The four-parameter growth function from Schnute (1981).

The four-parameter growth function from Schnute (1981).

Usage

Schnute(
  t,
  case = 1,
  t1 = NULL,
  t3 = NULL,
  L1 = NULL,
  L3 = NULL,
  a = NULL,
  b = NULL
)

Arguments

t

A numeric vector of ages over which to model growth.

case

A string that indicates the case of the Schnute growth function to use.

t1

The (young) age that corresponds to L1. Set to minimum value in t by default.

t3

The (old) age that corresponds to L3. Set to maximum value in t by default.

L1

The mean size/length at t1.

L3

The mean size/length at t3.

a

A dimensionless parameter that is related to the time/age at the inflection point.

b

A dimensionless parameter that is related to size/length at the inflection point.

Value

Schnute returns a predicted size given the case of the function and the provided parameter values.

IFAR Chapter

None specifically, but 12-Individual Growth is related.

References

Schnute, J. 1981. A versatile growth model with statistical stable parameters. Canadian Journal of Fisheries and Aquatic Sciences 38:1128-1140.

See also

See vbFuns, GompertzFuns, RichardsFuns, logisticFuns, and SchnuteRichards for similar functionality for other models.

Author

Derek H. Ogle, DerekOgle51@gmail.com

Examples

## See the formulae
growthFunShow("Schnute",1,plot=TRUE)

#> expression(E(L[t]) == bgroup("[", L[1]^{
#>     b
#> } + (L[3]^{
#>     b
#> } - L[1]^{
#>     b
#> }) * ~frac(1 - e^{
#>     -a * (~t ~ -~t[1])
#> }, 1 - e^{
#>     -a * (~t[3] ~ -~t[1])
#> }), "]")^{
#>     ~frac(1, b)
#> })
growthFunShow("Schnute",2,plot=TRUE)

#> expression(E(L[t]) == L[1] * e^{
#>     log ~ bgroup("(", frac(L[3], L[1]), ")") * ~frac(1 - e^{
#>         -a * (~t ~ -~t[1])
#>     }, 1 - e^{
#>         -a * (~t[3] ~ -~t[1])
#>     })
#> })
growthFunShow("Schnute",3,plot=TRUE)

#> expression(E(L[t]) == bgroup("[", L[1]^{
#>     b
#> } + (L[3]^{
#>     b
#> } - L[1]^{
#>     b
#> }) * ~frac(~t ~ -~t[1], ~t[3] ~ -~t[1]), "]")^{
#>     ~frac(1, b)
#> })
growthFunShow("Schnute",4,plot=TRUE)

#> expression(E(L[t]) == L[1] * e^{
#>     log ~ bgroup("(", frac(L[3], L[1]), ")") * ~frac(~t ~ -~t[1], 
#>         ~t[3] ~ -~t[1])
#> })

## Simple examples
ages <- 1:15
s1 <- Schnute(ages,case=1,t1=1,t3=15,L1=30,L3=400,a=0.3,b=1)
s2 <- Schnute(ages,case=2,t1=1,t3=15,L1=30,L3=400,a=0.3,b=1)
s3 <- Schnute(ages,case=3,t1=1,t3=15,L1=30,L3=400,a=0.3,b=1)
s4 <- Schnute(ages,case=4,t1=1,t3=15,L1=30,L3=400,a=0.3,b=1)

plot(s1~ages,type="l",lwd=2)
lines(s2~ages,lwd=2,col="red")
lines(s3~ages,lwd=2,col="blue")
lines(s4~ages,lwd=2,col="green")