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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 
"" 0 "" {TEXT -1 97 "The Maple notebook for Gavrilets, S. and M.Cruzan
 \"Neutral gene flow accross single locus clines\"" }}{SECT 1 {PARA 4 
"" 0 "" {TEXT -1 20 "Adult migration case" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 107 "Gene flow in a neutral locus linked to another locus und
er general fertility selection defined by matrix F\n" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 95 "X:=array(1..4,1..4):                    # genoty
pe frequencies in this generation in location 1" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 95 "Y:=array(1..4,1..4):                    # geno
type frequencies in this generation in location 2" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 85 "R:=array(1..4,1..4,1..4):               # pr
obability to get gamete i from parent j/k" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 551 "F:=array(1..3,1..3):                    # fertilit
y matrix; fertilities depend on the genotypes at the first locus\n f:=
proc(k,l,m,n) local I,J; if k<=2  then if l<=2  then  I:=1  else I:=2 \+
 fi fi;\n                                            if k>=3  then if \+
l>=3  then  I:=3  else I:=2  fi fi;\n                                 \+
           if m<=2 then if n<=2 then J:=1  else J:=2 fi fi;\n         \+
                                   if m>=3 then if n>=3 then J:=3  els
e J:=2 fi fi;\n                                            RETURN( F[I
,J] );     end;\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"fG:6&%\"kG%\"
lG%\"mG%\"nG6$%\"IG%\"JG6\"F.C'@$19$\"\"#@%19%F3>8$\"\"\">F8F3@$1\"\"$
F2@%1F=F6>F8F=>F8F3@$19&F3@%19'F3>8%F9>FIF3@$1F=FD@%1F=FG>FIF=>FIF3-%'
RETURNG6#&%\"FG6$F8FIF.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
86 "F[1,1]:=alpha[1]: F[1,2]:=beta[1]:   F[1,3]:=gamma:       # symmet
ric fertility matrix" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "F[2
,1]:=beta[1]:     F[2,2]:=delta:  F[2,3]:=beta[2]:" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 50 "F[3,1]:=gamma: F[3,2]:=beta[2]:  F[3,3]:=al
pha[2]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "print(F);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7%7%&%&alphaG6#\"\"\"&%%be
taGF*%&gammaG7%F,%&deltaG&F-6#\"\"#7%F.F1&F)F2" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 114 "R[1,1,1]:=1:           R[2,1,1]:=0:     R[3,1
,1]:=0:     R[4,1,1]:=0:                 # recombination distribution
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "R[1,1,2]:=1/2:        \+
R[2,1,2]:=1/2:  R[3,1,2]:=0:     R[4,1,2]:=0:                 # R(i,j,
k) is the probability" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 114 "R
[1,1,3]:=1/2:        R[2,1,3]:=0:     R[3,1,3]:=1/2:  R[4,1,3]:=0:    \+
             # that genotype (j,k) produces" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 88 "R[1,1,4]:=(1-r)/2:  R[2,1,4]:=r/2:  R[3,1,4]:=r/2:
   R[4,1,4]:=(1-r)/2:       # gamete i" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "R[1,2,1
]:=1/2:     R[2,2,1]:=1/2:          R[3,2,1]:=0:           R[4,2,1]:=0
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "R[1,2,2]:=0:        R[
2,2,2]:=1:             R[3,2,2]:=0:           R[4,2,2]:=0:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "R[1,2,3]:=r/2:      R[2,2,3]:=(1-r)
/2:   R[3,2,3]:=(1-r)/2:  R[4,2,3]:=r/2:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 81 "R[1,2,4]:=0:        R[2,2,4]:=1/2:          R[3,2,4]:
=0:           R[4,2,4]:=1/2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "R[1,3,1]:=1/2:    \+
 R[2,3,1]:=0:             R[3,3,1]:=1/2:        R[4,3,1]:=0:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "R[1,3,2]:=r/2:     R[2,3,2]:
=(1-r)/2:    R[3,3,2]:=(1-r)/2:  R[4,3,2]:=r/2:" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 80 "R[1,3,3]:=0:        R[2,3,3]:=0:             R
[3,3,3]:=1:           R[4,3,3]:=0:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 81 "R[1,3,4]:=0:        R[2,3,4]:=0:             R[3,3,4]
:=1/2:        R[4,3,4]:=1/2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "R[1,4,1]:=(1-r)/2:
   R[2,4,1]:=r/2:     R[3,4,1]:=r/2:     R[4,4,1]:=(1-r)/2:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "R[1,4,2]:=0:            R[2,
4,2]:=1/2:     R[3,4,2]:=0:       R[4,4,2]:=1/2:" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 76 "R[1,4,3]:=0:            R[2,4,3]:=0:        R
[3,4,3]:=1/2:    R[4,4,3]:=1/2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 76 "R[1,4,4]:=0:            R[2,4,4]:=0:        R[3,4,4]:=0:      \+
 R[4,4,4]:=1: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "NextX:=p
roc(i,j)  local Z,k,l,m,n; Z:=0:                          # genotype f
requency in the next generation" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "
for k from 1 to 4 do for l from 1 to 4 do for m from 1 to 4 do for n f
rom 1 to 4 do " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "                \+
                 Z:=Z+X[k,l]*X[m,n]*f(k,l,m,n)*(R[i,k,l]*R[j,m,n]+R[j,
k,l]*R[i,m,n])/2 " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "              \+
                   od od od od      end;" }}{PARA 12 "" 1 "" {XPPMATH 
20 "6#>%&NextXG:6$%\"iG%\"jG6'%\"ZG%\"kG%\"lG%\"mG%\"nG6\"F/C$>8$\"\"!
?(8%\"\"\"F6\"\"%%%trueG?(8&F6F6F7F8?(8'F6F6F7F8?(8(F6F6F7F8>F2,&F2F6*
*&%\"XG6$F5F:F6&FC6$F<F>F6-%\"fG6&F5F:F<F>F6,&*&&%\"RG6%9$F5F:F6&FM6%9
%F<F>F6F6*&&FM6%FRF5F:F6&FM6%FOF<F>F6F6F6#F6\"\"#F/F/" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 109 "NextY:=proc(i,j)  local Z,k,l,m,n; Z:=0:            \+
              # genotype frequency in the next generation" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 84 "for k from 1 to 4 do for l from 1 to 4 do fo
r m from 1 to 4 do for n from 1 to 4 do " }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 103 "                                 Z:=Z+Y[k,l]*Y[m,n]*
f(k,l,m,n)*(R[i,k,l]*R[j,m,n]+R[j,k,l]*R[i,m,n])/2 " }}{PARA 0 "> " 0 
"" {MPLTEXT 1 0 54 "                                 od od od od      \+
end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&NextYG:6$%\"iG%\"jG6'%\"ZG%
\"kG%\"lG%\"mG%\"nG6\"F/C$>8$\"\"!?(8%\"\"\"F6\"\"%%%trueG?(8&F6F6F7F8
?(8'F6F6F7F8?(8(F6F6F7F8>F2,&F2F6**&%\"YG6$F5F:F6&FC6$F<F>F6-%\"fG6&F5
F:F<F>F6,&*&&%\"RG6%9$F5F:F6&FM6%9%F<F>F6F6*&&FM6%FRF5F:F6&FM6%FOF<F>F
6F6F6#F6\"\"#F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "Eq:=proc(i,j)               \+
                        # equilibrium values" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 83 "(1-m-m0)*NextX(i,j)+m*NextY(i,j)-X[i,j]:            #
 excluding the case i=j=1 !!!!" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 " \+
                                     end;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#EqG:6$%\"iG%\"jG6\"F)F),(*&,(\"\"\"F-%\"mG!\"\"%#m0G
F/F--%&NextXG6$9$9%F-F-*&F.F--%&NextYGF3F-F-&%\"XGF3F/F)F)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 999 "pert:=[X[1,1]=1-m*x[1,1], X[1,2]=m
*x[1,2], X[1,3]=m*x[1,3], X[1,4]=m*x[1,4],                            \+
                                X[2,1]=m*x[2,1],     X[2,2]=m*x[2,2], \+
X[2,3]=m*x[2,3], X[2,4]=m*x[2,4],                                     \+
                        X[3,1]=m*x[3,1],     X[3,2]=m*x[3,2], X[3,3]=m
*x[3,3], X[3,4]=m*x[3,4],                                             \+
                X[4,1]=m*x[4,1],     X[4,2]=m*x[4,2], X[4,3]=m*x[4,3],
 X[4,4]=m*x[4,4],                                                     \+
        Y[1,1]=m*y[1,1],    Y[1,2]=m*y[1,2], Y[1,3]=m*y[1,3], Y[1,4]=m
*y[1,4],                                                            Y[
2,1]=m*y[2,1],    Y[2,2]=m*y[2,2], Y[2,3]=m*y[2,3], Y[2,4]=m*y[2,4],  \+
                                                          Y[3,1]=m*y[3
,1],    Y[3,2]=m*y[3,2], Y[3,3]=m*y[3,3], Y[3,4]=m*y[3,4],            \+
                                                Y[4,1]=m*y[4,1],    Y[
4,2]=m*y[4,2], Y[4,3]=m*y[4,3], Y[4,4]=1-m*y[4,4]  ]  :" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "subs(pert,Eq(2,2)): subs(m=0,\"); d
iff(\"\",m): subs(m=0,\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$&%\"xG6$\"\"#F'!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "x[2,2]:=0: subs(pert,Eq(2,3)): subs
(m=0,\"); diff(\"\",m): subs(m=0,\");" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$&%\"xG6$\"\"#\"\"$!\"\"
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "x[2,3]:=0: subs(pert,Eq
(2,4)): subs(m=0,\"); diff(\"\",m): subs(m=0,\");" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$&%\"xG6$\"\"
#\"\"%!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "x[2,4]:=0: s
ubs(pert,Eq(3,3)): subs(m=0,\"); diff(\"\",m): subs(m=0,\");" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$&
%\"xG6$\"\"$F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "x[3,
3]:=0: subs(pert,Eq(3,4)): subs(m=0,\"); diff(\"\",m): subs(m=0,\");" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,$&%\"xG6$\"\"$\"\"%!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 68 "x[3,4]:=0: subs(pert,Eq(4,4)): subs(m=0,\"); diff(\"\",m): sub
s(m=0,\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#,&&%&alphaG6#\"\"#\"\"\"&%\"xG6$\"\"%F,!\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "x[4,4]:=alpha[2]: " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "x[2,1]:=x[1,2]:  x[3,1]:=x[1
,3]:  x[3,2]:=x[2,3]: x[4,1]:=x[1,4]: x[4,2]:=x[2,4]: x[4,3]:=x[3,4]:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "subs(pert,Eq(1,4)): sub
s(m=0,\"); diff(\"\",m): subs(m=0,\");" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&,&\"\"\"F&%#m0G!\"
\"F&,&*&&%&alphaG6#\"\"#F&%&gammaGF&F&*(&%\"xG6$F&\"\"%F&&%%betaG6#F&F
&,&#F&F.F&%\"rG#F(F.F&F.F&F&F1F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "solve(\"=0,x[1,4]):       factor(\");" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#**&%&alphaG6#\"\"#\"\"\"%&gammaGF(,&!\"\"F(%#m0GF(
F(,,&%%betaG6#F(F(*&F.F(%\"rGF(F+*&F,F(F.F(F+*(F,F(F.F(F2F(F(F+F(F+" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "factor(1+denom(\"\"));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#*(&%%betaG6#\"\"\"F',&!\"\"F'%#m0GF'F'
,&F)F'%\"rGF'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "subs(per
t,Eq(1,2)): subs(m=0,\"); diff(\"\",m): subs(m=0,\");" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&&%\"xG6
$\"\"\"\"\"#!\"\"*&,&F'F'%#m0GF)F',&*(&F%6$F'\"\"%F'&%%betaG6#F'F'%\"r
GF'F'*&F$F'&%&alphaGF4F'F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 27 "factor( solve(\"=0,x[1,2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#,$*,,&!\"\"\"\"\"%#m0GF'F'&%\"xG6$F'\"\"%F'&%%betaG6#F'F'%\"rGF',(F'
F'&%&alphaGF/F&*&F2F'F(F'F'F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 57 "subs(pert,Eq(1,3)): subs(m=0,\"); diff(\"\",m): subs(m=0,\");
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&&%\"xG6$\"\"\"\"\"$!\"\"*&,&F'F'%#m0GF)F',&*&F$F'&%%b
etaG6#F'F'F'*(&F%6$F'\"\"%F'F/F'%\"rGF'F'F'F'" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 27 "factor( solve(\"=0,x[1,3]));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#,$*,,&!\"\"\"\"\"%#m0GF'F'&%\"xG6$F'\"\"%F'&%%betaG6#
F'F'%\"rGF',(F'F'F-F&*&F(F'F-F'F'F&F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 74 "x[4,4]:=alpha[2]; x[1,4]:=(1-m0)*alpha[2]*gamma/(1-(1
-m0)*beta[1]*(1-r)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6$\"\"
%F'&%&alphaG6#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6$\"\"\"
\"\"%**,&F'F'%#m0G!\"\"F'&%&alphaG6#\"\"#F'%&gammaGF',&F'F'*(F*F'&%%be
taG6#F'F',&F'F'%\"rGF,F'F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 52 "x[1,2]:=(1-m0)*beta[1]*r*x[1,4]/(1-(1-m0)*alpha[1]);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6$\"\"\"\"\"#*0,&F'F'%#m0G!\"\"F(&%%b
etaG6#F'F'%\"rGF'&%&alphaG6#F(F'%&gammaGF',&F'F'*(F*F'F-F',&F'F'F0F,F'
F,F,,&F'F'*&F*F'&F2F/F'F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
51 "x[1,3]:=(1-m0)*beta[1]*r*x[1,4]/(1-(1-m0)*beta[1]);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>&%\"xG6$\"\"\"\"\"$*0,&F'F'%#m0G!\"\"\"\"#&%%be
taG6#F'F'%\"rGF'&%&alphaG6#F-F'%&gammaGF',&F'F'*(F*F'F.F',&F'F'F1F,F'F
,F,,&F'F'*&F*F'F.F'F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "
simplify( x[1,3]+x[1,4]+x[4,4]);                        # frequency of
 the selected allele a" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,,&%%betaG
6#\"\"\"!\"\"*&%#m0GF(F%F(F(*&%&gammaGF(F+F(F)F-F(F(F(F(&%&alphaG6#\"
\"#F(,(F(F(F%F)F*F(F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "fre
qa:=\";" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&freqaG*(,,&%%betaG6#\"\"
\"!\"\"*&%#m0GF*F'F*F**&%&gammaGF*F-F*F+F/F*F*F*F*&%&alphaG6#\"\"#F*,(
F*F*F'F+F,F*F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "factor(1+
numer(freqa)); factor(1+denom(freqa));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "*&,&!\"\"\"\"\"%#m0GF%F%,&%%betaGF%%&gammaGF$F%" }}{PARA 11 "" 1 "
" {XPPMATH 20 "*&,&!\"\"\"\"\"%#m0GF%F%,&F$F%%%betaGF%F%" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "simplify( x[1,2]+x[1,4]+x[4,4]);   \+
                    # frequency of the neutral allele m " }}{PARA 11 "
" 1 "" {XPPMATH 20 "*(,@%\"rG\"\"\"*&F$F%%&gammaGF%!\"\"*&%%betaGF%F$F
%F(*(F$F%F*F%F'F%F%*&%#m0GF%F$F%F(*(F$F%F-F%F'F%\"\"#*(F-F%F*F%F$F%F%*
*F$F%F-F%F*F%F'F%!\"#*(F$F%F-F/F'F%F(**F$F%F-F/F*F%F'F%F%F-F%*&F-F%F'F
%F(*&F-F/F'F%F%*&F-F%F*F%F%*&F-F/F*F%F(F%,0F$F%F*F%F)F(F-F%F,F(F7F(F0F
%F(F-F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "freqm:=\":" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "numer(freqm);" }}{PARA 11 "
" 1 "" {XPPMATH 20 ",@%\"rG\"\"\"*&F#F$%&gammaGF$!\"\"*&%%betaGF$F#F$F
'*(F#F$F)F$F&F$F$*&%#m0GF$F#F$F'*(F#F$F,F$F&F$\"\"#*(F,F$F)F$F#F$F$**F
#F$F,F$F)F$F&F$!\"#*(F#F$F,F.F&F$F'**F#F$F,F.F)F$F&F$F$F,F$*&F,F$F&F$F
'*&F,F.F&F$F$*&F,F$F)F$F$*&F,F.F)F$F'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "factor( diff(\",r));" }}{PARA 11 "" 1 "" {XPPMATH 20 
"*(,&!\"\"\"\"\"%#m0GF%F%,(*&F&F%%&gammaGF%F%F%F%F)F$F%,&F$F%%%betaGF%
F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "factor(  -1+numer(fre
qm));" }}{PARA 11 "" 1 "" {XPPMATH 20 "*&,&!\"\"\"\"\"%#m0GF%F%,4*(%\"
rGF%F&F%%&gammaGF%F$*&F&F%F*F%F%**F)F%F&F%%%betaGF%F*F%F%*&F&F%F-F%F$F
)F$*&F)F%F*F%F%*&F-F%F)F%F%*(F)F%F-F%F*F%F$F%F%F%" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 13 "F:=\"/(-1+m0);" }}{PARA 11 "" 1 "" {XPPMATH 
20 ">%\"FG,4*(%\"rG\"\"\"%#m0GF'%&gammaGF'!\"\"*&F(F'F)F'F'**F&F'F(F'%
%betaGF'F)F'F'*&F(F'F-F'F*F&F**&F&F'F)F'F'*&F-F'F&F'F'*(F&F'F-F'F)F'F*
F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "factor( diff(F,m0))
;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**&%\"rG\"\"\"%&gammaGF%!\"\"F&F%*
(F$F%%%betaGF%F&F%F%F)F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "
" 0 "" {TEXT -1 19 "Seed migration case" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 220 "Gene flow in a neutral locus linked to another locus und
er general viability-fertility selection.\nFertilities are defined by \+
matrix F; viabilities are defined by matrix G\nplants don't move! - so
 it's pollen that migrates" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(
linalg):" }}{PARA 2 "" 1 "" {TEXT -1 71 "Warning: new definition for  \+
 norm\nWarning: new definition for   trace\n" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 97 "X:=array(1..4,1..4):                      # geno
type frequencies in this generation in location 1" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 97 "Y:=array(1..4,1..4):                      # \+
genotype frequencies in this generation in location 2" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "M:=array(1..4,1..4)               \+
       # genotype frequencies of fathers of the pollen coming to loc1
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "R:=array(1..4,1..4,1..4):      \+
         # probability to get gamete i from parent jk" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "Q:=matrix(4,4,[[1,0,0,0],[0,0,0,0]
,[0,0,0,0],[0,0,0,0]]):         # frequencies in the left-most populat
ions" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "print(Q);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "-%'MATRIXG6#7&7&\"\"\"\"\"!F(F(7&F(F(F(F(F)F)
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 553 "F:=array(1..3,1..3):  \+
                    # fertility matrix; fertilities depend on the geno
types at the first locus\n f:=proc(k,l,m,n) local I,J; if k<=2  then i
f l<=2  then  I:=1  else I:=2  fi fi;\n                               \+
             if k>=3  then if l>=3  then  I:=3  else I:=2  fi fi;\n   \+
                                         if m<=2 then if n<=2 then J:=
1  else J:=2 fi fi;\n                                            if m>
=3 then if n>=3 then J:=3  else J:=2 fi fi;\n                         \+
                   RETURN( F[I,J] );     end;\n" }}{PARA 12 "" 1 "" 
{XPPMATH 20 ">%\"fG:6&%\"kG%\"lG%\"mG%\"nG6$%\"IG%\"JG6\"F-C'@$19$\"\"
#@%19%F2>8$\"\"\">F7F2@$1\"\"$F1@%1F<F5>F7F<F9@$19&F2@%19'F2>8%F8>FGF2
@$1F<FB@%1F<FE>FGF<FH-%'RETURNG6#&%\"FG6$F7FGF-F-" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 2 "  " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
105 "G:=matrix(4,4,[[v[1],v[1],v[h],v[h]],[v[1],v[1],v[h],v[h]],[v[h],
v[h],v[2],v[2]],[v[h],v[h],v[2],v[2]]]);" }}{PARA 11 "" 1 "" {XPPMATH 
20 ">%\"GG-%'MATRIXG6#7&7&&%\"vG6#\"\"\"F)&F*6#%\"hGF-F(7&F-F-&F*6#\"
\"#F1F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "F:=matrix(3,3,[ \+
[alpha[1],beta[1],gamma], [beta[1],delta,beta[2]], [gamma,beta[2],alph
a[2]]] );" }}{PARA 11 "" 1 "" {XPPMATH 20 ">%\"FG-%'MATRIXG6#7%7%&%&al
phaG6#\"\"\"&%%betaGF+%&gammaG7%F-%&deltaG&F.6#\"\"#7%F/F2&F*F3" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 114 "R[1,1,1]:=1:           R[2,
1,1]:=0:     R[3,1,1]:=0:     R[4,1,1]:=0:                 # recombina
tion distribution" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "R[1,1
,2]:=1/2:        R[2,1,2]:=1/2:  R[3,1,2]:=0:     R[4,1,2]:=0:        \+
         # R(i,j,k) is the probability" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 114 "R[1,1,3]:=1/2:        R[2,1,3]:=0:     R[3,1,3]:=1/2
:  R[4,1,3]:=0:                 # that genotype (j,k) produces" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "R[1,1,4]:=(1-r)/2:  R[2,1,4]
:=r/2:  R[3,1,4]:=r/2:   R[4,1,4]:=(1-r)/2:       # gamete i" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 78 "R[1,2,1]:=1/2:     R[2,2,1]:=1/2:          R[3,2,1]
:=0:           R[4,2,1]:=0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
80 "R[1,2,2]:=0:        R[2,2,2]:=1:             R[3,2,2]:=0:         \+
  R[4,2,2]:=0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "R[1,2,3]:
=r/2:      R[2,2,3]:=(1-r)/2:   R[3,2,3]:=(1-r)/2:  R[4,2,3]:=r/2:" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "R[1,2,4]:=0:        R[2,2,4
]:=1/2:          R[3,2,4]:=0:           R[4,2,4]:=1/2:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 78 "R[1,3,1]:=1/2:     R[2,3,1]:=0:             R[3,3,1]:
=1/2:        R[4,3,1]:=0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
75 "R[1,3,2]:=r/2:     R[2,3,2]:=(1-r)/2:    R[3,3,2]:=(1-r)/2:  R[4,3
,2]:=r/2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "R[1,3,3]:=0:  \+
      R[2,3,3]:=0:             R[3,3,3]:=1:           R[4,3,3]:=0:" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "R[1,3,4]:=0:        R[2,3,4
]:=0:             R[3,3,4]:=1/2:        R[4,3,4]:=1/2:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 77 "R[1,4,1]:=(1-r)/2:   R[2,4,1]:=r/2:     R[3,4,1]:=r/2
:     R[4,4,1]:=(1-r)/2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 
"R[1,4,2]:=0:            R[2,4,2]:=1/2:     R[3,4,2]:=0:       R[4,4,2
]:=1/2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "R[1,4,3]:=0:    \+
        R[2,4,3]:=0:        R[3,4,3]:=1/2:    R[4,4,3]:=1/2:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "R[1,4,4]:=0:            R[2,
4,4]:=0:        R[3,4,4]:=0:       R[4,4,4]:=1: " }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 
"M:=proc(i,j)  (1-m-m0)*X[i,j]+m*Y[i,j]+m0*Q[i,j]:    end;  # frequenc
ies among pollen's parents" }}{PARA 11 "" 1 "" {XPPMATH 20 ">%\"MG:6$%
\"iG%\"jG6\"F(F(,(*&,(\"\"\"F,%\"mG!\"\"%#m0GF.F,&%\"XG6$9$9%F,F,*&F-F
,&%\"YGF2F,F,*&F/F,&%\"QGF2F,F,F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 229 "NextX:=proc(i,j)  local \+
Z,k,l,m,n; Z:=0:    for k from 1 to 4 do for l from 1 to 4 do for m fr
om 1 to 4 do for n from 1 to 4 do Z:=Z+X[k,l]*M(m,n)*f(k,l,m,n)*(R[i,k
,l]*R[j,m,n]+R[j,k,l]*R[i,m,n])/2*G[i,j]  od od od od     end;   " }}
{PARA 12 "" 1 "" {XPPMATH 20 ">%&NextXG:6$%\"iG%\"jG6'%\"ZG%\"kG%\"lG%
\"mG%\"nG6\"F.C$>8$\"\"!?(8%\"\"\"F5\"\"%%%trueG?(8&F5F5F6F7?(8'F5F5F6
F7?(8(F5F5F6F7>F1,&F1F5*,&%\"XG6$F4F9F5-%\"MG6$F;F=F5-%\"fG6&F4F9F;F=F
5,&*&&%\"RG6%9$F4F9F5&FM6%9%F;F=F5F5*&&FM6%FRF4F9F5&FM6%FOF;F=F5F5F5&%
\"GG6$FOFRF5#F5\"\"#F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 
"wmeanX:= sum ( 'sum( 'NextX(i,j)','i'=1..4)','j'=1..4):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 123 "Eq:=proc(i,j)       NextX(i,j)/wmeanX -X[i,j]:      \+
  end;                                                                \+
 " }}{PARA 11 "" 1 "" {XPPMATH 20 ">%#EqG:6$%\"iG%\"jG6\"F(F(,&*&-%&Ne
xtXG6$9$9%\"\"\"%'wmeanXG!\"\"F0&%\"XGF-F2F(F(" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 999 "pert:=[X[1,1]=1-m*x[1,1], X[1,2]=m*x[1,2], X[
1,3]=m*x[1,3], X[1,4]=m*x[1,4],                                       \+
                     X[2,1]=m*x[2,1],     X[2,2]=m*x[2,2], X[2,3]=m*x[
2,3], X[2,4]=m*x[2,4],                                                \+
             X[3,1]=m*x[3,1],     X[3,2]=m*x[3,2], X[3,3]=m*x[3,3], X[
3,4]=m*x[3,4],                                                        \+
     X[4,1]=m*x[4,1],     X[4,2]=m*x[4,2], X[4,3]=m*x[4,3], X[4,4]=m*x
[4,4],                                                             Y[1
,1]=m*y[1,1],    Y[1,2]=m*y[1,2], Y[1,3]=m*y[1,3], Y[1,4]=m*y[1,4],   \+
                                                         Y[2,1]=m*y[2,
1],    Y[2,2]=m*y[2,2], Y[2,3]=m*y[2,3], Y[2,4]=m*y[2,4],             \+
                                               Y[3,1]=m*y[3,1],    Y[3
,2]=m*y[3,2], Y[3,3]=m*y[3,3], Y[3,4]=m*y[3,4],                       \+
                                     Y[4,1]=m*y[4,1],    Y[4,2]=m*y[4,
2], Y[4,3]=m*y[4,3], Y[4,4]=1-m*y[4,4]  ]  :" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 57 "subs(pert,Eq(2,2)): subs(m=0,\"); diff(\"\",m): \+
subs(m=0,\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 
"" {XPPMATH 20 ",$&%\"xG6$\"\"#F&!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "x[2,2]:
=0: subs(pert,Eq(2,3)): subs(m=0,\"); diff(\"\",m): subs(m=0,\");" }}
{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",
$&%\"xG6$\"\"#\"\"$!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 
"x[2,3]:=0: subs(pert,Eq(2,4)): subs(m=0,\"); diff(\"\",m): subs(m=0,
\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",$&%\"xG6$\"\"#\"\"%!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 68 "x[2,4]:=0: subs(pert,Eq(3,3)): subs(m=0,\"); diff(\"
\",m): subs(m=0,\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 
11 "" 1 "" {XPPMATH 20 ",$&%\"xG6$\"\"$F&!\"\"" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 68 "x[3,3]:=0: subs(pert,Eq(3,4)): subs(m=0,\"); d
iff(\"\",m): subs(m=0,\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}
{PARA 11 "" 1 "" {XPPMATH 20 ",$&%\"xG6$\"\"$\"\"%!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "x[3,4]:=0: subs(pert,Eq(4,4)): subs
(m=0,\"); diff(\"\",m): subs(m=0,\");" }}{PARA 11 "" 1 "" {XPPMATH 20 
"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$&%\"xG6$\"\"%F&!\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "x[4,4]:=0: " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "x[2,1]:=x[1,2]:  x[3,1]:=x[1,3]:  x
[3,2]:=x[2,3]: x[4,1]:=x[1,4]: x[4,2]:=x[2,4]: x[4,3]:=x[3,4]:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "subs(pert,Eq(1,4)): subs(m=0
,\"); diff(\"\",m): subs(m=0,\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"
\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*(,(**&%\"xG6$\"\"\"\"\"%F)&%%b
etaG6#F)F),&#F)\"\"#F)%\"rG#!\"\"F0F)&%\"vG6#%\"hGF)F)*,,&F)F)%#m0GF3F
)F&F)F+F)F.F)F4F)F)*&%&gammaGF)F4F)F/F)&%&alphaGF-F3&F5F-F3F)F&F3" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "solve(\"=0,x[1,4]);" }}
{PARA 11 "" 1 "" {XPPMATH 20 ",$*,&%&alphaG6#\"\"\"!\"\"&%\"vGF&F(%&ga
mmaGF'&F*6#%\"hGF',,**F$F(F)F(&%%betaGF&F'F,F'F'*,F$F(F)F(F1F'F,F'%\"r
GF'F(*,F$F(F)F(F1F'F,F'%#m0GF'#F(\"\"#*.F$F(F)F(F1F'F,F'F6F'F4F'#F'F8F
(F'F(F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(\");" }}
{PARA 11 "" 1 "" {XPPMATH 20 ",$*(%&gammaG\"\"\"&%\"vG6#%\"hGF%,,*&&%%
betaG6#F%F%F&F%\"\"#*(F,F%F&F%%\"rGF%!\"#*(F,F%F&F%%#m0GF%!\"\"**F,F%F
&F%F4F%F1F%F%*&&%&alphaGF.F%&F'F.F%F2F5F5" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 36 "factor( subs( alpha[1]=0,denom(\")));" }}{PARA 11 "
" 1 "" {XPPMATH 20 "**&%%betaG6#\"\"\"F&&%\"vG6#%\"hGF&,&!\"#F&%#m0GF&
F&,&!\"\"F&%\"rGF&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 57 "subs(pert,Eq(1,2)): subs(m=0,\"); diff(\"
\",m): subs(m=0,\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 
11 "" 1 "" {XPPMATH 20 ",&*(,**(&%\"xG6$\"\"\"\"\"#F)&%&alphaG6#F)F)&%
\"vGF-F)#F)F***&F'6$F)\"\"%F)&%%betaGF-F)%\"rGF)F.F)F0**,&F)F)%#m0G!\"
\"F)F&F)F+F)F.F)F0*,F9F)F2F)F5F)F7F)F.F)F0F)F+F;F.F;F)F&F;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "factor( solve(\"=0,x[1,2]));" }}
{PARA 11 "" 1 "" {XPPMATH 20 ",$*.&%\"xG6$\"\"\"\"\"%F'&%%betaG6#F'F'%
\"rGF',&!\"#F'%#m0GF'F'&%&alphaGF+!\"\"F/F2F2" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 57 "subs(pert,Eq(1,3)): subs(m=0,\"); diff(\"\",m): \+
subs(m=0,\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 
"" {XPPMATH 20 ",&*(,***&%\"xG6$\"\"\"\"\"%F)&%%betaG6#F)F)%\"rGF)&%\"
vG6#%\"hGF)#F)\"\"#*(&F'6$F)\"\"$F)F+F)F/F)F3*,,&F)F)%#m0G!\"\"F)F&F)F
+F)F.F)F/F)F3**F:F)F6F)F+F)F/F)F3F)&%&alphaGF-F<&F0F-F<F)F6F<" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "factor( solve(\"=0,x[1,3]));
" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*.&%\"xG6$\"\"\"\"\"%F'&%%betaG6#F
'F'%\"rGF'&%\"vG6#%\"hGF',&!\"#F'%#m0GF'F',(*&F)F'F-F'F2*(F)F'F-F'F3F'
F'*&&%&alphaGF+F'&F.F+F'\"\"#!\"\"F<" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 75 "x[4,4]:=0; x[1,4]:=gamma*v[h]/(2*alpha[1]*v[1]-(2-m0)
*(1-r)*beta[1]*v[h]); " }}{PARA 11 "" 1 "" {XPPMATH 20 ">&%\"xG6$\"\"%
F&\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&%\"xG6$\"\"\"\"\"%*(%&gamma
GF&&%\"vG6#%\"hGF&,&*&&%&alphaG6#F&F&&F+F2F&\"\"#**,&F4F&%#m0G!\"\"F&,
&F&F&%\"rGF8F&&%%betaGF2F&F*F&F8F8" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 46 "x[1,2]:=(2-m0)*beta[1]*r/(alpha[1]*m0)*x[1,4];" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">&%\"xG6$\"\"\"\"\"#*2,&F'F&%#m0G!\"\"F&
&%%betaG6#F&F&%\"rGF&&%&alphaGF.F+F*F+%&gammaGF&&%\"vG6#%\"hGF&,&*&F0F
&&F4F.F&F'**F)F&,&F&F&F/F+F&F,F&F3F&F+F+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 75 "x[1,3]:=(2-m0)*beta[1]*v[h]*r/(2*alpha[1]*v[1]-(2-m0)
*beta[1]*v[h])*x[1,4];" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&%\"xG6$\"\"
\"\"\"$*0,&\"\"#F&%#m0G!\"\"F&&%%betaG6#F&F&&%\"vG6#%\"hGF*%\"rGF&,&*&
&%&alphaGF/F&&F1F/F&F**(F)F&F-F&F0F&F,F,%&gammaGF&,&F6F***F)F&,&F&F&F4
F,F&F-F&F0F&F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "simplif
y( x[1,3]+x[1,4]+x[4,4]);                        # frequency of the se
lected allele a" }}{PARA 11 "" 1 "" {XPPMATH 20 "*(%&gammaG\"\"\"&%\"v
G6#%\"hGF$,(*&&%%betaG6#F$F$F%F$!\"#*(F+F$F%F$%#m0GF$F$*&&%&alphaGF-F$
&F&F-F$\"\"#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "freqa:=
\";" }}{PARA 11 "" 1 "" {XPPMATH 20 ">%&freqaG*(%&gammaG\"\"\"&%\"vG6#
%\"hGF&,(*&&%%betaG6#F&F&F'F&!\"#*(F-F&F'F&%#m0GF&F&*&&%&alphaGF/F&&F(
F/F&\"\"#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 " factor( \+
subs(m0=0,freqa));" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*(%&gammaG\"\"\"
&%\"vG6#%\"hGF%,&*&&%%betaG6#F%F%F&F%!\"\"*&&%&alphaGF.F%&F'F.F%F%F/#F
%\"\"#" }}}{EXCHG {PARA 11 "" 1 "" {XPPMATH 20 ",$*&,**&%&gammaG\"\"\"
&%\"vG6#%\"hGF'!\"\"*&&%%betaG6#F'F'F(F'!\"#*(F.F'F(F'%#m0GF'F'*&&%&al
phaGF0F'&F)F0F'\"\"#F',(F-F1F2F'F4F8F,F," }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 91 "simplify( x[1,2]+x[1,4]+x[4,4]);                     \+
  # frequency of the neutral allele m " }}{PARA 11 "" 1 "" {XPPMATH 
20 "*.%&gammaG\"\"\"&%\"vG6#%\"hGF$,(*&&%%betaG6#F$F$%\"rGF$!\"#*(F+F$
F.F$%#m0GF$F$*&&%&alphaGF-F$F1F$!\"\"F$F3F5F1F5,,*&F3F$&F&F-F$F/*&F+F$
F%F$\"\"#*(F+F$F%F$F.F$F/*(F+F$F%F$F1F$F5**F+F$F%F$F1F$F.F$F$F5" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "freqm:=\":" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 9 "m0*freqm;" }}{PARA 11 "" 1 "" {XPPMATH 20 
"*,%&gammaG\"\"\"&%\"vG6#%\"hGF$,(*&&%%betaG6#F$F$%\"rGF$!\"#*(F+F$F.F
$%#m0GF$F$*&&%&alphaGF-F$F1F$!\"\"F$F3F5,,*&F3F$&F&F-F$F/*&F+F$F%F$\"
\"#*(F+F$F%F$F.F$F/*(F+F$F%F$F1F$F5**F+F$F%F$F1F$F.F$F$F5" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "subs(\{m0=0\},\");" }}{PARA 11 "" 
1 "" {XPPMATH 20 ",$*.%&gammaG\"\"\"&%\"vG6#%\"hGF%&%%betaG6#F%F%%\"rG
F%&%&alphaGF,!\"\",(*&F.F%&F'F,F%!\"#*&F*F%F&F%\"\"#*(F*F%F&F%F-F%F4F0
F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "factor(1/\");" }}
{PARA 11 "" 1 "" {XPPMATH 20 "*.&%&alphaG6#\"\"\"F&,(*&F#F&&%\"vGF%F&F
&*&&%%betaGF%F&&F*6#%\"hGF&!\"\"*(F,F&F.F&%\"rGF&F&F&%&gammaGF1F.F1F,F
1F3F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "\"*m0;" }}{PARA 11 
"" 1 "" {XPPMATH 20 "*,%&gammaG\"\"\"&%\"vG6#%\"hGF$,(*&&%%betaG6#F$F$
%\"rGF$!\"#*(F+F$F.F$%#m0GF$F$*&&%&alphaGF-F$F1F$!\"\"F$F3F5,,*&F3F$&F
&F-F$F/*&F+F$F%F$\"\"#*(F+F$F%F$F.F$F/*(F+F$F%F$F1F$F5**F+F$F%F$F1F$F.
F$F$F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "subs(m0=0,\");" }
}{PARA 11 "" 1 "" {XPPMATH 20 ",$*.%&gammaG\"\"\"&%\"vG6#%\"hGF%&%%bet
aG6#F%F%%\"rGF%&%&alphaGF,!\"\",(*&F.F%&F'F,F%!\"#*&F*F%F&F%\"\"#*(F*F
%F&F%F-F%F4F0F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(
\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "*.%&gammaG\"\"\"&%\"vG6#%\"hGF$&
%%betaG6#F$F$%\"rGF$&%&alphaGF+!\"\",(*&F-F$&F&F+F$F$*&F)F$F%F$F/*(F)F
$F%F$F,F$F$F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "freqa;" }}
{PARA 2 "" 1 "" {TEXT -1 27 "syntax error:\nfreqa;\n    ^\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{MARK "1 1" 
0 }{VIEWOPTS 1 1 0 1 1 1803 }