Predicting Diameter Distributions for Young Longleaf Pine Plantations in Southwest Georgia Lichun Jiang and John R. Brooks Parameter prediction equations for the Weibull distribution function were developed based on four percentile functions and a parameter recovery method for longleaf pine (Pinus palustris Mill.) in Southwest Georgia. Four percentiles were expressed as functions of stand-level characteristics based on stepwise regression and seemingly unrelated regression. Using a percentile-based parameter recovery method (PCT), estimated diameter distributions were obtained from available stand-level variables. The PCT method was also compared with a cumulative distribution function (CDF) regression method. The PCT method produced consistently better goodness-of-fit statistics than the CDF method. The results indicate that diameter distribution in longleaf pine stands can be successfully characterized with the Weibull function. Keywords: longleaf pine, Weibull distribution, parameter recovery, stepwise and seemingly unrelated regression T he Weibull probability density function has been widely used in forestry applications to describe the diameter distri- bution of trees. The ultimate purpose of modeling diameter distributions is to develop yield systems that provide volume esti- mates by diameter class. The Weibull function was introduced to forestry by Bailey and Dell (1973). Weibull parameters were initially predicted using empirical functions of whole stand characteristics (Smalley and Bailey 1974, Schreuder et al. 1979). Subsequently, the parameter recovery method replaced the parameter prediction ap- proach (Lohrey and Bailey 1976, Matney and Sullivan 1982, Burk and Newberry 1984, McTague and Bailey 1987, Bailey et al. 1989, Brooks et al. 1992, Knowe et al. 1997, Lee and Coble 2006). Re- cently, Cao (2004) evaluated different methods for estimating Weibull parameters and found that the cumulative distribution function (CDF) regression method was better than the PCT method (Cao 2004). This approach was later applied by Newton and Amponsah (2005), Nord-Larsen and Cao (2006), and Palahí et al. (2006). The objective of this study was to compare the two methods (PCT and CDF) for estimating the diameter frequency distributions of longleaf pine plantations using commonly mea- sured stand variables. Study Description The longleaf pine data are part of a growth and yield study based on 15 stands located in Lee, Worth, Mitchell, and Baker counties in southwest Georgia. Seventeen rectangular fixed area plots were es- tablished at different dates and have been remeasured annually; thus, the number of measurements available per plot ranges from two to nine. A total of 100 plot remeasurements are available for this study with age ranging from 3 to 20 years old and stand density ranging from 273 to 857 trees/ac and from 47 to 140 ft 2 of basal area (BA) per acre (Table 1). At each measurement date, dbh was measured with a diameter tape and recorded for every tree to the nearest 0.1 in. Total tree height was measured with a height pole (height, less than 15 ft) and an Impulse laser (height, 15 ft or more) and recorded to the nearest 0.1 ft. Initially, crown class was recorded for just the older stands (more than12 years) but they incorporated for all trees, regardless of age. The traditional definition of crown class was slightly modified to assign crown class to the younger stands. The younger plantations generally have a wider initial planting spac- ing and thus all trees receive full sunlight. The dominant and codominant crown classes were defined as those trees that make up the main crown canopy while intermediate and suppressed classes were assigned to those trees visually shorter (and usually less vigorous) than the trees that constitute the average crown height. Additional data set from 14 plots are available for validation. Received September 4, 2007; accepted December 19, 2008. Lichun Jiang (jlichun@yahoo.com), Northeast Forestry University, Harbin, China. John Brooks (jrbrooks@mail.wvu.edu), Division of Forestry, Forest Biometrics, West Virginia University, 322 Percival Hall, PO Box 6125, Morgantown, WV 26506. Appreciation is extended to Dr. Lindsay Boring of the Joseph W. Jones Ecological Research Center for his support of this project. Copyright © 2009 by the Society of American Foresters. Table 1. Descriptive statistics of stand variables for young long- leaf pine plantations in southwest Georgia. Variable Mean SD Minimum Maximum Fit data set PS 0.13 0.03 0.09 0.19 A 11.88 4.69 3.00 20.00 HT 29.83 11.45 8.63 49.69 BA 69.24 38.13 47.4 140.74 N 509.93 193.17 273.49 857.9 Validation data set PS 0.13 0.04 0.09 0.19 A 14.28 4.89 6.00 20.00 HT 37.08 9.21 19.41 49.92 BA 90.39 33.11 34.93 147.69 N 467.60 199.86 273.49 787.51 PS, plot size (ac); A, plantation age (yr); HT, average height of dominant and codominant trees (ft); BA, basal area per acre (ft 2 ); N, trees per acre. SOUTH. J. APPL.FOR. 33(1) 2009 25 ABSTRACT Downloaded from https://academic.oup.com/sjaf/article/33/1/25/4774752 by guest on 16 August 2022