Journal of Agriculture and Social Research, Vol. 13, No.1, 2013

Transcription

1 Journl of Agricultur nd Socil Rsrch, Vol. 3, No., 3 CROWN RATIO MODELS FOR TROPICAL RAINFORESTS SPECIES IN OBAN DIVISION OF THE CROSS RIVER NATIONAL PARK, NIGERIA *ADEYEMI, A.A., JIMOH, S.O. AND ADESOYE, P.O. Dprtmnt of Forst Rsourcs Mngmnt, Univrsity of Ibdn, Ibdn, Nigri *Corrsponding Author s Emil: dymidsoji@yhoo.com ABSTRACT Crown rtio (CR) is chrctristic usd to dscrib th crown siz, which is n importnt lmnt of forst growth nd yild. It is oftn usd s n importnt prdictor vribl for tr-lvl growth qutions. It indicts tr vigour nd is n importnt hbitt vribl. It is oftn stimtd using llomtry. Modifid vrsions of Logistics, Richrds, Wibull nd Exponntil functions wr usd to prdict CR for tr spcis in th Obn Division of th Cross Rivr Ntionl Prk. Systmtic smpling tchniqu ws doptd in th thr study sits (Aking; Ekng nd Old-Ntim) for plot loctions. Two trnscts of km long with distnc of 6m prt wr cut in ch of th study sits. Four smpl plots of 5m 5m wr thn lid ltrntly long ch trnsct t 5m intrvls. This procdur ws rptd in th clos-cnopy nd scondry forsts in th thr study sits. Forty-ight smpl plots wr usd for th study. Tr vribls (Dbh; dimtr t th middl nd mrchntbl top; crown dimtr; totl hight; mrchntbl hight; stm qulity nd crown lngth wr msurd on ll th trs with Dbh>cm. Th cnopy lyr to which ch tr blongs ws notd. All th msurd trs wr idntifid. Th Wibull nd Exponntil functions gv consistnt nd ccurt rsults in lmost ll th cnopy lyrs in th two forst typs with R ; SEE vlus of.7;.68 nd.7;.67 rspctivly for th dominnt cnopy,.75;.75 nd.75;.74 rspctivly for th co-dominnt cnopy. Exponntil function producd th bst fit modls in th study xcpt undr intrmdit cnopy lyr, whr it ws not found suitbl for crown rtio prdictions. Howvr, th diffrnc in rsults producd by th two functions is ngligibl. Thy r thrfor rcommndd for crown rtio prdiction studis in Obn Division of th Cross Rivr Ntionl. Kywords: Tr-crown, prdictions, functions, tr vribls, cnopy-lyrs INTRODUCTION Th siz of tr crown is strongly corrltd with th growth of th tr. Th crown displys th lvs to llow cptur of rdint nrgy for photosynthsis, ky procss in tr dvlopmnt. Thus, msurmnt of th crown is oftn don to ssist in th quntifiction nd undrstnding of th growth of trs in th stnd (Korhonn t l., 6). Th rtio of liv crown lngth to th totl tr hight is known s crown rtio. Crown rtio (CR) is th chrctristic usd to dscrib th crown siz (Hynynn, 995), which is n importnt lmnt of forst growth nd yild (Col nd Lorimr, 994). According to Short nd Burkhrt (99) nd Vlntin t l. (994), it is frquntly usd to prdict individul tr growth. In mny dimtr nd hight growth qutions, tr crown prmtrs r usd s xplntory vribls (Monsrud nd Strb, 996), nd crown rtio hs bn usd s prdictor of tr vigour (Hsnur nd Monsrud, 996); stnd dnsity; comptition nd survivl potntil of trs within forst (Olivr nd Lrson, 996). It is ftur of intrst in mngmnt of mny non-timbr forst 63

2 Journl of Agricultur nd Socil Rsrch, Vol. 3, No., 3 rsourcs, spcilly wildlif hbitts (McGughy, 997; Tmsgn t l., 5; Wltrt t l., 8). Tr crown rtio cn b prdictd dirctly from othr tr vribls such s totl hight nd dimtr t th brst hight (Hsnur nd Monsrud, 996; Pommrning, ; Tmsgn t l., 5; Adsoy nd Oluwdr, 8). It cn lso b prdictd indirctly from stimts of th hight to th bs of liv crown (Dyr nd Burkhrt, 987). Hsnur nd Monsrud (996) hv usd th logistic functions to prdict th mn tr crown rtio, which is lwys btwn nd. Th logistic function with norml distribution of rrors works undr th ssumption tht th rrors r normlly, idnticlly, nd indpndntly distributd with mn zro nd constnt vrinc. Thorticlly, undr th ssumption of normlity th rror trm cn ssum vlu from ngtiv infinity to positiv infinity nd th prdiction intrvl for CR cn b wll byond nd. Norml distribution pproch works fin for th prdiction of mn CR. Howvr, it might not work for th prdiction intrvl of CR, in ll othr circumstncs. An ltrntiv to ssuming norml distribution of rrors is to ssum th rrors follow bt distribution. This distribution ssurs tht th prdiction intrvls r lwys btwn nd (Cssll nd Brgr, ). Crown rtio is oftn usd s n importnt prdictor vribl for tr-lvl growth qutions, prticulrly for multi-spcis nd multi-lyrd stnds (Tmsgn t l., 5). Also, it indicts tr vigour nd cn b n importnt hbitt vribl. Msurmnt of CR for ch tr cn b tim-consuming nd difficult to obtin in vry dns stnds nd for vry tll trs, whr th bs of liv crown is obscurd but with n stblishd rltionship with othr tr growth vribls, n stimt of CR cn b obtind through th us of llomtric qutions (Tmsgn t l., 5). Although Tmsgn t l. (5) dvlopd crown rtio modls for multi-spcis nd multi-lyrd stnd in British Columbi, in tht study, only fiv spcis (Btul ppyrifr, Pic gluc, Pinus contort, Populus trmuloids nd Psudotsug mnzisii wr considrd. Th modls formultd wr, howvr, sit spcific nd not suitbl for prdictions in th Obn Division of CRNP. Similrly, Adsoy nd Oluwdr (8) dvlopd n intrim crown rtio modls for mixd Tcton grndis nd Gmlin rbor stnd t th Univrsity of Ibdn. Howvr, thir modls did not includ dt from th study r. Th objctiv of this study, thrfor, ws to dvlop crown rtio modls for svrl tr spcis in Obn Division of th Cross Rivr Ntionl Prk undr diffrnt cnopy lyrs. METHODOLOGY Th Study Ar Th study ws crrid out in th Obn Division of Cross Rivr Ntionl Prk (CRNP), Nigri. It lis within longituds 8 o ' nd 8 o 55'E nd ltituds 5 o ' nd 6 o 'N, nd covrs lnd r of 3km (Ogunjobi t l., ). It ws crvd out of Obn group Forst Rsrv in 99 for th consrvtion of rich biodivrsity. It is loctd in th Akmkp Locl Govrnmnt Ar of th Cross Rivr Stt (Fig. ). It shrs bordr with Korup Ntionl Prk of Cmroon in th st. It hs rining sson of t lst nin months (Mrch-Novmbr) nd rcivs ovr 35mm nnully (Ogunjobi t l., ). It is lrg lowlnd nd submontn rinforst situtd in th South-southrn prt of Nigri long th bordr with Cmroon. Th Cross Rivr nd its tributris drin northrn prts of Obn Division, whil southrn prts r drind by th Clbr, Kw nd Korup Rivrs. Th trrin is rough nd lvtion riss from th rivr vllys to up to m bov s lvl in mountinous r. Th tmprtur rngs from 5 o C to 7 o C in Jnury but in July, it riss up to slightly bov 64

3 Journl of Agricultur nd Socil Rsrch, Vol. 3, No., 3 3 o C. Rltiv Humidity is btwn 75% nd 95% in Jnury, but towrds Dcmbr, it rducs grdully s rsult of hrmttn (Bisong nd Mfon, 6). Ths uniqu combintions of high rinfll, humidity nd tmprtur hv intrplyd to dvlop n qully uniqu, highly complx nd divrsity rich vgttion, which is vrgrn throughout th yr. Fig. : Mp of th Study Ar Th vgttion is lowlnd, vrgrn tropicl rinforst nd chrctristic tr spcis includ Brlini confus, Coul dulis, Hnno klinn, Klindox gbonnsis, Khy ivornsis, Trminli ivornsis, Lophir lt, Strombosi spp nd Diospyros spp. In th lss ccssibl rs, th forst hs hd littl intrfrnc, but lswhr th vgttion hs bn much influncd by humn ctivitis. Exploittion in th buffr zon hs rsultd in scondry rgrowth. Four vgttion typs r distinguishbl within th prk, ths includ: high forst, ridg forst, scondry forst nd swmp forst (Udo, 7). Dt Collction Th systmtic (lin trnsct) smpling tchniqu ws doptd in ch of th thr study sits (Aking; Ekng nd Old-Ntim) for plot loctions. Th strting points of ch 65

4 Journl of Agricultur nd Socil Rsrch, Vol. 3, No., 3 trnsct ws dtrmind with th id of Compss nd Globl Positioning Systm rcivr. Two trnscts of m in lngth with distnc of 6m prt wr cut in ch of th study sits. Four smpl plots of 5m 5m wr lid ltrntly long ch trnsct t 5m intrvls. This procdur ws rptd in th two forst typs (clos-cnopy forst nd scondry forst) in ch of th thr study sits, thus summing up to 4 smpl plots pr km-trnsct, nd totl of 6 smpl plots pr study sit. Forty-ight (48) smpl plots wr usd for th study. Th following dt wr collctd on ll th trs with Dbh>cm within ch of th smpl plots: Dimtr t brst hight (Dbh); dimtr t th bs (D b ), middl (D m ) nd mrchntbl top (D t ); crown dimtr (CD); totl hight (THT); mrchntbl hight (MHT); stm qulity (SQ) nd crown lngth (CL). Th cnopy lyr to which ch tr blongs ws notd. In ddition, ll th msurd trs within ch of th smpl plots wr idntifid to spcis lvl. Computtion of Modl Vribls Bsl r computtion Th bsl r of ch tr within ch smpl plot ws computd using th formul: D BA Whr, BA = Bsl r (m ); D = Dimtr t brst hight (.3m bov th ground lvl). Th bsl r for ch plot ws obtind by dding individul tr bsl r in ch plot, i.. n BA p BA i Whr, BA P = Bsl r pr plot; BA i = Bsl r for ith tr in th plot. Th bsl r pr hctr ws thn obtind by multiplying th plot bsl r by 4 (4 bing th numbr of.5h-smpl plot in hctr). Volum stimtion Th volum of individul trs pr plot ws clcultd using Nwton s formul, s prsntd by Husch t l. (3): h V A 4A A b m t Whr, V = tr stm volum (m 3 ); h = tr totl hight (m); A b, A m nd A t r crosssctionl rs t th bs, middl nd top of th trs rspctivly. Di Sinc A i = 4 Th stm volum qution ws r-writtn s: V h 4 D 4 D D b m t Dtrmintion of th volum for ch smpl plot ws don by dding up th volums of individul trs within ch plot. Th volum pr hctr ws thn obtind by multiplying th plot stm volum by 4. Crown Rtio computtion Th individul tr crown rtio ws computd using: 66

5 Journl of Agricultur nd Socil Rsrch, Vol. 3, No., 3 CLi CR THTi Whr, CLi = individul tr crown lngth nd THT i = totl hight of th ith tr. This ws computd for ch of th spcis in th stnd s rspons vribl for th crown rtion prdiction modls. Crown Projction Ar Th crown projction r ws computd using: CD CPA Whr, CD = crown dimtr (cm) Crown Projction r for ch plot ws obtind s follows: CPA p n i CPAi Whr, CPA p = Crown projction r pr plot; CPA i = Crown projction r for ith tr in th plot. Th Crown projction r pr hctr ws thn obtind by multiplying crown projction r pr plot by 4. Dt Anlysis Comprisons of th growth Vribls btwn th two forst typs T-tst ws usd to invstigt significnt diffrncs btwn th tr growth vribls in th two forst typs. T-sttistics ws computd s: t S X X N N N N Whr, X = mn of th msurd vlus for prticulr growth vribl in th closcnopy forst, X = mn of th msurd vlus for th vribl in th scondry forst, N = numbr of trs smpld in th clos-cnopy forst, N = numbr of trs smpld in th scondry forst nd S = poold within-group vrinc (for indpndnt smpls with qul vrinc). Th t hs (N -) + (N -) dgrs of frdom. Anlysis of Vrinc On-wy nlyss of vrincs (ANOVA) wr crrid out to invstigt significnt diffrncs in tr growth vribls undr diffrnt cnopy lyrs. Th mthmticl modl for th dsign is: Y T ij i ij Whr, µ = ovrll mn, T i = ffct of th cnopy lyrs, i,j = xprimntl rror. Crown Rtio Modls Four non-linr rgrssion modls wr fittd to th tr growth vribls in th two forst typs. Th following non-linr rgrssion functions wr fittd to th tr growth dt. Logistics: 67

6 Journl of Agricultur nd Socil Rsrch, Vol. 3, No., 3 CR Richrds: CR Wibull: CR ( mcx ) ( Exponntil: / k ( mcx ) m kx kx )... CR ( )... 3 Whr CR, = th tr crown rtio; X = linr function of tr sizs; is symptot;,, c, k nd m r function prmtrs. Modl dscription Th vribls tht r commonly usd for crown rtio modlling r tr g; tr siz (dimtr, hight, hight/dimtr rtio); stnd dnsity (numbr of trs/h, bsl r); mximum tr dimnsion (dimtr); mn tr dimnsion (dimtr, dominnt dimtr), sit productivity (dominnt hight, sit indx) nd stnd-lvl comptition. For this study, tr g ws not includd sinc th g structur of n unvn-gd forst is highly htrognous nd its dtrmintion in prcticl forstry is not mningful, nd lso vry rr on rsrch plots (Liho t l., 995; Adkunl t l., 4). Thus, g is not vry importnt for modlling in tropicl rinforst. Svrl othr rsrchrs such s Vncly (994), Okoji (996) nd Akindl (5) hv usd surrogts of g (dimtr, bsl r nd sit form) during modlling. Givn tht th crown rtio modls wr intndd for multi-spcis nd multi-lyrd stnds, sit indx ws intntionlly xcludd from th modls (Vncly, 994 nd Akindl, 5). Th linr function X ws xprssd s combintion of tr siz (dimtr, stm qulity, mrchntbl hight nd totl hight) nd tr bsl r. All th growth vribls wr trid with individul tr crown rtio s th rspons vribl (Y). For ll th modls, th following sttistics wr computd: Stndrd Error of Estimts (SEE) SEE n i ˆ i n k Cofficint of Dtrmintion (R ) SSE R SST Whr, ê is th diffrnc btwn th msurd (y i ) nd th stimtd crown rtio vlus (y ˆ) ; SSE is th rror sum of squrs, SST is th totl sum of squrs, n is th numbr of trs in th modl-fitting dt st, nd k is th numbr of prmtrs in th 68

7 Journl of Agricultur nd Socil Rsrch, Vol. 3, No., 3 fittd modls. Evlution of th functions ws lso chivd through th obsrvtion of th ntur of contribution of th prmtr stimts nd th computtion of mn rsidul, stndrd dvition of th rsidul nd th cofficint of vrition (CV) of th rsidul (Adsoy nd Oluwdr, 8). Diffrnt vrsions of th logistic, Wibull, Richrds nd xponntil functions wr trid on ll th tr growth vribls. Th prmtr stimtion of ths non-linr functions wr bsd on th lst squrs mthod ssocitd with Qusi-Nwton minimiztion tchniqu of non-linr stimtion option of STATISTICA vrsion 7. (4). Both th significnc nd th stbility of th prmtrs stimts wr chckd bsd on th symptotic t-sttistic nd stndrd rrors of th prmtrs. Whn th prmtr stimt is not significntly diffrnt from zro th vribls nd th prmtr wr discrdd. Modl Evlution Modl vlution ws bsd on th computtion of th following sttistics for th comprisons of th slctd functions: Significnc of Rgrssion (F-rtio) This tstd th ovrll significnc of th modls. Th criticl vlu of F (F-tbultd) t p<.5 lvl of significnc ws comprd with th F-rtio (F-clcultd). Whr th vrinc rtio (F-clcultd) ws grtr thn th criticl vlus (F-tbultd), such qution ws significnt nd ws ccptd for crown rtio prdiction. Mn Prdiction Rsidul (MPR) MPR n i ( Obsrvd Pr dictd ) n Rsidul Cofficint of Vrition (RCV) Rsidul cofficint of vrition (RCV) ws computd to ddrss th wknss of rsidul stndrd dvition (RSD). It is should b notd tht stndrd dvition or vrinc cnnot b vry usful in compring two or mor sris whr ithr th units of msurmnt r diffrnt or th mn vlus r diffrnt. Cofficint of vrition thrfor tks cr of this problm. Th RCV ws computd s: RSD RCV MPR Prdiction Sum of Squrs (PRESS) sttistic This ws computd s: PRESS n i ( Obsrvd Pr dictd ) RESULTS AND DISCUSSION Tbl prsnts th t-tsts for th comprison of th mns of th tr growth vribls btwn th two forst typs. Th rsult shows tht thr wr significnt diffrncs btwn th mn tr totl hights (THT) nd dimtrs t brst hight (Dbh) undr th two forst typs (P =.) nd (P =.43) rspctivly. Th comprison of mn tr stm qulity (SQ) in th two forst typs rvld significnt diffrnc s P<.5. This implis tht th mn SQ in th clos-cnopy forst ws significntly diffrnt from tht obtind in 69

8 Journl of Agricultur nd Socil Rsrch, Vol. 3, No., 3 th scondry forst. Th tst for th comprison of th mn tr crown dimtrs (CD) btwn th two forst typs showd significnt diffrnc (P<.5). This implis tht th mn tr crown dimtrs in th two forst typs wr significntly diffrnt from ch othr. Th rsult rvld tht th mn tr bsl r (BA) obtind in th clos-cnopy forst ws not significntly diffrnt from tht obtind in th scondry forst s P>.5. Th tsts for th crown projction r (CPA), stm volum (SV) nd crown rtio (CR) rvld no significnt diffrncs in th two forst typs sinc P>.5 in ch of th css. This implis tht th mn vlus obtind in th clos-cnopy forst wr not significntly diffrnt from thos obtind in th scondry forst. Th lck of significnt diffrncs btwn most of th tr growth vribls in th two forst typs ncssittd th fitting of th rgrssion modls into th poold dt from th two forst typs. Howvr, thr wr significnt diffrncs mong growth vribls undr diffrnt cnopy lyrs, hnc, th four modls wr fittd to th dt st on th cnopy lyr bsis (Tbl ). Tbl : t-tsts for th tr growth vribls btwn th two forst typs Vribls Forst Typ N Mn S.D df t-stt p-vlu THT CCF SCF Dbh CCF SCF SQ CCF * SCF CD CCF * SCF BA CCF SCF CPA CCF SCF SV CCF SCF CR CCF SCF *significnt (p<.5); CCF: closd cnopy forst; SCF: scondry forst; THT: tr totl hight; Dbh: dimtr t brst hight; SQ: stm qulity; CD: crown dimtr; BA: bsl r; CPA: crown projction r; SV: stm volum; CR: crown rtio. Tbl : Mn sprtions for th tr growth vribls undr th four cnopy lyrs Cnopy lyr Mn vlus of th tr growth vribls THE MHT SQ DBH CD CL BA CPA Dominnt Co-dominnt b 3.86 b.5645 b b b.96 b.57 b b 7

9 Journl of Agricultur nd Socil Rsrch, Vol. 3, No., 3 Intrmdit.6 c c c c c c.93 c c Supprssd 3.55 d d d.589 d 4.64 d d.446 d.3635 d SV CR SF SC Dominnt Co-dominnt b.378 b.573 b b Intrmdit.73 c.393b c.556 c c Supprssd.397 c.393 c.534 d d NB: Mns with th sm lphbt s suprscripts undr ch column hding r not significntly diffrnt from ch othr Tbl 3: Tr crown rtio modls, prmtr stimts nd fit sttistics for dominnt cnopy lyr Function Prmtr Estimt SE t (df =7) P-vlu Logistic: * Cr * BA SQ * R =.7; SEE =.69 Richrds: Cr BA SQ 4 R =.7; SEE =.69 Wibull: / BA SQ Cr R =.7; SEE = * * * * * * Exponntil: BA ( SQ) Cr R =.7; SEE = * * * Tbl 4: Tr crown rtio modls, prmtr stimts nd fit sttistics for Codominnt cnopy lyr Function Prmtr Estimt SE t (df =38) P-vlu Logistic: * * * Cr BA SQ R =.73; SEE =.77 Richrds: Cr BA SQ 4 R =.74; SEE =.76 Wibull: / BA SQ Cr R =.75; SEE = * * * * * * Exponntil: BA ( SQ) Cr R =.75; SEE = * * * 7

10 Journl of Agricultur nd Socil Rsrch, Vol. 3, No., 3 Tbl 5: Tr crown rtio modls, prmtr stimts nd fit sttistics for intrmdit cnopy lyr Function Prmtr Estimt SE t (df P-vlu Logistic: Cr BA SQ R =.7; SEE =.78 Richrds: Cr BA SQ 6 R =.7; SEE =.78 Wibull: / 4 BA SQ Cr R =.7; SEE =.79 =6) * * * * * * * * * Exponntil: Cr BA ( SQ) Tbl 6: Tr crown rtio modls, prmtr stimts nd fit sttistics for supprssd cnopy lyr Function Prmtr Estimt SE t (df =53) P-vlu Logistic: * * * Cr BA SQ R =.43; SEE =. Richrds: Cr BA SQ R =.43; SEE =.9 Wibull: / BA SQ Cr R =.38; SEE = * * * * * * Exponntil: BA ( SQ) Cr R =.37; SEE = * * * Th slctd vrsion of th Logistics, Richrds, Wibull nd Exponntil functions, thir prmtr stimts nd fit sttistics for diffrnt cnopy lyrs r prsntd in Tbls 3, 4, 5 nd 6 rspctivly. Tr bsl r nd stm qulity wr found to consistntly prdict CR in ll th functions. In ordr to void convrgnc problms ssocitd with th fitting of Richrds nd Wibull functions to th dt st, th indx prmtrs (k nd m) wr rstrictd in th four sts of th modls. Th finl vlus of k = 4 nd m = - wr obtind for th two functions undr th dominnt nd co-dominnt cnopy lyrs; k = 6 nd m = 4 - wr obtind for th two functions undr th intrmdit cnopy lyr; whil k = nd m = - wr obtind for th two functions undr th supprssd cnopy lyr in th sts of modls. Th prdictors wr rthr rdundnt for th Exponntil function undr th intrmdit 7

11 Journl of Agricultur nd Socil Rsrch, Vol. 3, No., 3 cnopy lyr; hnc, no ccptbl qution ws obtind for CR prdictions undr this lyr. Thr wr minor diffrncs in th vlus of R nd SEE for th four functions undr diffrnt cnopy lyrs. In th dominnt lyr, th R vlus wr gnrlly high with low vlus of SEE. Th vlus of R rngd btwn.7 nd.7 (Tbl ). Th SEE vlus rngd btwn.67 nd.69. Undr this lyr, Wibull function gv th bst fit to th dt st with R =.7; SEE =.67. This ws followd by th Exponntil function with R =.7; SEE =.68. On th whol, th four functions gv good fits to th dt st undr th dominnt cnopy lyr. All th prmtr stimts rtind for th four functions undr this lyr wr found to b significntly diffrnt from zro. Tbl 7: Evlution of th four functions undr th four cnopy lyrs Cnopy lyr Function MPR RSD RCV PRESS Dominnt Logistics Richrds Wibull Exponntil Co-dominnt Logistics Richrds Wibull Exponntil Intrmdit Logistics Richrds Wibull Exponntil Supprssd Logistics Richrds Wibull Exponntil MPR: mn prdiction rsidul; RSD: rsidul stndrd dvition; RCV: rsidul cofficint of vrition; PRESS: prdiction sum of squrs sttistics. Undr th co-dominnt lyr, R vlus for ll th functions wr lso high with lowr vlus of SEE thn th dominnt lyr. Th R vlus rngd btwn.73 nd.75. Th SEE vlus rngd btwn.74 nd.75 (Tbl 3). In this lyr, ll th prmtr stimts for th four functions wr significntly diffrnt from zro s wll with Exponntil function givn th bst fit. Similrly, thr wr high R vlus nd low vlus of SEE for th Logistics, Richrds nd Wibull functions in th intrmdit cnopy lyr. Th R vlus wr btwn.7 nd.7 whil th SEE vlus rngd btwn.78 nd.79 (Tbl 4). Th Logistics nd Richrds hd th highst R vlu of.7 nd th lowst SEE vlus of.78 ch. Th Wibull function lst xplind th CR undr this lyr. Th prmtr stimts for th thr functions undr this lyr wr significntly diffrnt from zro. Howvr, th Exponntil function did not produc ny ccptbl modl for th tr CR in th intrmdit lyr, s th functions trid rvld tht th prdictors wr rthr rdundnt. Th four functions gv lowr vlus of R nd highr vlus of SEE undr th supprssd lyr whn comprd with th vlus obtind in th othr thr cnopy lyrs (R -vlus of btwn.37 nd.38) s shown in Tbl 5. Howvr, ll th prmtr stimts wr significntly diffrnt from zro. Th Logistics nd Richrds functions gv th bst fit to th dt st undr this cnopy lyr. Th Exponntil function list xplind th CR. Th vlution sttistics obtind for th four functions undr th four lyrs r prsntd in Tbl 7. Th tbl includs th msurs of prcisions nd th biss ssocitd 73

12 Journl of Agricultur nd Socil Rsrch, Vol. 3, No., 3 with th four functions undr diffrnt cnopy lyrs. Th tr bsl r nd stm qulity gv bst fits to th dt st nd wr found to b importnt in dfining th tr crown rtios for th two forst-typs in Obn Division of th Cross Rivr Ntionl Prk. Th suitbility of ll th othr tr growth vribls ws invstigtd. Thy wr, howvr, not significnt nd gv vry poor fits to th dt st. Ths othr vribls fild to xplin th tr crown rtios in ll th cnopy lyrs, nd wr, thrfor, not includd in th modls prsntd. Th R vlus for th four functions wr consistntly high undr th dominnt, codominnt nd intrmdit lyrs with vry low vlus of stndrd rrors of stimts (SEE). Th supprssd lyr, which gv much lowr fit to th dt st in ll th functions, howvr producd significnt rsults for ll th stimtd prmtrs in ll th functions. Th R vlus obtind for th four functions wr gnrlly highr comprd to thos rportd by prvious workrs for lss divrs cosystms (Tmsgn t l., 5; Adsoy nd Oluwdr, 8) with much lowr SEE vlus. This indictd bttr fits of th four functions thn thos rportd by prvious workrs. Th four functions, xcpt Exponntil undr th intrmdit lyr, gv consistnt rsults for th fit indics. Th mn prdiction rsidul (MPR) vlus ssocitd with ll th functions undr th four cnopy lyrs wr xtrmly low nd found to b ngligibl. Th rsidul stndrd dvition (RSD) vlus for th four functions wr somwht similr undr ch of th four cnopy lyrs. Howvr, th rsidul co-fficint of vritions (RCV) wr much diffrnt for th four functions in ll th cnopy lyrs. Th RCV vlus obtind for th four functions undr th four cnopy lyrs r lowr comprd to th vlus rportd by Adsoy nd Oluwdr (8) for th sm st of functions. Th vlus wr much lrgr for th Wibull nd Exponntil functions. Ths two functions lso hd th lowr vlus for th fit indics undr th four cnopy lyrs comprd to Logistics nd Richrds. Nvrthlss, th Wibull nd Exponntil functions gv th lst PRESS sttistics in ll th cnopy lyrs. Th PRESS sttistics obtind wr gnrlly lowr thn th vlus rportd by Adsoy nd Oluwdr (8). Th suitbility of Richrds nd Logistics functions wr furthr confirmd s obsrvd by Sors nd Tom () nd Tmsgn t l. (5). Morovr, th Wibull nd Exponntil functions wr found, vn mor suitbl in th study s thy gv highr R -vlus for ll th cnopy lyrs, xcpt th supprssd. This disgrs with th rports by Sors nd Tom (), Tmsgn t l. (5), Adsoy nd Oluwdr (8), whr suitbility of only th Richrds nd Logistic functions wr stblishd. This my b s rsult of th vribls usd in thir studis. It my lso b du to th lrgr dt st usd in this study, nd highr spcis nd structurl divrsitis in th cosystm. Nvrthlss, th fit of Exponntil function to th dt st undr intrmdit lyr producd no good rsult. CONCLUSION Bsd on th vlutions of th four functions usd in this study for tr crown rtio modlling, th Wibull nd Exponntil functions gv th most consistnt nd ccurt rsults in lmost ll th cnopy lyrs, going by thir fit indics. On th whol, xponntil function producd th bst rsult in this study. Howvr, th diffrnc from th Wibull function is ngligibl. Th two functions r thrfor rcommndd for crown rtio prdictions studis in th Obn Division of Cross Rivr Ntionl Prk, Nigri. Th Logistic nd Richrd functions lso gv significnt rsults, but th othr two functions r prfrbl. Th Exponntil function ws not found suitbl for tr crown rtio prdiction undr th intrmdit cnopy lyr of th r. Th four functions r tr bsl r nd stm qulity dpndnt. Sinc th four functions producd good rsults for th tr crown rtio modlling, thy r rcommndd for futur studis in th Obn Division of th Cross Rivr Ntionl 74

13 Journl of Agricultur nd Socil Rsrch, Vol. 3, No., 3 Prk nd othr rs with similr cosystm structur. For this study, th spcis wr poold, s mor dt r gnrtd in th futur, th suitbility of ths functions on spcis bss cn b invstigtd. REFERENCES Adkunl, V.A.J., Akindl, S.O., Fuwp, J.A., 4. Structurs nd Yild for tropicl lowlnd rinforst cosystm of South Wst Nigri. Food Agric. Environ., Adsoy, P.O. nd Oluwdr, A.O., 8. Intrim Crown rtio modls for mixd Tcton grndis nd Gmlin rbor stnd in th Univrsity of Ibdn, Nigri. Rs. J. For. (), Akindl,S.O., 5. Volum functions for common timbr spcis of Nigri s rin forsts. Intrntionl Tropicl Timbr Orgniztion (ITTO). Intrntionl Orgniztion Cntr, 5th Floor Pcifico-Yokohm, -- Minto-Miri Nishi-ku, Yokohm -, Jpn. Bisong, F.E. nd Mfon, P. Jnr., 6. Effct of logging on stnd dmg in rinforst of sourth-strn Nigri. Wst Afric. J. Appl. Ecol.,9-9. Csll, G. nd Brgr, R.L.,. Sttisticl Infrnc. Duxbury, Thompson lrning Inc. Col, W. nd Lorimr, C.G., 994. Prdicting tr growth from crown vribls in mngd Northrn hrdwood stnds. For Ecol Mng 67, Dyr, M. nd Burkhrt, H., 987. Comptibl crown rtio nd crown hight modls. Cn. J. For. Rs. 7: Hsnur, H. nd Monsrud, R.A., 996. A crown rtio modl for Austrin forsts. For. Ecol. Mng. 84,49-6. Husch, B., Br, T.W. nd Krshw, J.A. Jr., 3. Forst Mnsurtion. Fourth Edition. John Wily nd Sons, Inc., Hobokn, Nw Jrsy. Hynynn, J., 995. Prdicting tr crown rtio for un-thinnd nd thinnd Scots pin stnds. Cn. J. For. Rs. 5:57-6. Korhonn, L., Korhonn, K.T., Rutiinn, M. nd Stnbrg, P., 6. Estimtion of forst cnopy covr: comprison of fild msurmnt tchniqus. Silv Fnnic. 4(4): Liho, O., Lhd, E.A., Norokorpi, Y. nd Skss, T Stnd Structur nd th Associtd Trminologis. In: Skovsgrd, J.P. nd Burkhrt, H.E. (ds) Rcnt Advncs in Forst Mnsurtion nd Growth nd Yild Rsrch. Procdings from 3 Sssions of Subjct Group S4-. th World Congrss of IUFRO, Tmpl, Finlnd, pp McGrughy, R.J., 997. Visulizing forst stnd dynmics using th stnd visuliztion systm. In: Stl, W.A. (d) Procdings of th 997 ACSM/ASPRS Annul Convntion nd Exposition. Amricn Socity for Photogrmtry nd Rmot Snsing 4: pp Monsrud, R.A. nd Strb, H., 996. A bsl r incrmnt modl for individul trs growing in vn - nd unvn gd forst stnds in Austri. For. Ecol. Mng. 8, Ogunjobi, J.A., Mdun, A.J., Oni, S.O., Inh, E.I. nd Eny, D.A.,. Protction Stffs Job Prcption in Cross Rivr Ntionl Prk, Southrn Nigri. Middl-Est J. Sci. Rs. 5(), -7. Okoji, J.A., 996 Us of numricl modls for chrctrizing tr nd forst growth. Ghn J. For. (3),

14 Journl of Agricultur nd Socil Rsrch, Vol. 3, No., 3 Olivr, C.D. nd Lrson, B.C., 996. Forst Stnd Dynmics. John Wily & Sons, Inc., Nw York. Pommrning, A.. Approchs to quntifying forst structur. For. 75(3), Short III, E.A. nd Burkhrt, H., 99. Prdiction crown-hight incrmnt for thinnd nd unthinnd loblolly pin plnttions. For. Sci. 38, Sors, P. nd Tom, M.,. A tr crown rtio prdiction qution for uclypt plnttions. Ann. For. Sci. 58,93-. SttSoft, 4. STATISTICA softwr. Th Sttistics Hompg. Sttsoft Inc., Tmsgn, H.V., LMy, V. nd Mitchll, S.J., 5. Tr crown rtio modls for multispcis nd multi-lyrd stnds of Southstrn British Columbi. For. Chron. 8(),33-4. Udo, B.U., 7. Som spcts of cology of Mon Monky (Crcopithcus mon) in Cross Rivr ntionl Prk, Obn division. PGD dissrttion in th dprtmnt of Wildlif nd Fishris Mngmnt, Univrsity of Ibdn. Vlntin, H.T., Ludlow, A.R. nd Furnivl, G.M., 994. Modling crown ris in vn-gd stnds of Stik spruc or loblolly pin. For. Ecol. Mng. 69: Vncly, J.K., 994. Modlling Forst Growth ndyild. Applictions to Mixd Tropicl Forsts. CAB Intrntionl, Wllingford. Wltrt, M., Abgg, C., Ziglr, T., Hdi, S., Prit, D. nd Hodgs, J.K., 8. Abundnc nd community structur of Mntwi primts in th Plonn forst, North Sibrut. Oryx 4,