Berrill & Dagley 2014 Stocking Guidelines for Aspen Restoration STOCKING GUIDELINES FOR ASPEN RESTORATION: PREDICTING TREATMENT PERSISTENCE AFTER SUCCESSIVE CONIFER REMOVALS Lake Tahoe Basin aspen‐conifer stand at Blackwood Creek before and after mechanical removal of smaller conifers
FINAL REPORT FOR SNPLMA ROUND 10 SCIENCE PROJECT MAY 2014 JOHN‐PASCAL BERRILL DEPARTMENT OF FORESTRY AND WILDLAND RESOURCES HUMBOLDT STATE UNIVERSITY, 1 HARPST STREET, ARCATA, CA 95521‐8299 PHONE: (707) 826‐4220; FAX: (707) 826‐5634 EMAIL: PBERRILL@HUMBOLDT.EDU CHRISTA M. DAGLEY DEPARTMENT OF FORESTRY AND WILDLAND RESOURCES HUMBOLDT STATE UNIVERSITY, 1 HARPST STREET, ARCATA, CA 95521‐8299 PHONE: (707) 826‐1220; FAX: (707) 826‐5634 EMAIL: CHRISTADAGLEY@GMAIL.COM Citation: “Berrill, J‐P.; Dagley, C.M. 2014. Stocking Guidelines for Aspen Restoration: Predicting Treatment Persistence after Successive Conifer Removals. SNPLMA Round 10 Science Project P051 Final Report. 18p.” 1 Berrill & Dagley 2014 Stocking Guidelines for Aspen Restoration SUMMARY Quaking aspen (Populus tremuloides) forest communities in the Lake Tahoe Basin are undergoing succession to conifers that impact aspen vigor and stifle natural regeneration. Removal of conifers from aspen stands is undertaken around the Lake Tahoe Basin. However, little is known about stocking and treatment persistence: specifically, how much growing space must we provide aspen trees and their root sucker regeneration for vigorous growth to be sustained until the next restorative thinning1? This report introduces the Aspen Stocking Assessment Model and provides examples of its use in simulating aspen‐conifer stand development before and after restorative thinning. Tree data collected in 2 ½ acre (one hectare) plots around the Lake Tahoe Basin were used to initiate the model. Different diameter‐limit thinning prescriptions (i.e., cut all conifer below a defined size) were simulated by removing records for smaller (cut) trees from the plot data and then recalculating density and average tree size for input into the Aspen Stocking Assessment Model. This approach ensured that model simulations were based on realistic pre‐ and post‐thinning values. Treatment persistence – defined here as the time taken for stands to return to their pre‐treatment crowding levels – varied according to pre‐treatment stand density, species composition, and thinning intensity. Thinning a remote aspen‐conifer stand at Ward Creek in fall 2009 removed hundreds of small conifer saplings, and numerous trees up to 14 inches (35 cm) DBH. The abundant cut material was hand piled into 50 piles per acre (124 per hectare) which collectively covered 10% of the ground area. Thinning more heavily would likely have created an unacceptable fire hazard from excessive down wood in this inaccessible area. The Aspen Stocking Assessment Model forecasted a 15‐year treatment persistence, after which time the stand had returned to pre‐treatment stand density index (SDI), and a second thinning was scheduled. For the second treatment, we compared three alternatives: 20, 24, or 30 in. (50, 60, or 75 cm) DBH limit thinning, and again forecast growth of each tree species using the Aspen Stocking Assessment Model. These treatments had 23‐, 29‐ and 40‐year persistence, respectively. The heaviest thinning treatment generated ~28 US short tons ac‐1 (~64 metric tons ha‐1) of dry cut wood. We also simulated thinning in an extremely crowded aspen‐conifer stand south of Lake Tahoe adjacent to Highway 89, which had fewer small conifer saplings than the Ward Creek stand but had more conifer density in terms of basal area and SDI. Here, thinning first to the 14‐inch DBH limit was expected to provide the greatest possible relief from crowding without excessive exposure to wind, followed by a second thinning to either 20‐inch (50 cm) or 24‐inch (60 cm) DBH limits. The first thinning reduced stand density by 23% and had treatment persistence of 17 years, and the alternate second thinning treatments had either 22‐ or 36‐year persistence, respectively. The Aspen Stocking Assessment Model indicated that 36 years after the 24‐inch DBH limit thinning, once the stand had again exceeded pre‐treatment SDI, the new cohort of regenerating conifers collectively represented only 14% of stand density; the remainder being aspen or large residual conifers that had grown larger than 30 in. (75 cm) DBH. Thinning the stand again by cutting only the young conifers (i.e., cut 14% of SDI) would have short treatment persistence. Therefore – after two successive thinning treatments with progressively higher DBH limits ‐ any subsequent prescription calling for thinning more than 14% of SDI would necessarily involve cutting/killing some conifer >30 inches DBH. 1
For convenience we use the term “thinning” to describe conifer removal treatments designed primarily to relieve crowding but with the expectation that a new cohort will be initiated (usually defined as “partial harvesting”). 2 Berrill & Dagley 2014 Stocking Guidelines for Aspen Restoration ASPEN STOCKING ASSESSMENT MODEL The Aspen Stocking Assessment Model is a flexible, transparent spreadsheet‐based model that allows the user to schedule restoration thinning and ‘grow’ aspen‐conifer stands forward in time, before and after multiple thinning treatments. Thinning is specified by the user by entering a value for density (number of trees per hectare) of each tree species remaining after thinning and their average diameter (DBH; cm). The user obtains this information by manipulating a basic forest inventory ‘tree list’ in Excel: sorting by species and filtering on tree DBH to remove smaller conifers, then calculating density and average DBH of each species remaining. New ‘cohorts’ (age‐classes) of trees can be introduced at any time by entering density values for each regenerating tree species at the estimated time that species grows past breast height (4.5 ft.; 1.37 m above ground) and hence has DBH > 0. The Aspen Stocking Assessment Model comprises multiple worksheets that predict tree growth and calculate the associated changes in tree size and stand density in each cohort (Figure 1). These variables are used to calculate or estimate associated competition‐
induced mortality, change in crown ratio, tree height, and live crown base height, based on user‐defined DBH and density, in annual time steps. Individual tree growth models, height‐diameter models, and crown ratio models are implemented in Visual Basic functions embedded within the spreadsheet model. Figure 1: Aspen Stocking Assessment Model worksheets for development of DBH and SDI over time. 3 Berrill & Dagley 2014 Stocking Guidelines for Aspen Restoration LAKE TAHOE BASIN ASPEN MODELS A set of aspen models were developed using data collected in aspen‐conifer stands around the Lake Tahoe Basin and incorporated into the Aspen Stocking Assessment Model. The aspen growth model predicts tree basal area increment (BAI) as a function of DBH, crown ratio (CR), stand density in terms of basal area (BA), geographic location (east or west shore of Lake Tahoe) and elevation (Berrill & Dagley 2012). The aspen growth model depends on CR which was found to be influenced by stand density. Therefore an aspen CR model was developed using data from Lake Tahoe aspen‐conifer stands (Berrill & Dagley 2012). Competition‐induced mortality of aspen and its common conifer associates is predicted to occur when modeled stands reach the upper limit of stand density, defined by plot data from Lake Tahoe aspen‐conifer stands. This upper limit is lowest for aspen (SDI = 1700 metric), therefore mortality of aspen is predicted to occur at lower levels of stand density than mortality of conifer (Berrill & Dagley 2014). ANCILLARY MODELS A suite of ancillary models were developed and incorporated into the Aspen Stocking Assessment Model, enabling simulation of growth, tree size, and treatment persistence in various aspen‐conifer mixtures (Appendix 1). Height‐diameter equations were developed to predict total tree height (HT) from DBH for aspen, Jeffrey pine, lodgepole pine, red fir and white fir. Crown ratio models were developed for Jeffrey pine, lodgepole pine, red fir and white fir. The Aspen Stocking Assessment Model uses these models and logic to hold live crown base height at a steady height until sometime after thinning when the process of density‐induced crown rise resumes. Growth models were developed to predict BAI for Jeffrey pine, lodgepole pine, red fir and white fir growing in association with aspen around the Lake Tahoe Basin. Additionally, we developed ‘early growth models’ to predict growth of regenerating aspen and conifer ranging in size from zero DBH up to the smallest size of tree measured for data used to develop the aspen and conifer tree BAI models. The ancillary conifer BAI and CR models were fitted to data where conifers other than white fir were not well represented, and therefore should only be regarded as ‘preliminary models’ implemented within the Aspen Stocking Assessment Model to allow simulation of different aspen‐
conifer mixtures. 4 Berrill & Dagley 2014 Stocking Guidelines for Aspen Restoration THINNING SIMULATIONS Tree data collected in 2 ½ ac (1 ha) plots around the Lake Tahoe Basin were used to initiate the Aspen Stocking Assessment Model. Different diameter limit thinning prescriptions (i.e., cut all conifer below a defined size) were simulated by removing records for smaller (cut) trees from the plot data and then recalculating density and average tree size after this ‘thinning’. These new post‐treatment data were input into the Aspen Stocking Assessment Model which then ‘grew’ the thinned stand forward in time. This approach ensured that model simulations were based on realistic pre‐ and post‐thinning values. Treatment persistence – defined here as the time taken for stands to return to their pre‐treatment ‘level of crowding’ (i.e., SDI) – varied according to pre‐treatment stand density and species composition, and thinning intensity. Ward Creek Simulations Pre‐treatment data from the 2 ½‐ac (1‐ha, 200 x 50 m) monitoring plot in a remote, inaccessible part of the Ward Creek drainage at 6670 ft. (2033 m) elevation (WA38; Berrill et al. 2009; Berrill & Dagley 2010) were input into the Aspen Stocking Assessment Model; average DBH and density data were entered into cells for each species at ‘Year 0’ in the worksheets titled <DBH> and <Density>. Model output indicated that without any thinning or other disturbances reducing conifer tree and regeneration densities, succession to conifer would be complete after approximately 120 years. During this time, stand density rose above SDI = 1000 (metric) leading aspen to enter the so‐called “zone of imminent mortality” (i.e., > 60% of maximum SDI; Long 1985) where mortality gradually reduced aspen densities in approximate balance with aspen growth. At Year 67, total SDI exceeded the upper limit of SDI=1700 (metric) for aspen leading to rapid aspen decline and replacement by conifer (Berrill & Dagley 2014). Lodgepole pine also exhibited gradual decline as more growing space become occupied by shade‐tolerant fir in both the overstory and understory (Figure 2). A 14‐inch (35 cm) DBH limit thinning was implemented at WA38 in fall 2009 by the USFS, generating cut conifer wood manually piled in relatively small burn piles (av. 9.3 ft. diameter; range: 6.6‐14.1 ft.) numbering 50 per acre (124 piles per hectare) (Dagley et al. 2012). The stemwood volume (excluding branches/foliage) of cut conifers >8 in. (20 cm) DBH totaled ~1460 ft3 ac‐1 (42 m3 ha‐1). Conifers < 8 in. DBH were plentiful and presumably contributed a large volume of additional cut wood, branches, and foliage to these piles. This treatment reduced SDI by only 16%, with a modest ‘boost’ in average DBH (increase DBH of LP: 2 in. (9 cm); RF: 2 in. (10 cm); and WF: 4 in. (19 cm)) by removing the smallest individuals of each species and a large reduction in number of (smaller) trees per acre (reduced density LP 26%, RF 65%, and WF 44%). Model output indicated that the WA38 stand returned to pre‐treatment SDI after ~13 years, at which time aspen represented 15% of stand BA giving only 1% improvement over pretreatment composition of 14% aspen BA. In the absence of repeat treatment, the Aspen Stocking Assessment Model projected a decline in aspen to 5% of stand BA after 100 years and <2% after 120 years (Figure 3). To forestall this future decline, we simulated a second restoration thinning treatment in Year 15. Assuming that the first thinning treatment (Year 2) had enhanced wind firmness among residual trees at WA38, we simulated and compared three alternative thinning prescriptions: ‘light thin’ (20 inch/50 cm DBH limit), ‘medium thin’ (24 in./60 cm DBH limit), and ‘heavy thin’ (30 in./75 cm DBH limit) (Figures 4‐6). 5 Berrill & Dagley 2014 Stocking Guidelines for Aspen Restoration Figure 2: No treatment “do nothing” scenario ‐ simulated change in stand density index (SDI), WA38. Figure 3: One thinning cuts conifer <14 in. DBH ‐ simulated change in stand density index (SDI), WA38. 6 Berrill & Dagley 2014 Stocking Guidelines for Aspen Restoration The ‘light thin’ cut all conifer <20 in. (50 cm) DBH, reduced SDI by 29%, and removed 27 trees ac‐1 (67 stems ha‐1) of residual conifer and 80 trees ac‐1 (200 trees ha‐1) of regenerating conifer saplings. This enhanced aspen’s representation in the stand from 15% to 21% of total stand BA. The stand returned to pre‐
treatment stand density in Year 38, resulting in treatment persistence of 38‐15=23 years (Figure 4). Figure 4: Second thin cuts conifer <20 in. DBH ‐ simulated change in stand density index (SDI), WA38. The ‘medium thin’ cutting all conifer <24 in. (60 cm) DBH gave a 38% reduction in stand density. Removal of 37 trees ac‐1 (92 stems ha‐1) residual conifers 14‐24 in. (35‐60 cm) DBH and 80 trees ac‐1 (200 stems ha‐1) regenerating fir saplings shifted species composition in favor of aspen from 15% up to 23% of stand BA represented by aspen. The stand returned to pre‐treatment SDI in Year 44, giving treatment persistence of 44‐15=29 years (Figure 5). The ‘heavy thin’ would prolong treatment persistence but generated much cut wood. The 30‐in. (75 cm) DBH limit resulted in removal of 117 residual overstory conifers 12‐30 in. (30‐75cm) DBH and all fir regeneration arising after the first thinning. Lodgepole pine regeneration (4 trees ac‐1; 10 stems ha‐1) were retained. In total, the thinning reduced SDI by 54% (Figure 6). The remaining conifers comprised 2.4 WF trees ac‐1 (6 stems ha‐1) averaging 33 in. (84 cm) DBH, 1.6 RF trees ac‐1 (4 stems ha‐1) av. 48 in. (123 cm) DBH, and 6 LP trees ac‐1 (14 stems ha‐1) av. 36 in. (91 cm) DBH. These very large 10 trees ac‐1 (24 stems ha‐1) collectively represented 69% of stand BA. 7 Berrill & Dagley 2014 Stocking Guidelines for Aspen Restoration Figure 5: Second thin cuts conifer <24 in. DBH ‐ simulated change in stand density index (SDI), WA38. Figure 6: Second thin cuts conifer <30 in. DBH ‐ simulated change in stand density index (SDI), WA38. 8 Berrill & Dagley 2014 Stocking Guidelines for Aspen Restoration Therefore this ‘heavy thin’ treatment left aspen representing 31% of stand BA; a doubling in aspen representation in terms of BA. After thinning in Year 15, the stand did not return to pre‐treatment SDI again until Year 55; an estimated treatment persistence of 40 years. At that time, in Year 55, the young firs regenerating after the Year‐15 treatment comprised one third of stand density (Figure 6). The volume of conifer stemwood cut during this 30‐in. DBH diameter limit thinning amounted to 3021 ft3 ac‐1 (212 m3 ha‐
1
), from conifer trees averaging 19 in. (48 cm) DBH and 60 ft3 (1.71 m3) stemwood per tree (not counting cut branches and foliage). This massive volume of cut conifer wood greatly surpassed the conifer wood volume cut in year 2 which was hand‐piled into 50 relatively small piles ac‐1 (124 piles ha‐1) that collectively covered 10% of the ground area within the 2 ½‐ac (1‐ha) plot at Ward Creek. This suggested that the 30‐inch DBH diameter limit thinning created too much down wood for this inaccessible area, and that more frequent light thinning and associated pile burning treatments would be needed to relieve crowding and restore aspen dominance. Girdling a few larger conifers to leave the dead wood standing and leaving other large conifer logs lying intact as coarse woody debris are alternatives to hand‐piling and burning that merit consideration given the fuel disposal problem that otherwise precludes heavier thinning. Big Meadow Simulations Tree data from a 2 ½‐ac (1‐ha) monitoring plot at 7100 ft. (2165 m) elevation adjacent to Highway 89 at Big Meadow, south of Lake Tahoe (SSP24; Berrill et al. 2009; Berrill & Dagley 2010) were input into the Aspen Stocking Assessment Model. Aspen represented 24% of stand BA, with red and white fir representing 66% of stand BA. In terms of average DBH, the aspen were outsized by all other conifers. Aspen (52 trees ac‐1 /128 stems ha‐1) were outnumbered by white fir >8 in. (20 cm) DBH (142 trees ac‐1/351 stems ha‐1). Lodgepole pine (11 trees ac‐1/28 stems ha‐1) were more common that Jeffrey pine (3 trees ac‐1/8 stems ha‐1) and red fir (~1 tree ac‐1/3 stems ha‐1) > 8 in. DBH. In the absence of thinning, the model predicted that white fir would dominate at the expense of aspen (Figure 7). Thinning all small conifer <14 in. (35 cm) DBH (95 trees ac‐1/235 stems ha‐1 cut) improved aspen’s representation in the stand from 23% to 28% of stand BA. The stem wood volume (not counting branches and foliage) of cut conifers >8 in. DBH totaled ~1065 ft3 ac‐1 (75 m3 ha‐1). Conifers < 8 in. DBH were not common at SSP24 and presumably contributed a relatively small amount of additional cut wood, branches, and foliage for disposal. After the initial thinning in Year 2 reduced stand density by 23%, stand density returned to pre‐treatment levels around Year 19, equating to a predicted treatment persistence of 19‐2=17 years. After Year 19, residual white fir trees and a new cohort of red and white fir were predicted to progressively replace aspen that began to decline gradually once SDI exceeded 1000 (metric; lower limit of zone of imminent mortality for aspen) and declined rapidly once SDI exceeded aspen’s upper limit of 1700 (Berrill & Dagley 2014) (Figure 8). A second thinning was simulated in Year 19, removing conifers below a 20‐inch (50 cm) DBH limit including regenerating firs (4 trees ac‐1/10 stems ha‐1 of regenerating pines were retained). This treatment reduced total SDI by 27%, and shifted species composition from 27% aspen to 36% aspen in terms of stand BA. Conifer stemwood volume cut was similar to the first thinning, totaling ~1090 ft3 ac‐1 (76 m3 ha‐1) not counting branches and foliage. Stand density had once again returned to pre‐treatment levels by Year 41, giving a predicted treatment persistence of 41‐19=22 years (Figure 9). 9 Berrill & Dagley 2014 Stocking Guidelines for Aspen Restoration Figure 7: No treatment “do nothing” scenario ‐ simulated change in stand density index (SDI), SSP24. Figure 8: One thinning cuts conifer <14 in. DBH ‐ simulated change in stand density index (SDI), SSP24. 10 Berrill & Dagley 2014 Stocking Guidelines for Aspen Restoration Figure 9: Second thin cuts conifer <20 in. DBH ‐ simulated change in stand density index (SDI), SSP24. Figure 10: Second thin cuts conifer <24 in. DBH ‐ simulated change in stand density index (SDI), SSP24. 11 Berrill & Dagley 2014 Stocking Guidelines for Aspen Restoration Figure 10 depicts an alternative ‘heavier’ second thinning simulated in Year 19, removing conifers below a 24‐inch (60 cm) DBH limit including regenerating firs (4 trees ac‐1/10 stems ha‐1 of regenerating pines were retained). This treatment reduced total SDI by 42% and shifted composition in favor of aspen from 27% to 45% of stand BA represented by aspen. Conifer stemwood volume cut was double the volume cut in the first thinning, totaling ~2160 ft3 ac‐1 (151 m3 ha‐1) not counting branches and foliage. Under this 24‐inch DBH limit thinning, stand density had once again returned to pre‐treatment levels by Year 55, giving a predicted treatment persistence of 55‐19=36 years. By year 55, all residual conifers had grown >30 in. (75 cm) DBH. At this time, the regenerating conifers collectively represented only 14% of stand density, with the remainder being aspen or large residual conifers. Therefore any prescription calling for thinning more than 14% of SDI would necessarily involve cutting/killing some conifer >30 in. DBH. Thinning only 14% of SDI would have short treatment persistence. It appears that stand growth was predicted to slow beyond year 60, likely because so much growing space would be occupied by large old conifers with declining BAI and aspen growing slowly under the partial shade they cast. ACKNOWLEDGEMENTS We sincerely thank our collaborators Stephanie Coppeto, Kyle Jacobson, and Victor Lyon (USDA Forest Service), David Catalano and Mark Enders (Nevada Division of Wildlife), Tamara Sasaki and Silver Hartman (California State Parks), and Judy Clot (California Tahoe Conservancy). Field assistance was provided by Arron Cox, Chris Harrison, Chris Hightower, Jesse Jeffress, Christopher Kirk, Forest Kirk, Nick Knipe, Matthew Lyons, Brandon Namm, Kirk Perttu, Dustin Revel, and Chris Valness. This research was supported using funds provided by the Bureau of Land Management through the sale of public lands as authorized by the Southern Nevada Public Land Management Act (SNPLMA). LITERATURE CITED (Products of this SNPLMA‐funded science project are shown below in bold type). Berrill, J‐P.; Dagley, C.M.; Lyon, V. 2009. Monitoring Aspen Restoration Treatments in the LTBMU: Methodology and Pre‐treatment Data Summary. Final Report: LTBMU Aspen Monitoring Project. Berrill, J‐P.; Dagley, C.M. 2010. Preliminary stocking guidelines for aspen restoration in the LTBMU: Comparing thinning prescription diameter limits. Report prepared for Lake Tahoe Basin aspen forest managers. Berrill, J‐P.; Dagley, C.M. 2012. Geographic patterns and stand variables influencing growth and vigor of Populus tremuloides in the Sierra Nevada (USA). ISRN For. Vol. 2012, ID: 271549, 1‐9. Open Access. Berrill, J‐P.; Dagley, C.M. 2014. Regeneration and recruitment correlate with stand density and composition in long‐unburned aspen stands undergoing succession to conifer in the Sierra Nevada, USA. For. Res. 3(2): 1‐7. Open Access. Dagley, C.M.; Berrill, J‐P.; Coppeto, S.; Jacobson, K. 2012. Effects of slash pile burning after restoring conifer‐encroached aspen: interim pile building guidelines for aspen injury risk reduction. USDA Forest Service, Lake Tahoe Basin Management Unit Monitoring Report, December 2012. Long, J.N. 1985. A practical approach to density management. For. Chron. 61: 23‐27. 12 Berrill & Dagley 2014 Stocking Guidelines for Aspen Restoration APPENDIX 1: ANCILLARY MODELS Height‐diameter regressions Height‐diameter regressions were fitted to 2678 data for total height and DBH on all trees in nine 1‐ha plots around Lake Tahoe (Table A‐1; Figure A‐1). Data for trees with broken tops, dead tops, and forked stems were excluded. Table A‐1: Summary data for height (HT) to diameter (DBH) regressions for Lake Tahoe aspen‐conifer. AS JP LP RF WF Variable DBH (cm) Ht (m) DBH (cm) Ht (m) DBH (cm) Ht (m) DBH (cm) Ht (m) DBH (cm) Ht (m) n 1218
1218
102
102
200
200
255
255
903
903
Mean
27.7
17.9
51.0
23.9
43.4
23.1
40.2
18.6
44.6
22.0
s.d. 14.9 6.8 25.4 9.5 19.0 7.8 24.1 8.0 20.7 8.7 Min. 10.0 4.6 20.1 7.8 20.0 5.2 20.3 5.7 20.0 4.4 Max.
81.3
34.9
140.6
52.9
99.5
43.6
179.4
49.3
140.3
49.8
Figure A‐1: Height (HT) to diameter (DBH) regressions for Lake Tahoe aspen‐conifer stands. Fitting models without intercept to the response HT‐1.37 gave models the desirable property of predicting 1.37m HT at zero DBH (Berrill et al. 2009). HTas = dbh * 0.861 + dbh2 * ‐0.00845 + dbh3 * 0.000024 + 1.37 (R2 = 0.969) 13 Berrill & Dagley 2014 Stocking Guidelines for Aspen Restoration HTjp = dbh * 0.514 + dbh2 * ‐0.00171 + 1.37 (R2 = 0.972) HTlp = dbh * 0.673 + dbh2 * ‐0.00329 + 1.37 (R2 = 0.966) HTrf = dbh * 0.521 + dbh2 * ‐0.00165 + 1.37 (R2 = 0.974) HTwf = dbh * 0.6133 + dbh2 * ‐0.00249 + dbh3 * 0.000001567 + 1.37 (R2 = 0.977) Tree basal area growth Basal area increment (BAI) models were fitted to conifer increment data from two consecutive repeat measurements in five 1‐ha plots around Lake Tahoe (Table A‐2; Figure A‐2). BA, SDI, and SDIL (SDI of neighbor trees of same or larger size) were calculated for trees in 0.02 ha plot centered on each sample tree (n=717), with sums including the sample tree. Total height and crown height data were not collected on some trees; therefore crown ratio (CR) data were available for 547 trees. Table A‐2: Summary data for conifer BAI models for Lake Tahoe aspen‐conifer stands. Variable DBH (cm) Ht (m) CR DBHI (cm yr‐1) BAI (cm2 yr‐1) n
717
548
547
717
717
Mean
41.41
21.89
0.69
0.52
34.92
s.d.
20.36
7.71
0.14
0.27
24.97
Min. 20.00 6.70 0.23 0.03 1.20 Max.
140.30
45.50
0.94
2.40
166.47
The best‐fitting BAI model for conifers included dummy variables for species and species x Ln(DBH) interaction, Ln(DBH), CR, and SDIL0.5, fitted to the square root of BAI (cm2): (BAI+1)0.5 , transformed to correct for skewness in data distributions. A quadratic tree size term [(LnDBH)0.5 + LnDBH] best accounted for significantly changing growth rates as tree size increased. Species‐specific dummy variables modify the white fir (WF) base model: (BAI+1)0.5 = ‐32.7465 + 27.5716 * (LnDBH)0.5 + 3.4357 * CR ‐ 0.04205 SDIL0.5 + Species‐specific intercepts: (‐6.3165 JP) or (5.5097 LP) or (3.7779 RF) + Species‐specific slopes: lnDBH * (‐2.6726 JP) or (‐6.2192 LP) or (‐5.3745 RF) or (‐4.0763 WF) Where BAI =((BAI+1)0.5 )2 ‐ 1 14 Berrill & Dagley 2014 Stocking Guidelines for Aspen Restoration Figure A‐2: Tree basal area increment (BAI) models for conifer in Lake Tahoe aspen‐conifer stands, depicting the predicted influence of SDIL (stand density among trees of equal or larger size) (top; middle), and influence of tree DBH (bottom), while holding constant either DBH or SDIL and predicting crown ratio at that level of SDIL for each species: Jeffrey pine (JP), lodgepole pine (LP), red fir (RF) and white fir (WF). 15 Berrill & Dagley 2014 Stocking Guidelines for Aspen Restoration Crown ratio Dependence on crown ratio (CR) estimates for BAI predictions necessitated development of CR prediction models (Figure A‐3). A conifer CR model was fitted to data for 547 trees in five 1‐ha plots around Lake Tahoe. Dummy variables modified the intercept for each species, with respect to the WF base model. Tree size correlated poorly with crown ratio and was excluded. The best‐fitting model included SDI to account for the impact of stand density on live crown ratio. CR = 0.937 + (‐0.1344 JP) + (‐0.07906 LP) + (‐0.0069 RF) ‐0.00612* SDI0.5 where WF is latent variable, and other species are dummy variables where 1=yes; 0=no. Figure A‐3: Relationship between conifer crown ratio and stand density index (SDI) for Lake Tahoe aspen‐
conifer stands. 16 Berrill & Dagley 2014 Stocking Guidelines for Aspen Restoration Growth of regeneration Models of ‘early growth’ were fitted to data for conifer <30 cm DBH, and aspen <10 cm DBH, for prediction of growth of regeneration – i.e., smaller trees outside the range of applicable tree sizes for the conifer BAI models above and published aspen models (Berrill & Dagley 2012). Conifer data were almost exclusively WF (n = 128) (Table A‐3). Table A‐3: Summary data for young conifer BAI models for Lake Tahoe aspen‐conifer stands. Variable DBH (cm) Ht (m) CR DBHI (cm yr‐1) BAI (cm2 yr‐1) n 147 147 147 147 147 Mean
24.49
14.18
0.71
0.50
20.08
s.d.
2.87
2.73
0.15
0.27
11.84
Min. 20.00 6.70 0.29 0.03 1.27 Max.
29.90
21.60
0.93
1.37
63.22
A non‐linear ‘early growth model’ was fitted to BAI data for each conifer species: Jeffrey pine (JP), lodgepole pine (LP), red fir (RF) and white fir (WF), modeling the positive relationship with CR and negative impact of SDI on BAI, and predicting zero BAI at zero DBH. BAI = ((aCR + b * Log(SDI)) * Log(dbh + 1))2 With species‐specific coefficients: a = 2.5345: b = ‐0.0812 (WF, n=128); a = 3.4313: b = ‐0.1718 (RF, n=5); a = 1.9852: b = ‐0.1008 (LP, n=8); a = 2.7516: b = ‐0.1614 (JP, n=6). The predicted effect of DBH and SDI on early growth of WF is shown, based on CR predicted for selected levels of SDI (Figure A‐4). Figure A‐4: Basal area increment (BAI) model for young white fir in Lake Tahoe aspen‐conifer stands, depicting the predicted influence of tree size (DBH) at different levels of stand density index (SDI). 17 Berrill & Dagley 2014 Stocking Guidelines for Aspen Restoration An early BAI model for aspen was developed using repeat‐measures data for young aspen 0‐10 cm DBH after thinning to reduce stand density in five 1‐ha plots around Lake Tahoe (Dagley & Berrill, manuscript in preparation). The analysis revealed that aspen growth slowed in association with a greater proportion of fir trees as neighbors, whereas growth was faster among larger aspen with longer crowns. The model predicts DBH increment (DBHI; mm yr‐1), transformed here to predict BAI cm2 yr‐1 from inputs of DBH (cm) and proportion of neighbor tree BA in fir trees (range 0‐0.99, i.e., 0‐99% fir BA). eBAIas = (((eDBHIas / 10 + dbh) / 2) ^ 2 * 3.1415927) ‐ ((dbh / 2) ^ 2 * 3.1415927) where: eDBHIas = SqRtDBHIe ^ 2 ‐ 1 SqRtDBHIe = a + b * (dbh * 10) ^ 0.5 + c * CR + d * Fircomp ^ 2 a = 1.0088: b = 0.033: c = 1.7074: d = ‐0.5266 Predicting BAI for aspen and four common conifer associates revealed that pines have slower early growth than aspen and fir at SDI = 1000; the lower limit of the zone of imminent mortality for aspen (Figure A‐5). Figure A‐5: Basal area increment (BAI) model for young aspen and conifer: Jeffrey pine (JP), lodgepole pine (LP), red fir (RF) and white fir (WF), in Lake Tahoe aspen‐conifer stands, depicting the predicted influence of tree size (DBH) with stand density index (SDI) and predicted crown ratio held constant. 18