docLucía González Díaz Córdoba, 2012
download 
Report 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
publicaciones@uco.es
!
#
"
$
$
&
%
%
%
#
!
"#$"
!
% !
&
'
) '
$
'
%
(
&
'
%
(
! *
%
#
&
)* +
-
$
% %
!
,
)
& !
" -
/
!
"#$"
*) &
-.
0
1 "
#
!
2
#
$
23
+
,
! &
) *
&&
'9
( 5
"
0
&
!
%
4
&
6
%
%
5 2
-
.& !
$ 257 5 2 8*
)
' &
!
4
&
)
-
& &
'
.0 &
- )
' .&
)
&
! ! /
-1 &
2
!
*) &"*
34 ) %
2
-2
#
6
7
.
8
!
9,
.
-&
) '
!
7
!
'
0&
!
&.
'
&
6
&, 4
&
& '
'
; !
1 '
&
$<
& !
"#$$/ 3 & ! !
.
)))
4
$
%
%: %/ =
@
&
A !
3& ' &
3&
&
$<D$G$ +
0
&
&
'&
!
&
&
&
& '
-& !
3
& !
7
&
& !
&
&
&
"#$$ .&
&
+
> ' 2=
> &, 2 =
- ' &
,
&
"" BC"?BB"
&
0
&
&
$#D"#: + ! &
/
&
/
&
E3& '-F
) )? 1
)) - )H
& &
-
&
?
&
&
E3
&
& !
+"#$"/
'
! &
& F-
: $#"
&
*
&
&
.
&
-
.0 & &
&
.
!
":
%
"$
.&
-
& .
) )? 1 5
!
&
.
&
!
&
$
%
& '
%: %/
&
3 *
2
&
&
)=
> ' 2=
> &, 2 =
&
& !
,
&
3
'
&
2
(
$
*
1 &
'
%
%:
-
%/ )=
?
'
&
&
&&
!
,
+3
1
G:J?GI# ) >; BJC?C<?I$:?<B#G?# (
3 K
&
$
%
&
%
?
+"#$$/
'
!
&&
!
,
+3
1
GI$?GI< ) >; BJC?C<?I$:?<B#G?#
/
3
K
+"#$$/ %
3 *
2
&
!&
-
&
&
2
'
1 &
,
&
3
/
'
*
%/ )=
&
,
&
-
+"#$"/
&
&
'
' !
L
!
&
;M
&
&
13 ) 4* !
,
;
C$BD"#$"
&
&
'
!
&
'
, & !
!
&
0 ! &
'
&
&
&
*
? '
"##B
!
0
1
&
3
!
&
(
- 33((/
> & % A@
?
"#$#
!
0> ! , ! &
> 0 ! & +1 , !
2 O
> &,
?
"#$$ &,
0 0 & & +(
- 0 L @ &O (N/
;
&
:
2 !
2
*
!
-
&
!
"#$"
&
2
*
&
+%
1
&, (N/
3
&
)
,
' &
' &
-
%
"##C?##:<< +>
' &
.0 &
+
+
) /
) / )
&
&
&
0
' .&
-!
&
&
-
&
!
& /& !
!
/
&
)
& &
- &
'&
' .&
3? 13
&
!
&
,
, &
&
&
&
0
23 31
; &
)P P
0
*
"##B?#JCCG +) 0
-
!&
&
&
!
4
/
;
-
!
<
%
!
&
&
!
&
=
- -
&
& &
!
7
! & ! K
'
-
D
!
7 .-
!'
&
0&
7
! 7 & ! K
D
-& ! &
& !
!
,.
!' D
7
!
K
, -
!
0
&
&
! 0 !
! !
-
&
&
!
7
&
-
7
&
-
%
- - & !
&
,
!
'
7
! 7
&
&
!
7
!
!
! , &
3
&
'
!
Q
7
7
! &
'
0 ! ,
&
-
!
,
+
& !
&
!
& /-
+
&&
A!
0
&
&
!
!
7
! !&
!
R
0 &,
!& -
&
&
'&
7
,
'
&
,
3
!
A .&
0
7 .! &
'
0
7
& !
&
-
&
!
,
&
0
'
'
'
&
!
&
& !
&
'
0
&
-
&
& &
,
!
A
&
&
& !
'
&
3
&
7
'
!
!
!
&
!&
&
& &
&
0
! -
0 &
& -
&
&
& &
!&
7
!
-
& &
-
0 &
&
&
&
&
3
0
'
&
!&
3 !
!
7
&
-
&
'
&
'
&
0& &
&
&
&
!
&
'
!& !
7
-
+
& &
!
!
&
& !
!
7
&
&
- A
'
'
!
7
7
!
-
&
0&
!
&
&
A&
!
,
-&
7
!
&
'
&
!
&
A
,
&
A
!
&
!&
!
!
&
' !
,
-&
&
& &!
!&
/
!
!
&,
&
&
&
& !
&
>
!
!
!
A
'
&
3
7
- -
! &
&
'
'
&
&
& !
-
&
0&
!&
&
0 &
&
!
!
&
&
!
,
-&
-
,
!
!
!
&
(
!
!
,
&
'
!
!
!
!
7
'
! - .
&
' 0&
,
&
3
&
-& !
&
&
&
'
K
-
!
,
!
&
&
'&
&
'
&
!
&,
&
& / & !
'& -! 0
-
'
&
0
'
,
&
0
!
3
'
!
0
-
&
&
&
&
&
&
&
&
&
3 &
&
!
&
&&
!
&
3 !
&
& !
& !
!
!
&
'
,
3
& !
!
'
&
!
!
7
&
' ' &
&
!
&
&
!
&
0&
! &
&
&
&
*
!
!
&
&
'
&
' .&
&
'
&
&
&
&
&
& !
0
&
-
0&
& &
K
A
&,
7
-7
!
&
0& &
-
! -
!
&
-
,
'
7
&
!
!
0&
!
.
&
&
&
&
,
& !
-
&
, ! '
!
&
&
K
!
&
' &
&
'
-D
- &
&
&
&
&
&
3
&
!
&
&
-
&
&
&
&
K
7
&
&
!
&
&
!
&
'
!
&
&
&
&
+
&
?'
/ 3
7
&&
'
!
&
&
0 &
!
0& &
&
&
&
0
!
!
&,
&
-
!
&
&
0
,
!
0
&
&
!
!
&
&
&,
A
&
'
!
% ,
0
- !
,
&,
&
!
!
!
!
- & &
&!
&
&
A! &
&
&
!
!
!
&
,
&
A
0&
&
&
'&
!
-D
3
!
&
&
7
!
'
!
&
,
&
&
& !
,
&&
&
A
!
3 !
&
,
7
!
&
&
& &
!
,
'
!&
!
&
'.
&
3
!
&
!& -
&
&
,
7
&
&
'
& !
&
&
&
&
,
,
&
&
( !
0
- *
&
!
&
!
&
'
&
0 &
&
&
-
!
>
L
+@
,
&
-&
,-
& !
'&
&
!
/
@ ,&
!
! - '
' !
+- '
,
&
'&
!
! -
!
!
! A
!
A
&
,
-
,
&
!
&
!&&
'?
&
; @
&
! &
& !
&
00 &
?
O
@ , , ', &
- !& !
@
,
!
&
!
,
&
'?
4,
- @ , , &
'
'
, -
/ ,
&,
!
! !
' !
'
0
&
4
!
&
@
!
'&
,
0 &
7
!
0 ! @ O )
00
&
&
!
' !
4,
0
/,
!
&
!
' !
'
&
&
@
!
,
' !
@
,
,
0
&
0
!
' !
4,
&
!
',
'
4,
0
@ ,
&
4,
&
' !
@ ,
4,
' ! ! - '&
&
! ,
&
!&
- 0!
! ,
&
&
&
, 0
@
' !
'
'
@
O @
@
&
&
4, !
,
-
, 0 &
, &
&
@
-
, &
,
&
, &
&
,
&
&
&
&
-
-
!
!
&
& !
0
&
-,
! ,
&
&
A
&
, 0
!&
&
,
&
3&
&
@
0 @
@ @
&
0
, &
'
0
'
&
- 0
00 &
,
!
' !
0
,
&,
,
, ', &&
&
,
-
&
&
&
&, ! &
!
!
- A & !
0
@
&
)
'
,
R
&
!
, @
'
&
'
&
0
,
,
0
0 &
4, !
@
0
0
!
&
@
+
& !
0
,
@
&
,
A
,
, ' @,
!
@
O0
!
0
,
,
@
@
'
A
@ ,
, &
&
4,
'
!
&
' !
'
0
-
&
!
' @ &
@ ,
&
-
&
&
,
@ &
0&
@ ,
&, ,
L
&, '
-
'
, @
&,
0 , &
A
&
&
@
0
, ! '
&
@,
@,
-
-!
,
& &
,
&
&
&,
', &
@
@
@
* , 0
&
0
@ ,
'
,
!
'
7
,
!
&
%
' !
&
,
&
&
!
&
&&
!
'
0 &
&
&0&
?
&
,
@
' ,
,
,
0
0 ,
&
&
&
D
' ,
&
&
' ,
,
&
&
@
,
,
&
'
,
?&
,
0
&
-
?
,
!
-
@ ' 0 &
0 @ /
00
&
0 , ,
?
@, &, !
',
-
&
@ ,
,
@,
!
,
4,
!
&
' !
-
0
&
0
,
!
7
0 !
,
+
@ , ,
!
' -
,
?
!
D
00 & &-
&
0 &
0 @ @
!
A @
4,
&
4,
@ '
, &
, &
-
,
- -
&
@
, &
&
@
&
&
&
@
@
&
,
&
,
'
,
00 &
@
)
!
@
,
!
&
&
&
&,
, @
&
' ,
0
&
' 7
&
&
7
,
@
@ '
!
@
@
&
'
- 0 ,
4,
&,
@ ,
@
'
0 !
&, -
&
'
& 00 &
&
&
! ',
&
,
&
4, !
& &
4,
00
@ O !
&
- 0 , @
0!
' !
? > @
-
!
' !
&,
, O @
, @ !
&,
#
'
,
&
'
!&
00 &
00
!
'
&
&
,
'
-
@
@
-
- !&
,
@
&
&
,
@
&
7
&
&
-
@
&
&
& !
,
!"#$
%
&
'
(")*(+ )+, -# *)+
.
#/#0 -#($)+ ") *(+ /(")*(+
1
2
2
3
5
4
2
6
%
.
2
4
.
7
(,!* 0#($ " $ /#- +!85/(")*
4))"5 9(, -(/,)0#0#($ +!85/(")*
-($(/#- +!85/(")*
1
(")* , 9 /)0)9+ $" #$#0# * -($"#0#($+
$ :)/)$0 +09 0):#)+
.
1
1
1
1
1
11
1
1
1%
+))" 8 $; ")$+#0
1%
9(, #)*"
1<
$$! *#=)" $)0 9)0!9$
1<
>
1
>
2
6
4
6
3
6
66
6%
6.
6.
9(, +,)-#)+ (? 0@) 9(0 0#($+
6<
$"+- ,) +-)$ 9#(+ A B
1
6<
9(,,#$: +)C!)$-)+
%>
(,!* 0#($ /(")*
%
%1
%
%
%
5
5 1
56
%
5
D .A BD
2
5
.A B
D 6D
<
%.
1
%<
1
.>
1
2
.
2
.
3
2
2
.%
..
3
5
<
<
<
<
<
<
1
(,!* 0#($ " $ /#- +!85/(")*
<6
)$) ?*(E +!85/(")*
>1
0(-@ +0#- 9(!0#$)+
>%
9 /)0)9+ (? 0@) /(")* $" #$#0# * -($"#0#($+
>%
>%
)-0#($
F(*!0#($ (? 0@) @)98#-#")59)+#+0 $0
)-0#($
)+#+0 $-) / $ :)/)$0 +09 0):#)+
)-0#($
/,(90 $-) (? 0@) "#+,)9+ * F)-0(9 #$ 0@) )F(*!0#($ (? @)98#-#")
9)+#+0 $-)
1
,(,!* 0#($+
)-0#($ 1 )$+#0#F#0
$ * +#+
>%
5
2
1
4))" ,(,!* 0#($
1
)+#+0 $-) ?9)C!)$-
6
)+#+0 $-) +,9) "
%
2
2
%
1
1
>
1
1
4
1
4
1
4
3
2
%
3
2
2
3
2
%
$09("!--#G$ :)$)9 *
8H)0#F(+
!
$
! "
#
%
&'#(
#% %
)
(#,* + -
&& #'* +
"
,+
./0 10/0 &+ &2#
"
3
)
&++4
)
5
.6 # 2
#%
"
5
7
.6 #
7
2# $
"
5
!
"
8
7
,+
7 !
#
Superficie
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
26%
"
"
)
.0%> 0
2#
:
-
!
8
7
3
7
5 "
7 !
!
5 "
-
#> 5
7?
@ A>
. ,442 !
7
7!
B# %
"
"
8
7
!
"
!
5 #>
7
5 "
3
"
-
#
!
"
"
7
"
#0
7
" # C
8
!
7 8
"
-
"
-
.>8
9
&++ D 6
9E
7:
"
,, 2
"
.6
9E
5
5
7 :
"
,, 2# :
8
- 7 !
!
3
"
7
"
-
./
"
5
.1
. ,4I2
.
# &+
- G
-
" 7
"
5
# &++(2# $
9H
)
3
8
#
#
&++,2
27
-
8
# &++<2#
"
7
5 .F 89/
"
7
8
7
8
7
5
7
%
#
8
!
%3
-
7 0
7
8
8
)
!
)
"
,, D )
# ;
.:
# &++'D 1
0
7 0
# &++4D
"
5
)
#
# &+
,4,D C
2
"
-
7
#
-
7
0
7
)
#% 0
7
-
#
7
0
-
!
8
7
# %
8
8
!
0
"
7
) #
!
#
-
;
7
7
7
#
# 7
) 7 0
#
#
8
"
5 7
"
" 7 !
!
%
#
"
-
"
.1
"
<+9(+ )
7
.:
. 3
"
-
# &++42
7
5
# &++'D
7
"
#
5
# &+
,4,2 7
2 !
"
"
# %
-
-
3
!
7
.
5
9H
"
,4I2#
5
# .&+
8
2
"
-
7 -
# .&++42
# .&++'2 7 1
7
"
5
#
!"#$
-
)
7
>
#
!
7
5
#
# # &# # #
%
7
8
-
3
7
!
"
#H J 7K
<+
.&++ 2 -
)
#
@
"
7
8
#
0
L
7
.1
9M
,4'D &+
7
)
.
#
.
3
2
N/
2
#
7
#
#
2
.6 # I2 7
!
3
"
.6
9E
#
,,'2# 0
#
7
.0
#
,,+2#
2#:!9 1
.
8
7H
2 7
#
.
.0OC?;: &+ &2#
- 3
7
7 "
.
8
!
P I&2 .0
!
,,+2
"
(+
7
-
+
7 '
(9<+
-
&9I
7
5
.1
9M
,4'D &+
2 .6 # (2#
2
2>
@ > 9:
&++ 2#
.6
@
- 5
#
!
2
.6
!
3
#
2#:!9
5 2
&+ &2 7 2
%
"
.6
9E
#
7
!
,,'2# %
-
.6
9E
"
#
9
,4 D 0
.6
#
9E
'(
,, 2# : -
"
"
""
,, 2
#
,,'2 7
.0
#
-
8
7
.
# &++(2# %
8
.E
.:
!
-
0
#
7
, ,2
!
,,(2 !
"
5
" .E
)
7
, 4D :
-
0
#
,,(2# 0
.0
! 8
"
<(
#
,, 2
#
"
"
"
.6
9E
#
,4 2#
5
Q
#
<9&
!
.6
,4 2
"
-
%
.
8
90
5
76
9E
,, 2#
3
%
R
.H J 7 K
@
70
7
&++ 2# % 0
#
#
,4'2
3
9E
#.
"
)
" .C
,, 2# %
)
/
.6 # 2
7
) .C
,, D 1
#
,,'2#
.1
7
.& P I2 .
"
,4'2# %
8
&4
!
-
.1
2#
-
"
!
"
&+
- 5
7
<<
7
-
++9 &+
7 &9,
2
7
!
7
&+
#
7
3 "
.
"
,4'D 1
&+
!
7
I9
2 .6 # '2#
2#:!9 6
.
5 2
8
7H
.0OC?;: &+ &2#
%
!
.1
""
#
,,'2# %
) "
.1
#
,,'2
!
7
.6
-
9E
# &+++2#
7
)
7
7
!
"
7
5
.C
,, 2# $
'49,(
.6
9E
#
7
.6
,,'2
!
"
9E
#
7
"
8
7
7 "
Q
.6
9E
# &+++2
+++
8
Q
.C
!
'
!
,, 2# %
90
"
!
9E
5
76
# &+++2 7 !
9E
&++I2#
&<'
-
"
.6
.
,,'2#
5
-
2
2
2#:!9 %
2>
&+ &2 7 2
.6
.6
@ > 9:
@1
&++ 2#
# # &# # &# /
-
"8
7
7
-
.C-
7 /
"8
79:
3
-
,,'2#
7
""
#
7
#(
.H
# &++ 2
!
"
7 # %
-
!
.H
# &++ 2
.H
9/
# &++I2#
0
- 7!
)
7
"
!
-
-
"8
-
!
.
27
#
-
7
7
"
9
8
-
8
.H
# &++,2# %
&
(+
.:
-
8
0
.H
3
"
7
!
7
#
,,(2
# &++,2# :
#
"
"
!
!
.H
&9<
# &++ 2# 0
-
/
79:
-
,,'2# ;
77
"
!
7
,442#
"
"8
!
!
-
"
#%
7
5
.H
9/
3
-
-
5
# &++ 2 7
4
#0
# &++ 2 7
5
-
5
.H
-
7
&++I2
.H
7
!
# &++I2#
<+
7
"
./
.C-
3
.H
#
<
'
./
-
9/
-
- G
7
#
,, 2
# :
-
7
.C- 7 /
;
)
79:
-
,,'D / -
# &+ +2#
"
5
"
8
7
-
7 !
-
C
.0
,,+2#
"
3
"
.C-
7/
79:
!
8
-
,,'2# >
7
-
5
3
" .C
-
#
#
"
,, 2
7
# # &# # <# /
5
7
-
.:
&+ +2#
5
"
#
# .&+
"8
,4,D 0
2
,,+D C
)
7
"
0
-
"
7
8
"
7
0
"
7
5
5
-
.:
,4,2# %
!
8
-
!
"
8
"
8
7
!
"
- !
,, 2#
O
5
-
5
-
7
# %
9
.C
7 C
"
-
-
5
5
"
#
,, D
"
!
"
7 !
#
-
8
7
-
# %
7
.:
"
7
7
-
!
0
#
5
,,(2# %
5
7
. - -
# &++ 2
5
C
# :
.&++,2
5
7
.> 7
7
"
"
!
7
#
%
7
?
.C
-
-
-
&++,2# :
#
,, D
!
# &++<D
5
7 "
7 C
# K
&++,2
"
7Q
5
8
!
8
!
5
"
;
5
" 7
"
"
-
"
C
.6
#
9E
,4I2# %
.
#
#
-
,,(D
7 / L-
,,42
"
7
C
#
.&++,2
!
3
"
7
5
#%
7?
!
"
%
-
5
"
. ,,(2
,4ID
0
-
#
8
B .
!
A
2
3
-
#
7
8
!
!
5 7
!
8
"
#
"
-
!
"
-
.
7?
,,(D /
- G
0
"
#
,, 2#
5
"
)
7
"
5
.C- 7 /
79:
-
,,'D / -
# &+ +2#
3
!
.6
#
,4'D H
# &++,D
"
-
5
7C
&+ +2# %
9E
!
-
"
"
7
#0
"
8
"
75
!
7
-
.
>
# &++(D
5
7 C
&+ +2 -
8
.6
C
&+ +2# %
!
9E
#
!
,4'D
5
7
-
!
7
"
.6
&+
9E
2
#
"
,,4D H
# &++(D
.H
# &++I2 7
90
5
#
!
7
.6
:
7
9E
#
,,4D H
!
!
"
"
3
!
-
.O " 7 > G
&++(D H
6
5
.
90
9E
5
-
7
7> G
&++,D /
# &+
"
7 6
9E
"
!
-
7
90
5
76
9E
,, 2
90
5
7
!
.
,,<2# 0
:
-
-
:
.:: 2
7
>
7
"
5
9E
5
7
5
.
6
90
!
"
-
7
,, D
&++I2#
5
2#
8 7
6
# &++(D &++42#
7 8
# .&++I2 -
# % 0
::
5
3
!
-
"
#%
"
-
::
.
# &+
5
90
5
# &+ +D
90
5
2#
&
%
'
7
. - 9>
5
5 # &++ D H
,,42# %
"8
# &++,2 7Q
"
3
.C
,, D
3
-
&++'2 !
-
;
"
7
.?
3
7
#
5
8
#
"
#
%
5
5
8
3
#
/ -
-
.?
7 .&2
# &++'2 . 2
3
5
"8
3
"
7
5
69C?%O#
7
-
.
9
!
2
#
#
%5
"
9
7
#
7
7
7
./ 3G
7 ;S
%1%:
"
&++'2# %5
" #
3
5
!
/ %
-
7
- - !
9
#
3
9
# %
"
-
-
"
#$
"
!
6 # 4# %
"
7
7
"
#
.
90
"
5
&++42#
5
5 "
5
-
# %
"8
.
2
""
.
2
7
.6 # 42# %
5
5
"
!
-
.6
"
L
"
# &++42#
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
2#:!9 .
"
-
"
#
5
#
!
3
"8
.
!
- 7
L
,,42
. # #
2#
%
6 # 4
7
#
-
# &++ID H
9/
# &++ 2# %
"
.M "
# &++ 2 7
# %
-
7 !
.H
7
!
7
5 .?
9
# &++'2#
9
.
5 2
.>
5
# &+ &2#
(")*(+ )+, -# *)+
-
3
!
#%
"8
"
Q
7
"
#
%
9
7-
/ -
-
4+ 7
3
"
,+ .H
8
8
3
#
5
,4'D >
7 7
-
5 .>
L
# &++42 7
# &++,2# C
8
#
3
5
5
,,<2
7>
,,4D H
9/
.1 3
-
&++ID "
# &++4D
7
"
7
"
-
7
0
90
)
#%
/
-
.H
8
#
,4'D
9
,,(2#
"
# :
# .&++42
!
7
#? 7
!
9
7
!
7
9
7
!
7
#
"
"
5
!
"8
5
8
#0
9
7 !
7
!
#
9
.0
#
7-
,, D T
L7
"
!
7
8
5
"
5
-
&+++2# 0 !
7
# >
!
7
. # #
2
.
# &++42# %
"
)
8
.
!
2
!
"
# %
"
!
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
2#:!9 < /
2
! "
"
7 2- 3
#
"
"
7
.A
"
!
B2# %
"
# %
-
"
.6 # 42 7
27
"8
#
.
7
# # &# # &# /
. -
71
"
."
2!
-
,,<2
#%
5
"8
!
-
.
7
# &++42#
# # <# # #
)
7
"
%
)
)
! 8 !
7
!
D
)
! )
3
7
&++42
#
.
#
!
7
"
# :
)
!
!
7
#0
5
.
2
!
7
7
.T
!
L7
"
&+++2#
0"
)
)
3
"
.
# &++42# ;
5
!
"
)
"8
"
)
7
H
9/
# .&++ 2
"8
#
3
7
-
!
7
!
#
3
)
-
7 ?
7 .&+++2
"8
3
/ #
>
- 7 !
"
!
"
#
0
7
-
"
"
!
! )
.T
L7
5 "
7
&+++2# >
!
!
7
)
#
# # <# # &# ?
9
-
"
.
-
!
3
7
7 M
&++I2# >
5
3
!
#2# %
3
.M "
8
1
-
"
# .&++42
!
"8
"
-
7
9
"
7
"
# >
-
"
9
#
7Q
.
# &++42
5
!
"
.
8
.1 -
# &++&D > L
# &++42
-
-
#
90
,,,2 7Q
.H7
#
7 "
5
7
7 >
7
&++(D 1 3
-
7
5 "
.
"
# >
# &++42# %
"
#
%
Q "
-
#
Q !
"
"
.
8
-
.
7 ?
7 &+++2
3
# &++,2
A
)
,,(2
B.
2 .1 3
# &++42#
7
"
#/#0 -#($)+ ") *(+ /(")*(+
$
7
.6 # +2# 0 !
7
!
"
7
"
#>
!
!
-
2#:!9
7
#
># % !
#
$
!
.T
,4,2# 0
A"
"
"
-7
B7
7
.?
# &++'2#
"
! 8
# %
7
"
8
5 "
"
. # # "
"
2 !
# :
3
.:
- 7 1
5 "
,,(D > )
"8
7
# &++42# % / -
"
5
"
&++'2#
5 "
#>
7
"
- 7!
7
!
3
#:
!
!
!
.6
L
# &++42# %3
"
7
.
L
#
"
./
5
7Q
!
&++42# %
# &++ 2
"
-
./
! 8
7
3
#>
./
"
7
# &++ 2#
"
"
7
#>
!
"
7
# %
!
7
5 ./
7
&++42#
#
0
.
,I0!*( 2
,I0!*(+
!
"
"
8 7
"
7 8
#%
7
!
7
.
,I0!*( 2
C
#
9)F) ")+-9#,-#G$ ")* -($0)$#"( ") *(+ - ,I0!*(+ ,9#$-#, *)+
,I0!*(
3
!
.
- 3
#
2
&
+#4
- #%
@
-
9
" 7
# %
7
9
# %
-
!
7
#6
7
#%
#C
"
"
7
7
,I0!*(
#
3
!
.
2
#
5
-
++++ - # %
!
"
7
#%
9
5
#%
3
"
7
7
"
7
"
-
#:
5 "
5
"
"
,I0!*(
3
7
"
#
!
-
#%
.
2
- # %
)
7!
%
5
++++ -
7
8
#
%
7
#
# %
-
9
8
3
5 #%
5
7
"
-
7
!
5
7
-
!
5
3
"
# :
7
5
#
,I0!*(
C
#
#%
%
5 "
5
"
)
7
3
5
7
-
-
7
#
8H)0#F(+ )+,)-I?#-(+
9
3
. "
27
7
."
5
2
.
7 K2#
9 %
5
"
.
9%
-
7
7 K2#
"
3
-
5 .
9
8
.
1
5
.
7
7 K2 7
2
#
2
.&+
K
2 0
%
>
>
# -
@QQGGG#
# #
@ &+Q+(Q&+ &#
#8 9D
.
7
K2#
. ,,+2 H
#2 O7 #2
#8 9D
J
7
0
#%
-@( D
.
J
#H
O0 %
0
:
**)$D
# 7
#
. ,, 2 6
#T
J ($E))9 D
/ -
.
) #
J K 9 :(= D
#2 O7 #
**)$D
"
H
1
. ,, 2 0
#
-<
#
&,9<&#
-
G
7 (4 4 (94<I#
.&+ &2 :
%
) #-
@QQGGG#
- # #K
@
+<Q+<Q&+ &#
** 9LD
J -(,)*D
7
% "
J
# 0
,
''9 44#
@)9+ D
J M$-@)=D
-
. ,4'2 C-
7
# 0
%
7
9 #8 9D
J 4)+0)9/ $D
J
G
99(+D
2
99#G$D
"
J
+-@D
J )- +)$+D
7
J ")
#F
9F *@(D
#
#
99(+D
>
2
J
0
%
G
G-
/
&I 44+944'#
+-@D
J ")
9F *@(D
"
#
>
99(+(D
J 2)9$M$")=5N!#$0 $#** D
.&++42 %
9
&'
#
9
G-
J !#=D
J )9$ #=D
J )ED
.&++I2 :
J
)99 D
J M$-@)= ")*
!**D
9-(D
-
J
!#=D
J 2)9$M$")=5N!#$0 $#** D
-
J +-9#8 $(D
J
#T
99#(+D
1
-I
#
#
.&++I2 %
H
%
-
# C
# $ "
) #
* $-(5 (9)$(D
J
@ /(99(D
J
+ **)+D
J
)- +)$+D
G
1
&4 <,<9I++#
#
7
7
.&++,2
>
G -
7
4J
49 &4#
J 2)9$M$")=5N!#$0 $#** D
-
* $-(D
#
J !0/ $D
.&++ 2
- "
99(+(D
-
'49 4 #
F 99)0)D
J
7
G
- II
99(+(D
/
< 9 +<'#
#
1
<4+9<4'#
9
#
T
7I
.&++(2 %
3
"
.&++,2 %
J
$+D 2 3 .&++I2 :
7
- "
# T
- II <'(9<4'#
* $-(5 (9)$(D
J
V
@ /(99(D
J
$+D 2 3 .&++ 2 :
3
(*O+D
J #:(D
!+#D
J (E*)+D
#T
.&++ 2 6
+0*)D
J
#?
.&++(2 0
(/)9(D
J
G
+ **)+D
7 -
J
%
@ !@ $D
J
#**D
J
%
9)+0($D
"
7 ,4
7 ' <9 ''<#
$+D 2 3 .&++'2
"
:
%
)
) #
.&++ 2
7
,9 ' #
%
) #X
( V((# 0
) #
7 +< < 49<&(#
"
/ -
%
7
#F
@ /(99(D
H
&+'V& 4#
7 -
J
-I
K # K# %
.&++,2 %"
7 )9+D
> W
1
7
.
2
"
L# T
:
(I
#/ *(F
1
J (+(+(F K A&++,2# 0
@
G
"
-
"
#9!H)" D
J
#8 9D
,'
#9!H)" D
#>
J K 9 :(= D
&++'# 0
J
-
.&+
7
8)9$)9D
21
L
-
:
<
O
-
-
:
#:
-
7 &+< I(9('#
G
"
.&++,2
G
%
-
:
-
'(9 44#
9
#
-F
0
1
-'
I 9
(I#
#9!H)" D
J
-9
8)9$)9D
:
(*8 -@D
.&+ +2
#>
/
J )8 );)D
G
%
$ "
@
+
(!+)$+D
J
7>
)*: "(D
J
'4
J
-
0
ED
-
#
.&++42
@
" # ;3
1
7
-
G-
-
G
#0
J
#F
(90)$+)$D
#
7
J
J P-@+)D
)9@ 9"+D
J
# &4I9&4 # Y
9
.&+ &2 ;
O
2)9$M$")=5N!#$0 $#** D
- 7
1
6
-
7 (< & 4(9& , #
0
;
K #
8 %
:# 0# %
.% #K
8
7
G
#
$
>
0
&
7
&+ 9&
0
99(+(D
J )- +)$+D
G
- I+ &4 9&, #
J
$+D 3 J (9$)9D
7
@
7
J M$-@)= ")*
#
#
@ &+Q+(Q&+ &#
J
H#D
) #
!9*)D 7 .&++'2 /
-
#K
0
K
%#2
.&++(2
7 &I '<(9'I'#
# % @ 6
9
#T
%
.&++,2 %
%
:# 7 6
.&+++2
J ") 9 "(D
-
# . ,4'2#
#
"
- <4 <+ 9<+'#
J )9)"# D
J !+-@)#D
@QQGGG#
"
(9' #
#
2
-
. ,,42 :
+!$ D
9
#-;)D
' '9'&4#
(9)#9 D 2 .&+++2 H
") 9 "(D
"
I
.&+++2
J
(;@0 9#D
% "
C
:
< 9 II#
0@ /D
J
)F)+ D
<4+9 <44#
" G# T
#T
-
#
$:0#
(!+)$+D
!)9D
9
. ,,42
J !$0*) D
0
-
:
7
(**#$:@ /D
-
9-(D
""
2)9$M$")=5N!#$0 $#** D
J
F 99)0)D
. ,4 2 :
J
($=M*)=5 $"QH 9D
9
#
#
.
2 O7
2)9$M$")=5N!#$0 $#** D
J
F 99)0)D
%T1: :7
G
0
J (9$)9D
. #2
J
#>
,9 (# ;
J (9$)9D
J
$"QH 9D
- <
>
#
. ,4'2
#
J
F 99)0)D J (9$)9D
.
-
2 O7
J M$-@)= ")* 9-(D
# % @H
#2
#
-
9&<# >?ZC;/09%
2)9$M$")=5N!#$0 $#** D
J
6
9
%
J
G
) 7:
%
. ,, 2# /
7-
.% #
G
G-
#
X# 6# 7 6
/ -
%
-
9
) #
@
# % @
#76
9E
#2
#
) #
9-(D
J
J
8)9$)9D
.1 2
($=M*)= ($-)D
J #)8 +D
>
-
- %T1: /
:7
29)-;*)0($D
J !0@)9* $"D 4
J 4 0;#$+($D
J ") !- +D
J (9$)9D
G
7
. ,,'2#
) .% # :
)
9C
($=M*)=5 $"QH 9D
J M$-@)= ")*
%
F)"9 D
:# 0# %
2)9$M$")=5N!#$0 $#** D
J )- +)$+D
:
- &' <'(9<4<#
"
&'9I4# /
-
#
7
2)9$M$")=5N!#$0 $#** D
E
7 &< ,I(9,((#
. ,4I2 C-
#
F)99)0)D
1
%
- /
2)9$M$")=5N!#$0 $#** D
J M$-@)=D
-
# C- F
7
#T
""
J 2)9$M$")=D
J
F 99)0)D
. ,,42# $
-
/
#
<(<9<(,# /
6
J 0),@)$+D
@
#
.&++42 /
G
#F
0
%
7 I(
+(+9 +(4#
9-I 5
!"I$D
)
#1 "
@)9+ D
. ,4I2
%3
"
0
J (!+@D
"
.
7
2
49&+#
. ,,<2 :
-
G
#H :
I<
+,#
#**D
J (*/)+D
. ,,(2 %
#>
:
($=M*)=5 $"QH 9D
%
(
7
-
($=M*)=5 $"QH 9D
/
:# %# 7 6 - H# #2
G
G-
7
:
7
"
. ,, 2 /
# C- F
J 2)9$M$")=5N!#$0 $#** D
7
# % @ >
# <'' 9<'4+# %
J 2)9$M$")=5N!#$0 $#** D
79
($=M*)=5 $"QH 9D
9
<(&9<(4#
.&++42 T
7 K # K .% # F[
-
>
$Y#
-
0
. ,,<2 :
#
% 7
7
%
-
&
'9 &<#
7 &4
9&'#
+I9
($=M*)=5 $"QH 9D
7
J 2)9$M$")=5N!#$0 $#** D
.
2
"
.&++I2 /
G
7
7
#
>
&< '&<9
'&,#
($=M*)=5 $"QH 9D
J 2)9$M$")=5N!#$0 $#** D
=C!#)9"(D J )= !$D
1
*F(D
J
J 98 $(D
-
($=M*)=5 I =D
.&+
#
26
"
J
"
G
G-
#
- (+ 4<V44#
($=M*)=5 $"QH 9D
.&+
J 2)9$M$")=5N!#$0 $#** D
2 0
2
J
+0#" D 2 J
7
G
#T
($=M*)=5 $"QH 9D
1
-(
J )99 D
*F(D
J =C!#)9"(D
-
J )= !$D
7
.
<+I9<+,#
. ,,(2 /
- -
@ %
+0#" D 2 J
J )9) D 2 J M$-@)= ")* 9-(D
7
T
J
-
-
7
L
#F
0
7 <& ('49(4'#
($=M*)=5 $"QH 9D
J )99 D
J
(++D
L 7
#T
($=M*)=5 ($-)D
1
. ,,,2 /
. ,,42
:
I'
G
,'9'+(#
7
# T
- <4 I(<9I +#
(*+0D
J
+/!++)$D
J
-
+0#
#T
$?( :9( .&+ &2 >
=C!#)9"(D
J
(+L5
.&++'2 6
1
- I'
0
)- +)$+D
:
9I D
J
@QQGGG#
J
"
" G
#**D
#K
@ &+Q+ Q&+ &#
.&++<2 %
"
G
/
#
&< (&,9(< #
* $-(5 (9)$(D
J
9/)$:(0D
J )98));D
J ((/8)+D
J
$+D 2 3 .&+
7
\ 0
. ,,(2
7
"
.&+ &2
@QQGGG#
$ *#*D
#
J !+#D
-
J 9(E$D
G
#T
/
0
# #K
J )$0($D
#T
9+@ **D
C-
@
2 ? G
%
7
I( ''94I#
)/)9*)D
-
#
7
% "
7
9 I#
#-
G
7
G
J 2)9$M$")=5N!#$0 $#** D
0
$+D
:
G
1
- <( (+<9(+,#
0
7
/
0
#
@ +(Q+IQ&+ &#
J (E*)+D
.&+
21
"
-
7
G
(, & +9& '#
7 J ( 0/ $D
J !0/ $D
"
7G -
4 J C!#9)D
#T
J 4 9"D
1
7 .&++<2
- I< ''94,#
++ " D
J
-
#%
00@)E+D
9/)*D
.&++42
"
/
J *)E)** $D
-
J
RE)**D
)+-@;)D
J (E*)+D
-
S ($(F $D
J
G
J
($("D
!"D
"
-
1
J (E*)+D
- &4
'9'&#
.&+ +2 ?
9
#T
J
;(E+;#D
-
)F)D
J
#7F
(9+E(90@ D
:
(4 I
.&++ 2 $
F# T#2
7 J /#0@D 7
J K)*
D
(E*)+D
"
1
.&++(2 1
" 7
-(
J
4 J )ED
-
-
7
J (E 9"D
#T
J 0)E 90D
1
J )$$)00D
G - 7
:7
$5
$")D
"
,,V
&#
-
0
. ,,42 0
+
-
J
"
(H 9"#$(D
J -@/#"0D
J (E*)+D
J
G
%
.&++,2 H
7# T
7
C -
(!*"D 2 J **$)9D
L9)=5
%
9-I D
&&& I49(+#
0
#
# > 7
7
.
2
7 &< I+9I4#
. ,,,2 :
7 3
.
7 ,&
9
.&++ 2 /
6
) #
@
%
.&++I2 1 /@
G
)
J #**+D
"
)-;D
#
- <4 <'<9<44#
# %C: 0/ $ "
7
(I9
', <+(9<&(#
.&++ 2
$0)9D
.% #
#
G
0
@
-
# C-
#-)D
7
H# K# C- O -
G -
-
$$)**D
9I'&#
.&+ +2 /
#T
J
"
;
G
7
((9 ++# %
7 )F)D
- 7 7
#2
#% @T L
#D / L G L
7 .% # $
.
7
T
G
$Y#
#T
0
J
@
7
9
. ,442 :
E)$D
- G
G
# '9<<# 0H
7
#-@ )*D
- "
0
@
F)9+D
# #
G
- 4-0
.&++'2 $
G
L - G 1# %#2
$$ D
-
#
#% @O 9 /# Y# 7 H
. ,, 2
#>
E
J
7
& < I <9I '#
G
4I9 4(# C G
" 7
@O
2# F
#
-
7
"
#K
)99 D
J
($=M*)=5 $"QH 9D
G -
)0#0D
A ,,<2
L# C- F
J *#:$#)9D
J (*8 -@D
%
J ( $$($D
"
# 0
+# ++'Q <(,<9+ &9++,(94# K
#T)#9(D
;
J
"
)9)*/ $D
N! #*D
F
J
F
)- +)$+D
@QQGGG#
J
.&+ &2
?
-
#
#
H
.&++42 ? G
\%
/
&
"
<
@
9<&&#
# C%0 '( I'9( #
J
- , '& 9'&,#
#0
$ "
#
@ &+Q+ Q&+ &#
%
. ,,'2#
#
) .% # X "
)
:
6# 7 6
/ -
U00-@)9D
%
"
# % @
9E
#2
# I,9 I#
) #
.&++&2 /
9
7
-
- I& (&9 I#
.&+
2
/#D /
#% @6
9C
F 8 7/
J
@ /(99(D
K
0
# 7 :
#2
) #
J
$+D 2 3 .&++42 T
7
;
.% # H
#
# <&&9<&<# $ "
%
"
"
G
0
7
O% :
# 0
%
7
&I ,'9 +I#
(/)9( K 9-(D
C
;@
#
#K
) 7:
(/)9(D
% "
9
%
#T
(/)9(D
#
7
J =C!#)9"(D
J KE)9:)9D
H#D
7
"
-
-
#-@0)9D
9!)*(D
1
- &+
8)9$)9D
>?ZC;/09%
:
-
. , ,2
1
)- +)$+D
J
"
0
90)9D
0
.&+ &2 T
. , 42 : " "
#0
N! #*D
7
. ,,42#
90)9D
J @)$ #*D
" G# 0
"#
J
I(<9I <#
J ) ()!9D
!)9+-@/ $D
J )9$M$")=D
74
-
@ <+Q+ Q&+ &#
"#
!H " +D
-
J
-
"
. ,4'2
#% @6
:# 7 6
%#2
(/)9( K 9-(D
.&+
H#D
2
/#D /
9C
G
4'<944&#
"
J +-@ 9$0;)D
7
;
8 %
K
#7:
%
89#)*D
0
# <+&9<+4# Y
# % @ 6
F 8 7/
(+-@)E#0=D J
K
:# 0# %
0
#2
K #
.% # K
8 H#D
) #
;
.% # H
# <&(9<&'# $ "
#D
0
) #
J @#)+D
"
.&++(2 C-
3 7
# F
0
%
7 I&
(!RD 2 J
9#+D
-
J
)8(!"D 3 .&++42
7@
!#=D
J
G
-# >
99(+(D
J
G
)9$ #=D
#
M$-@)= ")*
J
J
9-I 5 (99)+D
#T
(+)D 7
1
(9$)9D
#
#$ "
J
F 99)0)D
%
) #
G
. ,4I2 C
# >
+,9
J
<# ;
J 2)9$M$")=5N!#$0 $#** D
7@
(!9#;D
"
#
- /
($=M*)=5 $"QH 9D
7
# $-@ D 2
#T
1
@
7
"
>
-<
7
- <
%T1:
#
. ,, 2 T
J F $ ")9 4)9?D 4 J
!
1
"
!
#
G -G
T
7
7
. ,,'2 C-
G
F $
. ,,(2 :
#C
-
J
G
I( <<'9<I&#
G
(9$)9D
7G
#
J 2)9$M$")=5N!#$0 $#** D
:7
. ,4,2
'' I,9 I#
**(9 5 /#0@D
:
"
- I4 <49I'#
9 9
8
#T
.&++42 C-
- <( I''9I4'#
. ,,(2 /
/
J
"
9&,#
1
J 2)9$M$")=5N!#$0 $#** D
0
7
#T
. ,, 2# H
@#**D
I
7
4 9 4'#
J (9$)9D
#%
8)9$)9D
9-I D
>
9-(D
J
- !
:
J 2)9$M$")=5N!#$0 $#** D
)+ 5
#
/#0@D
-
9
J !)F +D
:
G
/
7
F)"9 D
-
7
.
#2
<+ 9<+'#
0(/,@D
G -
.&++42
9
9
#
- I4 <&,9<<,#
#$ 0#)9D 2 J #R#)9D
J )
:)D
-
J ! -;D
2 J )+-(!99)0D 2 .&++,2 ;:/;:
7
7 3
# %
/
&&+ &&II9&&(I#
4 ** -@D
J
(??#$)0D
7
4((*-(-;D
-
#%
J (!+)$+D
-
"
/
.&+++2 0
II &,,9<+ #
-
7
#T
J I =5 #)99 D
#%
K F * D
!
G
K F * D
3
. ,4,2 /
J !9F)+D
J K) D
:
I4 &'9<I#
J 98#)0 D
.&++ 2 /
( 449,,#
J K) D
.&++I2 / -
"
#>
%
7 '
7
,'9&+'#
/
9
L
@
#()-($(/#- +, 0# ** )R,*#-#0 /(")* ?(9
E))" / $ :)/)$0 #$ "9 * $" -)9) * -9(,+
F *#" 0#($ $" *($:50)9/ )F *! 0#($ (?
/ $ :)/)$0 +09 0):#)+
2
3
4
5
2
5
"
7
!
-
-
5
9
"
# 0
-
7 !
# %
3
7
5
- "
3
#%
5
."
2
-
"
# :
"
"
5
#
"
-
7
3
"
# %
-
"
"
7
"
#%
5
"
!
# O
5
"
.'<&
Q
5
"
2#
5 !
7
#:
!
"
"
5
!
7
7
-
#
"
# %
!
7
5
#
5
5
-
-
7
#%
! 8
!
!
7
7
8
7
""
# %
"
5
7
-
5
#
* 89 + -* F)
5
6
-
"
-
"
"
7
"
-
3
7
-
- G
7
#
#
G
7 3
3
#
/
9
# 0
"
-
-
"
# ;
2
G
"
"
# C-
"
3
-
G-
- "
G-
G
- G
# C-
G -
-
G
G
G
.7
G
9
-
-
"
G
G
-
- G
"
#
G
"
G L
"
"
-
7
-
7
G-
-
"
G
"
#O
-
7
7 .'<&
Q
-
9
#? G "
G
7 G
- G
-
#%
-
G
-
G
"
G
-
-
7
7
-
7
-
- G
G
7
7
# ;
7
7
" 7
7 -
7
-
-
7 -
""
"
-
#:
7
7
7)
-
"
L G
#%
L
- G
" G
7
-
2# C-
GG
#
E(9"+
G
-
7 7
" 7
"
#
7
6
-
"
"
-
7
7
G .
6
90
9E
-
5
>
7
,,(2 G
&+ +2
"
-
"
L -
3
7 3
.T
C-
L
G-
- .?
,,&D
"
1
.C-
#
,4 D
5
6
7
,,'2# ? G "
G G
9E
5
"
6
,,<2# C-
9
- "
.
-
- G - -
9E
,,<2# ? G "
"
G
"
#
;
7
3
.>
.
# &++42
"
-
-
9
90
-
-
- "
G
-
7
-
]
3
,,<2
79:
-
-
"
.
-
- G
90
,,42# H
7
7
G7
/
-
G
7
L G
L
/
"
-
-
7
-
7
L
7
- G
"
7"
-
G L
-
7
G
7 "
7
7-
"
# C-
./ 3G
.
"
7
-
- - -
&+++2#
# &++'2# T-
G -
7
# &++'2
-
G
-
. !
.?
G
"
9
# &++<2# 0 -
-
G
3
. !
7
-
7
8
#
.
# &++'D K
"
# &++42# C# &++42 G - .:
,, 2# 6 G
L
-
-
-
1
.> )
,,(D > )
# &++4D
"
# &++,2 G- -
-
#
-
G
"
-
7 3
G
#
.
/
.1
"
,' D
./
#
,4(D
7
90
5
.?
!
7 -
-
!
7 -
./
5
&++<2# Z
-
!
-
-
9
-
- !
-
9
7 -
7
9E
-
# &++<2# ? G "
# &+++2#
6
G
4+
"
"
9
90
"
- "
-
2
# &++<2# C,, D
&+ &2# 6
.
:
-
.C
-
7
G
G - 7
"
# C-
9
- "
- "
&++ID >
-
# &++ID / 5
#
&++<2#
-
3
-
3
5
"
G L G
"
7
"
# C#6
G
-
-
G
G
7
G
:
# &+
7
4
"
5
-
7 #
2
C-
9-
7 -
" 7
-
2# C-
G
.:
"
G
7
#
- G
,4,D 1
7 -
# &++4D
9
7@
9
-
#
(,!* 0#($ " $ /#- +!85/(")*
C0
5
,,<D
90
5
G>
7
,,(2# H
7 -
G 9
7
++ ^ ++ - 3
.
G
G
7
9
9
# C-
G G
.>
-
-- 3
+#4'
-
5
-
G -
&2
!
.# # -
-
7
-
2# C-
-
-
G
G
-
-
-
"
.T
# &++<2#
C-
-
Gi
-
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+& -
- -
# &++ 2
9
3 7
" 7# ? G "
9/
# C-
"
-
G
# .H
9
C-
- "
G
7H
G
7
7 -
G
7
G-
-
G
#
CQ
-
7# :
9
"
7
-
- G
G
G 2 -
/>'# 0
7"
7
H
# .&+ +2 -
7
- G
#
- -
G
"
-
.&++I2 G-
-
-
-
"
9
"
7
"
-
# ? G "
-
#
/
:
7
" 7
7
G
-
7
G
- G
7
#
#
-
"
-
-
7>
7
" G
7
-
G
9
-
-
7
7 "
-
-
- - -
7
7
- # C-
G
"
7 7
- :
-
"
"
-
-
"
:
G
.&++ 2
# C-
-
-
G
G
- !
L
-
-
" "
- -
#
9
-
-
-
7
/>&D C
-
&2# C- -
/
90
"
7
5
7
-
6
# &++<D
5
"
-
G
-
7
-
. !
-
# .&++42
#
- "
. /><
G
G9
7
-
G L
G
-
G -
.H
-
-
-
-
G
7
# &++42
G -
-
.?1? />( /> 2#
7
G 7
-
-
/>'2
9
-
7
C-
-
.H
- 7
&++42# C-
7
:
/>I
-
-
"
&++,2# C-
- - -
-
3
7
C
-
./
G
.1;C ?:1
&++I2#
-
7 G- - - G
7
7
9E
3
!
-
"
"
-
?:1
-
- G
&++ID
-
#:
-
7
"
G
7
#
G -
7
-
.
90
- - 7-
5
6
7
-
9E
-
#0 -
- -
-
&++I2
- -
7
"
L -
-
L
-
" G
-
.O "
-
> G
"
&++(2 -
L
#
LG
-
7
"
7
.?:1
6
90
7G
-
5
6
- G
9E
&++ID H
-
-
-
3
7
"
-
-
7
;-
" "
#
- G
3
7 -
"
7
-
-
G
# C-
#0 "
G
- "
- -
-
-
-
-
-
L
#
#0
O -
G
- "
-
-
G -
7
G
:
9
G-
ANR
-
.6
7G
# T-
-
-
-
-
,,,2# C-
#
# C#
- G
-
-
-
-
E
7 -
- "
G
&++I2#
#H
7
"
9/
-
G
7
#> "
-
-
3
;O
-
7
-
72 -
.
7
G
5
7
-
G
#
7
.:
"
,4,2#
T
-
# C-
- -
G-
-
9
-
G
#
7
9
- 7 L G
G
7
G
L
7 -
-
L
.T
- "
# &++<2#
G
2
7
.# #
"
7
3
# ? G "
!
-
- G
7
-
7
-
G
-
73
-
G
7
-
-
-
L
# #
7 -
-
#
"
# C
"
- G
-
.0
.0
"
-
-
""
-
-
7
G- -
7
-
7
# CL -
;
"
7
7
,,+2# H -
-
,,<2
7
-
-
- G
-
7
G-
-
"
- "
"
"
-
7 3
-
-
-
2 G- -
# H
"
.
" "
#
-
7
# &+ &2
,,(D
!
Q
"
# &++<2#
-
G -
- "
G "
9
.
.&++ 2
G
-
!
.G -
-
-
G -
G
-
7# C-
"
-
"
7 :
-
G
/
#
"
-
7
3
"
#
-
7
7
#H
-
-
- !
-
-
- " G
9
G -"
G
"
#
2
:!#* 9D 2
J :P)9 D 2 J :!#* 9D
7
9 :($
4+(94
:9#-!*0!9)
), 90/)$0 .&++,2
7
!"+*) D
. ,,<2 ;
!*"D
J
((0)D
% "
%/
-
7
7# >-
#
: "
7
9F H *D 2 .&++(2 %
'
%
J
7
0
#
0
-
. ,,+2 OK0 %@
<+
& 9 &4#
7
:
-
G
-
# :
8
#
7
#
>
&
9
# 0
,#
#
99(+D
2
J
+-@D
J
9F *@(D
.&++42 %
9
#
"
#
>
99(+(D
J
F 99)0)D
)99 D
J
&'
J
!**D
#
-
J
$-@)= ")*
9-(D
J +-9#8 $(D
* $-(5 (9)$(D
4J
-
J
#T
99#(+D
1
-I
#
.&++,2
>
.&++I2 %
&4 <,<9I++#
G -
7
7
49 &4#
J 2)9$M$")=5N!#$0 $#** D
#
#
7
# >-# # C-
-
#$ "
#
* $-(5 (9)$(D
J
&
@ /(99(D
J
$+D 2 3 .&++ 2 :
3
@ !@ $D
J #**
#T
J 9)+0($D
.&++ 2
7
#9!H)" D
J !0/ $D
.&++ 2
!#=D
:
/
J 2)9$M$")=5N!#$0 $#** D
-
H
G-
+< 9 +<'#
- "
99(+(D
9
J
#8 9D
,'
#9!H)" D
&++'# 0
J
2# T
.&+
7
8)9$)9D
21
:
L
:
O
(I
<
-
-
&+'9& 4#
:
#:
++I9 + &#
G
"
.&++,2
G
-I
"
.
J K 9 :(= D
1
:
-
'(9 44#
9
-F
#
0
1
-'
I 9
H
7
$ "
7
(I#
(*8 -@D
J )8 );)D
G
A <<.B
7
(!+)$+D
@
" G# T
. ,4(2 0
:
I
7
' '9' 4#
G
7# 0
0
+' &<,9&(&#
(!+)$+D
J
0@ /D
#
>
J
ED
.&++42 >
@
-
@
7
"
# <(9 ( # ;3
$Y#
#-;)D
J
)9@ 9"+D
J P-@+)D
#
(99D
J
( *)D
J
?
9
(!+)$+D
G
7
G
. ,,&2 %
>
#
!9*)D 7 .&++'2 /
-
$$)**D
#
J
#
"
G-
(++D
#
. ,4 2 0
>
(
I<V (+#
&
-
<4(9<, #
J
>
&+ 9&
#
G
2)9$M$")=5N!#$0 $#** D
"
6
#
. ,,,2# H
@
-
9E
%
#D
) 7:
%
K
)
2)9$M$")=5N!#$0 $#** D
.&+++2
/#
/ J
#T
J
9-(D
J
)9@ 9"+D
9-(D
7
""
($=M*)=5 ($-)D
J #)8 +D
J ") !- +D
J (9$)9D
- %T1: /
:7
J
<(<9<(,# /
(90)$+)$D
J (@$+($D
#T
J (!+@D
. ,,<2# :
J
F 99)0)D
. ,,42# $
-
/
G
@)9+ D
@
J M$-@)= ")*
G
J 4 +)5 )+0)9D
7
J
8)9$)9D
.1 2
>
$+D 3 J (9$)9D
7
($=M*)=5 $"QH 9D
J M$-@)= ")*
G
# ,<9 +&# >?ZC;/09
- I+ &4 9&, #
2)9$M$")=5N!#$0 $#** D
J )- +)$+D
J
G
1
#2
#
J )- +)$+D
-7
B .% #
M
:
99(+(D
AH
6
#
. ,,'2 -
:
I(
-
#
+49
,#
G
#H :
I< +I9
+,#
#**D
J (*/)+D
. ,,'2 %
#>
:
($=M*)=5 $"QH 9D
G
(
7
7
($=M*)=5 $"QH 9D
:
. ,,<2 :
#
9
2
"
-
>
J 2)9$M$")=5N!#$0 $#** D
.
-
<(&9<(4#
J 2)9$M$")=5N!#$0 $#** D
G-
7
-
&
.&++I2 /
G
'9 &<#
-
7
7
#
>
&< '&<V
'&,#
($=M*)=5 $"QH 9D
.&+
J 2)9$M$")=5N!#$0 $#** D
2 0
2
+0#" D 2 J
7
G
#T
($=M*)=5 $"QH 9D
1
-(
J )99 D
*F(D
J =C!#)9"(D
-
J )= !$D
7
.
<+I9<+,#
. ,,(2 /
@ %
J
- -
-
7
#F
L
0
7 <& ('49(4'#
($=M*)=5 $"QH 9D
J )99 D
J
L 7
J
#
($=M*)=5 I =D
#%
F)"9 D
>
&&
:
7
0
I'
,'9'+(#
.&++<2 :
G
&,9 <<#
J F $ ")$ )9:D 2 J F $ ")$ (+-@D 2 J
G
3
. ,,,2 /
#T
($=M*)=5 $"QH 9D
G
(++D
7
&& ,4&9,,&#
($=M*)=5 $"QH 9D
-
.&+ &2
@
) ,D
.&+ &2 C-
0
: " 7
-
G
#-
@QQGGG#G
#
#
@ +(Q+(Q&+ &#
(*+0D
J
/!++)$D
J
+0#
-
$+D
#T
.&++'2 6
1
- I'
=C!#)9"(D J 2)9$M$")=5N!#$0 $#** D
.
#2
=C!#)9"(D
J
0
7
G
" G
7
-
"
7
J
#**D
.&++<2 %
"
G
/
#
&< (&,9(< #
J * $-(5 (9)$(D
:
"
7
"
@
II I<9((#
G
:
=C!#)9"(D
.&+ +2 :
J 2)9$M$")=5N!#$0 $#** D
-
7
9 I#
#0
)- +)$+D
G
J
"
@ /(99(D
J
7G -
($=M*)=5 $"QH 9D
#0
7
J
$+D 2 3 .&++,2
:
"
&,
I, 9I, #
- +0 D
J +0 *9#-@D
J
)-(D
7
.&++42
"
- +0 D
7
90
J
)-(D
#
- +0 D
J )$I0)=D
"
I(
+I9 +,#
# %
C
)-(D
.&++ 2 0
J )98));D
@
J ((/8)+D
"
7
. ,,(2
-
@QQGGG#
#
RE)**D
7
RE)**
#T
J
0
# #0
-
C -
-
&4 4 9,,#
G
1
- <( (+<9(+,#
6
% "
:
&+(9& &#
G
G
.% # $
-7 7
9
/# Y#
G
H
L - G 1# %#2
# '9
/# 0# $:0#
)""D
4J
!*"D
J 7)/,D
J
!9#+($D
. ,4(2 C-
7
0
1
-<
)+,*LD 2 J 9(!++)**#)9D
7
#%
<
+)** +D
/
G# 0
9<'#
J
#
-
.&++'2 $
<<# 0H
!
8
@ -
7
S ($(F $D
@O 9-
7
@ +Q+IQ&+ +#
. ,,&2 T
"
#
/
#T
7
90
7
"
.&++,2
8
< &<9&4#
) #C
)/)9*)D
" #C
.&++ 2
6
J
7
J ):)$")9D
44 ,9 4#
. ,, 2 %"
7
F
(H 9"#$(D
J
$$)**D
G
J (E*)+D
#T
(90)$+)$D
J
+0#
7
(++D
)F)D
:
(
$+D
J
L# T
.&++42 T
-@
1
$$)**D
G-
""
\T
!
-
"
1
- I4 <4,9<,<#
7
7 ,( I4(9I,&#
"
@ C-
G L
<,9 (&#
J )$$)00D
J
($H 9"#$(D
J -@/#"0D
J (E*)+D
.&++I2 1 /@
G
0
:7
9!)*(D
G
G #?
%
J 0)E 90D
-
-
" 7
#0
7
- I+ I,9 &#
"
.&++(2 ? -
. ,,'2 :
9
.&+++2 C-
"
$$)**D
9
',494+,#
00#$D
@
J (E*)+D
.&++<2# 0
T
0
#
', <+(V<&(#
J (88 : D
J
* D
J
!)$9(0@D 4 7 J !9;)D
"
-
. ,,42 6
7
# %
0
4
,I9&+ #
)*0=)9D
J 2)99#++D
J 2#0= (@$D
.&++42 >
7
)99 D
J
($=M*)=5 $"QH 9D
G -
#T)#9(D
J
"
#F
J
%
"#
J
-
"
(90)$+)$D
"
%
74
J
"
@
7 I( ( '9I'(#
-
!)9+-@/ $D
"#
!+-@)90D
0
-
. ,,<2
L# F
)9)*/ $D
G
I(<9I <#
9!)*(D
.&++42 ? G
\%
/
J H[9$+0 "D
'
-
J
&
(9"D
<
@
9<&&#
J )+;#$D
.F
"
.&++,2 : G
2# H
"
& ( <9
(',#
)- +)$+D
J
8)9$)9D
H
/
>?ZC;/09%
) 7:
))F)+D
1
?
%
(/)9(D
) .% # :
)
/ 7
#
X#
6
:
"
#
9E
# I,9 I#
G-
# T
#
.
#2
7
J
@ /(99(D
J
$+D 2 3 .&++42 T
7
"
G
7
O% :
# 0
%
7
&I ,'9 +I#
J +-9#8 $(D
J 2)9$M$")=5N!#$0 $#** D
G
7
.&++ 2 0
:
#T
1
7
-I
@
#2
('9 <#
"
!#=D
. ,,'2
%
. ,' 2 %
-
% "
J =C!#)9"(D
<',9<4'#
9
F)"9 D
-
J !)F +D
:
/#0@D
#
J
- !
)+ 5
9-I D
>
J
9-I 5 (99)+D
. ,,(2 /
/
9 9
. ,, 2 H
7
#T
**(9 5 /#0@D
:
7
"
# >-# # C-
#$ "
. ,,'2 C-
#
:
!
#
G
I( <<'9<I&#
F $ ")$ )9:D 2 J
;
G
#
8
J
7G
'' I,9 I#
0
@#**D
. ,4,2
4 9 4'
(+)D 7
#%
8)9$)9D
J
#**#: $D
J
)9")++)$D
G
J
9):(#9)D
J F $ ")$ (+-@D 2 .&+ +2
@
#T
1
- (+
I <9I&I#
#$ 0#)9D 2 J #R#)9D
J )
:)D
-
J ! -;D
2 J )+-(!99)D 2 .&++,2 ;:/;:
7
7 3
# %
/
&&+ &&II9&&(I#
4 ** -@D
J
(??#$)0D
. ,4,2 /
7
#%
4 $:D J 79(,??D
3
J
"
/
//)90D
II &,,9<+ #
J @9#+0)$+)$D
J
$+)$D
7 .&++<2 $
-
7
#%
4((*-(-;D
-
!
/
J (!+)$+D
G
0
@
G
&''9&4 #
.&+++2 0
#T
7
:
I4 &'V<I#
($09(**#$: $$! * E))"+ #$ -)9) *+ 8
"),*( #$: -9(, 9(0 0#($ 0 0@) * $"+- ,) +- *)
+ $ )R /,*)
4
3
%
-
"8
3
"
-
# :
"
"
"
5 # %
5
-
3
"
-
7
-
5
# :
5
5
"
5
"
"
"
# >
5
7
7
#1
"
7
5
-
!
8
7-
8
!
#
"
"
"
"
5
"
"
"
-
7
#
-
3
"
5
7
#%
-
"
"
7
5
7
5
"
"
"
-
"
#
7
" !
"
"
8
# $
-
* 89 + -* F)
"8
!
"
"
!
5 7Q
5 #
"
3
#
"
T
-
? G "
-
-
7
G
7
G
-
G
" #
-
G
9
-
- G
-
7
G
-
G 7
- # T
"
G
G
"
L
-
-
"
-
G
!
G -
#
G-
9
9
G
-
!
7
- -
- -
-
G
#
-
E(9"+
-
7
- G -
9
-
G
!
# %
G
7)
# T
-
G
Q
G
7
- G
-
-
-
G- - -
G
!
# C-
G
G
-
-
-
"
-
G
7-
-
-
3
#0
G -
7
- G
- "
G
3
# 0
G
G-
-
# 6
G
-
7
"
-
G
7
G-
7
"
G
7
-
-
"
-
"
-
7
3#
" G
-
G -
-
-
-
#
7
#
-
!
-
7 3
-
!
.C-
# &++,2# C-
3
G L
!
G- -
7
!
# &++42#
G
-
.
" 7
G- -
.F
-
-
7L
-
- G
"
,,<2# C-
- "
-
7
7
-7
7 - -
7
.F
# &++42 G- -
7
G
7
G
,4,2
-
7
-
7
- -
-
- "
3
G
-
"
9E
"
G
-
,,(D /
#0
"
-
7
- -
.
90
# &++(D "
7
G2# 0 -
-
G- -
G-
"
H
-
G
- G
. ,4+2 - G
7
- G
-
G
79:
-
L
7
-
. -
1
-
,,<2# /
"
,,'2#
-
7
7
"
"
L
7
-
"
-
.H "
&++'2#
- G
-
" .?
,,'2# C-
-
.?
-
-
-
-
.C-
C"
#
G-
- G
/
3
!
-
0
5
3
? G "
7 -
"
- G
G
.
#
#
# &++&D T
# .&++&2
-
"
- G
,, D ,,<2
# &+ +2# /
,,<2#
"
7
-
#
.:
- -
-
.F
7L
-
-
"
6
.
-
"
-
7 -
,, 2 -
7
7
G
7
-
- G - 9
9
-
"
7
-
G
-
3
-
7
"
-
.?
- G
-
-
,,'2#
9 "
- "
90
G
"
5
# .&++ 2
-
G
7
"
-
#
C-
!
7 G
-
"
"
-
G
7
G
"
-
"
G
-
# C-
-
# H - -
7
-
9
"
G
9
"
7
7 -
3
- G
#
0
5
/
:
79:
9
"
-
90
G
.:
7
9E
# .&++&2
H
G- -
<#(
G - V P ++
9
-
7
-
-
"
-
7
-
!
- :
3
-
-
:
-
"
.F
0
36
" 7.
-
!
-
"
#O
-
&+ +2
-
G
# &++,2# ;
G
G -
#% -
G
-
-
7 .6
- G -
G 9
V×V
#6
-
,4,2 G
,, 2
# .&+ +2
G
c& -
9
#
C-
&#
9E
,, D ,,<2# T G
"
G
#
3
-
-
.
,,(2# 0 -
"
6
6
#
.:
9
/
:
0
-
,4ID O "
5
-
7-
#
.
-
.C7
7
E
-
&++<2
,,'2
-
G
%
&#
- G
#'
G
-
G
#
G
7
-
-
!
7
-
# : -
# C-
-
-
"
!
G
3
-
7
G
G
7
7
-
-
-
G
#
-
!
-
T:T: G-
TG
:
G-
-
-
G 9
G -
-
7
-
"
7 -
7
"
G -
:
7
T
G
G
# 6
:
G
7
T
-
#
9(, +,)-#)+ (? 0@) 9(0 0#($+
T
- G
-
# H
G
.F
( # # -
9%3
G
. 2 .:
"
#
-
-
G
7
G 9
# &++(2
-
G-
0
.T2
9
G
.:2
-
,4,2#
$"+- ,) +-)$ 9#(+ A B
% -
!
G
"
"
-
-
/
-
&++I2# C-
G- -
7
# # "
G
G- -
G -
-
C
"
-
.&2
-
G-
"
7 !
G -
7
'
-
G
G - #
-
7
-
"
!
-
#O
" "
3
-
# >
"
.
7-
7
G -
"
7
-7
G
"
S
7 G
"
7
@. 2
G- -
-
"
-
# C-
-
7
!
:
:'
-
" 7 .C
G
G
2 G-
7 -
#
7
-
-
-
-
3
8*)
9 "
"
-
G-
7 -
7#
9(,+ 0 0@) * $"+- ,) *)F)* AWB
!$?*(E)9
):!/)
+
&(
(+
'(
++
++
'(
(+
&(
+
999
999
999
999
999
999
+
+
&+
&+
<<
+
++
++
+
+
&+
<<
&+
+
+
++
&+
+
<<
&+
+
4@) 0
A B
!"
&
<
I
(
!#
'
4
,
+
&
<
I
9(,,#$: +)C!)$-)+
1
-
-
37
G-
.
7L
G-
,,<2# T
7
G
-
7
3
# &++&2# 0
- -
-
!
G
-
T::T
G -
7
-
G
9
7
&# %
#
G -
A
C
7
7
G-
G
9
7
7
-
9
#
!
-
-
-
7
TT::
9
# &++&2
#
3
-
./
G
" 7
G -
- "
./
G
7
&
# 6
#: -
3 7
" 7
G -
7
-
!
C
# &++&2
7
-
T
G-
./
!
G - -
G-
3
&
G
B
7
C
G-
&
#
G -
"
G
"
8*)
1
G-
-
7
-
G 7 -
-
#
7
7
7
#
9(,,#$: +)C!)$-)+ ?(9 "#??)9)$0 #$#0# * -9(,+
4@) 0 A4B
!$?*(E)9 A B
T:T:
TT::
T::T
:T:T
::TT
:TT:
TTTT
:::::
T: T:
T :T :
TT::
T:: T
TT: :
T: :T
TT ::
T :: T
TT ::
T ::T
T::T
T T::
TTTTTT
: T: T
:T :T
:: TT
: TT:
: :TT
:TT:
: TT :
:: TT
::TT
:TT :
:T T:
::T T
::::::
):!/) A B
!"
&. 2
&. 2
/
!#
<
I
(.
(.
.
.
'.
'.
4.
4.
,.
,.
/
1
2
2
2
2
2
2
2
2
2
2
&
T: T:
:T :T
TT::
TT::
:TT:
:TT:
:: TT
TT ::
::TT
::TT
T::T
T::T
(,!* 0#($ /(")*
C-
L
G - 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
9
-
-
G
1
4
# 21
G
:&
: #
:,#
1
/
"
-
-
-
G-
G -
"
3
:
"
G
7
79:
- "
- G G
/
" #
-
-
L
"
G
!
G
-
#
7 G-
"
-
,,'2# ; -
-
"
G
# &+ +2# 6
G
-
.CG L-
/
- G
-
7
&++(2
- G "
-
7G
./ -
.C-
G
# /
G -
-
-
G
-
-
%
-
79:
7
7
-
- . ,,'2
- "
" 7
-
-
/
2# 0
G G- -
#
C-
#? G "
.6 #
G
-
-
-
# . ,4,2 - G
-
-
-- G
-
-
9
79:
-
,,'2
"
-
3
7 -
-
G-
-
- "
L
-
- - "
- "
- "
.:-
G
7
"
- G
7#0 -
-
.H "
&++'2
G
/
79:
-
,,'2
C-
G -
9
G LG -
-
7
G- G
- "
!
G
G -
"
G
G
3
G
#
- - G
# 6
#0 -
G
1
-
-
I . # # T :T :2
# C-
-
"
9 "
-
G
-
-
- G
"
-
#
-
-
7 #6
G- - 7
-
-
-
-
# C-
G
G
G
"
" G
G -
!
- G
# : -
7
-
L
G
G
#0 "
7 7
-
# &++ 2# :
# C-
-G
!
-
-
-
-
-
.
90
"
G
7
G -
G
.
- "
-
!
-
-
5
"
- "
# &++
-
# &++,2
- G
-
"
7 -
7 - G
7
" 7
"
- "
-
-
-
G
-
7
1
CG
- -
4 . # # TT ::2 G
-
-
.C-
-
-
- "
-
# C" G .H
# &++<2
-
"
7
7
"
9
-
L
G -
-
"
-
"
# T-
7
-
!
9G
- G
# C!
!
7
G
-
# CG-
-
-
-
G # 0
- "
-
-
7
-
9 "
-
G "
G - - G "
-
# ;-
!
-
"
-
.
7
-
# &++ 2#
"
7
7
- G
1
2
C-
" "
!
-
-
# 1
G
4<
G
,4
G
G-
-
7
-
-
.C
-
-
-
(2# C-
G
-
L
-
I
- G
9
? G "
9 "
-
-
-
-
G
- "
7
-
-
-
7 -
-
#6
-
G 9
-
G
L
G 7
!
./
"
-
G -
7
-
L
.H -
# &+
!
-
9
2#
7 -
G
-
L /
- G
# C- " 7 - -
G
- GG
G
G
# .&++&2 G - "
"
G-
G
- G
-
-
7
7
L
- -
# &++(2
G-
7
G-
-
-
!
G
-
"
'I
.T
7
-
-
4
G
# &++&2#
H
7
" 7#
G
-
9
- G "
#
" 7
7
+# '
-
'#, G-
-
-
7 -
7 G-
#
-
!
-
G -
G-
-
G
-
-
#
C- - -
"
G
- "
- 7
L
-
G - -
# .&+ +2#
7
-
G
G
7
"
-
-
-
7/
G
"
G
7
-
3
# .&++&2
"
- G- G-
G
-
G
G-
G "
G - - -
7
-
7
# CH
G-
!
7
G-
#0
G
G
" 7
G
7
:
: I
G
-
-
G
- 7
-
-
0
-
&
4
- G
#
-
C-
G
,
-
7
!
G-7# H
-
-
7
# C-
7
L 7
-
G - 9
"
4
-
-
-
"
: &
- G-
- G-
-
-
-
" G-
-
!
. # # T::T
7
"
TT ::2#
G - G- - -
G
"
7
-
-
-
7
-
7
9
- "
9
"
.
- -7
-
-
-
-
- -
1
G - G#
-
-
G- - G
-
-
,
-
G
G
G -
1
1
G
G
3
!
7
-
"
7
G 9
"
9 "
-
-
L
3 02#
1
7
cL P +#4(2 -
cL P +#,,2 - G
0
.T2
"
- G
# T-
G-
7 -
"
9
9
- G-
G-
. # # cS P +#,4
"
. # # cS P
.
9
3
-
"
-
# . ,4I2# T-
L
-
G
9E
"
3
G 9
"
7 76
-
- -
!
7
-
-
7
L
"
-
L
9
-
L
G-
# &++&D &++<2
-
G -
G-
# &++<2# 6
7"
-
./
-
/
# H
9
-
- "
-
G
G - G- - -
#
2
#8 9D
J
-@( D
.
#2 O7 #
J K 9 :(=
0
:
. ,, 2 6
#T
1
#
-<
&,9<&#
#
!*"D
J ((0)D
)$0($D
. ,4+2 0
J #-;)9 D
L 7\ C
%
)$F)$!0#D
T
#;L
J 4#*+($D
7
%"
4
.&++'2 T
H
7
(@ $D
'
J (E)9+D
+E)**D
(*8 -@D
J
-
-(
J
!:@0($D
J
E)+D
!
3
J C!#9)D
3
#
$:0#
*)9/($05
!,@#$D
J
#
J !++ $+D
J
G
L
7
) $ 9"D
7
A&++ 2
# :
%O%:Z:@
-
-
"
"
% "
"
I&&9I<&#
0
3-
7 -
I 9 ('#
@
1
-
-
J @ /,#($D
.&++ 2 /
#:
7@
4&9 44#
2 /
\T
"
"
/
)90)$+D 7 .&+
.&++<2 6
<I &4'9&,&#
#
# 0
%
7
4< &((9&'+#
(*8 -@D
J
($(;D
J
F#:$)D
.&++,2 0
7
9
-
.
9
#2# %
/
&&+
&9
'&#
(!+)$+D
J
(90#/)9D
G
. ,,(2 %3
.% #
!0?(90@D
1#
J 29 $-#+D
S
0
J
"
7#
/
0# /#2
$$)D
7
J
,9&
#
(90)$+)$D
$ "
J +;9#":)D 7
@
-# 0
@
7
7>
$Y#
A&++ 2 6
F
0
"
49 ' #
!)9D
-
J !+-@)#D
9
J
G
(90)$+)$D
#
2)9$M$")=5N!#$0 $#** D
%
J
7 &I '<(9'I'#
F 99)0)D
7
J (9$)9D
. #2
%T1: :7
@)9+ D
A&++,2 %
G
. ,,<2 :
I<
($=M*)=5 $"QH 9D
#
G
G-
:
- <
>
G
@
#
G
7
+I9 +,#
J 2)9$M$")=5N!#$0 $#** D
7
:
. ,, 2 /
# C- F
J 2)9$M$")=5N!#$0 $#** D
7
#>
,9 (# ;
-
79
($=M*)=5 $"QH 9D
-
#
- /
J (!+@D
\H :
. ,4I2 C-
0
. ,,<2 :
#
>
7
%
-
&
'9 &<#
7 &4
9&'#
($=M*)=5 $"QH 9D
J
S
:
* $0D
J 2)9$M$")=5N!#$0 $#** D
-
7
G
.&++ 2 /
-
G
#T
I, I IVI&&#
($=M*)=9 $"QH 9D
G
J
#
$+;#D
>
F
G
&,9 <<#
9
7
-
)*)$#!+D
.&++<2 :
&&
. ,, 2 :
H
F)"9 D
:
7 I&
@
"
'9<4#
. ,,'2 :
.%>/2@
#%
1
( $$($D
J 9(D
-
;
J @)$ #*D
7
0
J
J
(90)$+)$D
7
L#0
!9 "(5 R,G+#0(D
J
-
:
"
J (RD 7
F
H
G,)=5 9 $ "(+D 2 J
-
<9 '+#
A&++42
J 9)$=*(ED
G
(
!"9 D
#0
(9" $D
I( & + 9&
!$0 ")
:
-
&4 <',9<4'#
. ,,(2 :
7
7 4& <,+9<,4#
($=M*)=5 $"QH 9D
G:
#
J
G-
9
9-I 5 (99)+D
.&++(2
G
7
9
#
&#
$" *!-I .&+ +2 0
%
0
# 0
0
#
#)8/ $D
%
J
-;D
0
G
.&++I2
7 .% # /
)90)$+D
7J
@
.
0# %#2 9 '# H
#**#: $D
LG
:
J F $ ")$
L 7
#0
0
3
7
7
J
- G
(90#/)9D
E)$D
J (E*)+D
0
J !00($D
H
7#
@ /
H
G
7 , &&<9&&4#
.&++&2 T
#%
:
. ,4,2 ;
F 99)0)D J 2)9$M$")=5N!#$0 $#** D
A ,, 2 C-
&
9
(4 I
(!*"D
@
0
A&+ +2 ?
#T
J
"
(+-@D 2 A&++<2 %
7 J F $ ")$ (+-@D 2 J ))+0)98));D
#-@ )*D
2
$Y#
)90)$+D
G
#
< ,&9 &&#
:!99 $D
"
. ,,<2
&(9
I #
G
9I'&#
G
#T
&, &&,9&<4#
7
)99 D
J
#
($=M*)=5 $"QH 9D
G -
L# F
#T
1
. ,,<2
%
-<
&<9 < #
-
74
I(<9I <#
-
1
-
F)"9 D
:
J !)F +D
-
:
J
#
)+ 5
>
M$-@)= ")* 9-(D
4
J (9$)9D
#
@#90*#??)D
- "
:
-
($+D
G
.
2 7
A&++I2 :
7
7
7
7
!-@)9)*D
J
,#0 #$)D
J # !"D
J
J (!-@\9)D
!"9 D
J
#:$(*)0D
J -@)9/ $$D
.&++,2 C-
J
# #)09(D 2 J
9
# 0
%
7
% "
&+'9& ,#
@#**D
7
7
- <( I''9I4'#
9
<
. ,,(2 :
G
- II <449<, #
J 2( $$($D
J
7G
(< I (9I'+#
"
@)$ #*D
. ,4,2
4 9 4'#
1
J 7*#$:)8#)*D
1
9-I 5 (99)+D
.&++(2 -
#T
0)#$/ $$D
J
J 2)9$M$")=5N!#$0 $#** D
T
J $0=D
#T
9-I D
J
#T
**(9 5 /#0@D
:
!
G
I( <<'9<I&#
F $ ")$ )9:D 2 J
;
. ,,'2 C-
#**#: $D
J
)9")++)$D
G
J
9):(#9)D
J F $ ")$ (+-@D 2 .&+ +2
@
#T
1
- (+
I <9I&I#
4)+0)9/ $D
.&++(2 0
97
J #)8/ $D
7
-
J
)$ **)"D 2
" \K "
7
#T
:
J
)::)$+0 **)9D
J
.
2
(< <4,9<,&#
90=*)9D
J
7
#R($D
G 9
3
0
2
" 7
7
G
-
- 7
G
-
E
#
3
"
# . ,4I2
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
4I+
I (
<(4
+&
(+'
I&
<'+
I&&
-
G
-
#$#/!/ -($09(*
R /,*)Z
&2
J
F 99)0)D
. #2
G
J (9$)9D
#
- /
. ,4I2 C#
:
,9 (# ;
#>
>
- <
#
(")**#$: 0@) @)98#-#")59)+#+0 $-) )F(*!0#($
#$
,(,!* 0#($+ 0 0@) * $"+- ,)
+- *)
K
5
%
-
"
)
-
#:
-
%
5
-
#
-
3
5
"
5
5 7 "
3
#
-
5
-
7
-
#%
8
)
"
"
5 #
5
5
"
" "#
! 8
"
" 27
-
" .# #
.# #
-
2# %
75
5
3
8
# %
"
5
# :
-
5
!
-
8
7
"
.# #
5 # %
3
!
!
-
-
-
"
2# %
!
3
"
5
"
-
#
5
* 89 + -* F)
3
3
"
5
#
K
?
L 7
# ? G "
-
-
-
7
9
7 -
-
- G
-
-
"
" "
7 - G
-
- -
7# 6
"
-
-
" # C-
-
G
7 G"
7
7
.# #
.# #
"#
7
"
-
"
7
-
- -
#? G "
# C- - "
-
-
L G
"
7) E(9"+
3
7
9
-
"
"
- "
G
-
7
7
7 3
G
-
#
"
#
.# #
-
G
-
G
"
2# C3
-
-
- "
-
"
G -
-
-
-
#:
-
3
-
5
-
-
GG
9
-
-
2
2# C-
-
"
G
-
G- -
# C-
7
7
7
"
"
-
-
-
9
7 -
-
7
7 -
7 3
-
:
-
#
"
G
G
7
K
T
G
- G
# C- 7
7
. !
# &++<2# C-
7
L
.
5
"
"
#
C
&+ +2#
.F
<++ -
L
7
0
7
9
7 -
#
,, 2#
7 &+
&+
2 G -
2#
9
# &++'2#
:
-
G
-7
.
7
G
9
G
.?
.?
.Z
7
/
7
G - -
-
7
G
-
,4,2
3
-
7 -
-
# &+ +2#
- O
-
G-
:
G
-
-
- -
G
-
G - - - -
-
-
.&(
"
4+
L 7
" 72# 1
- G
-
-
-
.
- :
-
-
:
I'
G-
-
G
9
I,
&#(
"
G
,,+D
"
9
.
:
- G
.> G
9
7
.F
L
#
- L G
G
"
!
-
-
Z &+ +2# C-
-
-
7
-
7 -
-
,'4D
-
#
,, 2# %
G -
L 7
"
7
2
-
# &++<2# /
7
-
:
" 7#
- "
"
-
-7 G
7 #
-9T
#
C
/ 3G
- O
-
-
7 G
,, 2# C-
<#(
.
7
.C
#4
2
I<
G
-
G 0
7
G
- - -
"
-
.:
7
G -
7
#?
9
K
./ 3G
- G
#
-
7
-
G#6
,,+2# C- G
-
-
9
""
-
G
-
0
9
-
"
.H
.1 -
- "
&++ID 1 3
# #
-
"
-
&++'D 1 3
G L G-
# /
-
"
1
-
G
-
2#
-
:
# &++,2# /
# &+
3
# &++&D 1 -
# &++4D
7
-
- -
-
-
"
-
7 -
G - -
7
9
-
L
.1 -
-
# &++&2
9
-
# #
.1 3
# &++4D
# &++,2#
C-
7
-
"
"
-
-
" 7
"
7 G - G
-
G -
.1 3
# &++42# C-
-
L
7
-
G- - - "
# 0
7
-
3
# &++,2#
.# #
2
# T
G-
-
7
# :
G - "
7
-
# C L
7 3
-
G
"
C-
:
#
5
"
.&2 -
-
"
G L G-
G -
-
- "
7
G -
-
-
-
-
-
-
-
7 3
- :
G
- "
.
-
"
-
7
"
#
!
-
-
-
# C-
-
9
"
7
7 G
3
"
-
7
- G
. 2 -
9
9
-
"
G
7
K
"
.<2 -
"
"
C-
G- -
.I2 - L 7
7 3
G
R3R
++++
#0
#% -
2# C.:
-
9
-
&++,2
"
-
2
7
T
.(@I
-
6
-
-
2 .1
7 %
# 6
-
#0
G
++
9
9
. O% &+ +2# : -
- 6 # #0 -
8*)
-
9
:
-
7 - 7 G
G
-
G
!
!
-
G -RP
-
-
- 0
#
7
G
.C
"
G- -
- #:
3
" -
G
++# % - # C- R
7
L
G
3
-
-
-
#
-
5
- 0
. O%
&+ +2#
2
5 K
$#0 ?#)*" +#=)
2#)*"
A@ X?#)*"B
"#/)$+#($
&
<
I
(
+
(
&'
4
C-
-
. O% &+ +2@
G 97
- GG
(0 * ?#)*"
+#=) A@ B
)9) *
-9(,+ AWB
!$?*(E)9
-9(,+ AWB
&
'I
''
+4
(,
('
(
'<
&
I4
<+4
I4
(,+
4((
( &
(, <
4,
44
,
',
4
''
'4
''
&
<
&
,
&<
&&
&<
3
3&
&3&
&3<
&3(
<3(
<3,
,3,
&
I
'
4
!/8)9
(? ?#)*"+
G
-
- 0
G #
#:
G
G
G 7
9
G
G -
G
-
# C-
-
I&
"
.C
#0
2#
G
(4
G
9
G
K
2#:!9)
0
3
-
9
7
"
9
G
G
-
#H -
#
#>
G
9
-
G "
-
-
-
9
-
6 # &#
(,!* 0#($ " $ /#- +!85/(")*
C-
7
3
9
7
# CG-
7 -
!
-
7
7A
G G
.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
aA
G .:
G
#
,4,2
#
7
5
9E
7
7
G
- 0
-
7
-
"
# C7
-
"
7 G
- - .,<(
0
G"
#
7
"
7
:
-
# #
-
G -
7
- -
- "
-
7 "
3
-
7#
!
- -
-
G
G - -
-
&++I2 G-
-
-
-
7 G
6
2# 6
-
- "
90
" 7
" 77
"
9
7 - "
0 7
-
"
# 0
"
Q
-
-
&+
0
-
7 -
.
2# Z9 3
2#
:
"
"
L "
L
7
2 -
#
-
K
C-
"
"
- G
L# ; -
- G
- "
-
#
G
G
-
- G
-
3
G
-
-
7
#
.1 -
"
G
- -
" "
# C-
-# ? G "
%:C(2# C-
-
"
" 7
7
"
-
!
7
.%:CI
"
!
7
G
!
7 - - -
7
G
# C-
7
-
L
" 7
#0 -
-/
-
#
0
-
- -
9
-
-
- G
# &+
-
2#
-
- G
L G
-
G
G
-
!
7
-
-
G
!
7
"
.H
7
G -
# &++ 2#
G -
-
-
#6
-
7
-
"
# . ,,,2
-
1 !
G
7
-
-
7
#
G - -
7 " 7
G L
G- -
# .&++&2 - G
3
-
7
-
#> L
-
-
9/
"
"
3
-
7 -
-
7
-
G
7
7 - G
C-
-
.&++ 2
"
.
-
3
-
-
7
7
-
7
.H
"
- G
3
-
7
G
-
-
- -
"
-
&+
G
- "
"
- G 2 -
"
G - -
#:
-
7
L
G -
-
7
# &++&2#
-
# C-
G
" "
" 7
-
G
-
L
7 -
,,+2
G
-
-
C"
L "
G-
#
L -
G -
L
7
G
,, 2 -
G -
- G "
./ 3G
G
.C
G
-
7
K
-
.K 90
# &++( 2#
-
#
-
7
-
-
G
-
9
G
- G
7
- G "
9 '4 V
7
#0 -
.;G
# &+
- -
9
7
2# T
- -
.
1
-
7
&+
-
-
-
7
-
-
I+
- G
7
"
" 72
- G "
- "
# &++,2# 0
G -
G
7
.K 90
-
7
C-
-
-
-
"
#
"
7
.
-
- G 2#
4
C-
-
!
-
"
"
-
G
-
-
"
7
- "
7
G -
7 "
"
# &+++2# C-
- -
G
G
-
-
7
-
"
#1
-
#
7
-
9
9
-
G -
-
-
# C-
G- - " "
G
- G
G
7
-
" # C#
7
G -
"
7 -
-
-
7 7
"
"
G
G
# # -
- "
"
.
" 7
-
#
G
-
-
" # C"
9
G
-
-
C-
" 7
G
# C-
"
"
-
L
G
-
5
- "
- G
-
7
-
-
-
7
"
G -
-
-
-
3
-
G
"
G
# .&++( 2
-
-
7
# &++,2# K 90
7
0
7
9
.K 90
7
G - -
-
L
-
-
"
-
- "
-
G -
K
:
-
#
L
-
L
-
7
-
-
7
L
G
-
Q
L
7
-
7G - -
7 -
G
- - -G
G G
G
-
G
G-
-
-
- -
7 "
-
7# C-
- G
-
# C
" 7
G
."
H
-
-
7
7
L-
#
#
G
-
9
# &+ +2
G
-
5
"
7#
;-
9
-
-
3
-
.H L
.H L
1
&++,2
&++'2
7 -
- "
.
"
5
C
-
&+ +2
"
:
9
"
- G
9
9
-
"
9
"
#
L
. 87
-
7
"
-
G G
-
-
-
7
-
7
9
-
"
#
-
"
G
-
- "
#
9
G
- G
G- -
# C-
7
G
!
-
3
-
-
4
"
- - "
G
- -
3
" 7
-
# &+ +2# C-
G
" L
"
7 L G
"
#
-
7
-
" -
#
G
4
-
-
"
1
!
7
" 7G-
-
-
-
-
!
7
-
9
? -
-
# 0
"
-
- G
"
-
-
# C- G "
-
9
"
9
G -7 -
7
# #
-
9
G
- -
G
K
%3
.H
-
# &+++2 - "
-
G
"
-
-
-
-
7
7
-
# &++ 2# ? G "
G
-
-
-
-
.C
"
5
"
"
- G L# 0 -
-
.H
"
7 -
# &++42
7
-
" 7
7
-
"
"
.6 # '2
#? G "
-
#
,, 2
&++&D
#
-
7# :
-
9
'(
.
-
G
-
#
-
-
7
- G
3
L
# C-
"
-
G -
G
-
G
,4
-
9
# &+ +2# %"
-
I+
7
"
-
- "
-
-
- "
.
- G 2# C#? G "
-
"
7
-
-
-
"
-
"
-
-
'
L
#
-
- - "
- "
"
-
"
.
'' # 0
L
G
"
7
7 -
-
-
3
"
-
" 7
-
- G
"
1
-
-
- G
-
- G
-
- G 2# / 7
./ -
./ 3G
"
3
- -7
- G 2
- "
L
,,I2#
>
G
- -
.F
3
-
-
L
G
,, 2
"
G
&++ID
G
-
,,<2
-
"
- "
:
-
-
"
7 -
-
. # # 1 G
-
-
&++42# :
7
# 0
# C-
?
G - G
> G
-
L G
.H L
-
.1 -
"
"
-
!
"
#
-
#0- "
-
"
-
G- L G - G L
- "
"
K
-
"
G-
-
7 -
- "
-
- "
:
" # ; "
"
-
#0- "
-
7
8 h
7
7
# &+++2
- - "
"
7
G
-
/
79
G
#C
"
-
G
7 -
"
G
-
7 -
-
-
#;
-
-
- L G
- .
5
G
-
0
C
&++(2#
G
-
&+ +D > G
Z &+ +2#
-
-
.C
-
"
-
7
G -
- L G
-
-
T
-
-
7
7
#/ 7
-
# C-
-
- -
0 :9 -
"
G-
#
-
&++&D 8 7
.C-
-
G 7
-
- "
-
,,'D
-
7
-
-
-
9
7
"
G
#
2
*?(!9#)9D 2 J /8)90D
J @ 9/)0D
-
.&+++2 %"
%
#0
O0
-
7# C-
0
+
< 9
<4#
9 #8 9D
J 4)+0)9/ $D
G
)-;#)D
O
J
"
99#G$D
J )- +)$+D
7
.&++,2 %
#F
.&++'2 H
-
>
)-;#)D
J
:
'(
)-;#)D
-
#T
**D
C -
7&
%
7I
9
G
3@
9
-
G# >
(9 &4#
G
@-
3
7 &< < <9<'+#
* $-(5 (9)$(D
9
<4+9<4'#
&,+9&,,#
.&++42 :
J )8(!"D 3 .&++,2 :
C -
0
J
@ /(99(D
3
J
$RD 2 3 .&++ 2 :
#T
1
-I
&+'9& 4#
#T
K
!+#D
J
#-@)*D
J (E*)+D
J
L* )D
.&+
2
G
-
-
!
# 0
% "
%
7
7
I& I+<9I+,#
!+#D
J
!D N J
99)005 )$$ 9"D
J
-
(E*)+D
.&++42
# CF $D
J !++ $+D J
-
(++D
0
#T
J
-9
8)9$)9D
:
(*8 -@D
J
'
.&+++2 /
-
#9!H)" D
9
.&+ +2
#>
-
/
*)9/($05
-
:
!,@#$D
J
7
-
1
- I+ (
9( 4#
9
#
<4+9 <44#
) $ 9"D
.&++ 2
%O%:Z:@
"
"
% "
&4 9 &,+#
"
-
3-
G
#
# 0
%
7
4< &((9&'+#
!)9D
J !+-@)#D
-
9
L* )D
:
J
G
(90)$+)$D
#
%
.&++,2 %
7 &I '<(9'I'#
.&++(2 T
7
7
0
37
-
@
#T
(< '&49'I #
L* )D
J *\/)$0D
-
J )9$#$D 2 J @ !F)*D
7
J ) (99)D
G
.&+ +2 ? -
-
G
" #H
-
0
%
7
(+I9( &#
#::*)D
J
7
)F)D
J
/#0@D 2
-
.&+++2
J
99(+(D
G
1
J
J M$-@)= ")*
G
.1 2
9
- I< <' 9<4&#
$+D 3 J (9$)9D
7
($=M*)=5 $"QH 9D
J )- +)$+D
J
1
@
J M$-@)= ")*
7
9-(D
""
- I+ &4 9&, #
2)9$M$")=5N!#$0 $#** D
-
#T
J )- $+)$+D J
-7
#T
@)9+ D
-
G
2)9$M$")=5N!#$0 $#** D
>
.&++<2 ?
9-(D
J
J
($=M*)=5 ($-)D
8)9$)9D
J #)8 +D
J (9$)9D
G
- %T1: /
:7
90I$)=5 @)9+ D
J 9)E)9D
-7
J ") !- +D
J
F 99)0)D
. ,,42 $
-
/
<(<9<(,# /
J
7
.
J
E 9"D
(!+@D
#
6
#
. ,,I2 $
2# T
C -
G
7 4
<,9
I'#
#""#$:+D
J
#>
+++9 ++ #
-;F#**)5
@
/#*0($D
. ,,'2 C# C-
7
0
,I
K
($=M*)=5 $"QH 9D
7
J 2)9$M$")=5N!#$0 $#** D
.
2
"
.&++I2 /
-
G
7
7
#
>
&< '&<9
'&,#
9 /+@ ED
J 0)9$D 4
/
7
0
. ,''2 : " "
"
F
#
0
-
J #
2
9
7
"
" "
C-
#(D
.
#
- &4 ,<9 + #
. ,4'2 C#F
9/+D
# %
1
9)++)*D J ):)*D
7
H
-
@
7 '( <I,9<' #
. ,, 2 >
-
9
#0
G -
#F
>
>-7
7 <' ( <9
( ,#
) ,D
.&+
0
@
2 CQ
: " 7
Q
:
J
:
9^*L5
G
8)*D
#T
J
J
II
*/ D
0
(+L5
#2
9I D J
#
J
$+D 2 3 .&+
)-;#)D
J
J
F)"9 D
)
@QQGGG#G
0)F)$+($D
J
#
#
J
+0(9D
-
. ,, 2
%
+-(9# *D
!
)
:
/ -
.% #
#
@
< 9 I+#
@(/ +D
.&+++2 : " 7
2
.&+ +2
#0
#
"
/ -
.
9-I D
@ +,Q+(Q
L
-(
("9I:!)=5
# #0
:
1
9<' #
J
1
2T
7 I <
@!)- D
@QQGGG#
. ,, 2 C-
%
G
C -
(!9)#9(D
J
# &49 <&# :
T
#-
' 9 ,<#
@ 0
#T
L:\9)D
#-
(99#+($D
:
#/L$)=5 #" *:(D
9C
G
#
.&+ +2 O
+#)$#!;
-
0
J
9-I 5
79
!"I$D
0
J
7
37
-
#
($=M*)=5 $"QH 9D
J
-
7
G
:
#
>
&,
&I49 &( #
RE)**D
J
-
(!+@D
J
"(+)F#-@D
G
00@)E+D
#T
J *)E)** $D
4I9 4(# C G
J
)+-@;)D
G
0
C J (E*)+D
#>
#
. ,,+2 >
-
"
7
7 I &9 <#
. ,, 2
- 4-0
-
G
- "
0
7
@
K
)$-@ 9#D
J
/#**)9#D
-
J
#-@)D
@
J 9!$)D
9
G
J
E)$D
- G
)F)D
'
4
J (E*)+D
#T
9
:
(4 I
)F)D
J
/
#::*)D
:
J
/#0@D 2
G
94'I#
.&++42 :
#>
.&++ 2 T
-
.&+ +2 ?
0
G
J L* )D
-
# O G >-7
#-@ )*D
J )++ #$0D 2 J ) (99)D
G
9I'&#
"
7 -
I <,&9I+ #
J
(E*)+D
@
.&++<2 :
"
7
7 -
#T
1
- I< I+I9
I '#
)F)D
J
(9+E(90@ D
7 J /#0@D 7
J K)*
7 -
D
.&+ +2 /
#T
E)$D
J
#-@ )*D
J )$0($D
1
-(
J 0) "/ $D 7
G
7
)-;D
J
(!*"D 2 J **$)9D
,,V
J (E*)+D
# @
"
"
#T
1
-(
7 ,&
)9) 5 (99)+D 2 J
#*5 #8)+D
7 3
.&++ 2
@O
2# F
7
5
!
< &<9&'#
($=M*)=5 $"QH 9D
G -
. ,,<2
L# F
-
%
74
J !D N .&+ +2 %"
7
-
9
#
"
(E*)+D
7
. ,,,2 :
9
#0
J
2C G
.
%
)99 D
.&+
<<9 I #
@
%
&#
-
I(<9I <#
@
-
#0
1 " G
>
< '9<I'#
9)+0($D
J (E*)+D
.&++&2 %"
-
9
7 -
G
9 -
-
-
9
@
!
7
#?
7 44 49
<#
("9I:!)=D
"
79
% "
#-@0)9D
7&, <
#-@0)9D
7
J 4#): $"D 7 .&++,2 %"
9<
. ,,<2 >
/
3
>
7
#0
%
7
>-7
7 +&
.&++I2 6 G
G L G %
7
#
"# F
J ),,)*0D
-
@ -
J (E*)+D
,
G
'I ((9
9
#
+<'9 +I #
G
7
7
@
#
K
#-@0)9D
J KE)9:)9D
J
#T
(!RD 2 J
.&++&2 /
J
)8(!"D 3 .&++42
7@
-# >
7
>
&
F)"9 D
:
#
J $0=D
7
- "
J
/
:
)+ 5
#T
9-I D
:
7-
"
#
J
9-I 5 (99)+D
9-@)9D
7G
G
G
J )#-(+; D
%
0
.&++'2 :
('
.0"
-
@"
#
8
(*0!/D
2
&9'<#
. ,, 2 H
0
. ,4,2
(< I (9I'+#
0
,+
"
9&,#
.&++(2 -
#
J
I
7
4 9 4'#
,(; +D 7 J 2(9-)** D 2 J
8)9$)9D
-
7
>
@#90*#??)D
7
-
<<(9<I #
J !)F +D
9"#?D
7
G
(!RD 2 J )8(!"D 3 .&++'2 ?
-
9
- I& (&9 I#
9#+D
-
U00-@)9D
"
# >-# # C-
J
(E*)+D
#$ "
. ,,<2 ;
37
7
:
-
,
#
#
9
"
7
79
- 37
# >
' 9 4 #
@#**D
7
J
**(9 5 /#0@D
#T
9 $)*D
:
:
G
.&++&2 1
G
0 :9 -
-
@ T-
- " G
(+ '++9' &#
F $ ")$ )9:D 2 J
;
!
I( <<'9<I&#
J 49#:@0D
\T
. ,,'2 C-
#**# : $D
J
)9")$++)$D
G
J
9):(#9)D
J F $ ")$ (+-@D 2 .&+ +2
@
#T
1
- (+
I <9I&I#
#* 5 #!8D
J
)F)D
J (E*)+D
-
J
-
)F)D
J (E*)+D
.&++,2 6
J
)F)D
J 0) "/ $D 7
G - " "
J (E*)+D
.&++( 2 %
@ 7
-
" "
>I(+ -
4I '( 9' '#
9
!D N J
-
' '4'9', #
# O G >-7
#* 5 #!8D
7
0
# O G >-7
#* 5 #!8D
.&++( 2 1
#9$+D
J (E*)+D
7
.&++'2
7
#>
#F
0
7 -
%
!
&&( I,,9( <#
7 I& &449&,4#
0
-
-
K
3
C-
2
" 7
7
G
-
G
7 -
7
# C-
-
3
/
L G
-
-
-
7
- -
-
-
<+2 .H
-
9
-
!
#
+
-
?
G
"
# # -
7:
7 >
-
> G
# C-
-
7 -
G-
7 - - "
.&++&2
- "
C-
7
2
-
" 7
-
"
G- -
-
L
7
-
"
G
- 7
G
"
7 -
"
G- -
" "
-
- :
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
?
-
- 7
)?)9)$-)+
90 5
6
.&++I2
9E
Q
E
6
1 5
#
L
9
# . ,,42
# . ,, 2
> G
# .&++42
# .&++(2
>
/ K 90
.&++&2
-
"
-
2
3
)-;#)D
J
:
**D
'(
!+#D
J
.&++42 :
3@
9
G# >
(9 &4#
!D N J
99)005 )$$ 9"D
J
(E*)+D
-
.&++42
# C-
2)9$M$")=5N!#$0 $#** D
J )- +)$+D
J
G
0
($=M*)=5 $"QH 9D
J M$-@)= ")*
9-(D
J
-
7
'
($=M*)=5 ($-)D
J #)8 +D
:7
2
"
&4 9 &,+#
J ") !- +D
J
F 99)0)D
. ,,42 $
-
/
<(<9<(,# /
J 2)9$M$")=5N!#$0 $#** D
.
G
J (9$)9D
G
- %T1: /
($=M*)=5 $"QH 9D
J
8)9$)9D
.1 2
>
9
6
.&++I2 /
G
#
#
7
7
#
>
&< '&<9
'&,#
)$-@ 9#D
79
J @ !F)*D
J
7
37
0
#F
)-;D
J
9/)$- D
J L* )D
.&++42 6
G
0
%
-
L9
7 I( ,<,9,I'#
(!*"D 2 J **$)9D
. ,,,2 :
7 3
@
%
.
%
9)+0($D
G - -
7 ,&
J (E*)+D
9
2# F
#
.&++&2 %"
9
@O
7 -
G
9 -
@
!
-
7
#?
7 44 49
<#
H +); 9 $D 7 J
.-
9!* D
#2
,
(9 &I#
4J
$")9+($D
. ,, 2 :
7
-
# >
:
K
("9I:!)=D
"
79
% "
9<
F)"9 D
J !)F +D J
-
#
:
-
7&, <
#* 5 #!8D
-
J 4#): $"D 7 .&++,2 %"
)F)D
G
@ -
-
7
#0
7
%
#
)+ 5
9-I D J
>
J
9
9-I 5 (99)+D
. ,4,2
7G
4 9 4'#
J 0) "/ $D 7
9
J (E*)+D
.&++(2 %
@ 7
-
7
#F
0
%
7 I& &449&4,#
G
7
($-*!+#($)+ ?#$ *)+
K
2
#$
-
"8
5
7
5 # Z
!
"
#
&# $
7
5
-
#
!
7
5
"
# %
5
"
)
7
7
#
<#
-
8
7
5
I#
#
"
"
5
7
#%
"
# 0
"
5
"
7
8
"
"
7Q
"
-
(#
5
"
#
5
" "#
7
"
" 2 7
-
" .# #
.# # -
2
-
5
"
!
#
-
5
#
#%
7 5
8
"
3
"
5 #
K
'# %
7
-
"
!
5
-
3
>
#
-
!
5
!
-
5
"
5 #
4#
7
"
5 7
5
#%
"
7
7
! 8
!
7
-
7
""
7
8
7
#
,#
7
5
#
-
7
#%
5
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...