########################################################### ## Simple Examples -- Von B ( vb1 <- vbFuns ( ) ) #> function(t,Linf,K=NULL,t0=NULL) {#> if (length(Linf)==3) { K <- Linf[[2]]#> t0 <- Linf[[3]]#> Linf <- Linf[[1]] }#> Linf*(1-exp(-K*(t-t0)))#> }#> <bytecode: 0x00000237efcca370>#> <environment: 0x00000237efbd29a0>#> function (t, Linf, K = NULL, t0 = NULL) #> {#> if (length(Linf) == 3) {#> K <- Linf[[2]]#> t0 <- Linf[[3]]#> Linf <- Linf[[1]]#> }#> Linf * (1 - exp(-K * (t - t0)))#> }#> <bytecode: 0x00000239b4c64908>#> <environment: 0x00000239b4c8bcd0>ages <- 0 : 20 plot ( vb1 ( ages ,Linf= 20 ,K= 0.3 ,t0= - 0.2 ) ~ ages ,type= "b" ,pch= 19 ) ( vb2 <- vbFuns ( "Francis" ) ) #> function(t,L1,L2=NULL,L3=NULL,t1,t3=NULL) {#> if (length(L1)==3) { L2 <- L1[[2]]; L3 <- L1[[3]]; L1 <- L1[[1]] }#> if (length(t1)==2) { t3 <- t1[[2]]; t1 <- t1[[1]] }#> r <- (L3-L2)/(L2-L1)#> L1+(L3-L1)*((1-r^(2*((t-t1)/(t3-t1))))/(1-r^2))#> }#> <bytecode: 0x00000237efc83db0>#> <environment: 0x00000237ef9e3f38>#> function (t, L1, L2 = NULL, L3 = NULL, t1, t3 = NULL) #> {#> if (length(L1) == 3) {#> L2 <- L1[[2]]#> L3 <- L1[[3]]#> L1 <- L1[[1]]#> }#> if (length(t1) == 2) {#> t3 <- t1[[2]]#> t1 <- t1[[1]]#> }#> r <- (L3 - L2)/(L2 - L1)#> L1 + (L3 - L1) * ((1 - r^(2 * ((t - t1)/(t3 - t1))))/(1 - #> r^2))#> }#> <bytecode: 0x00000239b4c6b5b0>#> <environment: 0x00000239b4e55da0>plot ( vb2 ( ages ,L1= 10 ,L2= 19 ,L3= 20 ,t1= 2 ,t3= 18 ) ~ ages ,type= "b" ,pch= 19 ) ( vb2c <- vbFuns ( "Francis" ,simple= TRUE ) ) # compare to vb2 #> function(t,L1,L2,L3,t1,t3) {#> r <- (L3-L2)/(L2-L1)#> L1+(L3-L1)*((1-r^(2*((t-t1)/(t3-t1))))/(1-r^2))#> }#> <bytecode: 0x00000237efc7abd0>#> <environment: 0x00000237ef8cd408>#> function (t, L1, L2, L3, t1, t3) #> {#> r <- (L3 - L2)/(L2 - L1)#> L1 + (L3 - L1) * ((1 - r^(2 * ((t - t1)/(t3 - t1))))/(1 - #> r^2))#> }#> <bytecode: 0x00000239b4c6d780>#> <environment: 0x00000239b4f658a0>## Simple Examples -- Gompertz ( gomp1 <- GompertzFuns ( ) ) #> function(t,Linf,gi=NULL,ti=NULL) {#> if (length(Linf)==3) { gi <- Linf[[2]]#> ti <- Linf[[3]]#> Linf <- Linf[[1]] }#> Linf*exp(-exp(-gi*(t-ti)))#> }#> <bytecode: 0x00000237ef806420>#> <environment: 0x00000237ef7cd368>#> function (t, Linf, gi = NULL, ti = NULL) #> {#> if (length(Linf) == 3) {#> gi <- Linf[[2]]#> ti <- Linf[[3]]#> Linf <- Linf[[1]]#> }#> Linf * exp(-exp(-gi * (t - ti)))#> }#> <bytecode: 0x00000239b4ff2578>#> <environment: 0x00000239b502a278>plot ( gomp1 ( ages ,Linf= 800 ,gi= 0.5 ,ti= 5 ) ~ ages ,type= "b" ,pch= 19 ) ( gomp2 <- GompertzFuns ( "Ricker2" ) ) #> function(t,L0,a=NULL,gi=NULL) {#> if (length(L0)==3) { a <- L0[[2]]#> gi <- L0[[3]]#> L0 <- L0[[1]] }#> L0*exp(a*(1-exp(-gi*t)))#> }#> <bytecode: 0x00000237ef7ff560>#> <environment: 0x00000237ef56b5f0>#> function (t, L0, a = NULL, gi = NULL) #> {#> if (length(L0) == 3) {#> a <- L0[[2]]#> gi <- L0[[3]]#> L0 <- L0[[1]]#> }#> L0 * exp(a * (1 - exp(-gi * t)))#> }#> <bytecode: 0x00000239b5005060>#> <environment: 0x00000239b5127e50>plot ( gomp2 ( ages ,L0= 2 ,a= 6 ,gi= 0.5 ) ~ ages ,type= "b" ,pch= 19 ) ( gomp2c <- GompertzFuns ( "Ricker2" ,simple= TRUE ) ) # compare to gomp2 #> function(t,L0,a,gi) {#> L0*exp(a*(1-exp(-gi*t)))#> }#> <bytecode: 0x00000237ef7f3ce0>#> <environment: 0x00000237ef3306a0>#> function (t, L0, a, gi) #> {#> L0 * exp(a * (1 - exp(-gi * t)))#> }#> <bytecode: 0x00000239b5004378>#> <environment: 0x00000239b5238b98>( gompT <- GompertzFuns ( "Troynikov1" ) ) #> function(Lm,dt,Linf,gi=NULL) {#> if (length(Linf)==2) { gi <- Linf[2]#> Linf <- Linf[1] }#> Linf*((Lm/Linf)^exp(-gi*dt))-Lm#> }#> <bytecode: 0x00000237ef7e0e90>#> <environment: 0x00000237ef294790>#> function (Lm, dt, Linf, gi = NULL) #> {#> if (length(Linf) == 2) {#> gi <- Linf[2]#> Linf <- Linf[1]#> }#> Linf * ((Lm/Linf)^exp(-gi * dt)) - Lm#> }#> <bytecode: 0x00000239b5013760>#> <environment: 0x00000239b528d380>## Simple Examples -- Richards ( rich1 <- RichardsFuns ( ) ) #> function(t,Linf,k=NULL,a=NULL,b=NULL) {#> if (length(Linf)==4) { k <- Linf[[2]]#> a <- Linf[[3]]#> b <- Linf[[4]]#> Linf <- Linf[[1]] }#> Linf*(1-a*exp(-k*t))^b#> }#> <bytecode: 0x00000237ef1bca70>#> <environment: 0x00000237ef16da08>#> function (t, Linf, k = NULL, a = NULL, b = NULL) #> {#> if (length(Linf) == 4) {#> k <- Linf[[2]]#> a <- Linf[[3]]#> b <- Linf[[4]]#> Linf <- Linf[[1]]#> }#> Linf * (1 - a * exp(-k * t))^b#> }#> <bytecode: 0x00000239b52fd2d0>#> <environment: 0x00000239b53136d8>plot ( rich1 ( ages ,Linf= 800 ,k= 0.5 ,a= 1 ,b= 6 ) ~ ages ,type= "b" ,pch= 19 ) ( rich2 <- RichardsFuns ( 2 ) ) #> function(t,Linf,k=NULL,ti=NULL,b=NULL) {#> if (length(Linf)==4) { k <- Linf[[2]]#> ti <- Linf[[3]]#> b <- Linf[[4]]#> Linf <- Linf[[1]] }#> Linf*(1-(1/b)*exp(-k*(t-ti)))^b#> }#> <bytecode: 0x00000237ef1b07a8>#> <environment: 0x00000237eefc9e58>#> function (t, Linf, k = NULL, ti = NULL, b = NULL) #> {#> if (length(Linf) == 4) {#> k <- Linf[[2]]#> ti <- Linf[[3]]#> b <- Linf[[4]]#> Linf <- Linf[[1]]#> }#> Linf * (1 - (1/b) * exp(-k * (t - ti)))^b#> }#> <bytecode: 0x00000239b5301c90>#> <environment: 0x00000239b5435738>plot ( rich2 ( ages ,Linf= 800 ,k= 0.5 ,ti= 3 ,b= 6 ) ~ ages ,type= "b" ,pch= 19 ) ( rich3 <- RichardsFuns ( 3 ) ) #> function(t,Linf,k=NULL,ti=NULL,b=NULL) {#> if (length(Linf)==4) { k <- Linf[[2]]#> ti <- Linf[[3]]#> b <- Linf[[4]]#> Linf <- Linf[[1]] }#> Linf/((1+b*exp(-k*(t-ti)))^(1/b))#> }#> <bytecode: 0x00000237ef1aa938>#> <environment: 0x00000237eeea2408>#> function (t, Linf, k = NULL, ti = NULL, b = NULL) #> {#> if (length(Linf) == 4) {#> k <- Linf[[2]]#> ti <- Linf[[3]]#> b <- Linf[[4]]#> Linf <- Linf[[1]]#> }#> Linf/((1 + b * exp(-k * (t - ti)))^(1/b))#> }#> <bytecode: 0x00000239b5300250>#> <environment: 0x00000239b5555d70>plot ( rich3 ( ages ,Linf= 800 ,k= 0.5 ,ti= 3 ,b= 0.15 ) ~ ages ,type= "b" ,pch= 19 ) ( rich4 <- RichardsFuns ( 4 ) ) #> function(t,Linf,k=NULL,ti=NULL,b=NULL) {#> if (length(Linf)==4) { k <- Linf[[2]]#> ti <- Linf[[3]]#> b <- Linf[[4]]#> Linf <- Linf[[1]] }#> Linf*(1+(b-1)*exp(-k*(t-ti)))^(1/(1-b))#> }#> <bytecode: 0x00000237ef1a1288>#> <environment: 0x00000237eed8fbb8>#> function (t, Linf, k = NULL, ti = NULL, b = NULL) #> {#> if (length(Linf) == 4) {#> k <- Linf[[2]]#> ti <- Linf[[3]]#> b <- Linf[[4]]#> Linf <- Linf[[1]]#> }#> Linf * (1 + (b - 1) * exp(-k * (t - ti)))^(1/(1 - b))#> }#> <bytecode: 0x00000239b530a700>#> <environment: 0x00000239b569dd00>plot ( rich4 ( ages ,Linf= 800 ,k= 0.5 ,ti= 3 ,b= 0.95 ) ~ ages ,type= "b" ,pch= 19 ) lines ( rich4 ( ages ,Linf= 800 ,k= 0.5 ,ti= 3 ,b= 1.5 ) ~ ages ,type= "b" ,pch= 19 ,col= "blue" ) ( rich5 <- RichardsFuns ( 5 ) ) #> function(t,Linf,k=NULL,L0=NULL,b=NULL) {#> if (length(Linf)==4) { k <- Linf[[2]]#> L0 <- Linf[[3]]#> b <- Linf[[4]]#> Linf <- Linf[[1]] }#> Linf*(1+(((L0/Linf)^(1-b))-1)*exp(-k*t))^(1/(1-b))#> }#> <bytecode: 0x00000237ef195b80>#> <environment: 0x00000237eebe29d0>#> function (t, Linf, k = NULL, L0 = NULL, b = NULL) #> {#> if (length(Linf) == 4) {#> k <- Linf[[2]]#> L0 <- Linf[[3]]#> b <- Linf[[4]]#> Linf <- Linf[[1]]#> }#> Linf * (1 + (((L0/Linf)^(1 - b)) - 1) * exp(-k * t))^(1/(1 - #> b))#> }#> <bytecode: 0x00000239b53185f8>#> <environment: 0x00000239b581ef90>plot ( rich5 ( ages ,Linf= 800 ,k= 0.5 ,L0= 50 ,b= 1.5 ) ~ ages ,type= "b" ,pch= 19 ) ( rich6 <- RichardsFuns ( 6 ) ) #> function(t,Linf,k=NULL,ti=NULL,Lninf=NULL,b=NULL) {#> if (length(Linf)==5) { k <- Linf[[2]]#> ti <- Linf[[3]]#> Lninf <- Linf[[3]]#> b <- Linf[[4]]#> Linf <- Linf[[1]] }#> Lninf+(Linf-Lninf)*(1+(b-1)*exp(-k*(t-ti)))^(1/(1-b))#> }#> <bytecode: 0x00000237ef170720>#> <environment: 0x00000237eeaaa850>#> function (t, Linf, k = NULL, ti = NULL, Lninf = NULL, b = NULL) #> {#> if (length(Linf) == 5) {#> k <- Linf[[2]]#> ti <- Linf[[3]]#> Lninf <- Linf[[3]]#> b <- Linf[[4]]#> Linf <- Linf[[1]]#> }#> Lninf + (Linf - Lninf) * (1 + (b - 1) * exp(-k * (t - ti)))^(1/(1 - #> b))#> }#> <bytecode: 0x00000239b5316230>#> <environment: 0x00000239b5949580>plot ( rich6 ( ages ,Linf= 800 ,k= 0.5 ,ti= 3 ,Lninf= 50 ,b= 1.5 ) ~ ages ,type= "b" ,pch= 19 ) ( rich2c <- RichardsFuns ( 2 ,simple= TRUE ) ) # compare to rich2 #> function(t,Linf,k,ti,b) {#> Linf*(1-(1/b)*exp(-k*(t-ti)))^b#> }#> <bytecode: 0x00000237ef19dc08>#> <environment: 0x00000237ee9845e0>#> function (t, Linf, k, ti, b) #> {#> Linf * (1 - (1/b) * exp(-k * (t - ti)))^b#> }#> <bytecode: 0x00000239b5300b10>#> <environment: 0x00000239b5b4c1f0>## Simple Examples -- Logistic ( log1 <- logisticFuns ( ) ) #> function(t,Linf,gninf=NULL,ti=NULL) {#> if (length(Linf)==3) { gninf <- Linf[[2]]#> ti <- Linf[[3]]#> Linf <- Linf[[1]] }#> Linf/(1+exp(-gninf*(t-ti)))#> }#> <bytecode: 0x00000237ee901db8>#> <environment: 0x00000237ee8ca0f0>#> function (t, Linf, gninf = NULL, ti = NULL) #> {#> if (length(Linf) == 3) {#> gninf <- Linf[[2]]#> ti <- Linf[[3]]#> Linf <- Linf[[1]]#> }#> Linf/(1 + exp(-gninf * (t - ti)))#> }#> <bytecode: 0x00000239b5bab2b0>#> <environment: 0x00000239b5bad988>plot ( log1 ( ages ,Linf= 800 ,gninf= 0.5 ,ti= 5 ) ~ ages ,type= "b" ,pch= 19 ) ( log2 <- logisticFuns ( "CJ2" ) ) #> function(t,Linf,gninf=NULL,a=NULL) {#> if (length(Linf)==3) { gninf <- Linf[[2]]#> a <- Linf[[3]]#> Linf <- Linf[[1]] }#> Linf/(1+a*exp(-gninf*t))#> }#> <bytecode: 0x00000237ee8dedc8>#> <environment: 0x00000237ee7d9270>#> function (t, Linf, gninf = NULL, a = NULL) #> {#> if (length(Linf) == 3) {#> gninf <- Linf[[2]]#> a <- Linf[[3]]#> Linf <- Linf[[1]]#> }#> Linf/(1 + a * exp(-gninf * t))#> }#> <bytecode: 0x00000239b5ba7e60>#> <environment: 0x00000239b5d049a0>plot ( log2 ( ages ,Linf= 800 ,gninf= 0.5 ,a= 10 ) ~ ages ,type= "b" ,pch= 19 ) ( log2c <- logisticFuns ( "CJ2" ,simple= TRUE ) ) # compare to log2 #> function(t,Linf,gninf,a) {#> Linf/(1+a*exp(-gninf*t))#> }#> <bytecode: 0x00000237ee8eb4b8>#> <environment: 0x00000237ee6d17b0>#> function (t, Linf, gninf, a) #> {#> Linf/(1 + a * exp(-gninf * t))#> }#> <bytecode: 0x00000239b5ba71b0>#> <environment: 0x00000239b5e81db0>( log3 <- logisticFuns ( "Karkach" ) ) #> function(t,Linf,L0=NULL,gninf=NULL) {#> if (length(Linf)==3) { L0 <- Linf[[2]]#> gninf <- Linf[[3]]#> Linf <- Linf[[1]] }#> L0*Linf/(L0+(Linf-L0)*exp(-gninf*t))#> }#> <bytecode: 0x00000237ee8dbcf8>#> <environment: 0x00000237ee67f8d0>#> function (t, Linf, L0 = NULL, gninf = NULL) #> {#> if (length(Linf) == 3) {#> L0 <- Linf[[2]]#> gninf <- Linf[[3]]#> Linf <- Linf[[1]]#> }#> L0 * Linf/(L0 + (Linf - L0) * exp(-gninf * t))#> }#> <bytecode: 0x00000239b5ba6c00>#> <environment: 0x00000239b6028220>plot ( log3 ( ages ,L0= 10 ,Linf= 800 ,gninf= 0.5 ) ~ ages ,type= "b" ,pch= 19 ) ( log4 <- logisticFuns ( "Haddon" ) ) #> function(Lm,dLmax,L50=NULL,L95=NULL) {#> if (length(dLmax)==3) { L50 <- dLmax[2]#> L95 <- dLmax[3]#> dLmax <- dLmax[1] }#> dLmax/(1+exp(log(19)*((Lm-L50)/(L95-L50))))#> }#> <bytecode: 0x00000237ee8e30f8>#> <environment: 0x00000237ee585ba0>#> function (Lm, dLmax, L50 = NULL, L95 = NULL) #> {#> if (length(dLmax) == 3) {#> L50 <- dLmax[2]#> L95 <- dLmax[3]#> dLmax <- dLmax[1]#> }#> dLmax/(1 + exp(log(19) * ((Lm - L50)/(L95 - L50))))#> }#> <bytecode: 0x00000239b5bbb608>#> <environment: 0x00000239b6431dd0>########################################################### FSA
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