Modeling Diameter Growth and Self-Thinning in Planted Sugi (Cryptomeria japonica) Stands

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1 Th Opn Fost Scinc Jounl, 211, 4, Opn Accss Modling imt Gowth nd Slf-Thinning in Plntd Sugi (Cyptomi jponic) Stnds Tohu Nkjim *,1, Mitsuo Mtsumoto 2 nd Noihiko Shiishi 3 1 Lbotoy of Globl Fost Envionmntl Studis, Gdut School of Agicultul nd Lif Scincs, th Univsity of Tokyo, Yyoi, Bunkyo-ku, Tokyo , Jpn 2 Fosty nd Fost Poducts Rsch Institut, 1 Mtsunosto, Tsukub , Jpn 3 Lbotoy of Fost Mngmnt, Gdut School of Agicultul nd Lif Scincs, Univsity of Tokyo Yyoi, Bunkyo-ku, Tokyo , Jpn Abstct: Th objctivs of this study w to nlyz dimt gowth in ltion to ntul thinning in high-dnsity stnds in vn-gd, pu plnttion fosts nd to dvlop gowth pdiction systm bsd on Jpns pmnnt plot dt. Long-tm dt codd in vn-gd, pu, unthinnd stnd plots of Sugi (Cyptomi jponic) fosts w vilbl. Rltionships btwn log-tnsfomd vg dimt t bst hight (BH) nd stnd dnsity w nlyzd. In ddition, th slf-thinning tio (STR) ws nlyzd fom dt gthd fom unthinnd pmnnt plots. Rltionships btwn STR nd th yild indx, Ry (th tio of ctul stnd volum to tht t full stnd dnsity), w lso nlyzd nd modld. Bsd on ths nlyss, th dimt gowth t ws fomlizd s function of BH, stnd dnsity nd stnd g, using pmts divd fom full dnsity cuvs. Goodnss of fit of pdictions of dimt gowth in unthinnd stnds using th stimtd pmts w vlutd by comping pdictd stnd dnsity nd BH with thos obsvd in th pmnnt plots. Th vg o t, divd by vging th bsolut vlus of ll clcultd o ts fo th stimtd stnd dnsity, ws 1.8% with mximum of 6.4%. Th vg o t fo th BH ws 2.9%, with mximum of 8.1%. Th squd Pson s coltion cofficints of pdictd nd obsvd vg BH w btwn.97 nd 1.. Kywods: Cyptomi jponic plnttion, full dnsity cuv, gowth modl, slf-thinning. INTROUCTION Plnning, dcision mking nd th implmnttion of sound silvicultul pctics in fost mngmnt qui ccut pdictions of how stnd condition nd dnsity ltd nd likly to chng ov tim [1]. High qulity timb poduction hs minly lid on silvicultul pctics in mngd stnds, such s contolling stnd dnsity by thinning. It is lso impotnt to b bl to pdict gowth ts in unthinnd stnds, nd th quntity of dd-wood in thm in od to mk stimts of cbon stocks. Unthinnd stnds hv long bn studid in mny pts of th wold, including th Unitd Stts [2], Euop [3, 4], nd Asi [1, 5]. Gnlly, two kinds of modls vilbl fo nlyzing nd pdicting gowth in unthinnd stnds: pocss [6] nd mpiicl [7, 8] modls. Th im of pocss modls is to us knowldg of undlying cologicl pocsss to simult futu fost soucs. In contst, mpiicl modls cn b usd in conjunction with tditionl fost mnsution to nlyz th ltionships btwn vibls such s stnd gowth, slf-thinning nd stnd dnsity [8-11]. *Addss cospondnc to this utho t th Lbotoy of Globl Fost Envionmntl Studis, Gdut School of Agicultul nd Lif Scincs, th Univsity of Tokyo, Yyoi, Bunkyo-ku, Tokyo , Jpn; Tl: ; Fx: ; E-mil: nkjim@f..u-tokyo.c.jp Sinc fost owns nd mngs nd to collct lss dt in od to implmnt commndtions bsd on mpiicl modls, pst studis hv oftn bn bsd on mpiicl concpts such s th llomtic ltionship undlying full dnsity cuvs, i.. cuvs dscibing th coltion btwn th numb of ts p unit in full dnsity (unthinnd) stnd nd thi vg dimt [12-14]. Ely studis on slf-thinning in high-dnsity Jpns stnds in which mpiicl modls w mployd [15] oftn usd stnd dnsity contol digms [16-2] bsd on full dnsity cuvs [21]. Howv, ths studis w ll conductd btwn 14 nd 49 ys go, whn Jpns timb pics w high nd stndd Jpns vn-gd pu stnds could b mngd by ltivly fqunt thinning using stndd dnsity-contol cuvs [22, 23], lthough it ws known tht som dt sts usd to div full dnsity cuvs w indqut [21]. Sinc th citd studis w conductd, futh dt on high-dnsity stnds hv ccumultd though th piodic monitoing of unthinnd pmnnt plots [24], i.. xpimntl plots in th of intst (gnlly known s silvicultul tils in th USA), usd to collct tim sis of dt [25]. Nvthlss, ths li studis on pmnnt plots cn povid bnchmks tht cn b usd to vlut mo cntly clcultd full dnsity cuvs. Although mo thn hlf of th plntd fosts in Jpn ov 4 ys old, thi ottion piod hs bn xtndd by ducd logging [26]. It is thfo impotnt to invstigt thooughly ou bility to pdict / Bnthm Opn

2 5 Th Opn Fost Scinc Jounl, 211, Volum 4 Nkjim t l. stnd gowth ov th long-tm, und high dnsity conditions. Som pocss modls tht hv bn dvlopd using infomtion obtind fom unthinnd stnds in Jpn nbl us to pdict stnd biomss, litt fll, nd nt pimy poduction t th lvl of individul ts, by using mtooogicl nd biologicl dt [5]. Howv, it would lso b usful if fost mngs w bl to pdict dimt gowth nd stnd dnsity fom full dnsity cuvs pplicbl t th stnd lvl, bcus Jpns timb pics citiclly dpndnt on log dimt [27]. Moov, dclining timb pics discoug fost owns fom mnging plntd fosts, cusing dclin in thinning cnt studis [28, 29] hv suggstd tht mo thn hlf of ll Jpns vn-gd, pu plntd stnds hv not bn thinnd fo t lst 1 ys ccompnid by incss in th bundnc of unmngd, vn-gd, pu fosts [26]. Bfo timb pics fll, in lin with th pviling conomic conditions in Jpn, mny s of plntd fosts w fquntly thinnd ccoding to stndd dnsity contols bsd on stndd dnsity cuvs [23]. Howv, sinc th now incsing s of unthinnd stnds in plntd fosts in Jpn [28], it sms sonbl to pdict dimt gowth in ths high dnsity stnds using full dnsity cuvs. It is thfo impotnt fo stimting both timb poduction nd th cbon sink vlu of Jpns plntd fosts, to b bl to pdict gowth in high-dnsity stnds wh no thinning is bing undtkn. Th objctiv of th psnt study ws to tst th hypothsis tht vg dimt gowth could b stimtd by fomlizing function of xisting BH, stnd dnsity nd stnd g, using pmts divd fom full dnsity cuvs, nd to dvlop gowth pdiction systm bsd on pmnnt plot dt obtind fom plntd fosts in Jpn. MATERIALS AN METHOS 1. Study A Th Univsity of Tokyo Chichibu Fost (35 55 N, E) is in Chichibu municiplity, Sitm Pfctu, Jpn, btwn 53 m nd 1,98 m bov s lvl. Th tin is undulting with stp slops, nd most soils of th bown fost typ. Th fost is loctd in cooltmpt zon, with n vg nnul tmptu of 1.7 C, nd vg nnul infll of 1,294 mm. Th totl fost is 5,812 h, of which 3,11 h (53%) scondy fosts covd by minly dciduous bodlvd ts, nd 1,889 h (33%) pimy fost. Th mining 767 h (13%) plntd fost, of which 169 h (22%) Sugi (Cyptomi jponic) stnds, 291 h (38%) Hinoki (Chmcypis obtus) stnds, 27 h (27%) Kmtsu (Lix lptolpis) stnds, th mining 1 h (13%) Sw (Chmcypis pisif) nd oth plntd fost. Sinc 1955, mny pmnnt sch plots hv bn stblishd in plnttions of Sugi, which is th most common t spcis in vn-gd pu stnds in Jpn. Although most of th plntd stnds hv not hd ptd gound suvys conductd in thm, th plots listd in Tbl 1 hv spcilly long sis of msumnt cods. T hights, BH, nd stnd dnsity (stms p h) in unthinnd stnds hv bn codd ppoximtly vy 5 ys in ight pmnnt plots: Ytksw C1 (.2387 h), Ytksw C2 (.71 h), Iiym C3 (.128 h), Yohkusw C4 (.52 h), Idosw V1 (.957 h), Kosubisw V2 (.1234 h), Yohkusw V3 (.369 h), nd Iiym V4 (.554 h) [24] (Tbl 1). Th pmnnt plots ctngul. Th potntil vgttion nd vgttion cov of ths plots is hbl typ. Ths dt w ptitiond fo modl clibtion (C1-C4 of plot I) nd vlidtion (V1-V4 of plot I). 2. Mthodology W invstigtd th ltionships btwn stnd gowth, slf-thinning nd stnd dnsity. Th ithmtic mn of BH (cm) nd th stnd dnsity (stms/h) w clcultd fo ch st of cods fom th pmnnt plots, nd nlyzd with fnc to pst studis [21]. Rink suggstd tht th numb of ts p h t full dnsity vis with th vg tunk dimt in th stnd [13]. Bsd on this hypothsis, th cuv dscibing th ltionship btwn mximum numb of ts p h nd vg dimt, plottd on common log-log scl, is dfind s th full dnsity cuv in this study (fomul (1)). Th pmts d nd K in fomul (1) w stimtd by lin lst-squs gssion of log-tnsfomd BH ginst stnd dnsity. Sinc th study sits hd not bn Tbl 1. Cunt Chctistics of th Pmnnt Plots s tmind by Gound Suvy Plot I Altitud (m) Stnd Ag (y) Stnd nsity (Stms/h) Stnd Hight (m) Slop Aspct A (m 2 ) Numb of Msumnts Totl Bsl A (m 2 h -1 ) C Stp SE C Stp SE C Stp SE C Stp S V Modt E V Mdium E V Mdium SW V Stp S

3 Modling imt Gowth nd Slf-Thinning in Plntd Sugi (Cyptomi jponic) Stnds Th Opn Fost Scinc Jounl, 211, Volum 4 51 thinnd o distubd by ny ntul ctstoph sinc th stblishmnt of th pmnnt plots, it ws ssumd tht fomul (1) psntd th full dnsity cuv fo ths sits. log N = K + d log (1) wh: = BH (cm); N = stnd dnsity (stms/h); nd d & K pmts. Th pmt vlus stimtd in th psnt study w compd with full dnsity cuvs divd fom pvious studis [21]. Th slf-thinning tio (STR) of stms ws lso invstigtd. Following pvious studis [16, 17, 3], w nlyzd th ltionship btwn STR nd th yild indx (Ry), th ltt bing th tio of th ctul stnd volum to tht t full stnd dnsity. Ry is ltiv msu of stnd dnsity: tio btwn cunt stnd volum nd mximum stnd volum, nging fom to 1. Th high th vlu of Ry, th high th dnsity of th stnd nd th gt th comptition btwn ts. Ry ws plottd ginst th nnul STR fo incmnts of Ry (y -1 ). Ry ws stimtd by substituting th pmts divd fom stnd dnsity mngmnt digm [31], vg stnd hight, nd stnd dnsity, into th following fomul (2) [3]. H Ry = V H b + b = H b V Rf H H b + b (2) N wh: Ry = yild indx; V = stnd volum (m 3 /h); V Rf = full stnd volum (m 3 /h); H = vg stnd hight (m); N = stnd dnsity (stms/h); nd,,, b, b, b pmts. Following pvious studis [3, 31], vlus of.72, , 562, -2.87, , w substitutd fo th pmts,,, b, b nd b in fomul (2). Th dcs in stnd dnsity ws stimtd fom cuv divd fom th xponntil function in fomul (3), lting Ry to th slfthinning tio [32]. Th pmts in fomul (3) w stimtd by pplying th xponntil cuv to th ltionships btwn STR nd Ry using th nonlin lstsqus mthod tht is clld th qusi-nwton mthod, which is pplicbl to nonlin ltionships [38]. STR = A BRy (3) wh: STR = nnul slf-thinning tio p incsing of Ry (y -1 ); nd A & B pmts. Th following ssumptions w md in this study. Fist, pvious studis [33, 34] confimd tht stnd gowth could b stimtd s function of stnd g. On this bsis, it ws ssumd tht, bsd on th full stnd dnsity cuv, BH would incs ccoding to gowth function with fixd pmts. Pvious studis [33, 34] md us of th Richds o Gomptz functions fo stnd gowth pdiction. H, th Gomptz function, s givn in fomul (4), ws slctd fo stimting pmt vlus to pdict BH gowth bcus of its obustnss nd its simplicity. = m xp( nt) (4) wh: = gowth t fo vg BH (%/y); m & n pmts; nd t = stnd g (y). Scondly, pvious mpiicl studis hv suggstd tht th is n invs coltion btwn stnd dnsity nd stnd gowth und lxd intspcific comptition [35, 36]. Bsd on this mpiicl vidnc, w ssumd tht if th stnd dnsity lvl divd fom vg BH, nd th stnd dnsity plottd on log-log scl, diffd fom th full stnd dnsity cuv, thn th gowth t of BH could b djustd by this diffnc. Bsd on this ssumption, thfo, th low th stnd dnsity ltiv to th full stnd dnsity cuv, th lg th upwd djustmnt of gowth t. By combining fomuls (1) nd (4), th dimt gowth of ts in unthinnd stnds ws xpssd using fomul (5). In fomul (5), th fist nd scond tms show th dimt gowth t ccoding to th stnd g, nd th gowth t djustmnt fcto ccoding to th diffnc btwn th stnd dnsity lvl nd full stnd dnsity cuv, spctivly. Pmt p in fomul (5) indicts th dg to which stnd dnsity ffcts th gowth t with spct to BH. Although pvious studis focusd on thinnd stnds mngd ccoding to th stndd stnd dnsity contol cuv [23], obtind by pplying fomul (1) to plntd fosts with clssic thinning pctics, fomul (5) hs bn pplid to thinnd stnds thoughout Jpn [22, 37]. In Jpn, thinning fom blow ws common pctic in plntd fosts [24]. = m xp( nt) + p(k log N d log ) (5) Bsd on ths hypothss, Fig. (1) illustts th ovll ssumptions mbodid in fomul (5), showing th ltionships btwn th full dnsity cuv, vg dimts nd stnd dnsity nd plottd using log-log scl. Points 1 to 2 nd 2 to 4 in Fig. (1) psnt th duction in stnd dnsity s sult of slf-thinning nd th dimt gowth ft slf-thinning, spctivly. Fo xmpl, th mov fom point 1 to point 2 on th gph psnts dcs in stnd dnsity sulting fom slf-thinning, lthough th stnd g nd vg t dimt min unchngd (Fig. 1). At point 2 th dimt is smll thn tht xpctd ccoding to th full dnsity cuv (Fig. 1), nd thus th scond tm in fomul (5) is gt thn. Thfo, gt dimt gowth t t point 2 thn t point 1 is to b xpctd bcus of th ducd comptition t point 2 (Fig. 1b). In ddition, if th is no slf-thinning, th high gowth t (Fig. 1b) sults in ts with dimts lg thn would b xpctd ccoding to th full dnsity cuv, s fo xmpl t points 3 nd 4 in Fig. (1). In this cs, th low dimt gowth t t point 4 thn t point 5 is to b xpctd (Fig. 1b). In th psnt study, pmts K nd d w divd fom full dnsity cuvs s mntiond bov. By substituting th vg BH gowth t ( t ), stnd dnsity (N) nd vg BH () into fomul (5), pmts m, n nd p w stimtd by minimizing th totl squd os of th obsvd nd clcultd gowth tios fo th vg BH. Th mining pmts (m, n, p) w stimtd by pplying th nonlin lst-squs mthod (th qusi- Nwton mthod) to th BH gowth of ts in pmnnt plots. In od to stimt ths pmts fom this

4 52 Th Opn Fost Scinc Jounl, 211, Volum 4 Nkjim t l. log Gowth t (b) Fig. (1). Exmpls of () stnd dnsity dpnding on slf-thinning, nd (b) chngs in dimt gowth t bsd on th ssumptions undlying th nw modl. Th solid nd dottd lins in Fig. (1) indict, spctivly, th full dnsity cuv (fomul (1)) nd chngs in th vg dimt ( (cm)) nd stnd dnsity (N (stms/h)) plottd on log-log scl. Th solid nd dottd lins in Fig. (1b) indict, spctivly, th gowth t (fomul (4)) und th full dnsity cuv nd th gowth t dpnding on th chngs in vg dimt nd stnd dnsity shown in Fig. (1). Ech point btwn 1 nd 5 in Fig. (1, b) psnts th sm stnd g. F indicts th stnd dnsity lvl on th full stnd dnsity cuv. pocdu, th gowth t of th vg BH (%/y) ws obtind using fomul (6), which givs th gomtic mn of th gowth t btwn two tim points in th pmnnt plots. t = ( u t+u 1) 1 (6) t 1 2 5F 1F 4 2 logn wh: t = gowth t of th vg BH t g t (%/y); u = diffnc btwn two msumnt tim points. Finlly, th ccucy of th stimtd stnd dnsitis w chckd by comping stimtd nd obsvd vlus in th pmnnt plots (V1-V4 in Tbl 1). Aft confiming () 3 3 Stnd g Stnd g 1F 4 5F th ccucy of th stnd dnsity clcultd on th bsis of th pmts in fomul (3), th stimtd stnd dnsity (N) ws substitutd into fomul (5). Th obsvd BH, stnd dnsity nd stnd g t th tim of th fist msumnt w usd s th initil vlus fo stimting futu BH nd stnd dnsity ccoding to fomuls (5) nd (3). In oth wods, th obsvd stnd g, dnsity nd dimt t th tim tht th pmnnt plot ws stblishd (A ) w substitutd s initil vlus into fomul (5). Th dimt gowth ws thn clcultd ccoding to fomul (5) to pdict th dimt t th tim of th nxt obsvtion. Slf-thinning ws clcultd ccoding to fomul (3). Ths clcultions of dimt nd slf-thinning w ptd until th tim of th finl obsvtion. Th stimtd vg dimts w compd with th obsvd dt in th pmnnt plots. W clcultd th o t by dividing th diffnc btwn th obsvd nd stimtd vlus by th obsvd vlu. Th vg o tio could thn b stimtd by vging th bsolut vlu of th ll clcultd o ts. W usd Pson tst to chck th ccucy of th pdictd vlus divd fom fomul (5). Fo this tst, n (numb of dt) ws quivlnt to th numb of msumnts p plot (Tbl 1) nd sults w considd significnt whn p.1. Pson s coltion cofficints w lso clcultd in od to chck th ccucy of th stimtd vg BH divd fom th modl. RESULTS AN ISCUSSION Th ltionship btwn BH nd stnd dnsity cn b psntd by fomul (7). log N = log (7) Fig. (2) shows full dnsity cuv divd in pvious study [21], th cuv divd fom th cunt wok nd stndd stnd dnsity cuv [37] sulting fom clssic thinning pctics in plntd fost gion such s th psnt study. Th significnt diffncs (p <.5 lvl ft Bonfoni coction) btwn th stndd stnd dnsity cuv [37], tht divd in th cunt study nd th pviously divd full dnsity cuv [21]. Mo thn hlf of th stnd dnsitis nd vg BHs plottd on log-log scl pp bov th full dnsity cuv divd by Skguchi [21]. Howv, Skguchi s [21] dt w collctd in numb of gions [39-41] nd diffncs btwn cultivs of Cyptomi jponic in diffnt loclitis w not considd, bcus th w not nough unthinnd stnd plots t tht tim. Howv, in od to nlyz th ltionships btwn stnd dnsity nd vg BH it would b mo igoous to xmin dt fom singl gion. Bcus th dt st usd in this study ws collctd fom pmnnt plots in on gion mngd s on fost mngmnt unit, w consid tht fomul (7) dos xpss th full stnd dnsity nd is ppopit fo pdicting stnd gowth t th psnt study sit mo listiclly thn th pvious full stnd dnsity cuv. As shown in Fig. (1), th slop divd fom fomul (7) ws mo simil to th stndd dnsity cuv stimtd fo

5 Modling imt Gowth nd Slf-Thinning in Plntd Sugi (Cyptomi jponic) Stnds Th Opn Fost Scinc Jounl, 211, Volum g lo logn Fig. (2). Th full dnsity nd stndd dnsity cuvs divd fom pvious studis nd th psnt on. Bold, fin nd dottd lins show, spctivly, th full dnsity cuv divd in th psnt study, full dnsity cuv divd fom Skguchi [21], nd stndd dnsity cuv divd fom Nkjim t l. [27]. psnts BH (cm), nd N psnts stnd dnsity (stms/h). Th qutions fo th bold, fin nd dottd lins logn = log, logn = log, nd logn= log, spctivly. th thinnd [37] thn Skguchi s full dnsity cuv [21]. Pvious wok hs lso suggstd tht th stndd dnsity cuv hs simil slop to th full dnsity cuv [19, 42]. Vndschf t l. [14] suggstd tht, in such situtions, mixd modl would b btt bcus it tks into ccount intcoltd dvitions ssocitd with ptd msumnts fom pmnnt plots. Howv, sinc dnsity, nd pobbly dimt, did not diff much btwn th fou plots (C1-C4 in Tbl 1), th sults fo th pmts of th full dnsity cuv (K nd d) will b simil ispctiv of th modl usd. Thfo, it is considd tht nonusing mixd modl [14] would b not pticully impotnt in this cs. Whn stimting th stnd dnsity, th ppd to b lg quntity of dd-wood in th high dnsity stnds, i.. thos with Ry vlus gt thn.85 (Fig. 3). An xponntil cuv fittd to th ltionships shown in Fig. (2) sultd in fomul (8). STR = Ry 1.4 (8) Ry Fig. (3). Th ltionship btwn yild indx (Ry) nd slfthinning tio (STR). Th qution of th xponntil cuv is STR = Ry. Th slf-thinning modl cn b xpssd s th tjctoy of th ltionship btwn Ry nd th numb of ts. This ppoch, nd th slf-thinning cuv fom stnd dnsity mngmnt digms [16, 17], both dscib ddwood s bing dpndnt on th incs in Ry [3]. STR incsd s Ry incsd fom.85 to 1., with stong incs bov Ry vlus of.9 (Fig. 2). In od to STR(y -1 ) minimiz th mount of dd-wood in unmngd fosts, it is impotnt to implmnt thinning in high dnsity stnds. Th ccucy of th modl dvlopd ws chckd by comping th stimtd nd obsvd vlus fo stnd dnsity (Fig. 4). Howv, bcus th stnd dnsity in plot V1 lmost ntily ovlppd tht of plot V4, th fom is not shown in th figu. Th ng of o tios obsvd in ll pmnnt plots ws lss thn c. 1%. Ths sults suggst tht th dcs in stm numbs obsvd und th diffnt stnd conditions could b modld by th function of Ry divd fom xisting dnsity mngmnt digms [31]. As shown in Fig. (4), th high th initil stnd dnsity, th gt th subsqunt dcs in stnd dnsity. It ws confimd tht this tndncy of dcsing stnd dnsity could b xpssd on th bsis of th stimtd pmts h p s 15 m t S Stnd g (y) Obsvd(V2) Estimtd(V2) Obsvd(V3) Estimtd(V3) Obsvd(V4) Estimtd(V4) Fig. (4). Compison btwn obsvd nd stimtd stnd dnsity.

6 54 Th Opn Fost Scinc Jounl, 211, Volum 4 Nkjim t l. Th souc of th discpncy btwn th obsvd nd th pdictd vlus (Fig. 4) is pobbly th us of th sm pmt vlus fo ll th pmnnt plots. It is possibl tht th modl contining constnt pmts would b unbl to pdict slf thinning ccutly. Fo xmpl, ctstophic ntul distubnc in th futu could not b pdictd by this modl. Howv, bcus th vg o t of diffnc btwn th stimtd nd obsvd stnd dnsity ws btwn.5 nd 3.4% whn compd with th pmnnt plot dt, th modl could b usd to stimt dcsing stnd dnsity. Fomul (9), which includs gowth pmts fo pdicting dimt gowth, ws s follows. = xp(.169t) +.2(4.87 log N 1.19 log ) (9) If th pmt p, which flcts th ffct of stnd dnsity on dimt gowth, is positiv, this indicts tht dcsing stnd dnsity hs positiv ffct on dimt gowth. Fo xmpl, if stnd dnsity is blow tht modld by th full dnsity cuv, th scond tm in fomul (9) will b positiv. Thfo, th ffct of dcsing stnd dnsity on dimt gowth will b positiv. In this cs, th lg th diffnc btwn th stnd dnsity nd th figu bsd on th full dnsity cuv, th gt th ffct of stnd dnsity on dimt gowth. On th oth hnd, it is possibl tht stnd dnsity is gt thn tht modld by th full dnsity cuv [21], in which cs th scond tm of fomul (9) would b ngtiv. In such cs th ffct of stnd dnsity on dimt gowth would b ngtiv: th lg th diffnc btwn th stnd dnsity nd th figu bsd on th full dnsity cuv, th gt th ngtiv ffct of stnd dnsity on dimt gowth. Pmt p ssumd vlus btwn 1.6 nd 4.6 fo stnd dnsity ffcts on th bsis of th stndd stnd dnsity contols fo tditionlly thinnd stnds [22, 37, 43]. In contst it ws only.2 whn divd fom th full dnsity cuv, suggsting tht dcsing stnd dnsity hs lss ffct on th dimt gowth t fo th full dnsity cuv thn fo th stndd dnsity cuv. Gnlly, stnd gowth is dpndnt on t-cown volum [44, 45]. Futhmo, Zid [46] hs suggstd tht t-cown volums cn vy with stnd dnsity. Bcus cown volum und low stnd dnsity contol, s xpssd by stndd dnsity cuvs, is thought to b gt thn cown volum und th high stnd dnsity contol, s xpssd by full stnd dnsity cuvs, ou finding tht pmt p is smll whn dimts stimtd by th full dnsity cuv thn whn stimtd by th stndd dnsity cuv, sms sonbl. In ddition, whn stnd dnsity minly dcsd by contolld th ffct could b dscibd by th stndd dnsity cuv, whil dnsity tht dcsd s sult of slfthinning ws bst dscibd by th full dnsity cuv. With noml, mngd thinning, cown gowth incss immditly following th fomtion of cnopy gps. Howv, with slf-thinning, th cnopy gp only xpnds ft dd-wood flls o cldoptosis. This diffnc btwn th tims tkn to fom significnt cnopy gps und noml thinning o slf-thinning my b noth son why pmt p, nd its ffct on dimt, ws smll fo th full dnsity cuv thn fo th stndd dnsity cuv. In od to chck th ccucy of th dimt gowth pdictd using th nw modl, th stimtd dimts w compd with obsvd vlus (Fig. 5). Th vg o t fo th BH ws 2.9%, with mximum of 8.1%. Th squd Pson s coltion cofficints, indicting th ccucy of th vg BH stimtd by th nw modl, w btwn.97 nd 1. (p vlu <.1). This confimd th pow of th modl fo stimting vg dimt gowth. In th study, th stnd dnsity contol digm nd th dimt gowth modl bsd on th stndd stnd dnsity contol w dvlopd long with oth gowth modls, poducd by th govnmnt [31] nd oth schs [37]. Th bsolut o tios stimtd by comping vg dimt clcultd on th bsis of th stnd dnsity contol digm [31] nd th gowth modl bsd on th stndd dnsity cuv (Fig. 2) [37] with obsvd vlus collctd cntly fom th pmnnt plots ngd btwn 17 nd 35% nd btwn 15 nd 22%, spctivly. By comping th o t divd fom th nw modl with tht fom pvious modls, w confimd tht th dimt ws stimtd mo succssfully by th fom (Fomul (9)). Ths sults suggst tht incss in vg BH und diffnt stnd conditions could b modld using fomul (9). As shown in Fig. (4), th tndncy towds incsing vg BH could b xpssd using th stimtd pmts, suggsting tht it might b possibl to stimt th futu vg BH gowth, using th ssumptions mntiond bov. Although Gun t l. [1] stimtd gowth modl pmts fo ch pmnnt plot, th psnt study stimtd th pmts coss ll th plots. It my thfo b possibl to pply ths pmts to dimt gowth in oth unthinnd stnds, dpnding on th initil stnd condition. To pdict vg BH gowth fom fomul (9), stnd dnsity, vg BH, stnd hight nd stnd g quid. In compison with oth pocss modls, fomul (9) is si to us bcus if quis lss dt to b collctd. Fo xmpl, stnd volum cn b clcultd by substituting th vg BH nd stnd hight divd fom th hight gowth cuv [37], into th stnd volum qution [47]. Bcus th min Jpns cbon sink und th Kyoto potocol [28] is plntd fosts, including Sugi, it would mk sns to stimt th cbon sink using stimtd BH gowth by pplying fomul (9) to oth plntd fost s. Bcus this study is bsd on th fw unthinnd stnds tht xist, th nw modl could b pplid to high dnsity stnds. In ddition, bcus th pdiction piod in this study ws ppoximtly 3 ys, th nw modl should b ppopit fo pdictions ov such lngth of tim. uing th pdiction piod th stnds ngd fom 25 to 7 ys old. Th stndd ottion piod in th tgt is ound 6 ys, so th modl nds to b dvlopd futh to b usful fo pdicting th gowth of high dnsity stnds ov this tim spn. In this study, w confimd th hypothsis tht vg dimt gowth could b stimtd by using function incopoting xisting BH, stnd dnsity nd stnd g, with pmts divd fom vn-gd, monocultus of

7 Modling imt Gowth nd Slf-Thinning in Plntd Sugi (Cyptomi jponic) Stnds Th Opn Fost Scinc Jounl, 211, Volum ) m4 c ( H B3 g 2 v A Stnd g (y) Obsvd(V1) Estimtd(V1) 5 ) m4 c ( H B3 g 2 v A Stnd g (y) Obsvd(V3) Estimtd(V3) 5 ) m4 ( c H B3 g 2 v 1 A Stnd g (y) Obsvd(V2) Estimtd(V2) 5 ) m4 ( c H B3 g 2 v 1 A Stnd g (y) Obsvd(V4) Estimtd(V4) Fig. (5). Compison btwn obsvd nd stimtd BH gowth. Th coltion indxs in ch plot.98 (p <.1),.99(p <.1), 1. (p <.1) nd.97(p <.1), spctivly. fost ts in high dnsity stnds. Th stimtd pmts fo pdicting dimt gowth in unthinnd stnds w vlutd by comping th stimtd stnd dnsity nd BH, with obsvd vlus fom th pmnnt plots. It is possibl tht this ppoch to modlling th dimt gowth could b pplid to oth s by using dt collctd fom oth vn gd plntd t spcis nd gions in fomul (5). Bcus th min cbon sink in Jpn und th Kyoto potocol is plntd fosts [28], this gowth modl my b vlubl tool fo pdicting stnd gowth. Th nxt chllng is to chck th pplicbility of this gowth modl to oth t spcis nd gions. ACKNOWLEGEMENTS W thnk th stff of th Tokyo Univsity Fost in Chichibu fo thi vlubl ssistnc in collcting th dt st. This study ws suppotd in pt by Rsch Fllowships fom th Jpn Socity fo th Pomotion of Scinc. CONFLICT OF INTEREST Th uthos dcl tht thy hv no conflict of intst. REFERENCES [1] Gun BT, Lin S, Lin Y, Wu Y. Gowth fficincy-suvivoship ltionship nd ffcts of spcing on ltiv dimt gowth t of Jpns cds. Fost Ecol Mng 28; 255: [2] Pog NJ, Mshll, McCllln MH. Mximum Stnd-nsity Indx of 4 wstn hmlock-sitk spuc stnds in southst Alsk. Wst J Appl Fo 27; 22: [3] Monsud RA, Ldmnn T, Stb H. A slf-thinning constints ndd in t-spcific motlity modl? Fo Sci 24; 5: [4] Ptzsch H, Bib P. A -vlution of Rink s ul nd stnd dnsity indx. Fo Sci 25; 51: [5] Tod M, Yokozw M, Sumid A, t l. Folig pofils of individul ts dtmin comptition, slf-thinning, biomss nd NPP of Cyptomi jponic fost stnd: A simultion study bsd on stnd-scl pocss-bsd fost modl. Ecol Modl 29; 22: [6] Johnsn K, Smulsson L, Tsky R, t l. Pocss modls s tools in fosty sch nd mngmnt. Fost Sci 21; 47: 2-8. [7] Zid B. Anlysis of th 3/2 pow lw of slf-thinning. Fost Sci 1987; 32: [8] Zid B. Slf-thinning nd stnd dnsity. Fo Sci 1991; 37: [9] Chn K, Kng H-M, Bi J, t l. Rltionship btwn th vitul dynmic thinning lin nd th slf-thinning boundy lin in simultd plnt popultions. J Intg Plnt Biol 28; 5: [1] Hsnu H, Bukht HE, Stb H. Vition in potntil volum yild of loblolly pin plnttions. Fo Sci 1994; 4: [11] Hozumi K. Ecologicl nd mthmticl considtions on slfthinning in n vn-gd pu stnds. II. Gowth nlysis of slfthinning. Bot Mg Tokyo 198; 93: [12] Jck SB, Long JN. Linkgs btwn silvicultu nd cology: n nlysis of dnsity mngmnt digms. Fo Ecol Mng 1996; 86: [13] Rink LH. Pfcting stnd-dnsity indx fo vn gd fosts. J Agic Rs 1933; 46: [14] VndSchf CL, Bukht HE. Compison of mthods to stimt Rink s mximum siz-dnsity ltionship. Fost Sci 27; 53: [15] Minow M. A thoticl ppoch to fost gowth modling. (II) Futh discussion on th slf-thinning modl. J Jpn Fo Soc 1983; 65: [16] Ando T. Gowth nlysis on th ntul stnds of Jpns d pin (Pinus dnsiflo Sib. t Zucc.). II. Anlysis of stnd dnsity nd gowth. Bull Gov Fost Stn (Tokyo) 1962; 147: [17] Ando T. Ecologicl studis on th stnd dnsity contol in vngd pu stnd. Bull Govt Fo Exp St (Tokyo) 1968; 21:153.

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