{VERSION 3 0 "IBM INTEL LINUX" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{PSTYLE " Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading \+ 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple O utput" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 3 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 4 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 11 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 11 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 261 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 11 262 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 3 263 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 3 264 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } 3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 42 "Dynamics of baleen whale population growth" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "The model:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"xG6#,&%\"tG \"\"\"F)F),&*&,&F)F)%#muG!\"\"F)-F%6#F(F)F)*(F-F)-F%6#,&F(F)%\"TGF.F), &F)F)*&%\"qGF),&F)F))F2%\"zGF.F)F)F)F)" }}{PARA 0 "" 0 "" {TEXT -1 5 " where" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 262 "" 1 "" {TEXT -1 0 "" }{XPPMATH 20 "6#-%\"xG6#%\"tG" }{TEXT -1 40 " ... population de nsity at the year " }{XPPEDIT 18 0 "t;" "6#%\"tG" }{TEXT -1 46 ", rela tive according to the carrying capacity " }}{PARA 261 "" 1 "" {TEXT -1 0 "" }{XPPMATH 20 "6#%#muG" }{TEXT -1 19 " ... death rate" }} {PARA 260 "" 1 "" {TEXT -1 0 "" }{XPPMATH 20 "6#%\"qG" }{TEXT -1 92 " \+ ... maximum relative increase in fecundity as the population densi ty falls to low lewel" }}{PARA 259 "" 1 "" {TEXT -1 0 "" }{XPPMATH 20 "6#%\"zG" }{TEXT -1 78 " ... a measure of the severity with which \+ the density change is registered" }}{PARA 258 "" 1 "" {TEXT -1 0 "" } {XPPMATH 20 "6#%\"TG" }{TEXT -1 52 " ... the time to sexual matur ity (5 - 10 years)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 85 "The model is based on Report No. 29, International Whalin g Commision, Cambridge 1979." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 22 "Specify the parameters" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "mu:=0.5;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "q:=0.15; " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "z:=0.6;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "T:=8;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 257 "" 0 "" {TEXT -1 68 "Simulation of the population e volution and analysis of steady states" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 68 "You can c hange the length of simulation tmax and/or initial value x0" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "tmax:=120:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "x0:=0.91:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "X :=array(-T..tmax):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "for i from -T to -1 do X[i]:=1 od:" }}{PARA 0 "" 0 "" {TEXT -1 55 "The assigment of \"tail\" values can be changed as well." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 9 "X[0]:=x0:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "for i from 1 to tmax do X[i]:=(1-mu)*X[i-1]+mu*X[i-1-T]*(1+q*(1-X[i-T -1]^z)) od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "p1:=pointplot([[t,X[t]]$t=-T..tmax] ,style=point,symbol=circle,color=red):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 125 "p2:=pointplot([[t,X[t]]$t=-T..tmax],style=line,labels=[`t`,`x `],title=`Simulated evolution of the baleen whale population`):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "p3:=plot(1,t=-T..tmax,color=blue): " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "CharEq1:=lambda^(T+1)-(1-mu)*lambda^T-mu*(1-q*z)=0:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "S:=[solve(CharEq1,lambda)]:DominantLambda :=0:abs(S[1]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "for i from 1 by 1 to nops(S) do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 " DL:=abs(S[i]): " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 " if (DL>DominantLambda) then \+ DominantLambda:=DL fi" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 " od:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Stab1:=evalb(DominantLambda<1):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "CharEq0:=lambda^(T+1)-(1-mu)*lambda ^T-mu*(1+q)=0:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "S:=[solve(CharEq0 ,lambda)]:DominantLambda:=0:abs(S[1]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "for i from 1 by 1 to nops(S) do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 " DL:=abs(S[i]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 " if \+ (DL>DominantLambda) then DominantLambda:=DL fi" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 " od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Stab0:=ev alb(DominantLambda<1):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "if Stab1" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 73 " then lprint(`\\nPositive equil ibrium density is asymptoticaly stable.`)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 " else lprint(`\\nPositive equilibrium density is un stable.`)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 " fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "if Stab0" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 89 " \+ then lprint(`The zero density is an atractor. The population may go t o extinction.\\n`)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 93 " else lpri nt(`The zero density is repulsive equilibrium. The population is persi stent.\\n`)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 " fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "display(p1,p2,p3);unassign('p1','p2','p3'):" }}{PARA 6 "" 1 "" {TEXT -1 54 "\nPositive equilibrium density is asymp toticaly stable." }}{PARA 6 "" 1 "" {TEXT -1 73 "The zero density is r epulsive equilibrium. The population is persistent.\n" }}{PARA 13 "" 1 "" {INLPLOT "6(-%'POINTSG6`s7$$!\")\"\"!$\"\"\"F)7$$!\"(F)F*7$$!\"'F )F*7$$!\"&F)F*7$$!\"%F)F*7$$!\"$F)F*7$$!\"#F)F*7$$!\"\"F)F*7$F)$\"#\"* F=7$F*$\"$b*F:7$$\"\"#F)$\"%v(*F77$$\"\"$F)$\"&v))*F47$$\"\"%F)$\"'vV* *F17$$\"\"&F)$\"(v=(**F.7$$\"\"'F)$\")v$f)**F(7$$\"\"(F)$\"*voH***!\"* 7$$\"\")F)$\"+vV['***!#57$$\"\"*F)$\"+W+z&e*Feo7$$\"#5F)$\"+z:T(e*Feo7 $$\"#6F)$\"+')z9\"p*Feo7$$\"#7F)$\"+h3M%z*Feo7$$\"#8F)$\"+#Gl:()*Feo7$ $\"#9F)$\"+>H)H#**Feo7$$\"#:F)$\"+5B4b**Feo7$$\"#;F)$\"+dnMu**Feo7$$\" #F)$\"+Kh]8(*Feo7$$\"#?F )$\"+m0)er*Feo7$$\"#@F)$\"+)o7Uw*Feo7$$\"#AF)$\"+k!4O#)*Feo7$$\"#BF)$ \"+$QSn()*Feo7$$\"#CF)$\"+H*Hz\"**Feo7$$\"#DF)$\"+r.HZ**Feo7$$\"#EF)$ \"+#[!3n**Feo7$$\"#FF)$\"+_Z3%*)*Feo7$$\"#GF)$\"+V5R;)*Feo7$$\"#HF)$\" +h%H'y(*Feo7$$\"#IF)$\"+F2$=y*Feo7$$\"#JF)$\"+6_a5)*Feo7$$\"#KF)$\"+&p M\"\\)*Feo7$$\"#LF)$\"+$>,s))*Feo7$$\"#MF)$\"+2xg>**Feo7$$\"#NF)$\"+q: #[%**Feo7$$\"#OF)$\"+2*yT#**Feo7$$\"#PF)$\"+9dUy)*Feo7$$\"#QF)$\"+>BJQ )*Feo7$$\"#RF)$\"+&G<(>)*Feo7$$\"#SF)$\"+sr_B)*Feo7$$\"#TF)$\"+rx.V)*F eo7$$\"#UF)$\"+d&\\,()*Feo7$$\"#VF)$\"+$*HZ)*)*Feo7$$\"#WF)$\"+T$>T#** Feo7$$\"#XF)$\"+c.aF**Feo7$$\"#YF)$\"+\"e+%3**Feo7$$\"#ZF)$\"+!3Q0))*F eo7$$\"#[F)$\"+=J7e)*Feo7$$\"#\\F)$\"+WSl[)*Feo7$$\"#]F)$\"+I.#G&)*Feo 7$$\"#^F)$\"+6uEn)*Feo7$$\"#_F)$\"+f**Feo7$$\"#cF)$\"+sm80**Feo7$$\" #dF)$\"+^<%z))*Feo7$$\"#eF)$\"+Re-v)*Feo7$$\"#fF)$\"+L!o/()*Feo7$$\"#g F)$\"+^rxu)*Feo7$$\"#hF)$\"+k16'))*Feo7$$\"#iF)$\"+_3p,**Feo7$$\"#jF)$ \"+Mj9:**Feo7$$\"#kF)$\"+!)Rt?**Feo7$$\"#lF)$\"+Q<<<**Feo7$$\"#mF)$\"+ \"4av!**Feo7$$\"#nF)$\"+\"[do*)*Feo7$$\"#oF)$\"+)=J%*))*Feo7$$\"#pF)$ \"+aEo())*Feo7$$\"#qF)$\"+7\\(>*)*Feo7$$\"#rF)$\"+b>A,**Feo7$$\"#sF)$ \"+4m(>\"**Feo7$$\"#tF)$\"+@'**)>**Feo7$$\"#uF)$\"+E#QA#**Feo7$$\"#vF) $\"+>a->**Feo7$$\"#wF)$\"+9Xa7**Feo7$$\"#xF)$\"+p$>f!**Feo7$$\"#yF)$\" +5)4=!**Feo7$$\"#zF)$\"+?9r,**Feo7$$\"#!)F)$\"+Hl(e!**Feo7$$\"#\")F)$ \"+(pfG\"**Feo7$$\"##)F)$\"+c5'*>**Feo7$$\"#$)F)$\"+GrdC**Feo7$$\"#%)F )$\"++:UD**Feo7$$\"#&)F)$\"+Q4*G#**Feo7$$\"#')F)$\"+yog=**Feo7$$\"#()F )$\"+[@f9**Feo7$$\"#))F)$\"+X*RD\"**Feo7$$\"#*)F)$\"+h=T8**Feo7$$\"#!* F)$\"+D(Hq\"**Feo7$$FCF)$\"+dS2A**Feo7$$\"##*F)$\"+@\"*pE**Feo7$$\"#$* F)$\"++jRH**Feo7$$\"#%*F)$\"+,@fH**Feo7$$\"#&*F)$\"+0$Qx#**Feo7$$\"#'* F)$\"+!H#)\\#**Feo7$$\"#(*F)$\"+^#pE#**Feo7$$\"#)*F)$\"+++\">#**Feo7$$ \"#**F)$\"+8(yJ#**Feo7$$\"$+\"F)$\"+s66E**Feo7$$\"$,\"F)$\"+BVoH**Feo7 $$\"$-\"F)$\"+=&*pK**Feo7$$\"$.\"F)$\"+,jHM**Feo7$$\"$/\"F)$\"+i-DM**F eo7$$\"$0\"F)$\"+$zrH$**Feo7$$\"$1\"F)$\"+c)y7$**Feo7$$\"$2\"F)$\"+/l3 I**Feo7$$\"$3\"F)$\"+,$o+$**Feo7$$\"$4\"F)$\"+j]RJ**Feo7$$\"$5\"F)$\"+ $3'oL**Feo7$$\"$6\"F)$\"+,]?O**Feo7$$\"$7\"F)$\"+l<>Q**Feo7$$\"$8\"F)$ \"+vT;R**Feo7$$\"$9\"F)$\"+l!o!R**Feo7$$\"$:\"F)$\"+&*)[#Q**Feo7$$\"$; \"F)$\"+%>'HP**Feo7$$\"$<\"F)$\"+]:\"o$**Feo7$$\"$=\"F)$\"+oN\"F)$\"+1\")RQ**Feo7$$\"$?\"F)$\"+mw:S**Feo-%'COLOURG6&%$RGBG$\"* ++++\"F(F)F)-%'SYMBOLG6#%'CIRCLEG-%&STYLEG6#%&POINTG-%'CURVESG6$7]sF&F ,F/F2F5F8F;F>FAFDFGFLFQFVFenFjnF`oFfoF[pF`pFepFjpF_qFdqFiqF^rFcrFhrF]s FbsFgsF\\tFatFftF[uF`uFeuFjuF_vFdvFivF^wFcwFhwF]xFbxFgxF\\yFayFfyF[zF` zFezFjzF_[lFd[lFi[lF^\\lFc\\lFh\\lF]]lFb]lFg]lF\\^lFa^lFf^lF[_lF`_lFe_ lFj_lF_`lFd`lFi`lF^alFcalFhalF]blFbblFgblF\\clFaclFfclF[dlF`dlFedlFjdl F_elFdelFielF^flFcflFhflF]glFbglFgglF\\hlFahlFfhlF[ilF`ilFdilFiilF^jlF cjlFhjlF][mFb[mFg[mF\\\\mFa\\mFf\\mF[]mF`]mFe]mFj]mF_^mFd^mFi^mF^_mFc_ mFh_mF]`mFb`mFg`mF\\amFaamFfamF[bmF`bm-F`cm6#%%LINEG-Fdcm6$7SF&7$$!1nm mmU'*4_!#:F*7$$!1LLL$4pBy#F`dmF*7$$!1mmmmEWG_!#K&FdemF*7$$\"1LLL`?o$f&FdemF*7$$\"1 KLL\\\"*)e(eFdemF*7$$\"1*****fD^:7'FdemF*7$$\"1LLLhI(oQ'FdemF*7$$\"1++ +[k(4m'FdemF*7$$\"1*****f8L\"HpFdemF*7$$\"1******>&)e)=(FdemF*7$$\"1** ***z[pmZ(FdemF*7$$\"1mmm]I_NxFdemF*7$$\"1+++![/>,)FdemF*7$$\"1LLLLrMi# )FdemF*7$$\"1+++/r9O&)FdemF*7$$\"1lmmQ:x$z)FdemF*7$$\"1*****RIjI1*Fdem F*7$$\"1mmmE_ME$*FdemF*7$$\"1********p(>g*FdemF*7$$\"1MLLdJWn)*FdemF*7 $$\"1LL`k?*Q,\"!#8F*7$$\"1nmE;]\"3/\"F[\\nF*7$$\"1++!GTab1\"F[\\nF*7$$ \"1nm1`&3R4\"F[\\nF*7$$\"1LL8M)o#>6F[\\nF*7$$\"1++?$=3j9\"F[\\nF*7$$\" 1++S!H)=s6F[\\nF*7$FabmF*-Ffbm6&FhbmF)F)Fibm-%&TITLEG6#%SSimulated~evo lution~of~the~baleen~whale~populationG-%+AXESLABELSG6$%\"tG%#x~G-%%VIE WG6$;F'Fabm%(DEFAULTG" 2 774 381 381 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 10030 10061 10056 10074 0 0 0 20530 0 12020 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 263 "" 0 "" {TEXT -1 59 "Dynamics of killer wh ale stage-classified population growth" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 183 "The stage classified matrix population m odel published in the paper: Brault S., Caswell H.: Pod-specific demog rafy of killer whales (Orcinus orca), Ecology, 74(5), 1993, pp. 1444-1 454" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 200 " \+ Population is divided into four biologicaly defined stages, projection interval is set to one year, entries of population projection matrix \+ are based on report of the International Whaling Commision." }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "Population projection matrix: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "A:=array(1..4,1..4,[[0,0.0043,0.1132,0],[0.9775,0.9111,0,0],[ 0,0.0736,0.9534,0],[0,0,0.0452,0.9804]]):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Information s on model and its analysis" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "lprint(`Stage-clasification:`);" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "lprint(` 1. yearlings`);" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "lprint(` 2. juveniles`);" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "lprint(` 3. reproductive adults `);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "lprint(` 4. post-reprodu ctive adults`);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "lprint(`\\nPopul ation projection matrix:`);evalm(A);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "lambda:=evalf(Eigenvals(A, EigVecs)):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "k:=1:DominantLambda:= lambda[1]:ADL:=abs(DominantLambda):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "for i from 2 by 1 to op(2,(op(2,eval(lambda)))) do" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 23 " AL:=abs(lambda[i]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 " if (AL>ADL) then DominantLambda:=lambda[i]:ADL:=A L:k:=i fi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 " od:" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 39 "linalg[submatrix](EigVecs, 1..4, k..k):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "w1:=linalg[scalarmul](%,1/linalg[no rm](%,1)):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "lprint(`\\nThe domin ant eigenvalue of the projection matrix (entire population growth rate ):`);DominantLambda;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "lprint(`The stable stage distribution:`);evalm(linalg[transpose](w1));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "una ssign(`EigVecs`):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 " " 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Simulated evolution" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 53 "You can set initial \+ value and/or length of simulation" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "x10:=1:x20:=0:x30:=5:x40:=0:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 " tmax:=50:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "x:=array(1..4,0..tmax):X:=array(0..tmax):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "y:=array(1..4,0..tmax):" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 32 "xs:=array(1..4):xn:=array(1..4):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "x[1,0]:=x10:x[2,0]:=x20:x[3,0]:=x30:x[4,0]:=x40:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "X[0]:=0:for j from 1 by 1 to 4 do X[0]:=X[0]+x[j,0] od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "if (X[0]> 0) then for j from 1 by 1 to 4 do y[j,0]:=x[j,0]/X[0] od" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 " else for j from 1 by 1 to 4 do y[ j,0]:=0 od" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "for i from 1 by 1 to tmax do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 " for j from 1 by 1 to 4 do xs[j]:=x[j,i-1] od:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 " xn:=linalg[multiply](A,xs):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 " for j from 1 by 1 to 4 do x[j,i ]:=xn[j] od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 " X[i]:=0:for j f rom 1 by 1 to 4 do X[i]:=X[i]+x[j,i] od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 " if (X[i]>0)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 " then for j from 1 by 1 to 4 do y[j,i]:=x[j,i]/X[i] od" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " else for j from 1 by 1 to 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