are common. Then the basal measurement of one over that of the other is increased by increasing its altitude ; and measurements parallel to the base are increased by the same amount. Conversely, by increasing basal measurement of one over that of the other, its altitude is likewise increased. On the other hand, tree form apparently tends to change after release, as is brought out upon comparing figures 11D and 12D, though the time interval has not been long enough to affect significantly the relative tapers in 1928. In general, the periodic diameter growth of the virgin stand decreases slightly from breast height to a point about one-quarter of the way up and thereafter increases ; while the diameter growth of the cut-over trees decreases slightly from breast height to tip. Comparison of diameter growth of the virgin and cut-over stands by tree class is made in figure 2. The plotted points are the average deviations of the actual diameter growth from the estimated, for given percentage heights and height growth of the trees, added to the esti- mated diameter growth based upon average height growth of each tree class of the cut-over stand. CONCLUSION The results of the comparison of the trees from the virgin stand with those from the cut-over stand are not sufficiently definite to warrant an assertion that partial logging in western yellow pine is followed by increase of volume growth rate in the trees of the residual stand. From the diameter, height, and growth data of table 10, volume growth during the period 1910-1928 is about the same in the two stands. The greater diameter growth of the trees from the cut-over stand has been offset by the greater height growth of the trees from the virgin stand. 8m-10,'32