Stand Density Management: an Alternative Approach and Its Application to Douglas-Fir Plantations
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Forest Sci., Vol. 25, No. 3, 1979, pp. 518-532 Copyright 1979, by the Society of American Foresters Stand Density Management: an Alternative Approach and Its Application to Douglas-fir Plantations T. JOHN DREW JAMES W. FLEWELLING ABSTRACT. A methodof viewing standdensity as it relatesto volumeproduction and tree size is developedin the form of a simple density management diagram applicableto plantationsof coastal Douglas-fir, Pseudotsugarnenziesii (Mirb.) Franco, on all sites. Three prominentpoints in stand development,crown closure, imminent competition-mortalityand the maximum size- density relationshipare definedin terms of tree size and stand density, and their implicationfor standdynamics is discussed.A relativedensity index is presentedas a basisfor quantifyingtree growthand standyield as a functionof density.The trade-offbetween maximizing individual tree size or standyield is considered;this recurringdilemma for forest managerscan be rationalized on the basis of the density management diagram. FORESTSCl. 25:518-532. ADDITIONALKEY WORDS. Pseudotsuga menziesii, tree size, standyield, managementregimes. IN AN EARLIERMANUSCRIPT (Drew and Fiewelling 1977), we discussedthe the- oretical developmentof a generalprinciple of plant populationbiology, the max- imum size-densityrelationship, together with elements of yield-density theory, and introduced a concept of imminent competition-mortality.Here, we develop these conceptsinto an applied forest managementtool, which will take the form of a simple modelling approachto stand development. Our model adds to some of the fundamentalconcepts of growth, yield, and stand density that have arisen in the fields of forestry, biology, or ecology through the last century. Growth and development of forest standscan be forecast by a variety of models with differing objectivesand degreesof complexity. These modelscan be incor- porated into economic simulationswhich select optimum managementregimes. Most models, with few exceptions, such as Stage's (1973) prognosismodel, as- sume that random effects can be ignored; i.e., only mean trends for a class of standsare forecast. Thus, a consequenceof this assumptionis a possibility that the managementregime chosen as being optimum for the mean stand is not necessarilythe optimum regime for any particular stand. However, Adams and Ek (1974) have proposedusing stochasticmodels, which admit to uncertainty, in the evaluation of managementregimes. The uncertainty in growth and mortality patterns,particularly at high densities,are too importantto be ignored.Stochastic growth models have not been developed to any great extent, possibly because The authorsare, respectively,Tree ImprovementSpecialist, Tropical ForestryResearch, and For- estryBiometrician (currently enrolled in a Ph D programat the Universityof Georgia),both from the WesternForestry Research Center, WeyerhaeuserCompany, Centralia, WA 98531.Acknowledgment is madeto the many colleagueswho encouragedand contributedto the developmentof this manu- script;to the New ZealandForest Service, Nelson Conservancy for providingDouglas-fir growth and yield data; and the WeyerhaeuserCompany for supportingand authorizingpublication of this manu- script. Manuscriptreceived 23 August 1978. 518 / FOREST SCIENCE foresters are generally more comfortable with the assumptionof certainty (Bell 1977), needed error distributionsare not known, or becauseanalytical solutions are exceedingly difficult to obtain (Chapman 1967). The error distributions in growth and mortality are quite complex and cannot yet be determinedfrom ex- isting data bases with the precision required for the dynamic programmingmeth- ods (Hool 1966, Lembersky and Johnson 1975) available in forestry. We are proposinga simpler model which attempts to delimit stand conditions likely to result in particular patterns of growth and development. The error dis- tribution in mortality trends is recognized,though not specificallydefined. The resulting model, not a growth model per se, is similar in some respects to earlier hardwood stocking guides (Ginrich 1967, Leak and others 1969). This modelshould be easilycomprehended by nonbiometriciansand can, we feel, be extrapolated to untested management regimes with no more "heroic" as- sumptionsthan are required by the more complex approaches. Stand density manipulationhas the potential to make a major impact on indi- vidual tree size and stand yield. While the literature on spacing, thinning, and stand yield is voluminous,research to date has achievedlittle more than confirm "... what was formerly based on informal observation, namely, that there is an associationbetween the initial spacingand various tree and stand characteristics .... "(Evert 1971). In 1971 Evert could state that spacingand thinning studies have contributedlittle to the assessmentof differencesin degree in tree size and standyield that would allow decisionmakingfor the achievementof any particular managementobjective. His statementis essentiallytrue today, and thoughgrowth modelsfor somespecies give goodresults over limited rangesof age and density, there is still no general framework for relating tree size, stand yield, and stand density. Central to a discussionof stand density managementis an index to quantify the effects of density (trees per unit area) on growth. Stand density indices, functions which are used to estimate the effects of density, have historically been comparisonsof standsto reference stands,either in maximum stockingsituations or at crown closure. Examples of these are, respectively, Reineke's (1933) stand density index and crown competitionfactor (Krajicek and others 1961). These and other indices are discussedby Curtis (1970), who regards them as having approximately equal utility. One drawback to many of these indices is that they relate standsin terms of diameter and do not reflect the fact that "the space a ß . tree can utilize is related to both its diameter and height" (Briegleb 1952). Briegleb's (1952) index, based on a standardnumber of trees per acre by average diameter and average height, is highly regarded by Worthington and Staebler (1961) and Vezina (1964). However, Briegleb'sconclusion, that for standswith the samemean diameterthe taller standcan supporta greater numberof trees, may be subject to dispute: his conclusionis based on observed stand structuresimme- diately after thinning and cannot reflect tree space requirementsor growth po- tential. We define a relative density index, Pt, as the ratio of actual stand density to the maximum stand density attainable in a stand with the same mean tree volume. Because tree volume varies with both height and diameter, our density index reflects the same factors as does Briegleb's (1952) index; however, the effect of a greaterheight for a given diameteris viewed differently. The proposeddensity index is equivalentin conceptto a density indexing systemproposed by Tadaki (1964), first called a "management base line" and subsequently"relative den- sity." Tadaki's index is proportional to the ratio of a stand's mean tree volume to the maximum mean tree volume attainable at the same density. Though our relative density index and Tadaki's index have identical utility from a computa- tional viewpoint, the relative density which we have defined is directly propor- VOLUME 25, NUMBER 3, 1979 / 519 Mean Tree Volume (ms) (ft 3) 4.0 3.0 2.0 Maximum size-densityreiationship = 12.644-1.5 In 0(TPA)] 1.0 0.5 0.3 0.1 100 200 400 600 800 1000 2000 (trees/acre) I I I i 'l I I I i I i I I I I I I 300 500 1000 1500 2000 3000 5000 (trees/hectare) Density Figure 1. The maximum size-densityrelationship and the natural stand data used in positioning this relationship. tional to density. Thus, the new index may be more useful than Tadaki's for understandingthe effectsof densitymanipulation. The model discussedhere is partly quantitative and partly conceptual;above all it is simple.The approachwas adoptedin place of other modellingalternatives in part becauseof its easeof comprehension,especially by nonbiometricians,and its applicabilityto a wide range of stand conditions. THE DENSITY MANAGEMENT DIAGRAM FOR DOUGLAS-FIR The densitymanagement diagram, a graphicaltool for relating stand density, tree size, and stand yield, is a graph of mean tree volume and stand density on which the following relationshipshave been superimposed. Maximum Size-DensityRelationship.--We acceptthe conceptof maximumsize- density as a general principle of plant populationbiology: in pure even-aged 520 / FOREST SCIENCE stands, the maximum mean tree size attainable for any density can be determined by a relationshipknown as the -3/2 power law. v = a p-a/• (1) where v = mean tree volume a = constant p = standdensity. A review of the derivation and an example of the application of this relationship is presented by Drew and Fiewelling (1977). There is no rigorous statistical procedure available for selecting the limiting boundaryof a zone, given that someunknown randomvariation is to be expected. We chose to position the maximum size-density relationship by the following procedure. Volume computationsfor 1 to 9 repeat measurementsof 313 growth and yield plots in natural stands of coastal Douglas-fir, Pseudotsuga menziesii (Mirb.) Franco, from Washington and Oregon were graphically summarized on log-log scale (Fig. 1). The data base is essentially that described by King (1970), with some additions. The maximum size-density parameter in Equation 1 was selected for this data set by positioning a line of -3/2 slope near