: (GLMM) (pseudo replication) ( ) ( ) & Markov Chain Monte Carlo (MCMC)? /30

PlotNet 6 ( ) 2006-01-19 TOEF(1998 2004), AM, growth6 DBH growth (mm) 1998 1999 2000 2001 2002 2003 2004 10 20 30 40 50 70 DBH (cm) 1. 2. - - : kubo@ees.hokudai.ac.jp http://hosho.ees.hokudai.ac.jp/ kubo/show/2006/plotnet/ 2006-01-19 1/30

: (GLMM) (pseudo replication) ( ) ( ) & Markov Chain Monte Carlo (MCMC)? 2006-01-19 2/30

( ) TOEF(1998 2004), AM, growth6 DBH growth (mm) 1998 1999 2000 2001 2002 2003 2004 10 20 30 40 50 70 DBH (cm) ( ) ( ) 2006-01-19 3/30

( ) (1998-2004) : 1998 4 : (TOEF) : 2006-01-19 4/30

: 6 6? 1998 1999 2000 2001 2002 2003 2004 year growth6 TOEF(1998 2004), AM, growth6 DBH (cm) DBH growth (mm) 10 20 30 40 50 70 1998 1999 2000 2001 2002 2003 2004 6 (5 ) 6 2006-01-19 5/30

? (1) TOEF(1998 2004), AM, growth6 TOEF(1998 2004), AP, growth6 DBH growth (mm) 1998 1999 2000 2001 2002 2003 2004 DBH growth (mm) 1998 1999 2000 2001 2002 2003 2004 10 20 30 40 50 70 DBH (cm) 10 20 30 40 50 60 DBH (cm) TOEF(1998 2004), OJ, growth6 DBH growth (mm) 1998 1999 2000 2001 2002 2003 2004 ( ) : β 1 log(dbh) + β 2 log(dbh) 2 10 20 30 40 50 60 DBH (cm) 2006-01-19 6/30

? (2) 1998 1999 2000 2001 2002 2003 2004 year growth6 1998 1999 2000 2001 2002 2003 2004 0.0 0.5 1.0 1.5 year growth6 1998 1999 2000 2001 2002 2003 2004 0.0 0.5 1.0 1.5 2.0 year growth6 2006-01-19 7/30

( )? 2006-01-19 8/30

: 0.0 0.2 0.4 0.6 0.8 1.0 0 5 10 15 20 25 Temperature 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5 VPD 0.0 0.2 0.4 0.6 0.8 1.0 0 5 10 15 20 25 Temperature 0.0 0.2 0.4 0.6 0.8 1.0 0 2 4 6 8 10 Precipitation 0.0 0.2 0.4 0.6 0.8 1.0 0 10 20 30 40 50 60 PPFD : 6-9 ( ) VPD PPFD : 6 2-3 ( 16384 ) ( ) ( ) 2006-01-19 9/30

y1 A A "#%$# W y1 & B y2 B W y2 C C!! & #%$(') & : *,+(-. #%/0 1998 2003 2006-01-19 10/30

? (3) DBH growth (mm) TOEF(1998 2004), AM, growth6 10 20 30 40 50 70 DBH (cm) 1998 1999 2000 2001 2002 2003 2004 1998-2004 ; ( ) 2006-01-19 11/30

: = (fixed effects) (random effects) TOEF(1998 2004), AM, growth6 DBH growth (mm) 1998 1999 2000 2001 2002 2003 2004 10 20 30 40 50 70 DBH (cm) fixed effects ; Poisson random effects ; 1 Gamma (mixed model) Poission Gamma 2006-01-19 12/30

: ( ) L(β j, γ k, s {G i }) = i T r=0 [ R(r s) y Y ] P (G 6,y r, λ i,y ) dr, random effects R(r s) ( 1 s 2 Gamma ) fixed effects P (G 6,y λ i,y ) ( λ i,y Poisson ) P (G 6,y λ i,y ) = λg6,y i,y exp( λ i,y ), G 6,y! λ i,y exp( ) λ i,y = exp( X j β j x i,j,y + X k γ k w i,k,y ), + 2006-01-19 13/30

: R Random effects s 16384 1. 2. 10 fixed effects Akaike s Information Criteria (AIC) 1. 2. + 3. + + 2006-01-19 14/30

: (Acer mono) DBH growth (mm) TOEF(1998 2004), AM, growth6 ( ): 10 20 30 40 50 70 DBH (cm) temp.ps: best=16.4/width=4.6 ppfd: factor=0.02 vpd: factor=0.05 ( ): temp.mb: center=14.2/slope=1.0 rain: rbest=0.9/time=0.08 1998 1999 2000 2001 2002 2003 2004 density 0 1 2 3 4 5 6 7 0 1 2 3 4 5 posterior AM 2006-01-19 15/30

: (Acer amoenum) DBH growth (mm) TOEF(1998 2004), AP, growth6 ( ): 10 20 30 40 50 60 DBH (cm) temp.ps: best=16.4/width=5.8 ppfd: factor=0.05 vpd: factor=0.05 ( ): temp.mb: center=14.8/slope=2.0 rain: rbest=0.7/time=0.08 1998 1999 2000 2001 2002 2003 2004 density 0 1 2 3 4 5 6 7 0 1 2 3 4 5 posterior AP 2006-01-19 16/30

: (Ostrya japonica) DBH growth (mm) TOEF(1998 2004), OJ, growth6 ( ): 10 20 30 40 50 60 DBH (cm) temp.ps: best=16.0/width=5.8 ppfd: factor=0.04 vpd: factor=0.05 ( ): temp.mb: center=14.2/slope=2.0 rain: rbest=0.7/time=0.08 1998 1999 2000 2001 2002 2003 2004 density 0 1 2 3 4 5 6 7 0 1 2 3 4 5 posterior OJ 2006-01-19 17/30

: TOEF(1998 2004), AM, growth6 DBH growth (mm) DBH growth (mm) 10 20 30 40 50 70 DBH (cm) TOEF(1998 2004), AP, growth6 10 20 30 40 50 60 DBH (cm) 1998 1999 2000 2001 2002 2003 2004 1998 1999 2000 2001 2002 2003 2004 1. 2. ( ) 2006-01-19 18/30

- - ( ) 2006-01-19 19/30

{open, close} : 22 : 5m : 1 3 1 1,,,, CN,, 2004 10 : 1 ( ) 2004 10 2005 3, 7, 10 2006-01-19 20/30

:? :????? :? logistic p: ( 1 ) q: ( 1 ) p = exp(β CD + β LD L)/Z, L : 0, 1. q = exp(β CL + β LL L)/Z, Z = 1 + exp(β CD + β LD L) + exp(β CL + β LL L). 2006-01-19 21/30

: 1 3 1 1 : 1 ( )!?? 2006-01-19 22/30

Nest : - - : β x = β Hyperspecies x (Hyperspecies) (Species) (Individual) + β Species x + β Individual x 2006-01-19 23/30

: Markov Chain Monte Carlo (MCMC) Gibbs 2006-01-19 24/30

: β CD = β Hyperspecies CD + β Species CD + β Individual CD 2006-01-19 25/30

: 0.31 (close), 0.09 (open), 0.02 2006-01-19 26/30

( )? p: ( 1 ) A: ( ; ) L: N: ( % ) p = 1 1 + exp( (β C + (exp(β A ) + exp(β L )L)A + β N N)) 2006-01-19 27/30

: 2006-01-19 28/30

: average life (years) 1 2 3 4 Caj Clj Ms Sb St EjSl Rt Pe Sp Cs Pn Vo Sg Pt Cc Ia Qs Na Pj Ir La 1.0 1.2 1.4 1.6 1.8 2.0 nitrogen (%, spc mean) 2006-01-19 29/30

: Random effects ( ) plot data? MCMC TOEF(1998 2004), AM, growth6 DBH growth (mm) 1998 1999 2000 2001 2002 2003 2004 10 20 30 40 50 70 DBH (cm) 2006-01-19 30/30