Reproducibility and Reliability: How To Define the Population of Trees That Represent Site Quality For Longleaf Pine Plantations

We compared 13 definitions for the subpopulation of “site trees. ” Each subpopulation was defined (1) once at base age or at each measurement; (2) by crown class, diameter, or height; and (3) by the number of trees per acre. These subpopulations were applied to base ages of 25 and 50. For base age 25, the subpopulations defined at base age were superior to those defined at each measurement. The subpopulations defined by dominant and codominant trees were slightly superior to the subpopulations defined by the 40 tallest or thickest trees per acre. Generally, subpopulations defined by diameter were superior to subpopulations defined by height, and the subpopulations that included more trees were superior to those that included fewer. For base age 50, there was very little or no benefit from defining the subpopulations at base age. Among the subpopulations defined at each measurement, the one defined as dominant and codominant trees was superior. We selected this subpopulation for our site index modeling work. The results are largely explained by the stability of tree rankings within a plot over time. Ranking with respect to height is much less stable than ranking by diameter. Crown class was unexpectedly stable from measurement to measurement. 1 Principal Forest Biometrician and Information Technology Specialist, USDA Forest Service, Southern Research Station, Pineville, LA 71360, respectively. Citation for proceedings: Connor, Kristina F. , ed. 2004. Proceedings of the 12th biennial southern silvicultural research conference. Gen. Tech. Rep. SRS–71. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern Research Station. 594 p. INTRODUCTION Site index may be broadly defined as the average height of an arbitrarily defined subpopulation of trees in a stand at some arbitrarily determined base age. Site index is the most-used method to distinguish potential productivity of even-aged forests in North America (Carmean 1975, Goelz and Burk 1992). Site index is intrinsically a standor plotlevel variable (Sharma and others 2002), but it is obtained from measurements of individual trees (Zeide and Zakrzewski 1993). Base age is generally selected so that it is slightly less than the expected rotation age for the species and region (Goelz and Burk 1996); in North America, it is typically between 25 and 50 years, although it may be less for short-rotation species. One must choose what criterion to use to define the subpopulation of trees that indicate site quality. Various criteria specify the select subpopulation. Generally, regardless of the selection criteria for the subpopulation, damaged or defective trees are excluded, as such trees do not directly indicate site. The selection criteria are typically defined by crown class (Avery and Burkhart 1994), rank in diameter, or rank in height. When crown class is used, either the average height of dominants, or the average height of dominant and codominant trees combined, indicates site quality. When diameter or height is the criterion, either a fixed number of trees per unit of land or fixed proportion of trees on a plot define the subpopulation of trees that represents site quality. “Top height” is another term for the average height of the subpopulation of site trees (Zeide and Zakrzewski 1993). Zeide and Zakrzewski (1993) offered an alternative to using a single definition for the site tree subpopulation. Rather than using either a fixed number of trees per acre or a fixed proportion of trees per plot, they suggested a combined estimator that consisted of the “average of averages” of a fixed number and a fixed proportion of trees. For their data, this average of the averages cancelled out the biases of the two averages. In this way, it is roughly analogous to an antithetic variate type of estimator. Site index models may be produced out of a more general growth-and-yield modeling effort, or they may arise out of a site evaluation context. The data for these two contexts tend to differ. In a growth-and-yield context, height-development data arise from remeasured permanent sample plots. Height may be measured on all or some subset of trees on these plots; diameter is typically measured on all trees. In a site evaluation context, height-development data often arise from stem analysis (Duff and Nolan 1953) of selected sample trees. Although the trees may all be within a fixed sample area, other nonharvested trees may not be measured for diameter or height. The term “top height” is more often applied to the growth-and-yield context than the site evaluation context. It is simple to create a definition for the subpopulation of site trees and to determine the average height of those trees on a given plot. However, the trees that comprise that subpopulation change over time. As individual trees grow at different rates, a tree that was one of the 40 thickest trees at one measurement may not be in that class at some later measurement (Tiarks and others 1998). Given data from permanent sample plots, or even from stem analysis, it is possible to know or infer whether a tree belonged to the defined subpopulation at other ages. As this type of data is used to estimate site index equations, a model can specify membership in the subpopulation at base age, or can specify membership at each measurement. This is a critical decision: whether the trees in the subpopulation of interest should be defined at one time or redefined at each 043-Goelz1.pmd 2/26/2004, 3:13 PM 189 190 measurement. In the first case, we only consider the trees in the subpopulation at base age. In the second case, different trees represent the subpopulation at each age, and, thus, the average height includes different trees from measurement to measurement. Presumably, the first case produces models with smaller variance when fit to data, as one source of variation is removed. However, using only base age might be a false economy; the fit to our data might be improved at the cost of relevance in application. In a site evaluation application, a user cannot be certain which trees were in the defined subpopulation at base age, given measurements at some other age. So, the choice is between smaller errors in estimation or smaller errors (or objectivity) in application, or between reliability (small error) and reproducibility. Reliability suggests estimates that are more indicative of site quality. Reproducibility suggests greater objectivity, no need to guess which trees will be members of the subpopulation at any other time. In this paper we explore the issue of reliability (smaller error), discuss the processes that contribute to reliability, and incorporate the concept of reproducibility to guide decisions for a definition of site trees for a specific longleaf pine dataset. MATERIAL AND METHODS Data The data arise from seven studies in the Gulf Coast States to investigate the effects of spacing and thinning on growth and development of longleaf pine plantations (Goelz and Leduc 2001). The 267 plots have been remeasured multiple times at approximately 5-year intervals; most plots have been remeasured for > 20 years. Some of the stands are now > 60 years old. The protocol varied among the studies. Most recent measurements include height of all trees, and a subset of heights was measured during earlier inventories of some of the studies. The studies have been combined to form a uniformly measured database for growth-and-yield modeling of longleaf plantations (Goelz and Leduc 2002).