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This article is condensed from a paper of the same title presented at the 3rd IUFRO Workshop on Connection between Silviculture and Wood Quality through Modeling Approaches and Simulation Softwares, held in France on September 5-12, 1999. For a copy of the paper with complete description of the sample installations and analysis procedures, either contact one of the authors or obtain it from the SMC website, http://www.cfr.washington.edu/smc/).

In early 1998, the SMC defined and tested a procedure for routine measurement of individual tree branch data on its field installations. The results of the tests were reported at the Fall 1998 SMC Policy Committee meeting and the procedure was formally adopted for implementation. The procedure was designed to allow data to be collected on a reasonably large sample of trees within each treatment plot. It was designed for convenient data collection and repeatability with minimal impact on field crew time. The procedure obtains the horizontal diameter of the largest branch in the first whorl above breast height. The number of branches in the whorl and in the half-internode above and below it that are at least one-half the diameter of the largest branch are counted. The count data are segregated into “nodal” and “internodal” categories. These data are taken on the 42 trees that have been designated as a permanent subsample for height measurement on each plot. The first whorl above breast height was chosen because it is conveniently reached and these branches are unlikely to have been damaged or broken by personnel measuring DBH. Counting branches was restricted to those that are at least one-half the diameter of the largest branch to simplify counting by excluding the many smaller branches and “whiskers” that tend to rapidly self-prune. This focuses data collection on those larger branches that are likely to persist and impact products. Segregating the count into “whorl” and “internodal” components is expected to provide information on the relative persistence and self-pruning of these types of branches over time. Of particular interest is the ability of the internode to “clean up” and eventually produce clear wood.

During 98/99, 5 Type I and 8 Type III installations were measured with the branch procedure. For Type I’s, this paper presents results for the ISPA, ISPA/2 and ISPA/4 plots; other plots undergoing thinning or other treatments will be analyzed later. For Type III’s, this paper presents results for the six planting densities. A randomized complete block experimental design governed establishment procedures for both types of installations. Installations are blocks, and a complete set of treatments exists in every block. Preliminary analyses used this design framework to establish whether or not spacing affects either or both breast-high branch diameter and number. To quantify the factors leading to differences in branch diameters and numbers among stand, the data was re-analyzed using a factorial treatment design under a general linear modeling framework. Site index and density were considered as factors, while all the other variables listed above (and their interactions) were considered for inclusion in the models. To gain more detailed knowledge of what is happening to the relationship between tree size and branch size as affected by stand conditions, we also modeled branch diameter as a function of tree DBH using orthogonal quadratic polynomials. We used the coefficients from these polynomials as primary data and tested for differences in coefficients between treatments using analysis of variance and analysis of covariance techniques.

Figure 1 presents average height and average height to crown base versus initial stand density for the 5 Type I installations sampled and shows that the live crown is now above breast height except for a few of the less dense plots.

Figure 1: Total (HT) and Crown Base (HCB) Height versus Density on 5 Type I Installations

Figure 2: DBH Verses Density on 5 Type I Installations

Therefore, most of the bh- branches are dead. Figure 2 presents average dbh versus initial stand density for these installations. Installation 731, which is at the lowest site and highest elevation, has much smaller trees than the others.

Mean branch count ranged from about 6 to 11 branches per tree. Counts on individual trees ranged from about 3 to 20 branches. Remember that only branches that were at least half the diameter of the largest whorl branch were counted. Figure 3 presents trends of mean branch count versus stand density.

While there are weak trends within some installations, there is no overall consistent pattern and ANOVA found no statistically significant difference in branch count among the stand densities. Each installation was planted with the same seedling stock hence the lack of differentiation in branch counts was expected at this early stage in stand development. However, each owner planted seedlings that were likely different in both genetic origin and seedling type which may explain the differences in branch counts between installations. The current counts are likely to be maximum values and we expect they will decline in the future through self-pruning.

The usual expectation is that widely spaced trees will have more vigorous crowns, faster growth rate, and slower crown recession which combine to produce longer-lived, larger branches. This is confirmed by trends in Figure 4 which indicate larger branches at lower stand densities in each installation.

Furthermore, as stand density decreases, the rate of change in branch diameter increases greatly; the slope from ISPA/2 to ISPA/4 appears to be at least double the slope from ISPA to ISPA/2. Finally, when comparing installations, those that had lower original planting densities tend to have larger branches. The installations with lower original densities were likely to have had slower crown recession and hence developed larger branches. To quantify these observations, ANCOVA of branch diameter was conducted under a factorial treatment design. There was no interaction between site and density, hence this term was dropped from the analysis. In the final analysis, the ISPA, ISPA/2, and ISPA/4 stand densities were represented by indicator variables representing their respective means, 550, 250, and 125 stems per acre (1359, 618, 309 stems per ha). The indicator variable D125 was set to 1 if the stand was in the 125 stems per acre class, zero otherwise. A similar variable (D250) was set to 1 if the stand was in the 250 class. Both variables set to zero indicates the 550 class. Installations were placed into high or low site groups based on whether 50 year site index was above or below a value of 120 ft (36.6 m). The LOSITE indicator variable was set to 1 to represent the low site group, zero otherwise.

Branch diameter was significantly related to stand density, site, and an interaction between site and height-above-bh. Height-above-bh is a surrogate for the age of the bh whorl and its distance from the apical meristem; it includes both live and dead crown above bh. When stand density drops from ISPA (550 stems per acre) to ISPA/2 (250 stems per acre), branch diameter increases by 0.14 inches and when density drops from ISPA/2 to ISPA/4 (125 stems per acre), branch diameter increases by another 0.29 inches (Table 1); approximately double the change from ISPA to ISPA/2. As site changes from higher to lower, branch diameter decreases (see Figure 5).

Figure 5: Average Largest Branch Diameter vs. Density for different sites on 5 Type I installations with +/- 1 Standard Error bars

However, the effect of site cannot be fully interpreted without considering the interaction of site with height-above-bh which can be explained as follows. For trees of the same total height, those on a lower site are, on average, slower growing and therefore must be of a greater age. The bh branches on such trees are undoubtedly older than bh branches of faster growing trees on a higher site. Therefore, the bh branches of the lower site trees have more rings of accumulated growth on them and, on average, this has a positive effect on branch diameter. Conversely, bh branches on high sites have fewer rings of accumulated growth on them, and on average, this has a negative effect on branch diameter. An alternative perspective of this interaction is that, for a given stand density, a taller stand implies more shading of lower branches, reduced growth efficiency of these branches, and greater crown recession. Bh branches would either be very weak or dead. Thus, for a given stand density, greater height implies more shading and earlier branch suppression and death hence a negative effect on branch diameter. This would be more noticeable on a high site hence the negative sign for HABH coefficient for above average sites and positive sign for HABH*LOSITE (representing low sites).

It was expected that branch diameter and stem diameter would follow an allometric relationship. This was examined by estimating quadratic allometric relationships by regression analysis for the sample trees on each plot. The fifteen sets of coefficients obtained were analyzed with ANOVA as a randomized complete block design. The quadratic term, which was negative indicating a slight curvature downward for larger diameters, was not statistically significant. It was also found that intercepts were significantly different among densities and that the coefficients of the linear term of the allometric relationships differed significantly between installations but were not significantly influenced by stand density. Further investigation of the linear coefficients found that they were significantly and negatively influenced by height-above-bh; i.e., the linear slope of the allometric relationship is flatter for stands with a greater height-above-bh. This implies that, for a given dbh, a taller stand, hence a greater height-above-bh, has smaller branches. Taller stands tend to have bh-branches that are growing more slowly due to increased shading that reduces crown efficiency at bh.

Figures 6 and 7 present average height and dbh versus planting density for the sample trees in the 8 type III installations. There is a trend toward higher base of live crown with higher density but almost all presently have the base of the live crown at or below breast height hence virtually all branches are alive. Installation 905 has a pattern contrary to the others which we attribute to lack of site uniformity; the 100 and 400 stems per acre plantings are close together on a flat hilltop while the others are on its steep slope.

Figure 6: Smoothed Total (HT) and Crown Base (HCB) Height verses Density on 8 Type III Installations

In these installations, trees planted at the low densities are often smaller than those planted at the higher densities, a reversal of common expectations (i.e., that trees are smaller at higher planting densities). Note that seedlings of the same genetics and nursery stock were planted at all densities within a given installation. This phenomenon, where the relationship between tree size and planting density is reversed, is often referred to as the “cross-over” effect. This did not occur in the Type I installations which were planted at a uniform density, grew for several years and were then spaced. Since height nd diameter of trees on Type III installations are affected by the crossover effect, this may influence the effect of stand density on branching.

Although some apparent changes in branch count with stand density occur within some installations (Figure 8), no consistent patterns appear and ANOVA found no statistically significant differences. Apparent differences between installations are likely due to differences in genetics of the planting stock used by the various landowners.

Figure 8: Smoothed Number of Branches versus Density on 8 Type III Installations

Figure 9 presents trends of mean branch diameter with stand density. There appears to be a tendency toward larger branches with lower density (wider spacing). To investigate this, ANCOVA was conducted under a factorial treatment design with density and site as the factors. Analogously to the situation for Type I installations, indicator (or “dummy”) variables were set up to represent density classes (D100 = 1 if 100 stems per acre, 0 otherwise; D200 = 1 if 200 stems per acre, 0 otherwise; etc., five dummy variables in all to represent six densities). Again, two site classes were investigated, a “high” and a “low” class.

Figure 9: Smoothed Largest Branch Diameter versus Density on 8 Type III Installations

Branch diameter was significantly related to stand density, crown length, initial dominant height, and an interaction between initial dominant height and crown length. The stand density effect is only significant for 100 through 440 stems per acre versus 680 & 1210 stems per acre; at this time, there is little differentiation due to density except that the two highest stand densities have significantly smaller branches than the rest (Tables 2 and 3). At the present stage of development in these young stands, only the densest stands have developed sufficient crown closure to shade bh branches and suppress their growth. In the future, we expect the lower density stands to progressively develop more crown closure and shading that will suppress branch growth and eventually lead to crown recession. Crown length is also significant with larger branch diameters being associated with longer crowns. Presently, the base of the live crown is below bh for all densities but those with longer crowns are likely to be less shaded hence the bh branches are likely to be more vigorous and growing faster in diameter. Larger branches are associated with initially taller trees; those that are taller are likely to be more vigorous. Note that, due to the crossover effect, denser plantations tend to have taller trees.

Table 1: Final Model for Largest Breast-high Branch Diameter in Type I Installations.

Table 2: Final Model for Largest Breast-high Branch Diameter in Type I Installations

Table 3: Average Largest Branch Diameter for significantly different density groups on Type III Installations

The negative coefficient on the interaction of crown length and initial stand height may be explained as follows. An extra foot of crown length adds more to branch diameter than an extra foot of total height. Even though taller trees may have larger dimensions (through allometric relationships), taller stands would have more shading of the lower branches suppressing their rate of growth. An alternative perspective is that, for a given crown length, a taller stand may have relatively smaller bh branches; on a taller tree, a fixed length of crown would occupy less of the total height which implies faster crown recession. Consider again the crossover effect; planting at wide spacing tends to produce shorter stands but the breast-height region of the crown in such stands is less shaded and may be more vigorous and producing faster branch diameter growth. In contrast, the taller trees in the denser stands have more shading of the crown at breast height thereby suppressing branch growth. The denser stands will begin crown recession more quickly (see Figure 6) which will slow and stop branch diameter growth sooner and result in smaller knots. Thus the crossover effect may yield the paradox that the less dense stands produce smaller trees with larger diameter branches and knots than same-age high-density stands.

Site was not significant in explaining differences in branch diameter among the Type III installations. This may be due to the difficulty in obtaining meaningful measures of site index in young stands or because these young stands are all growing uniformly fast and have not yet begun to differentiate according to site.

As in the Type I installations the allometric relationship between branch diameter and dbh was investigated. The 8 installations on 6 densities produced 47 quadratic allometric equations that were analyzed with ANOVA as a randomized complete block design. As with the Type I installations, it was found that intercepts were significantly different but the linear slope was the same for all densities, but unlike the Type I installations, it was found that the quadratic term was statistically significant. There is a small tendency for the relationship to curve downward as tree diameter gets larger in the Type III installations which indicates a potential maximum, or asymptotic branch size which may be different for stands grown under different conditions.

In the future, branch diameter and count will be obtained on the remaining SMC Type I and III installations and all subsequent re-measurements. It is expected that branch counts and diameters will change as these installations are re-measured and branches eventually die and self-prune. This will provide useful information quantifying the effects of treatments and treatment regimes on number, size, and persistence of branches.

Articles of Interest

Modeling Number and Size of Branches in Young Coastal US Douglas fir Plantations as Affected by Silvicultural Treatment

David Briggs, Professor & Director Stand Management Cooperative Eric Turnblom, Assistant Professor & Silviculture Project Leader College of Forest Resources, University of Washington

Figure 1: Total (HT) and Crown Base (HCB) Height versus Density on 5 Type I Installations

Figure 2: DBH Verses Density on 5 Type I Installations