サイズ分布のべき乗関数モデルと森林樹木の更新動態の特性把握

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(1)Power Function Model for DBH-Class Distribution and the Way to Grasp the Regeneration Trait of Forest Trees. Synopsis I reviewed some ways to understand the regeneration traits of trees using DBH (diameter of breast height of trunks)-class distribution. When we consider the patch-mosaic structure in a forest, which structure is made by gap formation of the canopy tree, we can understand that Shimano's power function model for DBH-class distributions has a mathematical meaning for the forest structure. The power function is easy to fit loci of the distribution. More the power model is useful to understand not only the forest structures but also species' regeneration traits.. 1 . i$CtY'Il=. r t ~T, %& < a~%%fi;@/t.f ~ l j ~ - ~ m * a , z%izmb6+g%t%%Wbfihiz~L 5 2 LT3 torhea, g f i a ~ e ~ m i 5z2-4-5 ~ ~ k ~ z 2 2 73hb L T , QB+?a%Ra@,6fihb#Y f22Ti%&<fihb@9$'H3i-LT37:o 37z, El% fiiz;t;'L\T %g+$fif F a % i z f f t ~ $ &a) ~~~~6 fih2L\5,kT@E73ff'i-bhT$7coZ 5 L7z@% 13, &+$naB&%+%a)#ERf2 ?c 2 % filfi4-39 , ~ @ 2 K H a , m ~ i i ~ ~2 g~ f \~2s 6 .L- Z~ Tea? 5 L7:%&&f%%i~@ 9 Z 9 , -?a 5 2-T @%Shimano (2000) i t L 9 T % S$ h7:, @*a 94 X'%*iz~2%m@2%Tca&Tl~7%9 &fiq@-4-6lj?&2*zfi*6,. * %&EIkkY. B%T$%H5%-k>9- @!&!&EIYH%S T240-8501 %%%i%k&G!X%?%B 79-7 Department of Vegetation Ecotechnology, Institute of Environmental Science and Technology, Yokohama National University, Yokohama, 240-850 1 Japan. (1999 % 11 1 1 EI 9E).

(2) .. 1993, F Lh 1993 $6k") Kohyama (1993) 13, .th2I%9T&@DE%%l.*2EEL, - s i a k-V 3 ~ f i l b & % f i T D & f 2 % G a > q % t 9 f2 2'2% LTL\F3. Lfih L, .thiz%7T9~J€5,1~ Id%, % ~ H ? & & L " ~ - S BL' J~Ztfhi2fs G~ bfs~), 2 L ' q 7~p~'J%fi'h6~. Kohyama. 5. +t4;f'/n\*h\GE%4H%%L%&k6 Z h ba>*?./Lbd;, 2 BUka>@g26Ba'JQ&I ~ T ~ U € ? ' I L ~ ~ Y &$, ~ X 'X?-???rwqbT& , t 3 ~ 7 ~ b f s t f i 1 r ~ If;2~ L L \ . L ~ J ~ D L ,J A ~ ~ , @&%tfitz%ilHT3 a. zhia, % e a > 4 ~ 4X' DE73@%&a>%tfiT%, ? a > % 6 3 R ITfilbY 3 3 x i z $ 3 h 5 # d # % (@@) & n 7T 1 9rJa>7T 4 X'a>@77@2@@TShifR$b72%TT%s 9rJTS L (n i3Y4 X' 9' 3XD%) , 5 h i ~ 4 +a r 2 f i : + s ~ + ~ ~ ZR, i m~ .E F D M 9 4 XZq'B#fixRa>-tf4 X'iz@6 (h?j~\ib;?a> @2#+-H*rn#&&Eizb7?9 T@gTar 9 4 X'iz 2 2 3 6 ) @$?~$EP~T~U (%@7T9rJ 2 2id;+mT2t3a0 HZ, 5 % 10 q~ q g i ~ ~ h i f h a , n77ngU) & % t 3 6 2 2 i z h - > T R a > LT%r~?hfz9 QIgik2aj.6 2 L T % , BI ~f ~7'~94;t;'#&2#Z-j-6 2 L \ 5 %a>fi, ~ f s2 fi:$~\, t r h i a j q % s & q T 5 a>iz%j~@ rh2@izhTt3&623t&kX'Y-f79U, 9 4 f s ~ ~ z ~ ~+ +~7~ g ih~ ri a~1 i3 ~ z $~3 h ~5& x i z h T i 3 & 6 2 $137 yV-Y-7T3U (37ci3.g %TH@a>E%%t*2jEfE Lfs t3hiffsb fdL\ E 9 L f s L \ k 7 3 Y'y7-fT9IJ) 2 L i f h T L \ 6 , kL\jB+-?, 37z%ZtzR'iffTE:9TL\6 h 5 iZV& a>&g+A5?5~a>j@gT,10 q$$tzi3 r D T T ~ ~ ~ J ~ 9~ 4I X'L T(;li~a~id;%+^? , -9) V~flD#@7it?Tf&<,5DY4X.iZJZT6 A 3 < &%a>%?Rfi4Zb7T L Z jB+i~iB@ii @li$dl b%7ciz&32%7zm#2$B&3& a 2 L \ T6FFIEjRB%h a (SE 1999) 9 7c Z 2 fixT3 5 (Silvertown 1982, {F@C2fil ~ % f i a ) H * C a - - ~ i ~ /$J f\ s Y 4 xa> f,DfiT 1992, fflq 1998 7'6 P ) & < , A37'.%0i3'J.'f61r\. ZhSd;, @/*fix&E 372, %@7T9Ufi{Zbb f't3hi2, r a>$-tg& LTfT < i z - h % ~ @ l @2 a>%+@BT$E+2 i q X ? ~ 7 ~ % $ % 9 E T 5 %494X.ElJ@@% i~, iLfsk"izh9Tt&3ELTL\<r 2 d : R B T h a . D*#iz&&a%q+fix-Zizfs6. ZD7z&, h 372, B*izfshfsL\fff;*t%mfBDGG%.zDR, 5 x 5 - y7"a>Y4X%*id:?a,~a>xf y7"D 2 L T % t ? b h 6 . Kimmins (1987) 13, &#fi 9 4 X'%fia>S&fgizfsa7it32 fs9 , -ZTh ~H*fi:SR~%irE%fiL ~ b ~ h i f B f 3 % % 6 i 3 5 9 4 X'#&k2E@izjEfE-Fb r 2 fiV3 a. 32 J *?22%-Fk%xTL\6. 37z, H*a>E% r a>=W'1biri3,~ d Lh, &a> h .ifsA,&d% iz@fi:h6B+, Dlkif@%izA3 L ~ ~ 2'T~ f s 6. 3-T, #@7TPJ2-< 67c&iz, R$r~72&L\ A*d4$F%Cz$ < @ J h 7 ~ B + f2, s -@Wizjk% [email protected]@'IS Lfs t3hiffsb 7 ' s ~ \ , -3 9 , iEifif4FGL, r a> 2 S A * a > T ~ f 3 f &L T L \ ~ H Befihbra>fi$tfi&bh&L5 2 L T % , H*DY * a ~ f i f % ~ < ~;;-hl;a>~~.t-a-tt4~3 t i ~ ~ , 4 X'+E@2@ 5 Be, 5 q, 10 +a>%rH7fi:fihfihao 7x o g ~ f i< : ~a 2 3 fd: P, r$tgpg%fiiaip 9 ?c, r a > m # s t a g B t z m + t T , ~ ~ ~ i z i J w $%!a>Wz+F2t+-r 2 % & I a 0 r t ~ ~ d : 6#22TE\SLT& 9 , &%H*a>L 5 iz, RPEg Z-T, rh3Xa>.mfR2&@L, t 5 L7ziBfZE ~ H ~ T E % L T Lha>iZC3+BT;tja0 \< fih2 L \ C J %6fi;Pa>@trS%$hT37~fi~2&Tb\<. ? T , #@fT9rJa>&ss&@B@@a>m&izTa2 D h k T, & % # ~ + E % & @ ~ * E L ~ Z @Rtzfs->T L ~ L \~,T P I J s ~ ' I L ~ > ~ @T~ % c JShimano (2000) D + 7 ~ ~ 2 $ E fL, P ZhiZ JZ 6 & L 3 5 r 2d:*kc;h?5. %#S+E%%%a>%fi?&2RTL\ < Meyer (1952) i3$ J ?@!a>iBf3@/n\ai~@&fEl 4. j3i'i;hmZt % (y=a exp bx, x i3Ef3Pg2, y iT?a>Efg@ rht3, ~ f g p g ~ f i t z g t j ah,a e r H 7 h 79~, T D @ B , a, b i3SB) 2 % T 1 3 & 2 S & T L \ 6 0 h a 9 4 x - h f 9~ ~ @ ~ g i t =~a>a$ra'~x5g, Meyer (1952)62, 9 4 X ' ~ H ~ D E C @ ~ ~ T - Z T ~ ~ Y 7OtrErl~Y4x 3 7 tz@6iflJ+, &a>@V~!la~j;if if32 J *?2oBf3pg%*izE%m&fix&% L < 3 y 7 ' T % Z D 9 4 x3 7 X i Z 2 2"36iflJ&, &D T i 3 3 6 Z 2 ?!?$<TL\5, b \ - > 135 , Hett and %r~flXf~ 7 ' 3 T i z ? ~ - t fx4d l b E J E L L L Loucks (1976) , Shimano (2000) 13, E&MB2 Z 5ifW22'3hb$i-gLj T3nfEl&2%6oRt% &3%fEl% (y=aP, xi3iBt3Pi$2, y i350BfiE 2 LT@#??a % D T h 6 a$$* 1966, Hara 1993, @ T D @ @ % SL L L \ b Oa, b CTZ&) C)%32 3. qT3lj€F)b. 0. .. 0.

(3) SL, ~ 3 s m m o f i f i : h T c a &9 f i ~ \ z %j%j L T L \ 6 , H e t t and Loucks (1976) 63, E& 9 fi4k < f2fi17 f z O i 3 , 6. RZO)9 4 )L€T^)Lt:iiZ@I@i5+%a)-2 SlIJ m&a>% Meyer (1952) filfEs"P6 L 5 tZC31f4 XFi'la>@/jl/' Shimano (2000) 63, T-Py 7D%%$j@Z 3T b j $fi4-sTi3f&fi>97z7z&Th6,kg!tj% LTl,\ 6 l < y ? =EY4 P @ g a & f i T o E f g @ % & & 6 6 Z 5 L7z.L kfihb, Veblen e t a l . (1981) h , % k T b ' 6 0 *-? y ? E % 2 i3, % & g + e m f 2 @&a>B7's6 Nothofagus %a>jl$Ef3@%%&&3 FTAf3*fi%kkL6 2 , ?a>fi3TTf*% LTbl % B & & i % 9 THY$ L7z. .LkLbZ3$L%& r; 7z%&*i%amfi~%Efihb%&sh6 z 2 i z k (1986) 13, (y=a/x) %i877z0 37z, S & E L J 37z?D#@T%%CZL ! I @ E & @ b Kohyama (1986, 1987), El & (1993) i&it3'2-? 9 L, & @ ~ f t ~ 3 3 ~ 7 ' z ' t D f i 4 f i i % 2 & ~2 6b ,\ 5 4 7"a El& > (y=a,xh2exp(b, x) ) e l 8 7 Tjl$EtZPg% hDTh6, TLTZDL 5t ~ @ & L ~ b ~ 6 ~ 1 1 f 4 ;r;'a>M*%H (-;ffsbG b ) &-9a>l." ;kit?% L7z0 z a>EBC3, & & ? A Th%fih6 L 5 y ? 2 % i k J Z 5 L?z%S&P%a>Rf661<yFfi4 C~EBM&kd3%M&fi>bf29T% 9 To% € Y 4 9$iCZ< & g b $ 7 T b \ 6 g t $ g 7 5 l < y $$fd$h@fii%@!Th 6 o %CZ%47z L 5 iZ, BfZ ( BhI T6) . ~g/n'ma!z\-TL %3 k ~J ~ ~~ s7 b%- ~ , ? * ; ~ ~ 4 3 # ~ T %ir--%/J\ 2 b\BfsPBT@Efi47;fi4 6 z 2 fi4 &I 60 Zht-2, zB&@i:h5RBuka>A3 s (4% gfix 1.3mU4-?' 2rnUkfd P ) D4%*@jCj&bZ L7z 9 , %%b~1f-tf-fdFfiT%3"P67z2d,, CZ@l*D@Bfi~I&< fd 6 Z 2 fd Pfi4EKlTh 6 (st~-tt-tfo-&$&?j'E-?'x~J 9 @ !I$3, -@I% tz/J\ @tt4 ~'a>4%*%Efi~#RCz&<f d 6 .L 2 % h 6 ) 3 9 47 z5 $ 7J 9 3 2 5 3 < 3-j-z2 fi4TS Go 7 4 Y ~ b @ l @ y=c/bx/bc-1 exp-x/bc 6 , fl%{Z%$$,fG~&T, E!-IfZPB%&a>@'J%CZ Ltf L i f i g h k L 6 ( B a i l e y and D e l l 1973, 48 1984, %@ 1984, i%z. %% 1990) =C a>B&kt3 ~ 3 . a> 6 2 3 iEk!Z/rS;kiCZ f d 9 , c=l a>IR?$E&%;k;C~f26.37z, l/."S%-9 b 13, @ g a > a s (/n'&@a>*- Fa>g$) e %ToMasaki e t a l . (1992) C3, R&l~@fifXI7Z ZC J + ~ e @ f i ~ ~ / 7 i ~ k ! LZ~&Z .2:D% ~f~ G-, EB%&ta3$<~t~@fif;trz2ttfd9, f&b i3ZkL4?Ff9, %&, EB, B@i%&%T%L7zo Shimano (2000) 13, F T y 7°Ef$i~Ea>lzy 4 ZC J F!Pfi<A3< @fiS&] @tT9%@&%<z 2 ptlDH*%I3D?-4 x'2@@ogiL23ia>.L 5 fi4&56, L 5 L7z%;ki%!CZ%LTC1 Minowa and t r %E!Jl L T L \ (El ~ 1 +) ~ 6 3M , ~ D H i r a t a (1993) CL L 6I$ZiE$E&&@7"6P'fi4856 , f i $ t L T ~ \ a . ~ ~ ol~~?-tt Z h ba>=EY'1vi3, & & D l < 7% -9 2483 7 , 4 2'taGPRf6a>TJ r a>+ trs3, /I\$ f2H* (fi %&%!&Zk% LTb16. c a s < ~ r i % ~ 2 6A f iSs~, L ~ H * C ~ CL/ ~ ~ / ' ~ G < 2 Z 6d4, Z Z T @ * L ~ ~ = F Y . IMeyer ~~~, (1952) ~ > + E & € ~ . I L & @ I $@tr/rS;kia>j%2~ C~, fih@@T3f2b'o$b3a>-!f'f x k LT?a>Ef%(@ o i E % R $ T s 3 a ~ E $ C z h 7 ~ 66385 ) 2-9-6 2 , &kTf2?77b\6??1?Th6o ? a > k 2 d , j %sfm f d = E y ~ b 2tJdL\k6fi4&k@m2 C3L\kfdb\. 1f4xfi4 2fgCZf26 2 3 , % a o H z f i : & & 6 f i S C ; ~ ; ~ E ~9 L, ~g L gt~ 114 i g i ~ f ~ :a oa .;j4% Meyer (1952) , H e t t and Loucks (1976) CZ L 6 E C343%W% (y=aP, x CIHZDEt3, y Cd;?a> &M&a>s?~l.t&, ?kLfi4%3fih P 5 f i h C 3 E I J 2 L T , i E Z $ h T b \ 6 - t t 4 X ' P B F J T - ~ T ~ ~ ~ E ~ $BE, a, b C2$&) T S - ; f Z 2 fi:TS, %?ED% Eta y=ax-2T%$r2 7j4~3 6. =lt1,63,3 $Q E E T 3 5 , 6 T & @ m 2 b \ ; i 6 . Shimano (2000) 13, &;M;~a>@*~E%fixFa>&trBz 6 'r ()%?I ofiE@PE:'2 a>@E&%LTL'5 D7?7F, 1 DTCZZL7z.L 5 bZJ &j$fi:l<yF fih&%k, ?a> 5 k T d $ % M & % f ~ 5 d 3 T h 6 2 2 & @ ; % W l r ~ b \ f ~z. =C TIATz ~ ~ 4€Yl'29 @ E & R t ; , &&a>%g@pga>/<.;,?&. =*-. J. +m. -em. .. .. .. z).

(4) t $ J % t z g X I ~ ~ \~a ~ h h i r 2 D , &#~#TD. -!f4X - @ E W f % % y = a ~ i-r~f 6 6 r 2 8:#% 6.. $h. @E@#kEE%RB2S5%+@LTL\6 Did;@fBThaT-&, =I . t T @ f * a ) l f 4 X X k L-c 2,ss ~ L - C LD ~i d ; ~ z ~ ~ t m f aDH% 7FE%LTL'6 k 5 i r , # D E f 3 2 @ f 3 D E f 3 2 i~id;kflJN{%$%K$ $h6 (Shimano 1997 f6 F) , ? D T z & , % o ) % % D f 6 i 3 1 T D ~ 3 - ! f 4 r z ; ' C 2$$ ,. s<. a. 0I-Y-4X ' i ~ E 3 # 2 6 t 2 3fT36. T f 2 b h J &&f2%BE?@Dl{ y F & t $ J G $ i Z g O & # T D Ef3PE%47 ($$a>-tf4X'-@E %&) id; y = a ~ - ~ TEl!%T5t 2fi:T3 6 i 2 T T h 6 (B ZJ Shimano 2000) 3fz, Shimano (2000) 12, t t. .. -m%?;hTL\a d; 5 f2, ~ + ~ E G ~% fR 2 C 5 3 E t 2 f @ t 6 # % D - ! f 4 x%*id;$g&M&T STDid;3&gJTid;f6L\t 2 2%~-CL\6,, z8m7'sg49ifi:f'ibhJ & h f6-9-4 X'D 3 $b ( I ~ Y7 ) & $ j & # D E f 3 P % % 4 7 f i f g J $%! i r f 6 Z j D i 3 , *;ffi?$fta> y=ax-2i~@->Tb\Tzfih b 2L\%6. t h 5 2 T ~ + ARABi y h f i : - > T z , @ f Z i ~ d ;. 6 FiEi?2~~7%%I]& Shimano (2000) id; 9 4 / k 5 T'/k ( t i l e model) 2 1 0 , & # e # D E f 3 P % % 472:-2 % D 4 3 % M B T E l j % $ h 5 z 2 &Ef3 [y-&%;ffiD-2 %!3U (-2 power law f o r DBH-class d i s t r i b u t i o n ) 2 P F X I T L \ 6 . -2 %WUDhTb23 6 & # 2 1 q ~ F *€-tfl'43#iE@l%q%D2%2 fi1 6 id;?& a&#&, x q 7 9 - 9 ba>W$J2@@BZ&i%9 T G S t Z b d ; T h T L \ 6 2 h F 5 f i h & @ $ T 3 6. T. hifJ43 % E l j % T l q 7 % -9 b 6 - 2. L-iC, ?D&#fi<f2@T 5 L T z t k E i r f 2 6 fil2S ,%T63 - > 2 ~ t 3 i r ~6, 3. % & r ; k % ~ T h b % t r 9 f 2 d f - > T L \ 67"D 1~4 %3i 9 T h 6 , 2%W$hTL\bo ?a>'fz&%a) & 2 ~ ~ 4 7 " D % i d ; k f l 1 H L % i ~ fL686>~L J#3. DBMf6 F T M Z T % a > B ; f , 4 t & h T L \ < 2 %id; l's< f 6 9 T % ? D % D . ) ~ 4 7 ° i d ; # D ~ i r ? 3 $ d z TL\<. t 5 L T z Z k f i h b , &%L7z#%Ti2J J. %D&iL%f f2< T%(@/ZE@b2%$f6< 7%) $$D%E@Cd;%2TL~<-, Z h i r k - > T Shimano (2000) id;, #ifZD9 4 ~ k % - ~ ~ k ia>3 d ; ?3 IZ, I{ ~ s G r ) s E ~ m d ; B n n T 6 m a mLmT L \ ~ , r D f z & , kL\#id;#if3a> 94 ~ r k € ~ / k T % M $h6d;9%&<@GT3bt2trfd:o, ?ai$ f3PE%*~$h%id;~ -2 %Wrla>Thd; 9 %@*fihf2 % i ~ f 2 9 ,1 q 7 9 - 9 bik-2 k 9 %-?-?A$< (0 Li ~~2 z L ' i E ) f 2 a o 527z, Z E i z i 2 , J m 3 i @ j J f 35 d / h a U4i~f6bFfi%AL'fz1q.;)FTi2, I&*@+ zL$i\*~k!#% fi@ ;,ti $E LTL\6 1996) t 5 L?z/J\f3*0@$Ei2~ Ef3l%%47a>$h@&-2 %WlJD74 2.L 9 l t % , i ~ T 6 , T f ~ b t j ,I{?% -9b%-2L9%/J\$< OfihbEhZjJ.5 1): .fa$$%@& 6, Shimano (2000) id;, Shimano (1997) D M % L L z 4 3 % Y T Y 4 F M & (Power-sigmoid f u n c t i o n , r%Zj i~%flJ;j)2. (a@. i2L'J. T'-9fi1b#ZTizG&T64&*&R<. .. :. 2Tr 5L T z % % & M ~ ~ ~ ~ Z L T L \ ~ . t 5 L f z r 2 fif%R B % ~ C $ ~ f 2 7 5 ~ - > 7 ' z B E l 2 L-CiAJ - 9 i ~ i d ; & # T & & f~%BE?pga>Iq y 7&$bAK@D%sdfm%Tha t2 %5. -. 9 i 3 , :h3Tid;l<-Y*/k =I 2tozL-9iZd; 6 % ~ f 2 T ' - 9 D ~ ~ t * v ~ P - 9 3 YfiXB % T h - > ? z Z 2 f ~ F ; t ) f % t _ j r 6 h k 5. % % i ~ q L \ T J Shimano (2000) id;, & A f ~ % i Z E ? @ a ) ~ q7 4 &?,h@EL ( / q y F - Y 2 7 " ' I Y3"$!iJ Ohsawa 1991), ?h&%&LT&%2i$DB@S%T6 2b15 I ~ Y TFY 7 ' ' I 23"%&$& (ToMPS: t o t a l i n g @& 1993, 1994, method of patch samling, &@ 1996, Shimano 2000) & @ L \ , $ f 2 L \ z j 5. T&#D2#&<3f2<3sT6tkCrd;->T @RLTL\6. 7. ~S%Bd%@rn4@+9@~@E%*-@fiH. 4ZZD 9 4 / k € ? / k T i 2 ,. L f i h. o. L , /q y Fa). & % A i ~%2f 6 5 1 q ~ F h k D&EEI@ (BA: b a s a l a r e a . lQ&%iEi@&zt k % --ZD&#E @Ptlir&& a@f*%~l87iEi@a)&;ti2BAa L f 6 L \ (Shimano 2000) , Shimano (2000) i d ; t h % $ +. .. DEfZ2MZa>Ef3a>kfiJM&2f,. RtrA3 J;rY. 4xT%h6t 2 fihb%M L - C L \ 6 . 1q-4 7"€ T./k (Shinozaki e t a l . 1964a, b) Tid;, #id;. Shimano (2000) id;, Bf3Pg/n\;kia>& 2:gaj$lT DfiGtfi2J @* D + @ D E ~ ~ P E % ~ ~ %fTL\, ~ Z ~ L \ T &@DE%%++a>EE2%&TL\6. @id;, 6% iZ?!47id;&JzlFI~%a>1~79--9ba>fi$jR&&a>d; 5 i ~ f T 9 T L \ 6(B3) ~ i d ; @ f 3 ~ 9 4 / k 5 T . 1 k T h 5 .L\@id;-!f4 X. (@fa%. L < id;#OT$f3,. BlTi"6%jf5D-;L!Ol , %Bid; t:/8 C L ~ L G ~ ~ SfZid; 114, id;@l3 1/2, ir%id; 1/1, tZ+Z. E?;) d f z i g i r f 2 3 T z 2 3 L16, (3o/i ~h 6,. r a> d; 5. ZIT .i,F@&@TD@E.

(5) 3IH3Gkf Bailey, R. L. & Dell, T. R. 1973. Quantifying diameter distribution with the weibull function. Forest Science 19 : 97-104. Hara,T. 1993. Effects of variation in individual growth on plant species coexistence. J. Vegetation Science 4: 409-416. Hett, J. M. &Loucks, 0. L. 1976. Age structure models of balsam fir and eastern hemlock. J. Ecol. , 64: 1029-1044. El 6 1993. E3 $3lJ,!$i~;tj'b;'tj 6?3-a>%g 2% %%ga>aBZlL. 4L%%AT%Y@&t$*t% $gZ&Fz~~KPRB*. +G -zh IFjl%3!%% clr#$WlJB4%BiE?%1992. B@&%Y. 5 0 7 ~ ~g@/sE, . Rg. Kimmins, J. P. 1987. Forest Ecology. 531pp. Macmillan Publishing Company, New York, & ? ? @ - ~FfwP&7 h - C t T $1993. $%i%% a>#%$;% GT36a>$h. $$Y,63: 768-776. Kohyama, T. 1986. Tree size structure of stands and each species in primary warmy=a4a>j 6, bt-hY/I';f;'$x2{$1.~fd->?~k3a> temperate rain forests of southern Japan. -? LT, a aC-hei~/j\ts*a)gBe%+ Bot. Mag. Tokyo 99: 267-279. 1q7$-9T8560 b ; ~ - i c ,&&%Ega>Z%% Kohyama, T. 1993. Size structured tree t!k&R9#fEEb&,A3 f~{Ea> a 2-2 b; !I % $ CItz populations in gap-dynamic forest. -the /J\$b\ b { E e % q a 2i r f ~ 5giz, ~ +E+Ea> forest architecture hypothesis for the %Dl&,@$f&tr/J\$fd a 2 - 2 1 9 $A$b\ (7 stable coexistence of species. J. Ecol., 81 : 43 - X Efi0fi~iEb\)b l E 2 %9, Shimano (2000) kt, R Z z~~wa>7'3-%Tza>fi~tfiet7-37zo 131-143. Kohyama, T. 1987. Stand dynamics in a primary -? LT-?a>%%hhr;, Y - f , 4 Tt7-3-f2Pa>@@ warm-temperate rain foest analysed by the @&@7F9E+3FBj 7%9-€, y 3 97.f. Pa> diffusion equation. Bot. Mag. Tokyo 100: EIES*~!~#%~~&E$ET&~ a2 305-317. 9 6 29 to Masaki, T., Suzuki, W., Niiyama, K., Iida, S., Tanaka, H. &Nakashizuka, T. 1992. Community Zktb structure of a species-rich temperate Uka>b; 5 iz,Shimano (2000) b-h, &@Qqt forest, Ogawa forest reserve, cent'l'alJapan. ~ 7 ~ ~ ~ t ~ 1 r ; f =2 E aY 19~ q ~ ~~ ~ 7 ~%2 Vegeta tio 98: 97-111. 5 2 2 T,$ % = X ? 4 y 9 f$€?'~k@@Z L, 1q7$-- 9 e g ~ 1 ~ i z z m 2 5 a 2 ~ ~ ~Meyer, s 5 aH. A. 1952. Structure, growth, and drain in balanced uneven-aged forests. J. 2 Leo2 a>fS?ikt3, -;ST&#&Wa>Y/f Forestry, February 85-92. JwNij294 ? (WE, %$3, $f-%W%f2 Fa>S Minowa, M. & Hirata, Y. 1993. A modified b\, B-94 )\bS6f~@!ti>a°7 ElJt~k@T6t Exponetial distribution for describing the 2 irl!E;iaT&s5 L,I&%, -&%VtJa)#%r stand structure of Uneven-aged forests. J. 2 a>z%t&?)q7$ -9a>k-L@Kb;-3-icT% Jpn. For. SOC., 75: 449-451. tzLTE 2b'\;i,O. <. g$+e,. e//."?$ -. ezr;.

(6) %g%&l3b %@j'Lft;t$1990. $NH?. 243pp. a %+k, R Z . %,!&@$!i &I%%% LkD%%& 1986. ii!Zf3@%lj & & % 6 E Q & h T i 2 @ i ~6*%&E%@# L a>4+/,.#$ga>#tj9. 8 #%, 68: 361-367. Ohsawa, M. 1991. Life zone ecology of the Bhutan Himalaya 11. Lab. Ecol., Chiba Univ. 249pp. @Bj'L31996. El $&@ %F?%@yT%a>E%. B%a>SL\k?o>BB. f-%AFAYE$%F4 ~ @ % F ~ ~ $ I I I %106pp. X. Shimano, K. 1997. Analysis oftherelationship between DBH and crown projection area using a new model. J. For, Res., 2: 237-242. Shimano, K. 2000. A power function for forest structure and regeneration pattern of pioneer and climax species in patch mosaic forests. Plant Ecol., 146 : 205-218. .h?j!@j'67. 1999. wRa>y?$k, ?a>=&k%%.. $$i*%-k1966. if$^@ 2 #%, 48: 436-439. LEI 1998. @ %&% >a$8% ?& 9% -& & 7'. L T a>#/n\a>B$@ (1).. -a>GM. @&EIABB@$ZB24 : 11-20, kB#.I6!b. 1984. Efg%@i~g.f-6 @%!%&i (1). 74 7'~P5j@a>%5%f<7 9 -9 2 % E + 2 a>M$%%LUEE74YlP%6a>%g. 8 #. 3,66:253-261. Veblen, T. T., Donoso, C., Schlegel, F. M. & Escobar, B. 1981. Forest dynamics in south-central Chile. J. Biogeography 8: 211-247. $%L!~%l938. $f2#1@%. -&f2#&%1& $!%%@-. R#%.. %. RZ.. a. Shimano (1997). % V T s 4 FM&i2UF. a>L 5 ? & 6 ,. S%&%H%. W@rJ+. #& i@ 1993. %I%%%*&@, =@ Crrir/n';ftr.f-6 7'9- 4 3 Y-f#a>E%. El &%. @!@%GI. &%, 43: 13-19. ,!&@j'6Sj ;/tP@ $ %#a>E#j.. i@ 1994. ~Rj?ijZZi~%C3 6 yT &%%%, 44 : 283-291.. Shinozaki, K., Yoda, K., Hozumi, K. & Kira, T. 1964. A q u a n t i t a t i v e a n a l y s i s o f p l a n t f o r m . -The pipe model theory 1. Basic analyses. Jpn. J. Ecol. , 14: 97-105. Shinozaki, K., Yoda, K., Hozumi, K. &Kira, T. 1964. A q u a n t i t a t i v e a n a l y s i s o f p l a n t f o r m . -The pipe model theory 2. Further evidence of the theory and its application in forest ecology. Jpn. J. Ecol., 14: 133-139. Silvertown, J. W. 1982. Introduction to plant population ecology. 229pp. Longman Scientific & Technical, New York. (??ilBE - 8Blflk!$j AR 3% %B, 1992 r%@a>@ #%&%?I 274pp. %&A?LHk!!?, RZ). L L T , x l2$$a>Ef?6 (cm) , y b2HBfiS (m2) , ymx 62Z+@T$% bh6E%~a>.&AHZE@Th6 , ZOISb2, xdx/Jh$L\2 3a>@l,@& y=a2 TZfHT 3,$$a>Bf3a> 2 %iZlk@'LTHZa>fi@d~@AU. LT(TL\<L 2 2 Z L T L \ 6 , ?a>@, HZE@ y ir A 3 < f2 6 2 , HZfi@ y b2EAliE ymax, irQ% L T ? ~ U k ~ Z f i @ d ~Lfsb\ ~ A aL 2 43 A1 2 %,$ L T L \ 6 , Shimano (1997) 62l%?@ (1966) a>@?E%%%K%H#a>~'-9 dl 6 , a=O. 024, ymx=482.3 2 L \ 5 f$if?$$ttj L7?, Shimano (2000) 12, L a>lE2l!E- T I ~ TBa> Y ma a>H*d:Ya>@Ba>@zfi@2%7TL\6 A~f?gLH L, A*fih6?a>HZfi@2&%LTL\ 5 , hYZfi@a>%2+liEfi~~~ Y 9-a>fi@2BkTz 2 Z 5 T , ? h L KJ/J\$L\H*2#ZTir@7w-?5 2 Rf2 L7co.

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