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" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 110 "The evolution of dominan t gene frequency in population (denoted by p(t)) is modeled by the dif ference equation" }}{PARA 259 "" 0 "" {TEXT -1 16 "p(t+1)=F(k,p(t))" } {TEXT 256 0 "" }}{PARA 0 "" 0 "" {TEXT -1 5 "where" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "F:=(k,p)->p/(1-k*(1-p)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FGR6$%\"kG%\"pG6\"6$%)operatorG%&arrowGF)*&9% \"\"\",&\"\"\"F1*&9$F1),&F1F1F.!\"\"\"\"#F/F6!\"\"F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 119 "First, you can have a look to dependence of the function F (co nsidered to be function of x) on the growing parameter k." }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "animate(\{F(k,p),p\},p=0..1,k=-10..0.95,color=red,frames=50); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "Now, you can set a value of parameter k and simulate 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pp1:=pointplot([[ t,AA[t]]$t=0..tmax],style=point,symbol=circle,color=red):" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 62 " pl1:=pointplot([[t,AA[t]]$t=0..tmax],styl e=line,color=red):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 " t1:=textpl ot([1.02*tmax,AA[tmax],`AA`],align=RIGHT):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 78 " pp2:=pointplot([[t,aa[t]]$t=0..tmax],style=point,s ymbol=circle,color=blue):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 " pl2 :=pointplot([[t,aa[t]]$t=0..tmax],style=line,color=blue):" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 55 " t2:=textplot([1.02*tmax,aa[tmax],`aa`],al ign=RIGHT):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 81 " pp3:=pointplot([[ t,aA[t]]$t=0..tmax],style=point,symbol=circle,color=magenta):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 153 " pl3:=pointplot([[t,aA[t]]$t=0.. tmax],style=line,color=magenta,labels=[`generation`,`frequency`],title =`Simulated evolution of genotypic frequencies`):" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 55 " t3:=textplot([1.02*tmax,aA[tmax],`aA`],align=RIG HT):" }}{PARA 0 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