{VERSION 3 0 "IBM INTEL NT" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 0 12 0 0 
0 1 1 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Fo
nt 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 0 12 128 0 128 1 2 1 2 0 
0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 
257 1 {CSTYLE "" -1 -1 "Courier" 0 11 0 0 0 1 2 1 2 0 0 0 0 0 0 }0 0 
0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "restart:gc():" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "rv.mws" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 33 "Reproductive Value calculations. \+
" }}{PARA 0 "" 0 "" {TEXT -1 29 "RA Fisher defines births as b" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "births_at_age_x:=b[x];" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 45 "Fisher defines growth rate of a genotype \+
as m" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "pop_at_time_x:=dsol
ve(\{diff(N(x),x)=m*N(x),N(0)=N[0]\},N(x));" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 51 "value_at_age_x:=births_at_age_x/rhs(pop_at_time_x)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "prob_of_living:=l[x]/l
[a];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "future_value:=value
_at_age_x*prob_of_living;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
60 "pop_at_time_a:=dsolve(\{diff(N(a),a)=m*N(a),N(0)=N[0]\},N(a));" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "value_at_age_a:=1/(rhs(pop_
at_time_a));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "total_futur
e_value:=int(future_value,x=a..infinity);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 38 "RV:=total_future_value/value_at_age_a;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "simplify(RV);" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 98 "Note that N0/N0=1, and that la is a constant, so t
his simplifies to the expression on the handout." }}}}{MARK "0 0 0" 
13 }{VIEWOPTS 1 1 0 1 1 1803 }