Lucía González Díaz Córdoba, 2012
Transcription
Lucía González Díaz Córdoba, 2012
Lucía González Díaz Córdoba, 2012 TITULO: Desarrollo de modelos de dinámica en poblaciones espacialmente explícitos para el manejo integrado de malas hierbas anuales a diferentes escalas espaciales AUTOR: LUCIA GONZALEZ DIAZ © Edita: Servicio de Publicaciones de la Universidad de Córdoba. Campus de Rabanales Ctra. Nacional IV, Km. 396 A 14071 Córdoba www.uco.es/publicaciones [email protected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uperficie Producción 5 200 60 5 Superficie (x 10 ha) 62 250 Producción (x 10 t) 64 150 58 56 100 54 50 52 50 0 2004 2005 2006 2007 2008 2009 2010 2011 Años 2#:!9 %" 7 " % ) ./0 10/0 &+ &2# " 7 - ) 7 : " 9 .6 # &2# 7 0 # / - 7 " 2#:!9 : " % 0 ./0 10/0 &+ &2# 7 8 - " 7 9 " 7 - 5 .: " # ,4,2# " ! - " 7 5 7 8 " 8 ) 7 7 # : ! - #0 - 7 #% ! 7 - .60; &+ &2# 0 8 - " " " - - # 0 ! 7 &+++2# 8 7 "" " 5 . 7/ " " 7 ! 7 #$ - " " - 5 ) 7 6 # < ! " ) ) &+ + " - ! ! 7 #% % - & '* + = ! ! - " 7 ! # Varios 9% Insecticidas + Acaricidas + Nematicidas 31% Herbicidas 34% 2#:!9 &+ Fungicidas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establecimiento de adultos mortalidad de plántulas predación de semilla PLÁNTULA EMERGIDA Cultivo Cultivo LLUVIA DE SEMILLA ADULTO dormición germinación germinación fallida BANCO DE SEMILLA Mortalidad de semillas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tU ! " t# .> 7 # ,,4D 1 3 # &++42 7 " - 3 8 90 ! - 5 5 # ,,,2# . 90 5 - 3 7> " " 7 ,,(D 5 ! ! 7 ! 7 .6 # ,2# > . # # ! - 3 - 2 7 .> # ,,42# 2 2 a) b) x 1 1 1.4 y x 1 y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i - j - 1)# C- .1 - .- - # - 7 Nl,t[i, j] 7 - ,,'2 G "" <97 9 7 - # 0 sl - (t l P _<D G < 7 9 - - " ! 7 G - l "" 1) - - #; 2 - - t - L # t 7 - 7 G " 7 - gl 7 (t G - tG [i, j] 3 N t [i, j ] = sl g l N l ,t [i, j ] . 2 l =1 T 7 Rl,t[i, j] - l - j] t# C- Rl ,t [i, j ] = sl (1 − g l )N l , t [i, j ] G t - 7 " G- " - - "" 3 .l" 3 9 G - D - - - G7 - .t + 12# ; 7 " [i, - v S St [i, j ] = vN t [i, j ] 0 7 " - . 79 f - 7 5 6 9E T G " 7 .<2 7 " a - a &++I2 fSt [i, j ] 1 + aSt [i, j ] 79 7 G - 90 3 G - 9 0 .&2 # CTt [i, j ] = C- 3 7 .# # " " G - # 7 - " 72 N(+#<I +#+&')# C- G E L - 90 5 6 9 .&++I2# C- ." 2 - G ./ 3G 7 7 ;S - C 2 Q - 7 ` xP & < I# %!# < G Tt [i, j ] = " &++'2# C- "" 7 c3 f - ( c4 . C 5 > G .I2 G 7 7 .> 90 " ,,(2# : 5 90 5 &++ID .%! G G - G G- - # &++ 2# C- 7 # 9/ 3 - G 7 .H 3 .H - - + ` cx (1 − c1 )(1 − c2 )(1 − c3 )(1 − c4 ) fSt [i, j ] 1 + aSt [i, j ](1 − c1 )(1 − c2 ) G 90 2 G- - # &++,2# 2. c2 . 7 c1 1 - - ,,<D 90 5 > 7 ,,(D ,,,2 1 − exp( − d / 2 ) 1 − exp( −5d / 2 ) T- d - C- 3 7 # G - - & " (r # - .(2 - 1/6r &) " . - #T - r - 7 6r - 3 &2# % - # C- - 7 exp[−(2r − 1)d / 2] − exp[−(2r + 1)d / 2] 1 − exp(−5d / 2) CG- - G7 "" G - t - " - R0,t[i, j] L Rl,t[i, j] G - l P + _ < G - 9" " [i, j] . 2 7 3 7 " #> 7 90 5 . ,,<2 - - " P + ### < #T - 7 - 5 Rl,t[i, j], l 7 - G G - .> 7 + 90 5 ,,<2# 4))"5 9(, -(/,)0#0#($ +!85/(")* 9 G - -7 Yt [i, j ] = Y0,t [i, j ] 1 − C- 7 .L Q " 7 " 2 7 - " 3 : - - 7 77 G 7 2 7 N(&I++ &,<). C- " 2 Y0 .L Q 7 Y G- G G - .'2 G -G 7 ,4(2 kSt [i, j ] 1+ (k / b)S t [i, j ] # Y0 " 7 . / ./0 10/0 &++,2# C7 - -G ./ 3G - k - b 3 # -($(/#- +!85/(")* C- G . " " - > ,,&2# O 1 .NR =Q 2 7 NRt [i, j ] = Yt [i, j ]P − FC − HD − HA T.=Q 2 P " 7 FC .=Q C- - - 7 HD =QL # C" 7# C- HA - 3 - G 2# " - 9 .n 7 2 7 . ,,<2# C- 0 .42 O h 1 .ANR =Q 90 2 " 7 - 5 6 G 9E 3 G- n ANR[i, j ] = 1 NRt [i, j ](1 + h) − t h t =1 .,2 1 − (1 + h) − t (")* , 9 /)0)9+ $" #$#0# * -($"#0#($+ / " G G - .C " 3 " - " - G . - " 7 7 G2# C- L " 7 " - - - 2# C- .: 2 . ! G # &++,2# C- - - &++'2 - . ++ ^ ++ L 7 - # G ,,'D L # # $ :)/)$0 +09 0):#)+ " G 6 9E .C &++ID H - # &++4D " .> ,, D 5 5 &++,2# G " 7 " 7 90 C 7 - &2 .C 7 # 7 G - # " " 7 3 G ,,'2 SI = Dmax − Dmin T- - Dmax .# # L ! " 3 #0 " " 7 " 7 " " # C3 - G # G G " 3 - - - # C- C ANR2 G- " " 3 ! Dmin - SI - - . +2 - " " - 8*) / " 3 . - L " " @ sl 90 90 90 : L @ gl 90 90 90 : "" @v 6 7. Q 2@ f " #$ +#,< +#& +# & +#,I +#<( 999 +#,& +#&+ 999 +# I +# I + +#4+ +#4+ 999 +#<I +#<I 999 6 9E # .&+++2 +#' ,<( +#,( &(+ +# ' ' 6 9E # .&+++2 )?)9)$-)+ - E 1 : 90 5 .&++I2 9E 6 9 9 .&+++2 #( + +#+ H # .&++ 2 + +#,,' + + +#,,( 90 5 .&++I2 6 9 E @ c2 @ c3 +#,+ +#'+ +#,, +#'' +# + +#I' 9 @ c2 @ c3 +#4+ +#I+ +#,& +#I +#II +#&& 90 5 .&++I2 9E . ,, 2 6 E 6 C +#(+ +#4+ + @ c1 77 G7 9H 96 ? @ c2 96 * *1 9? * *1 ? - > > c3 @ c4 k b 7 .=QL 2@ P 63 .=Q- 2@ FC 9O 9? ? 7 .=Q- 2@ HA ? .=Q- 2@ HD 0 # .&++ 2 90 5 6 .&++I2 # . ,,'2 @d H - R E 6 > 2# O # ) $ : 3 @h E # . ,,42 90 5 6 .&++I2 # .&++42 ? . ,,'2 +#++( +#,( +#++4< +#++ , +#', +# +#& +# < /0 10/0 .&++,2 < ' <(< 4#I <( <4' 4#4 &4 < ' '#,4 0 0 0 I 0 H 1 ? <4 +#+( <, ! 9 # .&++<2 / .&++ 2 .&++,2 / .&++ 2 # .&++,2 # .&++ 2 : .&++,2 8*) # / # 889)F# 0#($+ ;O T ? ? @ @@ 79 61? ?1? 1;C ?:1 Ga ? ? .- ? . 2U- U- U. U. U.U.2U- - a CG 97 -# C- /> />& />< />I />( /> />' 2 2U- 2 2U- - -G G 7 - 7 - # " &++ 2# C# .&++ 2# H > b+ 7 G " - G ^& & ++ &++& + C- - - T G - 8 @ # 7 ,4,D : :! " " - G G - 1 ,,(D / " .1/: 2 c2 P +#II c3 .> ) # " - &++& # @ "# ,, 2# C- P +# C 7 G 2# " 2T &++4D / &# +#( ^ +#( . " - - G - . 9 7 G ^ + - # 7 H G- &++<2 G 3 P +#&& G 9/ 7 .&++ G- .H - > b+I2 7 : - > b+& > b+< & - - / / G G O ! - 8 # r2 7 7 - - 3 ,, D > ) 7 >) - " .T # &++42# T # .&++42 - - 1 - C- S .$2 .> # ,,42 G- # C- " 3 - 2 $ . $ . @ 2 &2 C - G "9: G 3 "S - " - 2# G- - - " .K <2 : " .0 7 G # &++(2# H ! - " Q C- " " G "# G G- " " - G > b+< G - - " - 7 7 # - .6 # 2# C- r2 - - 7 > b+ - G #: - " - " # " ,+9I++ -#0 - G - G - # &++,2# G - - G G- Y - . @ $ " - - G - - - " " " - - G " +#'(9+#4,# C- 3 " G - G 7 - " G 3 - 7 - # G -7 - P G G - C- 1/: 3 - P+G 7 G - - " " .C G 3 7 > b+ - -7 G G - - - " > b+< G- - - - $ # +#<<# <2# C- - # - G > b+I - <2# - > b+& G .C - > b+& .C <2 " C- - 79 - - G- G " > b+< > b+I " .6 # 2# 6.00 12.00 Plot_01 Plot_02 5.00 4.00 8.00 Observed Observed 10.00 6.00 3.00 2.00 4.00 Obs = 0.70 + 0.86 Pre 2.00 Obs = 0.01 + 1 Pre 1.00 2 r2 = 0.87 *** r = 0.75 *** 0.00 0.00 2.00 4.00 6.00 8.00 10.00 0.00 0.00 12.00 1.00 2.00 3.00 5.00 6.00 7.00 7.00 Plot_03 6.00 Plot_04 6.00 5.00 Observed 5.00 Observed 4.00 Predicted Predicted 4.00 3.00 2.00 1.00 2.00 3.00 4.00 Obs = -0.52 + 1.44 Pre 1.00 r2 = 0.89 *** 0.00 0.00 3.00 2.00 Obs = -0.41 + 1.31 Pre 1.00 4.00 5.00 6.00 r2 = 0.80 *** 0.00 0.00 7.00 1.00 2.00 3.00 Predicted 2#:!9) ; " "# G - - Pre 8*) G- > 4.00 5.00 6.00 7.00 Predicted # C- @ # T- 7 - - Obs " G- - # - - > b+& > b+< > b+I2# C- C- S $ .$ 7$ .> b+ 2 1/: G G- # *(0V> +#4 aa +#'<aa *(,) $0)9-),0 8# + AWB +*(,) AWB )99(9 AWB *(0V> +#+ O: +#++& + +#,,4 +#<<+ 8 O: ≥ +#+( 1/: @ 1 - a c +#+( / :! *(0V> #< aaa 9+#I aa O: aa c +#+ " aaa c +#++ # # " - - G - Y C- *(0V>1 #IIaaa 9+#(&aa "9: G" # - .> b+ . > b+&2 7 - G 2# C- > b+ - > b+& - - G G G - G .6 # &2 - " - > b+& G G - G - - " - " - - .6 # &2# 4 Plot_01 2 3 1 2 0 -1 -2 Plot_02 1 0 -1 -3 8 6 -4 10 8 4 6 12 10 -2 X -3 8 4 2 0 6 10 2 Y 6 > b+I - Residuals Residuals 3 .6 # &2# C- > b+< 6 4 0 2 2 Y 4 Plot_03 X 4 8 12 10 0 0 Plot_04 5 3 3 Residuals Residuals 4 2 1 2 1 0 0 -1 8 6 -2 10 8 4 6 8 4 2 0 6 -1 X 10 2 Y 2#:!9) 12 10 - .> b+ .C 2 0 X 0 > b+& > b+< - G 9 4 2 Y 1 - 6 0 C- 4 8 12 10 L > b+I2# - I2# +))" 8 $; ")$+#0 L ! <'(4 7 G - 7 />'2 .C ! I2# - 7 7 #0 7 .C - - Q 5 G & 3 . '<& Q I2# C- - - 7 7 7 - 79 G2 4' . 7 8*) 1 L " ! 7 7 # +))" 8 $; A ))"+X-)** ) 9B <'(4 T ? ? @ @- 9H 96 ? - - 9*) #)*"a A;:X@ ) 9B <,' $$! *#=)" $)0 9)0!9$a AYX@ B 9(&I +I4 && 4 &+ ( <I, 9'& 9&&( <<&I &II4 4'( ( + + I 9& & 9( < +4, '&( 9&&& 7 G '(I ( & '&( + 9<+( 7 G + I , & &+I' + 7 G I,& (+( & ,I + 9, 7 G &+<4 '+ (< + 9, 7 G +(( ,,( I4< ''( + &&+I 9 < 7 G d /> />& 9H 96 />< 9H 96 />I 9H 96 />( 9H 96 /> 9H 96 />' aO - - " d /> .? .H 79 G />& .H U- 2 />I .H 79 U- - G U- 79 79 - 2 />' .? 7 .'<& (+ 7 C 2 />< U- 2 /> .H 79 U- G U- 2# - - 9 Q U- - U- - #O 7 G G " - 9 &< # U- - 2 />( .H - - 9I, Q Q . ,, 2 2 GG- - I+ - " 2# C- G - - - " 7 7G Q & G G - . +I4 # C- " - G 7 - G - - # C- G 7 .C T - />I . 2 - G - G G G G - 7 7 U .C - - - - U 79 ! G 2 - G 2 .C .- - - - 7 79 2 /> /> .- G G I2# C- - - U - - />& . U # G 79 - U - - 7 />< . 2 6 79 7 79 G />' .- - 2 - G I2# - - C- 79 - U U - 9 .C - I2# 7 U - - 2 />( . 7 - U I2# 9(, #)*" O 7 7 : .C I2# 4< &I++ L Q- .C 2 ! " 77 G - - - - - G />' />I .C - 7 G 7 7 7 9 - - " .C 3 " - - - 7 # C- 0 - " - G - I2# 7 G I2# C- 7 G # C- " - " />& G - '+ - 7 4 - # $$! *#=)" $)0 9)0!9$ C- G " - # C- 7 />< .C # - - - - .- - />&2 - - " 72 G G -- G - I2# 0 =Q- G G .9( < =Q- 7 G - G /> .- 9& & =Q- - ! 9<+( # % - U- - 2 - - - G- - - .C - . /> 2 G - . - C- " 7 7 G U- - 72 .C - " I2# C@ />< 9 " - 7 />I# - 3 7 61? ?:1 /> 9 />I "" G # .C - .C 7 .C 72 G />&# 6 7 G - /><9 />' - G - (2# " 7 - - G (2# C- - - (2# ANR G 3 7 7 61? ?1? /> - - .# # "" - 7G L G - 0 " (2# C- />' /> - G .C ?1? 1;C />( />' G G " " 7 7 G - /> />( G - - " 77 G G - - 9 < =Q- # : G " G - - I2# @ 1;C ?:1 - ANR G .C ;O# 6 - (2# 1 T - " 7" - 3 - G - - G G- G G - - G - 7 3 7 # - - > b+ " G- - 7 G- 7 .> b+&2 - # C- > b+I - G - G G " " G- G - " - > b+I - - > b+< - 7- " # G - G 2# ; " > b+< 7 7 " . - - > b+I# C- G - G- # - ! " > b+ " 7 G - GG - - " " 7 - " G G- - - 7 : - " 7 />' .? - - U- - a ;O .G - % C- i 9 ANR .=Q- 2 > $ 7 f 9: L 9 ANR .=Q- 2 9: L 9 ANR .=Q- 2 "" 9: L 9 ANR .=Q- 2 6 : d s 7 g G 9&<' >>% 5 16 9 + <+ 9<+< 9 I(4 9 < '4 9 7# 2 />( .H 79 U- - />& .H 2 61? .- v " L "" 9: L 9 ANR .=Q- 2 : L 9: L 9 ANR .=Q- 2 : 8*) 79 9& <.> 9<< 2# G U- - < 9 ( 9&4 94& 9 (I I, 9 2 ?1? .- - 9 <4 I&4 9 <+ 9 4 <+& 9 <& 9< 4 94& &' 9 + 2 U- SI < - 79 2 1;C . 9&,I &(+< 5 >< &I 9 <+ 9< 9'&< 9 & <, 9 4 2 />< .H - 7# 9 4+ 1 5 (' 9 I& 9&+, 9 +( 9 I ', 9 ' - 2 /> .H G 79 9&&+ I'+ 9&&< 9 4 ( 9& 9<4+ 9 &' &( 9 I - . G < 9 <I < 79 U- 9 ,& &II 9& + 5 9< < 9 << (+ 9 ' Z G ! U- 2 ?:1 .- - 9'+ I' 9(' & 9 &44 9 I 9 , 9(< I< 9' L 2 />I .H 9(I '(I 9< & + &(, 9I, 4+ 9I <+ 9 1 - 79 G 6 9 ( 9, & 9 ( 9I< 9 +I 9 +, 94 <, 9 & U- - 2 /> .? 9 <+ .1> 9 &I <' 9 '& 9 &4 9<+ 9,I + 9 < 72 U- - 9,+ 6% 9'+ , 9 <++ 94 9,4 9(( 9' % 2 U .ANR2 % C- />' .? - - U- - a ;O .G - $ 9: L 9 ANR .=Q- 2 2 61? .- 79 G 2 />( .H U- - />& .H " c HD + HA 9 ANR .=Q- 2 9 ,< 63 FC 9 ANR .=Q- 2 ? '( 7 P 9 ANR .=Q- 2 H 9 & b 9 ANR .=Q- 2 > 8*) 2# 79 G U- - 2 ?1? .- - 5 .%< I(' 9,, 9 ,< 166 9( 2 U- 9,,& 1 % 9(& 9 ,< < < 9<& 9 ,< &+' 9 +I - 79 2 1;C . 5 > 4' 2 />< .H - 7# 9' &+ 9 &+ ( 9(< 2 /> .H G 79 G 5 .<6 1. 9(& 9 ,< I ( 9 ( 79 U- 5 <. , 5 > > &< 9 9 &+ <% 9& G U- 2 ?:1 .- - 9 &+ + 9I' Z 2 />I .H 5 1 &+( 9 9 &+ > 9 1 - 79 G 5 .>> & , 9<& 9 &+ % 9 U- - 2 /> .? 9& <' 6 9<& 9 &+ &(' 9 + 6 U- - 9II, &II 9,, 9 ,< 1< 9& % 2 U G - 7 7 ! - G- - 3 " 7 - - - - 7 - - G- G ! L7 - 7 7 - - - G- # C- 9/ # .&++ 2 &2 . ++ - G - G G - 7 . ,,<2 - G- - G - - - " " 7 L . ,,42 " 7 - C II++ #; .&++I2 3 GG 7 " 7 90 3 - 5 5 - 6 C - " L 3 3 />' G - - - G " . # # />< />I />( - - " - - # # T 9 - 7 - .&++,2 7 9 - G " - - 9E G - - #6 7 - - " - 7G 7 7 # - G " 9 7# C- # .&++<2 G - - 7 7 & G - - - ! Q 9 7 S . ,, 2 &+++ C- 7 - 7 ! - G 7 - 3 G# 0 7 # G " - # - 7 7 - - - - " - - L - # C- 3 - - - - G " 7 7 7G - G- " > b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×V #6 - ,4,2 G ,, 2 # .&+ +2 G c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i ∈ {1,...,V } " - t j ∈ {1,...,V } # C" - f( )( t # # 7 M t [i, j ] = N t [i, j ] f ( N t [i, j ]) G - 7 N t [i, j ] G / . 2 # . ,4,2 # # f ( N t [i, j ]) = g (1 − cx )(1 + agN t [i, j ]) G - x = {W, S, L} −b .&2 G -g - - " cx - b .C <2# - 3 G - .0 # 7 7 .6 G # G G - ,, 2# G - 7 - G,4I2# / " '( G - # # #T G- G 7 / .6 . 7 ; G O " 2 7 9 F 72 7 G . 7 cx G- - 7 9 . 7 ,4I2 - G A - - G B G S / G G- - G G- 7 "" ,,(2# C- G cW = 0 G.C G # -2 # : - 7 G 9E 9 . - G - - G x ; 9 9E " a G 3 7 - 3 7 - 7 - - " " 7 6 - 3 9E # . ,4I2 <2# 0 9 G - G- - dx 7 G " - ! 7 G % +2# C- - - - % # - - .:- " G G- .: &++(2# H 5 - - 3 # C- G " L - 7 I[i, j] " 7 L sN G - s N t +1[i, j ] = M t [i, j ] − Et [i, j ] + I t [i, j ] + sN t [i, j ] G - E[i, j] dS # d L # # # dW P + dW P +#+ I G "" G - G - G ,,(2 - 3 7 . # # dW ) + " 0 7 &++ID :- .: - - Y - G dW P +# & " # 7 &++(2 O " G- - " # .<2 - 8*) > " G /8(*+ # *!)+ $#0+ +#&(a g > G- 7 <&# (d : > a > b d : "" s +# (a cW + cS +#,,e 9 cL +#,<f 9 T- dW +D +#+ IgD +# &aa dS + dL + Q +#++Id G 9 T9: G : 9: G 9 a L "" / .: - 0 # ,,(2# d> 90 G 5 6 9E . ,,<2 G 7# e C- G L 3 G 7 G9 " L C7 " G fO g: 7 " G # D ,4I2 2 .: 3 # 6 - G - 7 - G 7 I97 G 7 " Y - &++I2 G- - - # 9E G L " 7 . .:. 7 " " # 6 9 # - - G 7 .6 Nt+1 - - Nt+1 - &9 L - 7 - - - ++ aa : " - ,4I2 7 Nt+1=Nt g(1-cS)(1+agNt) +sNt G - Nt Nt+1=Nt g(1-cL)(1+agNt) +sNt G - Nt # G- - -b ,4I2 G -b 9E 7 E " L 6 G 7 7 cS G " 7. # G G G # . ,4I2# CG -7 G - " 7# : ! 3 G 9G 9E " G 7 - 7 6 G 7 G9G 3 G % &++(2# - 2 - . # 7 C- G - / %3 L 7G G G - ,4,2 # # - G . + " H # 6 - G & Q G K 7 " I #/ G - " " - - - ! " > - " # - .Nt+1[i, j]2 G G - .: - - " 7 &2 Q # C " 7 ! " 90 " " 5 . ,,<2 G - - N t +1[i, j ] = floor(N t +1[i, j ] + U ) = N t +1[i, j ] + U G - U G 7 N̂ G ! + .I2 # C- 9G " 7 V Nˆ = V N t +1 [i, j ] V − 2 .(2 i =1 j =1 C- 9 L 7 - " G &++ 2# H - - - " 7 C- # CG L &7 k =1 7 @ Nˆ k . 2 p 7 - 9 - G - - G- p N= - - " p - - . G C- 7 3 " N G G - ! 7 - G - - 9 - # - - - 7 # 9 % 6 G- 7 - G - - " - - L 3 - G 9 - " " ++ 7 9 - - G7 .6 # 2 " 7 . - G 2# 6 # C- G .6 # G - 2 - 3 - ! " 7 - - G - G " 7 .6 # 2# 2 2 4500 2100 No dispersal Low dispersal High dispersal 4000 3500 No dispersal Low dispersal High dispersal 1800 Ν (seeds/m2) Ν (seeds/m2) 1500 3000 2500 2000 1500 1200 900 600 1000 300 500 0 0 0 10 20 30 40 50 60 70 80 90 100 0 10 20 Years of simulation 2#:!9) 50 60 70 80 90 100 7 7 G 7 . dW P +#+ ID - : 2 - - dW P +# &2 9 2 - 7 G 9 :'# 5 5 1 56 - . :& : : I2 G- - " 7 7 - 7 " 9 .C 9 I G G G (2# C- ! - G .C " I (2# ; " 7 - 7 - - 7 - .C 9 " " " 7 G #: 3 40 Years of simulation / dW = +D 6 30 " 3 . 7 I 1 - (2# C- G- - 3 &. 2 G-7 (. 294. 22# : L 7 " - 7 G- - - G . - - G 2# ! G G .C G - - G- I (2# O G G - - - - G " .C " G G ID :&2 - I2# 6 .C (2# ? G " - - G 2# ;" & 7 G " 9 G- - - 1 - 4G - .dW P +# &2 1 - I - 1 - 9 # G .dW P +#+ 42 < I 1 4# 6 G- - # %! - - - 1 - G .C 3 . 1 " " , " 7 : & 6 # & " G- - ! G 7 7 - - " . 2 7 .C I (2# 1 - 4 7 1 # # 1 ' - G - - G - - .C (2# / 7 L 7 - " - G G - - G G 7 G - " G- G 7 ( 7 G " G - - I 1 - G G - - .C G - < - - - 3 7 (2# C " " - - # Z G- - G G - G G- G - - G - 7 - - " G- G- ' 4# C- :, G : <. - G 2# : I G - G G- G G - G L G # CG- - - 1 G - - - G - 7 ! 7 : + - -- - - - " 7 9 :4 : G - a :% &. 2 / &9 . 8*) 1 / 7 R /,*)D E@) 0 + #$#-# * -9(,+ TTTT T:T: TT:: ! 2# & G 9 - " I' I(& I(& &I + +a >> 1 + .c I'< II4 > <+I I(& I & I ( , < >> 1 &<&4 ,(( &+,, > > - > G 2# &2 T.&( 2D :.'( 2 G- Q T.+ 2D :. ++ 2 " . < & I(& I&&4 > '+& (I& I&&' >> 1 + &( , & I&+( > #+,)9+ * ?9 -0#($ AdWB I&+ I(& <I > I ( , <I+ >> 1 &<<+ ,(( <&+ > $"+- ,) +-)$ 9#( A B 1 T.(+ 2D :.(+ 2 T.'( 2D :.&( 2 I'' I(& 4I( > I' I(& 4I(I >> 1 I'< II4 4II( > 6 T. ++ 2D :.+ 2 8*) / ! . Q &2 - - 9 &9 I . G- G 7 " 2# $"+- ,) +-)$ 9#( A B 1 T.<< 2D :.<< 2D .<< 2 / & R /,*)D E@) 0 + #$#0# * -9(, > >> 1 > TTTTTT &4 4a &4<I T. + 2D :.&+ 2D .&+ 2 T. ++ 2D :.+ 2D .+ 2 #+,)9+ * ?9 -0#($ AdWB > >> 1 > > >> 1 > &4 & ( <' ( (+ ( 4I( 4I(( 4II( &, &(4 &(4 &(' '< < T: T: &(4 <+, 'I+ &(4 I T :T : 'I , I+& 'I (. 2 TT:: &'< (,4 (++ . 2 TT: : & I&+ &I '. 2 TT :: ( <<I <+< 4. 2 TT :: &< &(' + I ,. 2 T::T && &'4 I' - " a :% .c &I ,+ << 'I 'I <+ (<< &' <<4 <<4 << &< <'( ,,4 & & & + '( &,< +<+ ,< ,< ,& I< &&4 '4< < < < & ( (I& && && && &&( 2# 1200 Rotation 3 Rotation 4 Rotation 8 Rotation 9 Ν (seeds/m2) 1000 800 600 400 200 0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Seed dispersal fraction 2#:!9) %! - G - 9 5 D .A BD 2 7 G G - < I 4 , : &2 5 .A8B " " - .# # 1 9 dW # - 6 G - D 6D 1 G - 9 G .C " - < I2# 0 :& . :& 7 - : 9 L : 2 - 7 G - ! .6 # < 2# 6 : I - - " " - G - . - - - G 2# 6 - 9 7 G - - . 2 .6 # < 2# . : I2# ")$+#0#)+ A+))"+X/ B 8 -9(,,#$: ) 9 T:T: 1% a 1 . &. 2 TT:: <% 1 < T: T: I T :T : (. 2 TT:: 1 6 % . < > &I'( I&4 &I'( I&4 &I'( I&4 &I'( I&4 4& <( ,'( I ' (', 1 6. %< 6 %6 (', >1 %% < <+I 1 6 < . 2 TT: : 1 > % '. 2 TT :: .% 6 6 4. 2 TT :: 6 1%1 ,. 2 T::T %> . - 9 - - R /,*)D E@) 0 + #$#0# * -9(, - G - :, - G " % - G dW P +#+ I G - 4 8*) 6 %! $ (2# 0 7 1 G G - :4 :, :, G - 7 . 2 4 .C " 7 1 9 7 - ,'( I I " <( '' <, <+I '' <, <+I '' <, 6 . % & I<< & & ( <4 &' > %. . I + ' ,< &+ '4 4 4' ( <& 4 ( . & I'I &(& ( << 4 <1 '+ <4 < &I& I ,I 1 - 4& (', 16 - a :% I ' 6. - &I'( I&4 " .c ' # 2# 1 / - " - G G #1 - ! G - G - 7 - - - 7 G 7 - G- " # G G " 7 - ! - " - G " 7# C- - G - - G G 7 - " 3- G # C- - - - 3 - 2 2 500 3000 Rotation 8 (a) Rotation 8 (b) Landscape scenario 2 Landscape scenario 6 400 Ν (seeds/m2) Ν (seeds/m2) 2500 2000 1500 1000 300 200 100 500 0 0 0 5 10 15 20 25 30 35 40 45 0 50 20 40 2#:!9) :- 9 7 - 2 C- 7 60 80 100 120 140 Years of simulation Years of simulation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cL P +#4(2 - cL P +#,,2 - G 0 .T2 " - G # T- G- 7 - " 9 9 - G- G- . # # cS P +#,4 " . # # c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cS - G 6 cL 9 G - - " # C 0 - G - - 3 - - " " - - 7 - G- - L 7 - - G- - " G- G # T3 1 & " - G - - G G G - ! - L " " G - 1 # 8*) / ! . - - cL cS G I. : Q #0 : I2 &. < I (. . '. 4. ,. cS]> <.e 4 d T:T: TT:: T: T: T :T : TT:: TT: : TT :: TT :: T::T 2 2 2 2 2 2 a # # G- " 7 6 9E 3 cS] e cL]> <<f + 4 < ' +&+ 4< (+ ,&, I(& I' &(4 'I <<4 & ,< < && 44( '<' + + + + + + + + + + + + + + " .c 2# #S . ,4I2 3 - # CG L 3 " G ! G G " 7 - #6 - G E # . ,4I2 fO " # #% - - - G - - 2 " G G 7 " cS G " 7 " L 76 9 # L Nt+1=Nt g(1-cL)(1+agNt) +sNt, G - Nt 7 7 .6 Nt+1 - I 7 7 " 9E G " 7 L 7 - # 3 2)9$M$")=5N!#$0 $#** D 7 %T1: :7 - G # C- 7 -b ,4I2 7 Nt+1 - - G G 9G L - G - - 7 - Nt+1=Nt g(1-cS)(1+agNt) +sNt G - Nt " 7# C7 G9G 3 - - 7 G9 -b G G 7 " -7# " G- 7 7 - 7 G 3 R#/!/ -($09(* cS]> <<e N cL]> < f G C- )? !*0 -($09(* # d :% e 6 +#+ I# cL]> . f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aA2 C- G 7 - - G - G 7 7 7 " # C- - G - G # C- 7 - G 7 - G 9 - - - 9 5 a # # 0 - " - - 7 7 7 @ - 7 .aa2 .AA2# 9 G 7 # : " 7 - .6 # &2# 3 " K harvester ppo qpo k s SL g1·c1 SB1 t1 SC SB1 1-m1 SB1 SB2 SB2 SB2 1-m2 SB2 SB3 SB3 SB3 1-m3 SB3 t2 t2 SB3 CG t3 SB2 t1 t1 SB1 SB1 ES SR f g2·c2 g3·c2 CCG t2 t2 SB2 10 cm SB1 1-d t1 AD v g1·c2 g2·c1 g3·c1 5 cm h IS SB3 20 cm 2#:!9) / - G 7 L # C- L SB L G 9 - SC - - - - "" G G "" G - "" L 7 C- -9 7 .SBini2 ? ! 7 - " CG - G - 7 qpo# C- - t 7 m - L d h - 7 f# - # 0 - 7 ( .F 7 L # 7 - - ! # C- + - G G - - 7 ! ,, 2 pini# - 7 F 7 7 - L 7 G 0 3 7 - - - 79T - c - L + G- - "" ( - " 7 - - k K# &# # # # : SR# ; - ppo s 3 v - 7 - - - - - CCG( - G - g 9 - - " 7 7 - ! -9 - - G - 9 - G AD ES - G IS G " SL - - - " - - 0 G 7 G # 0 G - G L -9 G - - K " - G - G - " 71 - # .&++&2# C- 7 " - .SB1 SB2 SB32 - 7 C- " - - G G- 7 7 - .SL2 - - - .AD2 - t 7 7 " , y G - " . - G 7 . xx G - " aa aA C- 2G - G - 7 - G " 7 7 t2 . AA2# - - 3 - 7 .SR2# [i, j] Z ty,xx [i, j ] = (SR[i, j ], AD[i, j ], SL[i, j ], SB1 [i, j ], SB2 [i, j ], SB3 [i, j ]) y,xx - L Z1t ,xx - Z t9−, 1xx # " 1 [i, j ] Z1t ,xx [i, j ] = Z 9t −, xx C- 3- G 7 " - n G- - G G 7 & # C- <G - 3 G- - 3T 3 - 7 G -" - 9 0 G " 7 .> - 7 " 7# " #0 - G # C- - & 0 - 7 Tl,n G - l - - . 2 - - - - - - - G - 9C 7 91 - " " G &++ 2 Z t2, xx [i, j ] = T1n ⋅ Z1t ,xx [i, j ] 0 0 0 G - T1n = 0 0 " 0 0 0 0 0 .&2 0 0 0 0 0 0 0 t111, n 0 t112, n 0 0 0 t121, n t122, n 0 0 0 t131, n t132, n 0 0 0 t113, n t133, n t133, n K C- 3 " 3 t1 # # t132 ! - : " - - 7 < - - 7 & # - - G 5 7 " G 7 L " 7 - 7- " 7 7 - 7- " .H # &++,2# C- G " 7 - - d 3 D# Z 3t ,xx [i, j ] = D ⋅ Z t2 ,xx [i, j ] G - D= 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1− d 0 0 0 0 0 0 1 0 0 0 0 0 0 1 - - G G - G .C ,, 2# ? : " - - 7 G G - G 7 - - " - G - # 7 " G L .<2 G - 3 G .> 9C - G91 &++ 2# C- G ( ) Z t4 ,xx [i, j ] = T2 n ⋅ G1 ⋅ Zt3 ,xx [i, j ] 0 0 0 G - T2 n = 0 0 0 0 0 0 0 s 2n 0 0 0 0 0 0 0 0 0 0 t 211, n t 212, n 0 0 0 t 221, n t 2 22, n 0 0 0 t 231, n t 232, n t 213, n t 233, n t 233, n .I2 K 0 0 0 G1 = 0 0 0 C- - " 0 0 0 0 0 0 0 0 0 g1c1 g 2c1 g 3c1 0 1 − g1c1 0 0 0 0 1 − g 2c1 0 0 0 0 1 − g 3c1 L - - 3 G1 . - .gc12# C7 0 0 0 0 0 0 3 " - 7 g. 7 - - 3 2 7 - 3 7 - 7 .1- gc12 7 2 c1 G - s2 - "" - # 0 G - " ./ - - # &+ +D F 89/ G -G : - C- G - 7- " L - 7 # G 7 CCG G - " 2# C- - G G - &+ # C- " - 3 G- - " - 7 CCG tn−, 1xx [i, j ] = (0,0,0, CCGn, xx [i, j ],0,0 )n , xx t −1 Z 5t ,xx [i, j ] = Z t4, xx [i, j ] + CCG tn−,1xx [i, j ] ; - G - &- - - 7 Hn . 3 9 "" 7 - G - - D G - G L " "" ( - ) Z 6t ,xx [i, j ] = T3n ⋅ H n ⋅ G 2 ⋅ Z t5 ,xx [i, j ] 0 0 0 0 0 s 3n 0 0 0 0 0 0 0 - # C- 9 2# C- 0 0 0 G - T3n = 0 0 - - .(2 0 0 0 t 311, n t 312, n 0 0 0 t 321, n t 322, n 0 0 0 t 331, n t 332, n t 313, n t 333, n t 333, n - 3 . 2 K 0 0 0 0 Hn = 0 0 0 0 0 0 (1 − hn,xx ) 0 0 0 0 0 0 0 0 0 G2 = 0 0 0 T - c2 - - 0 0 0 0 0 0 - G 7 hn,xx, - - # 90 5 - 0 0 0 0 0 0 1 " 7 # C- 3 - & s3n 7 - - - 79 . 0 0 0 1 0 0 0 0 0 0 0 0 1 g1c2 g 2c2 g 3c2 0 1 − g1c2 0 0 0 0 1 − g 2c2 0 0 0 0 1 − g 3c2 G 0 0 0 1 0 0 - "" 0 0 0 7 6 9E - 7# C- " &++I2 5 3 v 3V "" # Z t7 ,xx [i, j ] = V ⋅ Z t6 ,xx [i, j ] .'2 0 0 0 0 0 0 0 0 v 0 0 0 G - V= 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 K# &# # # &# : C- - " G 7 . C- - - " # ;" . 2 7 G2 7 - - " - 3 7 # G K 7 - " - - # T - 7 " . 2 7 - 79 xx 90 5 6 OVxx[i, j] G - -7 9E 7 .&++I2# OVxx [i, j ] = ADxx ⋅ f n 1 + b ⋅ ADtotal [i, j ] .42 G - ADtotal [i, j ] = ADaa [i, j ] + ADaA [i, j ] + AD AA [i, j ] C- SRtotal[i, j] SRtotal [i, j ] = OVaa [i, j ] + OVaA [i, j ] + OV AA [i, j ] C" 7 C- ! 7 - - - 9 9 p q " p[i, j ] = OV AA [i, j ] + 12 OVaA [i, j ] SRtotal [i, j ] . +2 q[i, j ] = OVaa [i, j ] + 12 OVaA [i, j ] SRtotal [i, j ] . ! 7 # C- pm - .,2 - k 2 G ! - qm G ppo[i, j] G- - p m [i, j ] = p[i, j ] − k ⋅ p[i, j ] + k ⋅ q[i, j ] . <2 q m [i, j ] = q[i, j ] − k ⋅ q[i, j ] + k ⋅ p[i, j ] . I2 qpo[i, j] - ! L " - - 7 - - . 7 2 ! 7 - GFxx G GFaa [i, j ] = q po [i, j ] ⋅ q m [i, j ] . (2 K GFaA [i, j ] = p po [i, j ] ⋅ q m [i, j ] + q po [i, j ] ⋅ p m [i, j ] . GFaa [i, j ] = p po [i, j ] ⋅ p m [i, j ] 0 C- 7 " . '2 7 - - L 2 - 3 Fxx# 7 7 - 3 M#C- Z 8t ,xx [i, j ] = M ⋅ Z t7 ,xx [i, j ] + Fxx [i, j ] 0 0 0 G - M= 0 0 0 0 0 0 0 0 0 . 42 0 0 0 0 0 0 0 0 0 0 0 0 0 1 − m1 0 0 0 0 1 − m2 0 0 0 0 1 − m3 SRtotal [i, j ]⋅ GFxx [i, j ] 0 0 0 0 0 Fxx [i, j ] = C- 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 " 6 0 0 0 0 7 - 0 0 0 0 0 0 0 0 7 m1 m2 - - G 7 # - - m3 # # - - - G # Z t9 ,xx [i, j ] = S ⋅ Z 8t ,xx [i, j ] G - S= 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 . ,2 K 0 " " G " 7G - - G- 7 - - " 7 - - " G " #T - - G " 9 " # )$) ?*(E +!85/(")* G ! 7 G 7- " 9 - @ - # C- " 3 - - G - 7 # # " 7# K# &# # &# # > C- G - " &++&2 # # 7r %!# .&+2 7 L - - " G- - - z ! 7 - - .1 - 3 7 # # C- / " z 7 # C- G / - " 9 7 - - PO G - - - 7 # C- 7 - j+r z PO[i, j ] = SR[i, j ] ⋅ pol 0 + i+r SR[u , v ] − v = j − r u =i − r T - ! - " 7 - - ppo - - " SR[i, j ] ⋅ pol 0 ⋅ p m [i, j ] + G qpo j+r p po [i, j ] = .&+2 - qm " ⋅ pol r # - ! SR[u , v] r ⋅8 - - i + r −1 v = j − r −1 u = i − r −1 r =1 G - pol0, pol1, …,polz - G j + r −1 z r =1 i+r " # C- SR[u , v ] ⋅ p m [u , v ] − v = j − r u =i − r #? ! - j + r −1 7 ! 7 PO[i, j ] - pm - i + r −1 SR[u , v ] ⋅ p m [u , v ] v = j − r −1 u =i − r −1 r ⋅8 G ⋅ pol r .& 2 K q po [i, j ] = 1 − p po [i, j ] K# &# # &# &# : T " " - .&&2 " - " - 7 " G # C- - - - " G " G - G - - " - G 9 " # C- G7 L .SB12 - G - #: 7 G- - 9 7 - - " .con2 G- G 7 - - " gat# 0 - # 7 G- " - " - " - 7G Z9 # CG - - " " 7# C- ! " " G 7 ES - IS # C- " G - 3 7 - - G " - - ES G 3 - - G 0 0 0 1 − CG − ES 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 " " - " - - " Z t9 ,xx [i, j ] = S ⋅ Z 8t ,xx [i, j ] + IS xx [i, j ] G - S= - # T - - " G - - 7 G - - 7 - - " 3 G 0 1 0 0 0 0 1 0 0 0 0 1 .&<2 K 0 0 0 IS xx [i, j ] = IS xx [i, j ] 0 0 G - ext - CG = gat n ⋅ con n .&I2 ES = gat n ⋅ (1 − conn ) ⋅ extn .&(2 IS xx [i, j ] = SR xx [ihar −1 , j har −1 ] ⋅ ES .& 2 3 " - - " - [ihar-1, jhar-1]# - " - 1 - " " 7 - - " - " # C- " - " T - 3 7 - " - S .&++,2# C- - " G " ; 0 L G - .# # - - 2# ! * * & C- 3 G -G - " - " 7 - G - " G # C- - - G G - sr CCG1, xx [i, j ] = ⋅ yield 7 # - G yield - SR xx [i, j ]e ⋅ CG e =1 .&'2 size 3 - G- G size G - sr - - - CCG1 G - #0 7 # C- G %!# .&'2 L # 7 size [i, j]e - " - CCG2 P +# K 0(-@ +0#- 9(!0#$)+ C " " - " - G - - 7 > . O " &++42 " 7 90 5 G . ,,<2 - - X = floor( X + U ) = X + U G -U G + .&42 X - # # AD[i, j] SR[i, j]# 1 9 /)0)9+ (? 0@) /(")* $" #$#0# * -($"#0#($+ C- - - - C #0 - " - C- G - 7 " G- 7 - ! &++<2# C- " # # - " G - - &+ " L - " O " - " 3 - . - " " - " & - G 7 G 7 ! C G - - - P %:C+2# G # - # ,(,!* 0#($+ G " # G F(*!0#($ (? 0@) @)98#-#")59)+#+0 $0 - G G - G )-0#($ - # C- ! > L 7 G - 7 G - .# # # # C- # C- G " " " 0 " 7 G - " - - 7 : 7 G - " L - - - - - G " 9 - & G . G - " G 2# > G- - 9 " - aa C- gO f C- e0 ! d 0" # 7 7 - G ! L a C- : 6 8*) 7 - G # C- 7 G # : 9 G # t2 7 t3 t1 - ! " - 7 L 3 # G 7 t321 t322 t323 t121 t122 t123 t221 t222 t223 CCS0aa CCS0aA CCS0AA pini - G 7G - t331 t332 t333 t231 t232 t233 t131 t132 t133 L 0 - + + aa +#4+f +# < +#+' +#(,f +#<I +#+' - &# # 0‡ 0 0 - + +# < +#'I +# < + - # G# 7 3 + + +#+ +#+ +#,4 +#+ +#+ +#44 Q- a * +9(d +#I +#(+ +#+, &#' * + )9) * -9(, /8(* SBini G - #S .&++'2 "" t311 t312 t313 t211 t212 t213 t111 t112 t113 " +#4+f +# < +#+' +#4(g +# ( + - &# 0‡ 0 0 - +# < +#'I +# < +#< +# , + - # +#+ +#+ +#,4 + +#+I +#, +#+ +#+< +#, Q- a * +9(d +# ( +#(< +#<& &#' * + +#'+f +#&+ +# + 7 # !$?*(E)9 -9(, G L L L : : " : : > ? 79T # .&++'2 # .&++'2 # .&++'2 # . ,4,2 > G .&++&2 )?)9)$-)+ K ? ? ,,42# gg C- ff 0" ee C- dd C L O > G & 9 9 - 7 7 7 9: 9: 9: " : "" 9: 9 C? 1 8*) - & < - - G - - G "" G -G 7 7 - - 9 - - - 7 G # - - + " 7 " # # G - " s1 s2 haa haA hAA v f c1 c2 g1 g2 g3 d /8(* - # # 7 " ,<( - +#,( + + +#' +gg Q +# (ff +#<( +#(<ee +#&' +#+& 3 7 )9) * -9(, +#( dd 7 - 7 ,<( - + + + +#' Q +gg +gg +# (ff +#<( +#(<ee +#&' +#+& # !$?*(E)9 -9(, +#( dd - # E 6 ;G F 8 H # .&+ .6 2 9E 9E 90 5 .&++I2 9? 6 # # .&+++2 9 # . ,, 2 )?)9)$-)+ # .&++,2 K - O ,, 2# C L K ? " 96 91 - - " - - - - & - -7 - G - 7 / / 3 - " : 7 7 9: / > 8*) 7 7 - 7# C- - & < L - G - - G - G- - - 7 7 - L - - - - " # pol0 pol1 gat con ext z k G - m1 P m2 P m3 b /8(* # ++9 - - 4+ - 5 +#+&, +#, +#+4 +#+& &#'* +94 +#<+ # )9) * -9(, +#++++<I - - 7G # # - G- - +#+&, ++ + &#'* +94 +#<+ G 3 !$?*(E)9 -9(, +#++++<I - - " .:- :- ? E - - G . ,, 2 . ,''2 % % - G - &++(2# ./ .&++(2 # . ,,'2 # . ,,'2 / : )?)9)$-)+ 90 5 6 .&++I2 G # 9 K K )-0#($ )+#+0 $-) / $ :)/)$0 +09 0):#)+ / 7 - - - " - 7 " # C" 7 - Q G - G- G - 7 - 7 - %:C< 7 G - .%:C 2 # # ++ - # 9 G G - (+ G ! - - ++ " - .%:C& 7 - G - G #? - # C- G G - G # C- 7 - - " # - " 72# H - - G - .%:CI2 - - - .%:C(2# C- - G 7 - " G G - - - G - - G # " @ G - 5 - G 7 " 7 ++ G # %:C( G- - - ,, 2# G %:C G .%:C " %:C - C )-0#($ 2 - - 7 - G G .%:C & ./ - G %:C( . 3 %:C&2 %:C (2 .%:C 2 <# /,(90 $-) (? 0@) "#+,)9+ * F)-0(9 #$ 0@) )F(*!0#($ (? @)98#-#") 9)+#+0 $-) " G - - " ! ! " - - 9 ! 7 G 9 " G " - # C - .G - - 72 G : 9 G 7 - - ! - - # C- " 7 G - ! G @ 5 - 9 G 7 G " 7 - - " - # G G # C- 7 K 7 3 - G ,4 8*) ./ - - # &+ +2# : .# # 2 # )+-9#,0#($ %:C+ %:C %:C& %:C< %:CI %:C( %:C %:C' %:C4 %:C, %:C + %:C %:C & %:C < %:C I %:C ( %:C - I& - ++ )-0#($ 1 )$+#0#F#0 " 7 7 G G . T &++,D O " - " G -- - - - (+ - ++ - ++ - " $ * +#+ # C" - 1 1 : G : %:C U %:C< %:C< U %:CI %:C< U %:C( %:C U %:CI %:CI U %:C( %:C U %:C( %:C U %:C< U %:CI %:C U %:C< U %:C( %:C< U %:CI U %:C( %:C U %:CI U %:C( %:C U %:C< U %:CI U %:C( 1 : - - " 90 .# # 7 5 G 6 9E 2 L G &++ID 1 # &+ +2# C- - - 7 - - # # # C- G G - 7 " - G - 7 - 7 " ! 7 - : 7 G 7 # C- 7 # C7 " G - - - - G - " 7 - " K " " - G " #H -G 7 <# C- - " " 7 - - " " " - 7 .&++,2 - " 2 5 G - G - - - - - 7 G # 3 # C- " G " L 9 7 L# C- L 3 - - G 9 - - " L .6 # <2 G#H G G 7 7- 7 - 3 0# % - - .6 # <2 " ! - 0 - - 6;1% O - # 7 " - - " L G - G L - " - - T - C- 3 " 71 G- C- - " - - L - - - L # Frequency of phenotypic resistance 1,0 0,8 0,6 0,4 Adult plants Seed bank 0,2 0,0 0 5 10 15 20 Years of simulation 2#:!9) C " - ! 7 - - 9 " - # C- ! 7 - - 9 - G L .6 # I2 GG - - 97 7 - ! - - 3 " # 7 K Frequency of phenotypic resistance 1,0 0,8 0,6 0,4 sunflower-cereal rotation cereal-sunflower rotation cereal monoculture 0,2 0,0 0 5 10 15 20 Years of simulation 2#:!9) 1 C " 0 - - 7 7 # 7 .6 ( G- - .O " # &++<2# 0 9 L " - 2# 0 G L - 7 - G .6 - ( - 9 G &+ Cellls (x 103) with evolved resistance 9 - - - G - - - ! 7 - - 9 - 9 - G 2# 10 8 6 4 2 0 0 5 10 15 20 Years of simulation 2#:!9) C " - - # C.AA .- 2 7- L 7 aA 9 G- L " &+ - 7 7 2# 4))" ,(,!* 0#($ C- G ' 2# C- L " " - %:C - - " # O G - " . 2 - " - .6 # - 2 G L %:CI . G %:C( . 7 " 2 K - 7 %:C+# C" 7 - - " - " 7 - - .%:C&2 - L " .%:C<2 - G G " Year 4 Year 6 Year 8 &+ SBaA + SBAA = 0 &+ 0 < SBaA + SBAA 2#:!9) 6 1 - - 7 G %:C - - (+ I - - G 7 G # T- SBAA SB SB 47 7 - " 7# C- G - - " 3 L .SB = " - # .6 # ' 2# %:C < - L " %:C ( - (+ SB < SBaA + SBAA SBaA + SBAA 7 SBAA + SBaA + SBaa2 L SB " SB - .6 # ' 2# Year 1 SBaA G - %:C - - &+ 7 - - G G L .6 # ' 2 " # : - G - 7 - L# 0 L " - L - %:C < # L %:C K 2 35 6 Seeds/cell (x 10 ) 30 25 20 15 10 5 0 0 5 10 15 20 Years of simulation EST0 EST1 EST2 EST3 EST4 EST5 2 35 Seeds/cell (x 106) 30 25 20 15 10 5 0 0 5 10 15 20 Years of simulation EST0 EST6 EST7 2#:!9) % %:C( EST8 EST9 EST10 L 7 2 " - %:C %:C4# %:C ( " C %:C EST11 EST12 EST13 - EST14 EST15 EST16 2 %:C - " %:C - %:C %:C < 7 %:C+# %:C I - - # ./ - <2# )+#+0 $-) ?9)C!)$C- ! 7 %:C(2 - ! .6 # 4 2# %:CI " " %:C( G # C- L7 " " 7 %:C+# ? G " L (+ .%:C - G %:C %:C& %:C< - G K G - 7 7 G 7 7 %:C& %:C<# C%:C< " G - G 7 9 G- %:C( G- - G " " G - G - - .%:C' - .%:C I %:C (2 .6 # 4 2# %:C %:C & G - G- - " G %:C 7- G- - " G 7 %:C&# .6 # 4 2# 0 %:CI " - - %:C C- 7 - " " - - %:C 2 7 .6 # 4 2# .%:C < %:C 2# )+#+0 $-) +,9) " T - " 39 " - - 7 - - %:C( - %:C L %:CI 7 %:C& - - %:C<# %:C& 7 " : .6 # , 2# 0 " " - - 7 " - %:CI 7 %:C' %:C( %:C L G 7 - .%:C " %:C I %:C < " " - %:C < " - - G %:C & - - G- - " " 7 " .6 # , 2# %:C 7 397 - " - %:C<2# %:C " 9 3 " 397 " %:C .6 # , 2# ! %:C # C- G %:C< - 7 - - &+ 7 .6 # , 2# 2 C- 2 " 7 " G " @ - " - - - - - - " ! .6 # + 2# ? G " 7 - 7 G - # 7- .6 # + 2 - " 7 - " + G 9 7 .6 # - G 2# - G - K - " " # ? " .6 # + 2 - - - G " " G - - - - " G - .6 # + 2# 2 Frequency of phenotypic resistance 1,0 0,8 0,6 0,4 0,2 0,0 0 5 10 15 20 Years of simulation EST0 EST1 EST2 EST3 EST4 EST5 2 Frequency of phenotypic resistance 1,0 0,8 0,6 0,4 0,2 0,0 0 5 10 15 20 Years of simulation EST0 EST6 EST7 2#:!9) . C " 2 - - C %:C ( <2# ! " %:C EST8 EST9 EST10 7 %:C EST11 EST12 EST13 - - %:C %:C I 9 %:C( 7 %:C+# %:CI EST14 EST15 EST16 2 L " - %:C+ %:C4 - %:C - - # ./ %:C %:C & - " - K 2 Cells (x 103) with evolved resistance 10 8 6 4 2 0 0 5 10 15 20 Years of simulation EST0 EST1 EST2 EST3 EST4 EST5 2 Cells (x 103) with evolved resistance 10 8 6 4 2 0 0 5 10 15 20 Years of simulation EST0 EST6 EST7 2#:!9) < C " - 2 - %:C 7 0 . %:C - %:C + C <2# C- 7 .AA aA 7 - G 2# CG 9 %:C( 2 %:C ( L " - %:C %:C+ %:C, - %:C 7 - L G- - %:C4 # ./ &+ 2# G 7 EST14 EST15 EST16 7- 7 %:C+# %:CI " " EST11 EST12 EST13 .- 2 " %:C' %:C & - EST8 EST9 EST10 7G GG- - # C- " G 7 G - 9 G K 7 #4 - - 7 , G - G- 2 G # Harvester Sowing weed-contaminated crop seeds Pollen flow Distance from focus (m x 100) 300 200 100 6 4 2 0 0 0 5 10 15 0 20 5 10 2#:!9) > 2C " - - .- 2 2 - L - - 7- 9 - " 7 .AA L 7- 9 " G2# C7 20 9 - 9 - 15 Years of simulation Years of simulation G G 2 Harvester Sowing weed-contaminated crop seeds Pollen flow " G 8 400 Cells with evolved resistance G- G .- " G L 7 aA G- 2# K &+ - # 1 1 C- G .6 # " - G 2# K 7- - 7 L - 2 .6 # G (+ 2 - - - 2 .6 # - 7 .# # G " - - - G " - # C- L " L. - G 2 7 - G9 7 7 9 - # C- 7 7 - G 2# ; - L 7 + . .6 # 7 - G 2# - .6 # 3 G . - G 2# - G 7 - - " - - - - G " 7 - G 97 - 7. " G -5 - # C7 - - &+ 9 " C- - 2 - " - - -7 " - - .# # 7 - " - " 7 - - - - - G 2 2# C! G 7 - K 2 2 Potential fecundity Mutation rate Fitness cost Herbicide control 8 7 6 5 4 3 2 1 -1.0 -0.5 9 Years to resistance evolution over half of the cells integrating the landscape Years to resistance evolution over the landscape 9 0.0 0.5 Potential fecundity Mutation rate Fitness cost Herbicide control 8 7 6 5 4 3 2 1 -1.0 1.0 -0.5 2#:!9) : " 7 7 2 - - - " - " 2 - # C- - - " " " " 7 7 C7G- - 7 aA " 7 - 9 G G 7 G- &+ &+ - G L " 7 - .6 # & 2 - G 2# 0 7 " - G - G G- G - - - " " 2# . - - " " .AA 1.0 " - # C- 0.5 - - - 7 0.0 Standardized domain of uncertain Standardized domain of uncertain " ! - - &+ " - 7 - # C- - - G- - - G .6 # & 2# C- 6;1% O " . 7 - - - G 2 - L G - " ; 0 - - " " <&&+ # " - - # 1 ; - 9 - G G - - 7 G 3 G- " 7- ,,<2 - # - 7 - 3 7 0 37 - 37 G G G 7 # C- G - - - 7 - G G - " " 7 7 7 9 ,,<2# : - 37 # &+ " " - 37 . ? 2 .0 7 - .C G- - 2# C- # - - " " " 0 7 7 .C # K - ./ - # &++ 2 " & 7 ? G " - ! " " " 7 7 " # - 7 G G - 7 &2# Q 2 2 10 Cells (x 10 ) with evolved resistance after 20 years of simulation 10 Cells (x 10 ) with evolved resistance after 20 years of simulation G G - - .&+ 0 - - - ,, 8 6 6 4 3 3 4 8 2 Tail length of the pollen distribution 0 -1.0 -0.5 0.0 0.5 2 Harvester movement 0 FOREIGN mov. 1.0 LOCAL mov. Standarized domain of uncertain 2#:!9) : - " " 7 " - 2 - . # # 6;1% O 7C- 7 " ; 0 9 G- 7 .? &+ - 2 .- 2 &+ 7 - - - - 7 # 7 .AA a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h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j <# CL " " - " - " " i9 - 6;1% O ! G 7 " 7 " 7 - " .&++,2 . 7 - 7 ! - " " - - G - # - 7 G L G - G L - - : - #4I * +9(2 T " 7 - * +9( 7 1 ! - " - - # C- .&#' * + (#I * + 2 " - ,,,2# C- .&# - G # . ,4,2 7 G 7 " - - G - " # C- G " " <+++ 0 # - " &++42# 0 - C - +2 - H L - " " . 9 " - 7 - - " G - 7 - - G " . : - G 7 - - L - - 7 G 7 " - G L - # &++42# C- G 7 G 7 G- - - # 6 " # C. - " 7 - - G - " " # .&++42# 0 7 " " @ - 7 # C- " 7 " 7 " - ! G - " - .> L # " 7 G # K 8*) > > haa / k 6 s a / 3#@ 3 " d / #@ *!)+ 3#a@ &(+ Q #d@ ' 3#@ #@ +#4( 3#@ (* +9' #@ +9, 3#@ +#< #@ + / / / / / / / / 7 f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
Similar documents
b hwTln-aitJivii^ijng
1un^wviiJ'3in{]':i'iSm^'M^1wvil0H0l'iJ*l'uvn'3vi^?ii'i0'U0n^'wilvii,nwpmjj1dnJu5'5'5ii'l'u niia0u^'^t^0nMfinjs;n'5iajniimLunjni^£i0U(^(^i.30n'3'iEJ'3nulT4LviPiu'i£ivin'u m0^^i^sun'i^sj?iuf=n^ onian...
More information