Empirically Derived Optimal Growth Equations for Hardwoods and Softwoods in Arkansas

Accurate growth projections are critical to reliable forest models, and ecoiogita l ly based simulators can improve siivicultural predictions because of their sensitivity to change and their capacity to produce long-term forecasts. Potential relative increment (PRI) optimal diameter growth equations for loblolly pine, shortleaf pine, sweetgum, and white oak were fit to data from the Arkansas portion of the Eastwide Forest Inventory Data Base (EFIDB). Large sample sizes are necessary for successful application of the PRI mathodology, and in aggregate almost 29,000 trees were used to develop these models, In the final model versions, only a handful (< 30 per species) of the fastest growing trees given their species, size, and growing conditions were retained from the Arkansas EFIDB. Shortleaf pine, sweetgum, and white oak all generated skewed model curves, while loblolly pine p r o d u c e d a m o n o t o n i c a l l y d e c l i n i n g c u r v e . C o m p a r i s o n o f t h e s e o p t i m a l i n c r e m e n t m o d e l s across tree size indicated that loblolly pine had higher potential than the other species until 10 cm in diameter at breast height (d.b.h.), after which sweetgum and white oak overtook it at intermediate sizes. However, loblolly pine optimal performance decreased at a lesser rate than any of the other species, so that by 60 cm d.b.h. it once again had the greatest potential. The other taxa outperformed shortleaf pine throughout most of the diameter range considered, while sweetgum proved intermediate between shortleaf and white oak. These optimal diameter functions are a valuable first step in the development of forest simulators. INTRODUCTION Foresters have increasingly used models to predict longte rm s tand dynamics . Emp i r i ca l l y based g rowth and y ie ld models, e.g., Lynch and others (1999) Wykoff and others (1982), are popular because they are relatively easy to parameterize. However, the rigid nature of these designs, their finite analysis options, and their lack of ecological mechanism have limited their applicability beyond shortte rm growth-and-y ie ld p red ic t ion . Eco log ica l p rocess mode ls a re becoming more w idespread, e .g . , Bo tk in and others (1972), Bragg (1999), Pacala and others (1993), in part because of their greater complexity and flexibility. However , these mode ls o f ten lack an emp i r i ca l founda t ion and somet imes re ly upon ques t ionab le assumpt ions . B lend ing the pos i t i ve fea tures o f empi r i ca l and eco log ica l mode ls shou ld improve the re l iab i l i t y o f longte rm fo recas ts of forest dynamics. Most forest simulators include some kind of individual tree growth mode l . A fundamenta l goa l o f th is inc rement mode l is to predict realized growth accurately, and there are at least two different ways to approach this problem. Most emp i r i ca l mode ls use a f i t t ed s ta t i s t i ca l response where increment is either added or subtracted from a standard level, depending on how favorable conditions are for growth, e.g., Wykoff and others (1982). While commonly applied, this design limits the growth function to a specified set of modifiers, thus restricting its adaptability. The other pr imary approach employs a po ten t ia l inc rement func t ion that is resealed downward based on departures from optimal growth conditions, e.g., Botkin and others (1972), Bragg (2001). Thus, one predicts realized growth from its depar tu re f rom opt ima l g rowth us ing appropr ia te mod i f ie r function(s). In principle, this strategy has greater flexibility fo r eco log ica l mode l ing because env i ronmenta l response func t ions can be more soph is t i ca ted and mechan is t i c . However, one of the biggest challenges to optimal growth mode l ing l ies in the deve lopment o f an acceptab le response curve . Researchers have deve loped and eva luated numerous des igns o f po ten t ia l g rowth equat ions (Botk in and o thers 1972, Moore 1989, Pacala and others 1993, Zeide 1993). Most recently, Bragg (2001) developed the Potential Relative Increment (PRI) methodology to fit inventory data to an eco log ica l l y robus t func t ion , thus l ink ing des i rab le theore t i ca l and s ta t i s t i ca l p roper t ies . Th is paper p resen ts optimal PRI increment models for loblolly pine (Pinus taeda L.), shortleaf pine (P. echinata Mill.), sweetgum (Liquidambar styraciflua L.), and white oak (Quercus alba L.) in Arkansas using data from the Eastwide Forest Inventory Data Base (EFIDB) (Hansen and others 1992). METHODS The details of the PRI method are beyond the scope of this paper (see Bragg 2001). Briefly, all records of the species of interest with positive growth were selected for processing. After identifying this initial group, those individuals growing at the greatest rate for each 2-cm diameter at breast height (d.b.h.) class (one tree per size c lass) were segregated in to a max ima l ac tua l inc rement ‘Research Forester, USDA Forest Service Southern Research Station, P.O. Box 3516 UAM, Monticello, AR 71656 USA Citation for proceedings: Outcalt, Kenneth W., ed. 2002. Proceedings of the eleventh biennial southern silvicultural research conference Gen. Tech. Rep. SRS-48. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern Research Station. 622 p.