vbModels(), GompertzModels(), RichardsModels(), and logisticModels() to see the equations for each growth function.vbFuns(type = c("Typical", "typical", "BevertonHolt", "Original", "original",
"vonBertalanffy", "GQ", "GallucciQuinn", "Mooij", "Weisberg", "Schnute",
"Francis", "Laslett", "Polacheck", "Somers", "Somers2", "Fabens", "Fabens2",
"Wang", "Wang2", "Wang3"), simple = FALSE, msg = FALSE)
GompertzFuns(type = c("Ricker1", "Ricker2", "Ricker3", "QD1", "QD2", "QD3",
"KM", "AFS", "original", "Troynikov1", "Troynikov2"), simple = FALSE,
msg = FALSE)
RichardsFuns(type = 1, simple = FALSE, msg = FALSE)
logisticFuns(type = c("CJ1", "CJ2", "Karkach", "HaddonI"), simple = FALSE,
msg = FALSE)
vbModels(family = c("size", "seasonal", "tagging"), cex = 1, ...)
GompertzModels(family = c("size", "tagging"), cex = 1.25, ...)
RichardsModels(cex = 1, ...)
logisticModels(family = c("size", "tagging"), cex = 1.25, ...)=FALSE; DEFAULT) or whether all individual parameters must be specified in separate arguments (=TRUE).=TRUE) or not (=FALSE; DEFAULT)."size" (DEFAULT), "tagging", and "seasonal" (only for the von Bertalanffy models).Funs return a function that can be used to predict fish size given a vector of ages and values for the growth function parameters and, in some parameterizations, values for some constants. The result should be saved to an object that is then the function name. When the resulting function is used, the parameters are ordered as shown when the definitions of the parameters are printed after the function is called (if msg=TRUE). If simple=FALSE, then the values for all parameters may be included as a vector in the first parameter argument. Similarly, the values for all constants may be included as a vector in the first constant argument (i.e., t1). If simple=TRUE, then all parameters and constants must be declared individually. The resulting function is somewhat easier to read when simple=TRUE, but is less general for some applications.
The functions ending in Models return a graphic that uses plotmath to show the growth function equations in a pretty format.Schnute for an implementation of the Schnute (1981) model.###########################################################
## See the equations
windows(8,5)
vbModels()
windows(6,5)
vbModels("seasonal")
vbModels("tagging")
windows(5,5)
GompertzModels()
GompertzModels("tagging")
RichardsModels()
logisticModels()
###########################################################
## Simple Examples -- Von B
( vb1 <- vbFuns() )
ages <- 0:20
plot(vb1(ages,Linf=20,K=0.3,t0=-0.2)~ages,type="b",pch=19)
( vb2 <- vbFuns("Francis") )
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
## Simple Examples -- Gompertz
( gomp1 <- GompertzFuns() )
plot(gomp1(ages,Linf=800,gi=0.5,ti=5)~ages,type="b",pch=19)
( gomp2 <- GompertzFuns("Ricker2") )
plot(gomp2(ages,L0=2,a=6,gi=0.5)~ages,type="b",pch=19)
( gomp2c <- GompertzFuns("Ricker2",simple=TRUE) ) # compare to gomp2
( gompT <- GompertzFuns("Troynikov1"))
## Simple Examples -- Richards
( rich1 <- RichardsFuns() )
plot(rich1(ages,Linf=800,k=0.5,a=1,b=6)~ages,type="b",pch=19)
( rich2 <- RichardsFuns(2) )
plot(rich2(ages,Linf=800,k=0.5,ti=3,b=6)~ages,type="b",pch=19)
( rich3 <- RichardsFuns(3) )
plot(rich3(ages,Linf=800,k=0.5,ti=3,b=0.15)~ages,type="b",pch=19)
( rich4 <- RichardsFuns(4) )
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) )
plot(rich5(ages,Linf=800,k=0.5,L0=50,b=1.5)~ages,type="b",pch=19)
( rich6 <- RichardsFuns(6) )
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
## Simple Examples -- Logistic
( log1 <- logisticFuns() )
plot(log1(ages,Linf=800,gninf=0.5,ti=5)~ages,type="b",pch=19)
( log2 <- logisticFuns("CJ2") )
plot(log2(ages,Linf=800,gninf=0.5,a=10)~ages,type="b",pch=19)
( log2c <- logisticFuns("CJ2",simple=TRUE) ) # compare to log2
( log3 <- logisticFuns("Karkach") )
plot(log3(ages,L0=10,Linf=800,gninf=0.5)~ages,type="b",pch=19)
( log4 <- logisticFuns("HaddonI") )
###########################################################
## Examples of fitting
## After the last example a plot is constructed with three
## or four lines on top of each other illustrating that the
## parameterizations all produce the same fitted values.
## However, observe the correlations in the summary() results.
## Von B
data(SpotVA1)
# Fitting the typical paramaterization of the von B function
fit1 <- nls(tl~vb1(age,Linf,K,t0),data=SpotVA1,start=vbStarts(tl~age,data=SpotVA1))
summary(fit1,correlation=TRUE)
plot(tl~age,data=SpotVA1,pch=19)
curve(vb1(x,Linf=coef(fit1)),from=0,to=5,col="red",lwd=10,add=TRUE)
# Fitting the Francis paramaterization of the von B function
fit2 <- nls(tl~vb2c(age,L1,L2,L3,t1=0,t3=5),data=SpotVA1,
start=vbStarts(tl~age,data=SpotVA1,type="Francis",ages2use=c(0,5)))
summary(fit2,correlation=TRUE)
curve(vb2c(x,L1=coef(fit2)[1],L2=coef(fit2)[2],L3=coef(fit2)[3],t1=0,t3=5),
from=0,to=5,col="blue",lwd=5,add=TRUE)
# Fitting the Schnute parameterization of the von B function
vb3 <- vbFuns("Schnute")
fit3 <- nls(tl~vb3(age,L1,L3,K,t1=0,t3=4),data=SpotVA1,
start=vbStarts(tl~age,data=SpotVA1,type="Schnute",ages2use=c(0,4)))
summary(fit3,correlation=TRUE)
curve(vb3(x,L1=coef(fit3),t1=c(0,4)),from=0,to=5,col="green",lwd=2,add=TRUE)
## Gompertz
# Make some fake data using the original parameterization
gompO <- GompertzFuns("original")
# setup ages, sample sizes (general reduction in numbers with
# increasing age), and additive SD to model
t <- 1:15
n <- c(10,40,35,25,12,10,10,8,6,5,3,3,3,2,2)
sd <- 15
# expand ages
ages <- rep(t,n)
# get lengths from gompertz and a random error for individuals
lens <- gompO(ages,Linf=450,a=1,gi=0.3)+rnorm(length(ages),0,sd)
# put together as a data.frame
df <- data.frame(age=ages,len=round(lens,0))
# Fit first Ricker parameterization
fit1 <- nls(len~gomp1(age,Linf,gi,ti),data=df,start=list(Linf=500,gi=0.3,ti=3))
summary(fit1,correlation=TRUE)
plot(len~age,data=df,pch=19,col=rgb(0,0,0,1/5))
curve(gomp1(x,Linf=coef(fit1)),from=0,to=15,col="red",lwd=10,add=TRUE)
# Fit third Ricker parameterization
fit2 <- nls(len~gomp2(age,L0,a,gi),data=df,start=list(L0=30,a=3,gi=0.3))
summary(fit2,correlation=TRUE)
curve(gomp2(x,L0=coef(fit2)),from=0,to=15,col="blue",lwd=5,add=TRUE)
# Fit third Quinn and Deriso parameterization (using simple=TRUE model)
gomp3 <- GompertzFuns("QD3",simple=TRUE)
fit3 <- nls(len~gomp3(age,Linf,gi,t0),data=df,start=list(Linf=500,gi=0.3,t0=0))
summary(fit3,correlation=TRUE)
curve(gomp3(x,Linf=coef(fit3)[1],gi=coef(fit3)[2],t0=coef(fit3)[3]),
from=0,to=15,col="green",lwd=2,add=TRUE)
## Richards
# Fit first Richards parameterization
fit1 <- nls(len~rich1(age,Linf,k,a,b),data=df,start=list(Linf=450,k=0.25,a=0.65,b=3))
summary(fit1,correlation=TRUE)
plot(len~age,data=df,pch=19,col=rgb(0,0,0,1/5))
curve(rich1(x,Linf=coef(fit1)),from=0,to=15,col="red",lwd=10,add=TRUE)
# Fit second Richards parameterization
fit2 <- nls(len~rich2(age,Linf,k,ti,b),data=df,start=list(Linf=450,k=0.25,ti=3,b=3))
summary(fit2,correlation=TRUE)
curve(rich2(x,Linf=coef(fit2)),from=0,to=15,col="blue",lwd=7,add=TRUE)
# Fit third Richards parameterization
fit3 <- nls(len~rich3(age,Linf,k,ti,b),data=df,start=list(Linf=450,k=0.25,ti=3,b=-0.3))
summary(fit3,correlation=TRUE)
curve(rich3(x,Linf=coef(fit3)),from=0,to=15,col="green",lwd=4,add=TRUE)
# Fit fourth Richards parameterization
fit4 <- nls(len~rich4(age,Linf,k,ti,b),data=df,start=list(Linf=450,k=0.25,ti=3,b=0.7))
summary(fit4,correlation=TRUE)
curve(rich4(x,Linf=coef(fit4)),from=0,to=15,col="black",lwd=1,add=TRUE)
## Logistic
# Fit first Campana-Jones parameterization
fit1 <- nls(len~log1(age,Linf,gninf,ti),data=df,start=list(Linf=450,gninf=0.45,ti=4))
summary(fit1,correlation=TRUE)
plot(len~age,data=df,pch=19,col=rgb(0,0,0,1/5))
curve(log1(x,Linf=coef(fit1)),from=0,to=15,col="red",lwd=10,add=TRUE)
# Fit second Campana-Jones parameterization
fit2 <- nls(len~log2(age,Linf,gninf,a),data=df,start=list(Linf=450,gninf=0.45,a=7))
summary(fit2,correlation=TRUE)
curve(log2(x,Linf=coef(fit2)),from=0,to=15,col="blue",lwd=5,add=TRUE)
# Fit Karkach parameterization (using simple=TRUE model)
log3 <- logisticFuns("Karkach",simple=TRUE)
fit3 <- nls(len~log3(age,Linf,L0,gninf),data=df,start=list(Linf=450,L0=30,gninf=0.45))
summary(fit3,correlation=TRUE)
curve(log3(x,Linf=coef(fit3)[1],L0=coef(fit3)[2],gninf=coef(fit3)[3]),
from=0,to=15,col="green",lwd=2,add=TRUE)Run the code above in your browser using DataLab