Historic, archived document Do not assume content reflects current scientific knowledge, policies, or practices. : At a¥, 7 i Le 8 So gree gr rte ee te eet Sang nt trey gt ia ‘ J ied ot ~ - i Sh Tae f a IS Sf 7 , i o, (b YUo United States Department of Agriculture Forest Service Intermountain Research Station Research Note INT-RN-429 September 1996 David C. Chojnacky Abstract—Diameter growth measurement is difficult for pinyon and juniper trees because they are slow-growing, multiple-stemmed, and poorly suited to measurement meth- ods used for other temperate tree species. This paper de- scribes a model designed to estimate diameter growth for individual pinyon and juniper trees from a small subsample of growth measurements. Data for model construction in- clude 10-year radial growth sampled from 1,536 trees on 176 plots spread throughout Arizona and New Mexico. Species include Pinus edulis, Juniperus monosperma, J. deppeana, J. scopulorum, and J. osteosperma. The model predicts past 10-year diameter growth from stand-level growth-index measurement, tree diameter, and number of basal stems in a tree. Keywords: individual-tree model, drc, tree rings, inventory, log regression Estimating diameter growth is an important aspect of forest management and inventory. Coring trees and counting rings, a common method to estimate growth, is not easy to do in the field for pinyon-juniper species. Also, juniper trees often have multiple stems originat- ing from a single root system, creating additional measurement complications (Chojnacky 1990). Meas- uring a few trees and extrapolating results to a larger population would be simpler. With this approach, an individual-tree model (Chojnacky, in preparation) was constructed to estimate diameter growth of all trees on a plot from growth measurement of a few trees: Indrc, = By + By Indre + Bodrc? + Bs Inginder (1) David C. Chojnacky is a Research Forester, with the Interior West Resource Inventory, Monitoring, and Evaluation Program, Intermountain Research Station, located at the Forestry Sciences Laboratory, Ogden, UT. Currently he is visiting assistant professor at Purdue University, West Lafayette, IN. Estimating Diameter Growth for Pinyon and Juniper Trees in Arizona and New Mexico | where drc, = 10-year diameter growth at drc (cm) stems dre = | ¥ d? i=l d; = stem diameter near the root collar, above groundline forks and major diameter swell (cm) stems = number of stems near the root collar with diameter (d;) 3.8 cm or larger = (Pamd, [stems ) for pinyon, (Jama, V stems) for juniper = 10-year gmd growth of the median gmd (median-sized tree) from a plot’s pinyon distribution (cm) = 10-year gmd growth of the median gmd (median-sized tree) from a plot’s juniper distribution (cm) gmd = drc/Vstems In = natural logarithm with e as a base B = equation parameter Sindex Pqmd, Jqmd, This model was patterned after growth and yield mod- els developed for temperate forests (Edminster and others 1991; Hann and Larsen 1991). It differs in using a stand-level growth index (/;,¢x;) instead of a site quality variable and in not using any variable to de- scribe tree competition within plots. This strategy was necessary because site quality and stand competition in pinyon-juniper forests are not understood well enough to develop variables to measure these processes. The purpose of this paper is presentation of an individual-tree model (eq. 1) thatis applicable to Arizona and New Mexico. The equation 1 model form was devel- oped from only New Mexico data (Chojnacky, in prepa- ration). Now available Arizona data (Chojnacky 1988) are added and tested to estimate a single set of param- eters for equation use in both States. Data Pinyon and juniper growth were available from 176 plots (fig. 1). Most plots were subsampled from inven- tories (Conner and others 1990; Van Hooser and others 1993) conducted in the 1980’s by the U.S. Department of Agriculture, Forest Service, Interior West Resource Inventory, Monitoring, and Evaluation Program through its Forest Inventory and Analysis activity (commonly called FIA). In Arizona, 94 plots were sys- tematically selected from FIA plots on private, State, Bureau of Land Management, Prescott National For- est, and Hopi Indian Reservation land ownerships (Chojnacky 1988). Arizona data were collected concur- rent with the 1985 FIA inventory, which limited the sample to lands surveyed by FIA that year. Navajo, San Carlos, Fort Apache, Hualapai, and Havasupai Indian Reservations, and Kaibab, Coconino, Apache- Sitgreaves, and Coronado National Forests were not included in these surveys. In New Mexico, 82 plots were randomly selected in 1986 and 1987 from prior FIA and National Forest inventories (Chojnacky, in preparation). Arizona @ Diameter growth plot (176) * FlA inventory plot (2,065) All 176 growth plots were fixed-area and circular: 81 were 0.08 ha; 93 were 0.04 ha; and 2 were 0.02 hain size. Tree measurements from these plots included species identification, diameter at groundline near the root collar (drc), total tree height, the number of stems (3.8 cm and larger) at drc, and 10-year radial growth cores. Trees were defined as having one or more stems originating from a single root system with at least one stem at adiameter of 7.6cm. Increment cores were taken by diameter classes from trees randomly selected within each pinyon and juniper genus. This design subsampled about half the trees on each plot and it covered all tree sizes. Two or more 10-year radial increment cores were collected from each tree subsampled for growth. Increment cores were glued into holders in the field and were later sanded and measured under magnification. Although researchers dispute how well ring counts assess growth rates, Despain (1989) has shown that ring counting can estimate 10-year diameter growth if some error can be tolerated. For Utah juniper in Arizona, Despain (1989) found that a 5 percent error should be expected for most trees, but errors exceeding Mexico Coordinates unavailable for most National Forest inventory plots (402) Figure 1—Diameter-growth data from 176 plots were used to estimate parameters for the growth model (eq. 1). Data represent a subsample of 2,467 plots from the Forest Inventory and Analysis (FIA) database for pinyon-juniper forest types. There are 402 plots in the FIA database supplied by the National Forests that have no geographic coordinates. 20 percent need only be expected for about 20 percent of the trees. Tree-ring cores for Arizona data were collected by FIA crews, and measurements were done at Colorado State University. The New Mexico data were collected by asingle study crew, and measurements were done at Utah State University. Ten-year growth was meas- ured as the distance from the first visible ring (after the vascular cambium) to the eleventh ring. False rings were not identified; all rings were counted. Growth data for Arizona and New Mexico (table 1) totaled 774 pinyon (Pinus edulis Engelm.), 375 oneseed juniper (Juniperus monosperma [Engelm.] Sarg.), 275 Utah juniper (J. osteosperma [Torr.] Little), 70 alliga- tor juniper (J. deppeana Steud.), and 42 Rocky Moun- tain juniper (J. scopulorum Sarg.). Forty percent came from Arizona’s 94 plots and 60 percent of the trees came from New Mexico’s 82 plots. Modeling Computing Growth Index The individual-tree growth model (eq. 1) was formu- lated differently than growth models for other temper- ate forest species. Because of difficulties finding suit- able site quality and stand competition variables, an alternative “growth index” was used as a surrogate for site and stand description. A variant of Meeuwig and Cooper’s (1981) work was utilized to devise an index representing diameter growth of the median-sized tree for each pinyon and juniper genus found on each plot. This method first computes the quadratic mean diam- eter (qmd) for each tree: qmd = —=—— (2) where stems = number of stems within a tree at drc with diameter (d;) 3.8 cm or larger dre = "Sd i=l d; = stem diameter near the root collar, above groundline forks and above major diame- ter swell (cm) Next, past 10-year diameter growth for pinyon (Pqmd,) and juniper (Jgmd,) is determined for each plot from trees corresponding to the median qmd for each genus: Pqmd, = Aor + Op Pamdsop (3) Jqmd, = Bop + Biz Jqmdson (4) where @ = parameters estimated within each plot (k) from all pinyon stem diameters (d;) sampled for growth, average R? = 0.32 and aver- age n = 6.4 stems per plot Pqmds5 9, = the median gmd from the pinyon distribu- tion of each plot (k) B = parameters estimated within each plot (z) from all juniper stem diameters (d;) sampled for growth, average R? = 0.29 and average n = 6.2 stems per plot Jqmdso, =the median gmd from the juniper distribu- tion of each plot (2) These equations were constructed using a separate linear regression for each plot. About six stems per plot, Table 1—Pinyon and juniper diameter (drc) growth data sampled from Arizona and New Mexico, 1985 to 1988. No. Median 90th percentile Multiple- of 10-year No. of 10-year No. of stem State Species trees growth drc Height stems growth drc Height stems trees ----cm---- m ----CM---- m Percent Arizona Pinyon 157 1.8 16.5 4.0 1.0 3.6 32.8 7.0 1 3 Alligator juniper 16 2.0 16.6 3.4 ds) 3.9 65.4 7.0 5 50 Oneseed juniper 177 187, 26.7 3.4 3.0 3.2 59:27 2O'5 10 63 Utah juniper 269 Wes) 23.9 4.0 1.0 3.5 52:6, 5:8 5 36 Total juniper 462 1.6 24.8 3.7 1.0 3.3 55:25 5:5 tf 47 New Mexico Pinyon 617 io 16.8 52 1.0 2.2 2977, 9 1 i Alligator juniper 54 We 18.6 4.3 1.0 2.4 38.4 6.1 3 39 Oneseed juniper 198 1.5 22.7 3.4 3.0 2.6 43.7 4.9 8 73 Utah juniper 6 0.8 33.9 4.4 2.0 1.6 53.8 5.2 4 50 Rocky Mountain juniper 42 13 18.9 4.3 1.0 2.5 33.3 6.1 2 26 Total juniper 300 1.4 21.0 3:7 2.0 2.6 42 25:2 if 60 Total Juniper 762 Was 23.1 ChI/ 2.0 3.1 50.3 5.5 7 52 Pinyon 774 1.4 16.8 4.9 1.0 2.6 30:20" 7:9 1 6 spanning the range of pinyon and juniper stem diam- eters (d;), were available for each regression. Regres- sion slopes were both positive and negative; 58 percent of 118 pinyon and 58 percent of 152 juniper regression equations had positive slopes. Even though R? values were low and regression relationships alternated between negative and posi- tive slopes, I was not concerned because only the mid- range of each regression equation was used to esti- mate a single value for each plot. If regression end points or extrapolations had been needed, linear re- gressions would not have been used. But from previous model construction experience (Chojnacky, in prepara- tion) equations 3 and 4, which relied on the robust nature of medians, were found superior to indices based on mean, minimum, or maximum growth. Estimating Parameters Before estimating parameters, State and species dif- ferences within the growth data were examined sta- tistically for possible data separation. A category for multiple- and single-stem trees was not included in the tests; instead, these two groups were initially made because of measuring differences. An F-test (Graybill 1976, p. 247) showed little ad- vantage for separating the Arizona and New Mexico data (table 2). Only single-stem pinyon trees tested significantly different between Arizona and New Mexico. And even for these data, the smaller Arizona sample (152 of 728) did not have enough replication from some tree sizes to warrant separate equations for each State. An F-test was also used to compare possible species differentiation for combined Arizona and New Mexico data. An initial test showed a significant difference (Prob > F = 0.008) among species for multiple-stem trees. However, this result was highly influenced by a few trees greater than 70-cm drc. With recalculation, after excluding the 13 (out of 441) trees over 70-cmdrc, no species differences were evident among multiple- stem trees (Prob > F = 0.136). Therefore, all data (including trees over 70-cm drc) for both States and for all species were combined into multiple- and single-stem groups for parameter esti- mation (table 3). This strategy provided considerable data for both equations; yet the model still expressed some site and species differences through the growth index variable. Because a growth index was indepen- dently estimated for each plot, it automatically in- cluded some species and site effects. Graphs of regression residuals supported grouping data by State and species, since no unreasonable pat- terns were observed (fig. 2). Although the residuals showed considerable variation, the lack of patterns gives confidence for unbiased model predictions for large sample sizes. The growth index was the model’s most important variable (fig. 3). Successive stepwise regressions showed that it accounted for more than 95 percent of variation explained by the model. Summary Parameters were estimated for an individual-tree diameter growth model from pinyon-juniper data Table 2—F-tests comparing full? and reduced® growth models between Arizona and New Mexico data. Tree No. of trees form Species Arizona New Mexico F-value Prob > F Multiple-stem Alligator juniper 8 21 0.99 0.4361 Oneseed juniper 111 144 2.17 0.0732 Utah juniper 97 3 0.88 0.4780 Rocky Mountain juniper 0 11 0.00 1.0000 Pinyon 5 41 0.44 0.7803 Single-stem Alligator juniper 8 33 1.10 0.3738 Oneseed juniper 66 54 0.73 0.5716 Utah juniper 172 3 0.31 0.8682 Rocky Mountain juniper 0 31 0.00 1.0000 Pinyon 152 576 4.41 0.0016* aFull model: Indrcy = Q% + Oy Indre + Q dre? +04 INgindex +No +M Indre + Nz drc* +3 INGinder- where a = parameter estimates for Arizona data, and 0 for New Mexico data. 1 = parameter estimates for New Mexico data, and 0 for Arizona data. >bReduced model: Indrc, = Bo + By Indre + B, dr < +B INindex where B = parameter estimates for Arizona and New Mexico data combined. *For the a-level set at 0.05, the full and reduced models are significantly different. Table 3—Parameters for estimating pinyon and juniper diameter growth in Arizona and New Mexico. Tree Parameter estimates® No. of Regression statistics® form Bo B; Bo By trees R2 C.V. Bias Percent Multiple-stem 0.777 0.1088 —0.0000913 0.8647 441 0.60 35 1.0684 Single-stem 0.661 0.1932 —0.0001594 0.9473 1,095 0.60 36 1.0705 aDiameter growth equation: drcg = Bo drcB\ exp(B2 drc?) (ginder)?3 where drc, = past 10-year diameter growth at drc (cm) Stems dre = = d; (F3 d; = stem diameter near the root collar, above groundline forks and major diameter swell (cm) stems = number of stems at drc with diameter (d;) 3.8 cm or larger index = (Pamdg stems ) for pinyon, (Jqmdg a stems ) for juniper Pqmd, = 10-year gmd growth of the median gmd (median-sized tree) from a plot's pinyon distribution (cm) Jqmd, = 10-year gmd growth of the median gmd (median-sized tree) from a plot's juniper distribution (cm) qmd = dre| v stems >The coefficient of determination (R2) and coefficient of variation (C.V.) were recomputed in original diameter-growth units. °The By parameter was corrected by this amount to compensate for log regression (Flewelling and Pienaar 1981). 5 Oneseed juniper: m-stem 3) Oneseed juniper: s-stem € E © & 2 2 a oO =) —. 3 3 2) 7) @ 3) ira iv 0) 1 2 3 4 5 0 1 2 3 4 5 Predicted drc growth (cm) Predicted drc growth (cm) 3; Utah juniper: m-stem 3) Utah juniper: s-stem § 5 2 2 5 E 7 a7) c Figure 2—Regression residuals (observed minus predicted) for Gules Dia is leas ORS ee > 3 4 5 10-year diameter-growth data fit Predicted dre growth (cm) Predicted drc growth (cm) to equation (1). Residuals are ex- pressed in original units (not logs), 31 Pinyon: m-stem 3) Pinyon: s-stem and include the log bias correction (see table 3). Residual data are E d = Z Z separated to show that no discern- Cee Oe Chea ible patterns can be seen from fit- 2 ; 2 e.. e ting data combined by State and 3 9 oh 3 e —ta7>. species. Seven x,y data points— o -1 Ph a (5.1, -1.9), (2.4, 3.1), (5.3, 0.1) for a c oneseed juniper; (5.3, —0.6), (5.8, 74 Ari =2 ot om TERA: 2.3), (3.4, -3.3) for Utah juniper; -3 -3 and (5.7, 1.0) for pinyon—are omit- 0 ! 2 3 4 5 ) 1 2 3 4 5 ted from graphs because they are Predicted drc growth (cm) Predicted dre growth (cm) outside the axes ranges. Growth Index Median gmd growth, No. of stems S>= 3 cm, : stems . Nera spantnoransvensasssstcaseegy, qs BaP ELIT T) Past 10-year drc growth (cm) 0 10 20 30 40 50 60 70 Dre (cm) Figure 3—Past 10-year diameter (drc) growth (for either pinyon or juniper) predicted from drc and a growth index (index) by using equation (1). Compo- nents of the growth index—median-sized tree growth from the plot's quadratic mean diameter (qmd) distribution and number of stems—are illustrated for individual-tree predictions. collected in Arizona and New Mexico (table 3). Mea- surements needed to use the model include drc, num- ber of stems at drc, and growth index. The growth index requires estimation of pinyon and juniper growth indices, Pgmd, and Jqmd,, for each plot or stand. In this study, growth indices were estimated from within-plot regressions by using past 10-year growth measurements from about six stem diameters (d;) per plot for each pinyon and juniper genus. In practice, a regression to estimate growth indices may not be desirable for each plot. It might be prefer- able to directly measure growth of the median-sized (qgmd) pinyon and juniper on each plot. Or one might want to average the growth of the median-sized stem with additional stems close to the median. If a field method — other than a regression for each plot—is used to estimate the growth index, it should be compared to the regression approach because the model is cali- brated to a regression estimate for median-sized tree growth. If radial cores are utilized to estimate 10-year diameter growth, I recommend at least three cores per stem (Chojnacky 1990). Generally, a growth model is designed to predict growth without requiring any grewth measurements, but since this model requires measuring median-sized pinyon and juniper growth, it is more like a traditional stand-table projection method (Husch and others 1982) where trees are assumed to grow at an average rate based upon initial measurements. However, until fur- ther research is done on pinyon-juniper growth pro- cesses, this model fills a present knowledge gap by allowing estimation of diameter growth from available inventory measurements and a “growth index.” References Chojnacky, D. C. 1988. Modeling volume growth for Arizona’s pinyon- juniper forests. In: IUFRO proceedings, forest growth modeling and prediction conference; 1987 August 24-28; Minneapolis, MN. Gen. Tech. Rep. NC-120. St. Paul, MN: U.S. Department of Agriculture, Forest Service, North Central Forest Experiment Station: 247-254. Chojnacky, D. C. 1990. Subsampling diameter growth within multiple- stem juniper trees. In: Proceedings, IUFRO, research in forest inventory, monitoring, growth and yield; 1990 August 5-11; Montreal, Canada: Publication FWS-3-90, School of Forestry and Wildlife Resources, Virginia Polytechnic Institute and State University, Blacksburg, VA: 32-41. Chojnacky, D. C. [In preparation]. Estimating diameter growth for pinyon and juniper trees. Ogden, UT: U.S. Department of Agri- culture, Forest Service, Intermountain Research Station, For- estry Sciences Laboratory. Conner, R. C.; Green, A. W.; Born, J. D.; O’Brien, R. A. 1990. Forest resources of Arizona. Resour. Bull. INT-69. Ogden, UT: U.S. Department of Agriculture, Forest Service, Intermountain Re- search Station. 92 p. Despain, D. W. 1989. Radial growth relationships in Utah juniper (Juniperus osteosperma) and pinyon pine (Pinus edulis). Tucson: University of Arizona. 153 p. Dissertation. Edminster, C. B.; Mowrer, H. T.; Mathiasen, R. L.; Schuler, T. M.; Olsen, W. K.; Hawksworth, F. G. 1991. GENGYM: a variable density stand table projection system calibrated for mixed conifer and ponderosa pine stands in the Southwest. Res. Pap. RM-297. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, Rocky Mountain Forest and Range Experiment Station. 32 p. Flewelling, J. W.; Pienaar, L. V. 1981. Multiplicative regression with lognormal errors. Forest Science. 27(2): 281-289. Graybill, F. A. 1976. Theory and application of the linear model. North Scituate, MA: Duxbury Press. 704 p. Hann, D. W.; Larsen, D. R. 1991. Diameter growth equations for fourteen tree species in southwest Oregon. Res. Bull. 69. Corvallis, OR: Oregon State University, Forest Research Laboratory. 18 p. Husch, B.; Miller, C. I.; Beers, T. W. 1982. Forest Mensuration, 3d ed. New York: John Wiley and Sons. 402 p. Meeuwig, R. O.; Cooper, S. V. 1981. Site quality and growth of pinyon-juniper stands in Nevada. Forest Science. 27(3): 593-601. Van Hooser, D. D.; O’Brien, R. A.; Collins, D. C. 1993. New Mexico's forest resources. Resour. Bull. INT-79. Ogden, UT: U.S. Depart- ment of Agriculture, Forest Service, Intermountain Research Station. 110 p. You may order additional copies of this publication by sending your mailing information in label form through one of the following media. Please specify the publication title and Research Note number. 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