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1979
Uneven-Aged Forest Management: State of the Art (or Science?)
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USDA Forest Service General Technical Report lNT - 50 Aprll 1979 THE AUTHORS
DA VlD W. HANN is Assistant Professor in the Department of Forest Manage ment, Schoo! ~f Forestry, at Oregon state University, Corvallis, Oregon. From 1971 through 1978 he was a Research Foreater working on prohlems of inventory techniques for the Renewahle Resources Evaluation research work unit in Ogden, Utah. He holds a B.S. in forest management (1968) and an M. S. in forest mensuration (1970) from Oregon State University, and a Ph. D. in forest mensuration (1978) from the University of Wash Ington, Seattle.
B. BRUCE BARE is Associate Professor of Forest Management and Operations Research, College u' Forest Resources, Universltyof Washington, Seattle , UNEVEN·AGED Washington. Heholds B. S.F. (1964) and Ph.D. (1969) degrees from Purdue University and an M. S. (1965) from the University of Minnesota. For the FOREST MANAGEMENT: past 8 years, his work has involved the applIcation of quantitative methods State of the Art (or Science?) to wildland use planning, timber harvesting and forest operations scbedlu lng, and taxation prohlems. David W. Hann and B. Bruce Ba re
INTERMOUNTAIN FOREST AND RANGE EXPERIMENT STATION Forest Service U. S. Department of AgrIculture Ogden, Utah 84401 RESEARCH SUMMARY
Examioes some Importaot historical factors that have caused widespread preference oftbe even-aged management system over the uneven-aged. Ma.for CONTENTS declsloos facing forest managers loterested 10 applying uoeveo-aged maoage Page meot are defloed aDd a review Is made of techolques tradLtLooaLly used, or receotLy proposed, for use 10 making these declsloDS. FloaLly, problem areas THE ROLE OF MANAGEMENT AND SILVICULTURE Deeding further research aDd developmeot are Ideotlfled. EARLY HISTORY OF THE PROBLEM
THE PROBLEM TODAY • • 3
MANAGEMENT DECISIONS 4
AN EARLY ATTEMPT TO ANSWER QUESTIONS
DE UOCOURT'S CONSTANT "q" VAWE. 5
RECENT WORK . 6
WHAT'S NEXT .
COMPUTER AND ALGORITHM CAPABIUTIES
INTERFACING SIMULATORS TO NONLINEAR PROGRAMING
GROWTH AND YIELD SIMULATORS.
SPECIES COMPOSITION • • • • • 10
SCHEDULING OF COMPARTMENTS 12
SUMMARY •• •• •• 16
PUBUCATIONS CITED 17
c.. The phi losophy of uneven- aged ma nagement was devel oped ma i n ly in Fr ance a nd S\oo'it!er land aft er the advancement of t he eve n-aged phi losoph}' . It \oo'3S based on the concept that fOl'es~ m.magemcn t is pr i m;;. ri 1)' an a r t t ha t r e lics heavil y upon the cont i nuous i n THE ROLE OF MANAGEMENT AND SILVICULTURE put of the fores ter ' s ecol og ica l experi ence ( ""'ith i t s scientific base) and s ilv i cultura l judgment in order to i mp l ement t he ma nagement p l a n and to meet the s t a t ed objectives . This ph:losophy is compati b l e t.d th the uneven-aged s ilvi cultural system of selection harve s t ing where s t rong empnasiS is a l so p l aced on t he for ester' s experience ana Jud ~ Over the centuries, two often conflicting fores t management systems- - even- and me nt (Davis 1966 ; Knuc he l 1953; ~ t c}'e t' a nd others 1961 ) . uneven- aged management--have been !lpplied to fores ts throughout the world. !:.i.::; tori c ally, both systems arc rooted in the principles of s ilviculture , but have been expanded A r eview of contemporary fores t man agement literature reveal s that uneven-aged to include forest management obj ectives and the organization of the forest property. ma nagement i s s till trea t ed morc as an art than a science (U.S. Departme nt of Agricul Today. we recognize silviculture and management as separate b!.lt related disciplines. t ure 1975 , 1976) . Add i t i onally , the d istinc tion between uneven- aged s ilvic ulture and Si 1 vicul ture concentrates on <:.he establishment. tending. and hal'vesting of f orest stands ma nagement i s oft e n so blurred that man y s tudents of fores t science have come to and mana gement focuses on decisionmaking, organization, administration, planning, and be lieve that uneven-aged mana gement a nd s ilv i culture are ins eparable . In this paper, control of operations on a forest prope rty to best achieve specified objectives. we s how t ha t the sc i ence of uneven-aged management i s readiJ y di stinguis habl e from uneven-aged si l viculture and t hat unevcil-aged management is jus t as ame na ble to system Silv icultural systems are clas s i fied either as even- or uneven-aged depending a t ic t rea t me nt 3S i s even-aged man agement. primarily upon the type of harvest-regeneration method emp l oyed. Stands containing trees of about the same age that develop under full-light condi t 1ons without Significant As ide from obv ious s il v i ·.:: ul t ural and regulatory di ffe r c nces. the t""·o manageme nt border competition are silviculturally classified as even-aged (Davis 1966). Stands phi.losophies can be diffe r entiated by what for e st managers perceive to be the objec containing trees of several ages that develop with significant interaction with sur t ives o f fores t ma napement, the relative we i ght ass i gned to each objective, and the rounding trees of different ages are classified as uneven-aged. me thod s used t o ac hieve them. Knuc ht! l (1953 , p . 12), a Swis s forester who favored
uneven-aged management J de fined the obj ect i ves of f ores t management 3S follows: From t his ecological-silvicultural basis, the forest manager must decide ,,,hether the individual stand is large enough to be recognized and managed as a separate trea t I . ~ I ai nten a nce of the health a nd r esi s t ance to damage of the forest; rais ment unit. A treatment unit compos ed o f a single even-aged stand is usually managed ing the produc tive capacity of the s oil and of the s tands to the high under the even-aged system of management. and a unit composed of a pure all-aged stand est volume pos s ible on t he s ite and ma intaining that productive capacity. is managed unde r the uneven-aged system. Stands that are too small to be recognized a s separa te treatme nt units are managed under the uneven-aged management system. Such 2. Con ti nuous production of t he hi g}l est possible vo lume of valuable t i mbe r . a treatment uni t might be composed of s evera l small even-aged stands or c lumps --each too small to be treated s eparately. Thus. the choice between even- and uneven- aged 3. Prorr. ot i ng the pr ot ect ive e ffect of the forest in the wides t sense (pro management systems is dictated by s ilvicultural as well as economic and operational t ection agains t soi 1 e r osi on. a va l anches a nd flooding. prot ection of cons iderati ons . From a regulatory perspective. control variables of the two sys tems t he scene r y, pr ot f'c t ion o f the na ti ve flo r a a nd f a una ) . also differ . The major regula tory control vari able in even-aged management is sta nd a ge (size) whereas the ma jor control variables in uneven-aged management are stand 4. Pr ovision o f r egu l a r employment f or the loca l i nhabi t a nts, especi a lly s tructure and s tocking. during the t i me wh en l a bor i s not wanted for agricu l ture.
The r ema inder of this paper focus es on the major decisions facing fores t managers 5 . Pr oviding the h ighest poss ibl e financ i a l y ield. who have adopted the uneven-aged s ystem of management . We assume throughout this repo rt tha t uneven-aged s ilviculture i s a feas ible alte rna tive where its use i s implied . 6 . The f or e :-; t shoul d wor k in a sense l i ke a savings bank , i n tha t in tim"" La s tly . i n the d iscussion tha t follows . the terms "treatment unit" and "stand" are used of need i t i s i n a posi t ion to s upp l y a gr eat er yield o f lJla t e ria l tha n interchangeab l y . A s t a nd is v i ewed as the smallest sized uni t that can be e ffic iently in no rma l times, without los ing its pr oducti ve capacity . managed . \vh i l e t hese objecti ves could a l so be me t by even-aged manageme nt , ::,~ n y pr opone nts of the uneven-aged phi l osophy bel i eve tha t even-aged ma nageme nt f a il s t o meet objec t ives I , 2 , 3 , a nd 6 . They be lieve tha t even -aged management r esults in the devel opme nt of a monocu lture f avoring a few spec i es (pri ma rily coni f e r s) r a i sed in singl e spec i es EARLY HISTORY OF THE PROBLEM age-homogeneous s t a nd s t hat a r e more s us ce ptib l e t o various damaging agents . Th ey a l so contend tha t even-aged ma nagement has r esu l t ed in t he conver s i on of "natu ra l sit e" species t o "int roduced" species oft e n ..... i t h d isast rou s effec t s; the c utting of i mma ture The phi los ophy of even-aged management, developed in Germany and Austria, is based trees i nstead of producing t he " ... highest poss i bl e vo lume of va l uabl e timbe r "; gr ea t e r on the conv i cti on tha t for est management i s primarily a s cience for which me nsurational di s t urbance o f the site wi th r esul tant i mpac t s upon soil pr oduc t iVi t y , soil s t abil i t y , scenic amenities. a nd na t ive fl or a a nd fauna ; a nd ma nagement p l ans tha t are disrupt ed a nd f inancial fonnulas can be developed and used in a sys tematic manner. The concepts when actua l cuttin,g deviates s ign ificantly f r om the schedul ed cut . of the ful l y regula t ed or norma l f or est and the doc trine of s oil rent are outstanding examp l es of this form o f thi nking. Othel exampl es include the myriad of methods for det e r mi n i ng r otation l e ngth and a llowahJe ;.arvest l eve l s --two of the major decision The phi l osophy of uneven-aged ma nagement emp hasizt:s protection a nd imp r ovement of points i n even-aged t imbe r regula tion . Interfacing this philosophy with even- aged a s t ab l e fo r est e nvironme, t , t he gua r a nt ee of tor <'! st sus t e nt ion and pr oduction of s ilvicultura l pr act ices i s na tura l becaus e even-aged silviculture i s an eas ily unde r l arge-sized, h igh- qua li ty timber . Its proponent s be-l i eve tha t these object ives shou l d s t ood syst em compa t ibl e wi th the concept tha t f or est manageme nt can be syst emati zed not be sacrificed fo r hi gher ra t es of ret urn on for est capita l , greater wood fiber, and (or ) ma nagement simpl icit y . (Davis 1966; Knuche l 1953; ~le ye r a nd others 1961) . Forest management in t he Un i ted States today genernl l y follOl~'s the even-aged MANAGEMENT DECISIONS philosophy. Reasons are va ried but r; an be attributed primarily t o (a) the attractive ness of even-aged managemen t as an effective means of converting a forest compo sed o f decadent o r high- graded s t ands to a regu l ated forest, (b) the da\\'11in g of the :-ge of Befor e an examinat ion and evaluat ion of uneven-aged m AN EARLY ATTEMPT TO ANSWER QUESTIONS The early attract iveness of de Liocourt1 s i deas was probably due to the following: the method provided a quant i tative bas is for determining an "idea l !! or "normal" selec tion forest to use as an object ive; i t was useful in determini ng conver sion strategies a nd a l lowab l e cuts; and the method was easy to use at a time when most calculations were Matthews (1930) made an early a ttemp t t o quantify some of the aspect s o f uneven tediously done by hand . The r ecent literature would indicate that thes e features are aged manageme nt in this country in order to answer quest ions concerning conver sion s till va lued (~Io ser 19 76~ U.S. Dep. Agriculture 1975, 1976; and Alexander and Edminster s trategies . length of cutting cycle. "rotation" l ength (age o f o ldest tree in the 19773, 1977b) . s t and), and allowable cut. Lacking better information, he assumed that the uneven-aged s t a nd could be viewed as a composit e of sma ll, equal-s i zed, even-aged component s that Some of t he questions not answered by de Li ocourt I s me thods were : (a) what "q" are well mixed throughout the s t and. Therefore , his concept of the " i deal " structure value and l argest tree size combi nations were optimal; (b) were the conversion strate of the uneven-aged s tand could be determined by data taken f rom normal yield t ables o f gies optimal or even d .. sirable; (c) what about species composition, cutting cycle even-aged ::t t and s . Th is concept of the structure of uneven- aged stands ""3S later laid length, dat e of entry, and conversion period length; and (d) what compartment schedules to r est by Walker (1956) and Reynolds (1 954), Na lker concluding that t o charact erize were best f or a given set of objectives? uneven-aged stands in such a manner was" . . mi s l eading, inaccurate, and a waste of t ime. " rolore fundamentally, i s a balanced dis tribution, such as that described by de Liocourt, necessary for sust ent ion? Might not other diameter distributions be just as sustainabl e and yet prove t o be better abl e to meet management objectives? These "q" questions were prcbabl y on Davis 1 (1966) mind wh en he conc luded that, " ... a good ,H~_ DE LIOCOURT'S CONSTANT VALUE me t er distribution is determined by the biol ogy o f the forest and the pur pos es of management anti not by mathematics .... " Leak and Fi lip (1977), in discuss ing the use of group se _tion in northern ha rdwoods, supported that conc lusion. In another attemp t t o quantify somf of the aspect s of uneven-aged management, ro1eyer (1943, 1952) and ~ I eyer and other s (1961) took the work of French for ester de Liocourt, expanded upon it, and applied it to forest s in ~ I exico and t he United States. What de Liocourt found was that a balanced, or sustainab le, diameter distri bution was craracteri zed by a constant "q" value, ca lcula ted as the ratio of the number of t r ees i n a given diamet er c l ass divided by the number of trees in the next l arger RECENT WORK diame ter c lass. a nd by the diamet er of the l argest tree in the s t and . This r e l a tionship gener ates a geometric series and, when plotted, forms the we ll-kno",," r everse-j shaped curve. Meyer demonsl: rated how know l edge of the balanced diamet er distribution, coupled Some of the mo s t important r ecent work dea ling with the quest ions of uneven-aged with additional information concerning pr esen t s t a r.d s tructure and gr ow th, could be management has been that of Adams (1974) and Adams and Ek (1974, 1975). Thei r wor k used to develop a conversion strategy and to est imate f uture yields . involves the interfacing of a stand simulator with nonlinear ma thema tica l programing t o answer quest ions concerni ng optimal s tand diameter distribution, cutting cyc le l ength . Duerr and Bond ( 1952) next examined how, aft er the best "q" va lue, species, and and conver sion s trategy. Their stand model was a modified version of a pr eviously largest tree size were dete rmined , the economic criterion of ma r gina l value gr owt h developed stand s imulator (Ek 1974). percent could be used to determine optimal s tocking, in terms of volume per acr e. Op timal stock ing was defined as the stocking level a t ""h ich marginal . .!~ .!t! growth This simulator was used t o det ermine the optimal s tand s tructure that would maxi percent e' .:l1s the a lternative percent r ate of r eturn. .ni ze value growth for a fixed ba sal ar ea s tocking level, cutting cycle l ength . species mix, and site quality while meeting the cons traints of sust ainabilit y. This pr ocess Hough (l9S4) used doubl e sampling t o collect gr ow th and diame t er distribution was repeated for various basal area s tocking l evel s and the resulting d i fferent diameter data. He used these data to determine a targeted "q" value and a maximum tree s i ze distributions were compared by using the margina l va lue growth percent crite rion to based on the objectives of management and the form of the original diameter distribu determine the final, optima l di s tribution for a fixed cutt i ng cyc le length , species mix, t i'm. Then he compared the balanced diame ter distribution to the predicted diamet e r and si t e qual ity. Adams (1976) subsequentl y has shown how this same procedure can he distribution at the end of the first cutting cycle t o determine the number of trees used to determine the optimal diameter distribution based on "value" s t ocking r a ther t o cut in each diameter class . For each ar ea ur der contrOl, this process was repeated than basa l area s t ocki ng. Distributions de r ived in th is f ashion are "investment just prior to ;ic heduiec.i ha r vesting . Hough theol lIed that thi s repetitive technique e ffi c i ent" because they maximize percent net worth for the investment made in the gro\oo~ n g would cause the tal-ge ted "q:! value to approach, over time, the idea l "q" for the given s tock. species and sit e. One requireme nt of this procedure is that the cutting cyc l e be cqua l t o , or an integer multiple of, the growth per iod l ength of the model. In thcir example, Adam s COMPUTER AND ALGORITHM CAPABILITIES and Ek (1974, 1975) used a cutting cyc le equa l t o the gro\o"th peri od ; however, they 31 so :; howed how t o incorpor ate l onger. mult ip l e per iod cutting cyc.:lcs into their optimiza- t ion process. In applying t hei r techni(lUes, Adams and Ek ( 1975) found tha t the ~o l lition process fas t appr 0ached the I imits of e i t her the mathema tica l progr aming a l go rit~m s or the Aft e r cstablishing t he optimal stand diamete r dis tribution, Adam s. and Ek ( 1974 , computer when the cutting cycl e exceeded three t i mes the growt h per iod ) en~t h . A s im 1975) used nonl inear mathcmat ica I programing to find the opt ima l conv e rs ion st rategy ilar prob l em exist ed when s olving for the optimal conversion s trategy. In 1: t, is case, that maximized present net wo rth o f the stand fo r a fixed convers ion cyc l e l ength , they discovered that transit ion per iods exceeding four times the gr ow th peri(.ld could s pecies mix, and sit e quality during the transition from exi sting stand diameter di s tri not be hand 1ed . bution to optima l dis tribution. Like the cutting cyc le l ength , t he convers i on cyc l e length must be an i nteger mu ltipl e of the growth period. It is also possible to app l y They found a l so that it was sometimes difficult, if not impossible, to find sol u the same technique for different trans ition periods in order to determine the optimal tions t o thes e non linear pr ogr ami ng problems . But, as they s uggest, there is reason t o conv"-sion per iod l ength on a stand basis. believe that some of these problems and l imi t a tions soon will be over come either by applying new mathema tical programing techn iques , such as the optimal control theory or the decompos i tion theory, and (or ) through imp r oved computer capabil i t ies. INTERFACING SIMULATORS TO NONLINEAR PROGRAMING WHAT'S NEXT An i mportant requirement of the Adams and Ek (1 974, 1975) approach i s a s t and sim ulator that explicit l y expresses the change in number of trees in a diamt'ter c l ass as a function of -:-he number of t r ees i n the diameter c l a s s and as a funct ion o f any othe: Th e milestone work of Adams and Ek (1974, 1975) opens the door to a new set o f applicabl e i ndependent variables. Ek ' s (1974) modified s t and simulator is the onl y tools for answering uneven- aged management questions and i llustrates t hat uneven-aged uneven-aged s imu l ator reported to dat e that mee t s this requirement. Although other management is s ubject t o much mor e rigo rous ana l ysis than man y previousl y thought. modeling techniques do not provide the required explicit equations , it i s possibl e Never the less, t he development of uneven-aged management syst ems s t ill lags behi lld t hat to use numerical analysis procedur es to prov ide estimates accurate enough to determine of even-aged management. solut ions without the explici t functions (Adams 1974) . While t heor etica lly possi bl e, further r esearch is needed to t est the feasibili t y of this approach . On e potential Whi Ie Adams and Ek 1l~74, 1975) have incorporated conceptually most of the major problem might be the difficul t y in combining the nonlinear mathematic3l program, the decisi on points facing a manager, their entire analysis was directed at sing l e st ands . program for the numerica l analysi s procedure, and the growth and y iel d s imulator Co n s \~q u e ntl y, t hey did not consider the scheduling of compartment or s tand treatments t ogethe r on the same computer. v iewed f r om a forestw ide position. Second l y , their appr oach d i d not adequat e l y treat the pr oblem of det ermining optimal ~ reci cs mix within a given s t and . La s tly , some comput ational probl ems remain when mo r e complex situations are encountered . tn r eview ing t he work of Adams and Ek (1974 , 1975), we believe that five problem areas, some overlapping , need additional work before their (or any other new) tools can be made GROWTH AND YIELD SIMULATORS fully operational . These probl em ar eas are: 1. Improvement of computer and al gori t hm capabi lit ics. Given that the pr ac tical problems with interfacing nonlinear programing to a growth and yield s imulator can be worked out, one is then faced lI'I'i th a wide choice of 2. Development of techniques for i nterfacing stand simulators to nonlinear simulator types to choose from . Munro (1974) c l ass ified s imulator s into three cate programing mode l s . go r ies: Sing l e trce/dis tance dependent , single tree/distance independent, and whole s tand/ d i s t ance independent . 3. Deve l opment of uneven-aged growth and yield s imulators. Single tree/di s t ance dependent simulat ors utilize tree coordinates to apprai se 4. Development of techniques fo r determ ining opt imal species mixes. i~tertree .:ompetition between a given tree and its neighbor s. An examp l e of a s lmulator o f t hi s t ype with the potent ial for us e i n uneven-aged s t ands is the one 5 . Development of optimization t ool s for s chedul i ng compartment treatments r epo rted by Ek and t-Ions erud (19711a , 1974,) . The theoretica l advantage of thi s type on a forestwide basi s . o f s i mu lator is that it can provide the gr eates t amoun t of information concerning both tree and s tand deve l opment. However , the s ing le tree/ dist ance d;;pendent s imulators publi s hed t o date have not demonstra ted an abilit y t o predict individual tree deve l op ment accurately, a nd they do not s eem to predict s tand a ttributes any bette r than the o ther types of simu l ators . It i s possibl e that these results will improve as the "state of the art" improves . The whole s tand/dist ance independent t ype of simulator is easier to develop, There are several disadvantages to using 3ingl e tree/distance dependent s imulators cheap~r to initia lize and run ~ and takes less computer core than do the Singl e tree for answering uneven- aged management questions. First ~ this type of simulator is varieties. Also, its smal l er computer core requirements make it more likely to be inter difficult and expens ive to develop because data with individual tree coordinat es are faced wi th nonl inear programing. The main disadvantage is that individual tree informa not common. The simul ators are a l so more costly to operat e because o f the tree tion is comp letely lacking and , for the very simple whole stand simulators, stand coordinate c ata needed to initialize them and because of the l arge amount of computer s tructure information is sometimes l acking. However, as was mentioned. the lack of time and sf.ace needed to run them . individual tree i nformation i s not critical at this time for two reasons: (a) the i nformation i s not needed to answer most of the uneven-aged management questions, and Second. much of the data generated by this type of s imulator are not needed t o (b) simul at ors that produce individua l tree information have not: demonstrated an ability answer uneven-aged management quest ions. Thus. there is al so a real potentia I for t o do so reliably. overloading the information system with extraneous data. We believe that r e l atively sma ll uneven-aged. whole stand/distance independent Third. the small plot s usually generated by sing l e tree/d ist ance dependent simu simulat ors can be devel oped that wil l provide more detailed information than do pre lator s may not be large enough to represent the uneven-aged s tand accurately. Finally, sent who l e s tand simulators about s tand s tructure and about the growth and vigor of because of the large amount of computer space and time needed. it is doubtful that a tree c l asses within the s tand. The progress of our work tends to confirm this hypoth siruulator of this t ype can be interfaced wi th nonlinear programing. es; s. Once our s imula tor is comp l eted. we hope that a numerical analysis linkage to a nonlinear pr ogr aming routine can be developed and tested for feasibility. Some modelers. who have developed singl e tree/ distance dependent simul ators. have tried to circumvent the expense and difficulty of requiring tree coordinates when the simulator is initializ.ed by artificially generating tree coordinates. This basically converts the s imulator to a distance independent type i nsofar as later usage is con cerned (~tunro 1974) . An example of a single tree/dist ance independent s tand simulator that has the potential for adaptation to uneven-aged stands is Stage's (1973) "progno sis model. II St age ' s approach has several advantages over the distance dependent t ype. Besides the SPECIES COMPOSITION obvious advan-.::a ges of not requir i. ng tree coordinates, his approach does not r equire the complete enumeration of the plots to be "prognosticated." Instead, it is based on s amples drawn from throughout the stand. This lessens the amount of data to run the Both r.10ser ' s (1972, 1974) and Ek ' s (1974) whole s tand/distance independent simu mode l and makes it possibl e to apply the model to uneven-aged s tands. which a re oft en lator s were developed from mixed species data. None of the simul at or s recognized l arge in size. individual speci~s; so the esti ma ted yields r epresent only the species mix found in their data. Oe t e r mi ning an optimum species mix i s an important ques tion for fores t The disadvantages of sing l e tree/distance independent simulators are that their managers interest ed in practicing either even- or uneven-aged forest management. Adams programs are s till large and generate a large amount of information not presently and Ek ( 1975) conc luded that the best way to approach the species composit ion problem needed t o answe r uneven-aged managemen t questions. Because of their siz.e ~ the inter was t o use a s ing le tree/distance dependent simulator and a growth maximization fac i ng of the distance independent simulator s with nonlinear programing is as doubtful a lgor ithm. They r eject ed using whole s t and/ dis t ance independent s imula tors because as wit h the distance ('.;:pendent t ype. It is also generally acknowledged that sing l e they believed that (a) multispecies Khole stand simulators would be a lmos t as complex tree/distance indeper Jent simulators ar e not designed to provide accurate individual as Single tree types and (b) determining the parameters i n the nonlinear, mul t ispecies tree development ip .ormation . Also, their advantage over whole s tand/dist ance inde equations would tax o r exceed exist i ng nonlinear regression programs . pendent simu lat o r ~ for pr edicting s tand development has not been demonstrated. We do not agr ee. ~tultispecies who l e stand simulat or s undoubted l y will be more Whole c: .. ", ... J/di stance i ndependent simulator s can range from the simple t o the comp l ex than s ingle tree s imulators , but we 10 not feel that they wi ll approach the comp l ex. ;·:.:.::.e r' s (1972) set of first-order, ord inary differential equations for comp l exity of individua l tree/ distance dependent s imulat or s. The problem of non- expressing change in the total number of trees (or in t ot a l basal ar ea) of the s t and is I inear r egress ion lim i tati ons can a I so be avoidec' through t he use of other mode 1 ing a n example of a s impl e uneven-aged whole stand simulator. The differential equations s trategies . were used t o express gr oss growth. mo rtality, and ingrowth rates for all trees 7 i nches or greater in size. In a later version, ~1oser ( 1974) divided the s t and into six Ne base these conclusions on OUT work in developing a who le stand/ distance inde diameter classes (1.6- 4.5. 4.6-9.5 . 9.6- 14 .5. 14.6-19. 5 . 19.6 -24 . 5 . a nd 24.6+inches). pendent simulator for uneven-aged ponderosa pine . In this simul ator. ponderosa pine This improvement al l owed the monitoring of changes in diameter dis tribution becaus e of ha .. been divided i nto two vigor c lasses , "blackjack pine" and "ye llow pine ." based on different treatments . For each diameter c l ass, differentia l equations were again used bark color of the tree . Each vigor class i s represented by a separ at e diameter class to mode l gross gr o·... ch, morta l i ty, and ingrowth, this time expr essed as basa l ar ea. distribution. As a result. each vi gor c l ass has been handled in a manner analogous t o cubic-foot volume, or number of trees . the trea t ment of separate species in a multispecics model. Separate gr owth and mortality functions have been developed that interrelate both vigor components of the s tand. Ne Ek's (1974 ) uneven-aged s tand simulator is also fairlx s imple. He divided the have not encountered insu r mou!"ltabl~ probl ems mode ling these two vigor c l asses, and we stand into 2-inch diameter c l asses and then used a t echnique ana l ogous to s t and tabl e do not believe the s imulator is overly complex. A simi l ar approach i s worth trying projection to move the trees through the d iameter c lasses. The c hanges i n the number for multispecies simulators. of trees in each diameter class due t o ingrowth, upgrowth. and mortal ity were modeled as nonl inear functions . Given that a simulator can be developed for nrultiple species. the optimization problems are merely logical extensions of Adams' a~d Ek'~ work. ~s a~ ex~mple, the SCHEDULING OF COMPARTMENTS following formulation is uied to determine the optlmal diameter dlstrlbutlon for two species (X and 1) and a specified l evel of stocking (L): The preceding discussion of management decisions 1 through 4 shows that foresters only recentl y have begun to apply modern decisionmaking tools to help solve uneven-aged management problems . Further, a review of the literature indicates that most of this recent work i s directed at the individual treatment unit or stand and not at the forest in its entirety . In fact. little attention has been paid in the literature to the scheduling of uneven-aged compartments for treatments. Loucks (l~64) observed that linear programing could be used to schedule treatments in uneven-aged forests, and Norman and Curlin (1968) applied linear programing to the management of a Tennessee Valley Authority (TVA) forest organized for uneven-aged management . The Forest Service subject to: Timber Resource Allocation Mode l (Timber W1) also is capable of handling uneven-aged management cptions (Navon 1975). Further, we understand that the mathematical programing D= I, N • t.XlO, system, ~1a.x-\.fi 11 ion (Ware and Clutter 1971). used extensivel y to schedule harvest operations in the Southern States has been modi fied by some users to include uneven-aged D= I, M· 6YD~O, management options. Thus, it is apparent that linear programing can be used to facil itate scheduling when an uneven-aged management system is used. To clarify this. we r,;(f(D) ' (Xdt) • Jeft))) L will examine the scheduling problem in more detail, pointin~ out difficulties to be overcome. A simplified linear programing fOI'1J1Ulation and two alternative formulations are then proposed. Each formulation is to illustrate one way to interface stand-level N Xeft)?o, D= I, information, such a s might come from the work of Adams and Ek (1974, 1975), with a fores twide optimization model. Jeft ) ?O, D= I, M In this formulation, V and U a re value functions of diameter f or species X and Y, Although optimal stand structure, species compOSItIon, and conversion strategy rna)' D D be determined for each stand, it i s highly unl ikely that these optimal stand solutions respectively; lJ.X and 6Y are the changes in the number of trees in the Dth diameter will lead directly to an optimal forestwide scheduling solution. Preliminary work D D class after one growth period; f ( D) is the function that determines diameter class indicates that the decision points for each stand that can be determined by schedul ing stocking; and XD(tJ and YD(tJ are the initial ntDIlber of trees in the Dth diameter are ti~e of first entry, cutting cycle length, and conversion length. Therefore, the a lternative treatme •. ::, schedules for each uneven-aged stand are a series of yie lds that class . By eliminating all terms involving species YI the exact one-species formulation are the result of determining optimal stand structure. species composition, and of Adams and Ek (1974) results. conversion strategy for a sel ected set of alternative cutting cycles, conversion lengths, and times of first entry. An unexplored area is the feasibility of linking a multispecies model with a l'ie a s sume at the outset that the forest area has been organized into geograph nonlinear programing routine. Although theoretically possible. such a model might ically i dentifiable compartments, with each compartment composed of one or more encounter computational limitations. Additional research is needed before definite ihdividual treatment units or stands. We further assume that all stands are to be conclusions can be drawTl . treated and managed as uneven-a ged stands . However, this assumption can be relaxed without major impact on the formulation that follows. The planning horizon (that is, the number of years over which we wish to plan) is spl it into a series of p lanning periods, each of constant length, and an equal multiple of the growth period. This latter a s sumption i s necess:J.ry if Adams' and Ek's (1974, 1975) stand optimization procedures are to be used to produce stand-level inputs. However, this limitation may be eliminated if a different approach to stand simulation is adopted. I\s previously noted, the cutting cycle and conversion length are a l so restricted to even multiples of the growth period. We also assume that the scheduling of management activities is done at the com partment level and not at the stand level. Later. we alter this assumption by elimin ating compartment boundaries and, in essence, treat the whole forest as a single com partment made up of many stands. For treatment activities, it is necessary to recog nize individual stands within compartments. We deal with this by aggregating stand information within a compartment , but ","'e preserve the integrity of the compartment for scheduling purposes. 12 11 For each stand in a given compartment, a set of management alternatives is gener While the date of first entry is a useful descriptive variable, it is not used as ated. As shown in table 1, each management alternative is characterized by its cutting a control variable in the compartment level optimization. However. it mu s t be equal to cycle, conversion length . ::.~c! J.::.t'!.' :of [i:'~t entry. One of the management alternatives or evenly divisible by the cutting cycle and conversion period in O..lr formulation. is assumed to reprO!sent the optimal cutting cycle, cOi!version period, and conversion strategy for a given s t and provided by a procedure simi1ar to that of Adam s and Ek The manner in which management alternatives are defined for each stand within a (1974. 1975). H~wcver, this condition can be eliminated '~ithout affect ing the formul a· compartment can greatly affect the computationa l feasibility of the approach being tion of the scheduling problem. The remaining management alternatives for each stand deve loped. For instance, if a common definition of management alternatives is forced arc clearly not optimal, but are included to facilitate ·the compartment l evel optimiza upon each stand in a compartment (as in table 1) J the total number of alternatives to tion. Compart'llent surmnaries are obtained by t otali n~ all stand variables (weigh!'ed by examine will be equal to ifla where a = the number of alternatives per stand and c = stand size) over a given planning period. the compartments. Table I.--E:rample of rmnagemen t alt ernat ive 8peei[ieatiml [ 01'mQ t However, if each s tand in a given compartment adopts a unique definition for its Si management al ternatives, then the total number of alternatives mushrollms to ~ a i=1 and 8 i = number of stands in the ith compartment. S- ye3r planning period A compromise solution to this problem is possible if a priority ranking of Net present Management alternatives value management alternati ves of each stand within a compartment is determined. This would unJoubtedly lead to suboptimization. but would be better computationally than the compartment i Stand 1 first approach and more feasible than the second. 'cc· 10 Based upen one of the above options, we can proceed to formulate the compartment 1 2DE .. I ' v level scheduling problem as a linear program. Although we assume that our objective i s to maximize net present va lue over the planning horizon, other objectivp.s are equally possible. In so doing. we also assume that the demand for stumpage is perfectly e l a s tic bet",'een Uk and Lk (see below). We define cc • DE = x .. the number of acres in compartment i to ffi.lnage under management 'J alternative j V •• the harves t volume ppr acre removed from compartment if managed cc • S 'J under management a lte rnative j DE • 3 Stand 2 i the compartment index where i = I, 2, ... m cc • 10 DE '" I j the management alternatives index where j I, 2, •• • n cc • 10 DE = 2 k the planning period index where k = I. 2, ... t cc = OE = net present va 1 ue (NPV) per acre if compartment i is managed according to management a 1ternati ve j the upper bound on the desired harvest vo lume in planning cc • period k DE • Lk the lower bound on the des ired han'est volume in planning period k Summary for compartment i A1.' = the maxir.lum a creage in compartment avai l abl e for management We then have ~Ia x NPV = Lex i j ij ij lec .. C:u tt i ng cycle. 2DE ". Da t e o f entry. lV .. Vo l ume removed at time of ha r vest . 13 14 subject to r r SUMMARY x .. ,,; for all k = I, 2 , i j V ij ~J Uk X •• for all k = 1, 2, V ij ~ Lk f J ~J The use of uneven-ageJ forest management has been limited in this country. One r X •• ,,; A. for all i = I, 2, m reason for this might be the bel ief that the practice of uneven-aged management is J ~J ~ more of an art than a science. As a result, historically, few tools have been devel Under this formulation, X is treated as a continuous decision variabl e implying oped to aid the manager interested in applying uneven-aged management . However, recent ij Congressional and administrative decisions, along with increased public concern and that a compartment can be managed under more than one alternative. This further implies involvement ~ n forest management decisionmaking, are forcing uneven-aged management to a management strategy,..ror a compartment that involves different cutting cycles and be reevaluated as an alternative to current practices . With increased interest has different dates of first entry. However, as long as all of the above cycles or come initial developrr:ent of tools that can help the manager answer some pressing periods are equal multiples of each other, the management strategy presents no serious questions about uneven-aged management. Some aspects of uneven-aged management may scheduling problem. The real problem lies in the fact that if a stand is managed remain an art but evidence is growing that more science can be introduced into it under two or more management alternatives, no guidance is given for locating the portion than previously was thought. of the stand to be managed under each alternative. As an alternative to the above formula.tion, we may wish to treat the whole compart ment using one management alternative. To accomp lish thi~, we redefine same of our variables. In this case, let the proportion of compartment i managed under management al ternative j the total net present value from compartment i if managed under management alternative j the total harvest volume from compartment if managed under management al ternat i ve j We also require that X takes on the value of 0 or 1. ij Generally, the above integer programing problem will be more difficult to solve computationally than the linear programinf formulation previously presented. Thus, if an integer solution is desired. a common definitioll of management alternatives probably would be required to reduce the computational load. The I inear and integer programing problems presented above have been based on the premise that the compartment is the basic unit of management and the s tand the opera tional unit for which a specific silvicultural treatment is specified. Thus, both formulations restrict entry into s tands in a given compartment. Since the cutting cycles for all s t ands in a given compartment are equal multiples of each other. one or more stands are treated during each planning period. As an a lternative, we may do away with compartment boundaries entirely and schedule individual s t ands. In thi!= ~ase, the maximum number of management altern- atives to consider i s .fa·s .. where a, c, and 8. are as previously defined. t.= l t. t. Under this approach, a s t and could s t ill be managed under two or more management alternatives. This can be avoided if an intege:- programing formulation is adopted. However, as mentioned earlier, the computational difficulty associated with solving this type of problem mounts rapidl y as management alternatives increase in number. Techniques for scheduling treatments for uneven-aged stands do not differ markedly from those used for even-aged management. Further, it makes no di fference if even-aged stands are intermingled with uneven-aged stands . Thus . we believe that with few excep tions. uneven-aged management systems can be developed for large forest properties. However. actual case studies of this approach are not available in the literature . IS 16 PUBLICATIONS CITED ~1eyer, H. A. 1943. ~fanagement without rotation. J. For. 41: 126-132. Adams, Darius M. ~feyer. H. A. 1974 . Jeriv3tion of optimal management guides: a survey of analytical approaches . 1952 . Structure, growth and drain in balanced uneven- aged forest. J. For. In Forest modeling and inventory--selected papers from 1973 and 1974 meetings 50:85-92. of midwest mensurationists, p. 1-9 Der . For. J Sch . Nat. Resour . • Call. Agri.:.. Meyer, H. Arthur. Arthur B. Recknagel, Donal d O. Stevenson. and Ronald A. Bartoo. and Life Sci., Univ . Wis •• Madison. 1961 Forest management. 2nd ed. 282 p. The Ronald Press Co .• New York. ~Ioser. W., Jr. Adams J Darius M. J. 1976. A note on the interdependence of s tand stnlcture and best s tocking in a 1972. Dynamics of an uneven-aged forest s t and. For. Sci . 18:184-191 . selection forest. For. Sci . 22: 180-184 f.k> ser, John W•• Jr. Adams, Darius M•• and Alan R. Ek . 1974. A system of equations for the components of fa-rest growth. In Growth models 1974. Optimizing the management of uneven-aged forest stands. Can. J. For. Res. for tree and stand simulation. p. 260-287, Fries (Ed.) Dep . For. Yield Res., Royal 4: 274-287. CoIl. For. , Stockholm. Res. Note 30, 379 p . Adams, Darius M. , and Alan R. Ek. ~foser, John W.. Jr. 1975. Derivation of optimal management guides for individual s tands. In Prac. 1976. Specification of density for the inverse J-shaped diameter distribution. SAF workshop on systems analysis and forest resource management in Athens, For. Sci. 22:177-180. Georgia., p . 132- 147. ~lunro, Donald D. Al exander, Robert R.. and Carleton B. Edm; nster. 1974. Forest growth models--a prognosis. In Gr owth models for tree and stand simu 1977a. Regulation and control of cut under uneven- aged management. USDA For. Serv o lation, . p. 7-21. Fries (Ed.), Dep. For. Yield Res., Roya l ColI. For .• Stockholm. Res. Pap. RM-182, Rocky Mt. For. and Range Exp. Stn., Fort Collins, Colo. Res. Note 30. Alexander, Robert R., and Carleton 8. Edminster. Navon, Daniel I. 1977b. Uneven-aged management of old growth spruce-fir forests: cutting methods and 1975. Timber RA.'I User's ~lanual Part II: Forester's Guide. USDA For. Servo Pac. stand structure goals for the initial entry. USDA For. Servo Res . Pap. Rt-1-186 , Southwest For. and Range Exp. Stn •• Berkeley, Ca l if. Rocky Mt. For. and Range Exp . Stn . • Fort Call ins, Colo. Norman, E. L., and J . W. Curlin. Davis, Kenneth P. 1968. A linear programming model for forest production control. Oak Ridge Natl. 1966. Forest management: regulation and valuation. 519 p. 2nd ed. McGraw-Hill Lab. Dep. 4349. Book Co., New York. Reynolds, R. R. Duerr, William A.• and W. E. Bond . 1954 . Growing stock in the all-aged forest. J . For. 52:744-747. 1952. Optimum stocking of a selection forest. J. For. SO: 12-16. Smith. David Martyn. Ek, Alan R. 1962. The practice of silvicul'ture. 578 p . John Wiley & Sons. Inc., New York. 1974. Nonlinear models for stand table projection in northern hardwood stands. Stage, Albert R. Can . J. For. Res. 4:23-27. 1973. Prognosis model for s tand development. USDA For. Serv. Res. Pap. INT-137, Ek, Alan. R., and Robert A. Monserud. 32 p. Intermt. For. and Range Exp. Stn . , Ogden, Utah. 1974a. FOREST: a computer model for simulating the growth and reproduction of mixed Steering Committee for Indian Reservation Forests. species forest stands. Res. Rep. A2635. Sch. Nat. Resour., CoIl. Agric. and Life 1977. f.tak ing dollars and sense out of forestry. Proc. Na t ional Indian Timber Sym., Sci., Univ. Wis., Madison. February 23-25, Seattle. Wash . Ek, Alan R., and Robert A. Monserud. U.S. Department of Agriculture, Forest Se;vice. 1974b. Trials with program FOREST: growth and reproduction simulation for mixed 1973. Silvicultural systems for the major forest types of the United States . USDA species even- or uneven-aged forest stands. In Growth models for tree and s tand Agric. Handb. 445. simulation, p. 56-73, Fries (Ed . ). Dep . For Yield Res. , Royal ColI. For ., Stock U.S. Department of Agriculture, Forest Service. holm, Res. Note 30. 1975 . Uneven-aged sil vicul ture and man agement in the Eastern United States . Proc. Hough, A. F. in-Service workshop, July 15- 17. f.lorgantown, W. Va. 1954. Th e control method of forest management in an age of aerial photography. J. U. S. Department of Agricul ture, Forest Service. For. 52 : 568-574. 1976. Uneven-aged s il vicul ture and management in the Western Uni ted States . Proc. Knuchel, Hermann. i n-Ser vice workshop, Oc t . 19-21, Redding. Calif. 1953. Planning and control in t he managed forest. 360 p . Translated Mark L. Anderson. Wa l ker, ~::. t. Oliver and Bo yd. London. 1956. Growing s tock vo!tlmes in unmana ged and ::Ianaged forests. J. For. 54: 378-383. Leak. William B. Ware , G. D., and J. L. Clutter. 1964 . An expression of diameter distribution for unbalanced, uneven-aged stands and 19:-1. A mathematical programing system for the management of industrial forests. fores t s. For. Sci. 10 :39-50. Fo r . Sci. 17 : 428- .1 45. Leak, William 8., and Stanley f.1. Filip. 1977 . Thirty-eight years of group selection in New England northern hardwoods. J. For. 75 :MI-643. Loucks Daniel P. 1964. The development of an optimal program for s us tained-yield management. J. For. 62:485·490 . Matthews, Dona ld M. 1930. Management plans for a ll age forests. J. For. 28 : [057-1069. 17 18 Hann, David W., and B. Bruce Bare. 1979. Uneven-aged forest management: state of the art (or science ?). USDA For. Serv. Gen. Tech. Rep. INT-50, 18 p. Intermt. For. and Range Exp. Stn., Ogden, Utah 84401. Examines some Important historical factors that have caused widespread preference of the even-aged management system over the uneven-aged. Major deciSions facing forest managers interested In applying unevenaged management are defined and a review is made of techniques traditionally used, or recently proposed, for use In making these decisions. Finally, problem areas needing further research and development are Identified. KEYWORDS: uneven-aged, even-aged, forest management, silviculture , management deciSions, stand simulation, rrathpmatlcalprogramlng, optimi zation, compartment scheduling. Hann, David W., and B. Bruce Bare. 1979. Uneven-aged forest management: state of the art (or sclen.ce ?). USDA For. Serv. Gen. Tech. Rep. lNT-50, 18 p. Intermt. For. and Range Exp. Stn., Ogden, Utah 84401. Examines some important historical factors that have caused widespread preference of the even-aged management system over the uneven-aged. Major decisions facing forest managers Interested in applying unevenaged management are defined and a review is made of techniques tradltlonally used, or recently proposed, for use in making these decisions. Finally, problem areas needing further research and development are Identified. KEYWORDS: uneven-aged, even-aged, forest manag ment, silViculture, management deCiSions, stand simulation, mathematIcalprogramlng, optimi zation, compartment scheduling.