fishgrowth (version 1.0.2)

gcm: Growth Cessation Model

Description

Fit a growth cessation model (GCM) to otoliths and/or tags.

Usage

gcm(par, data, silent = TRUE, ...)
gcm_curve(t, L0, rmax, k, t50)
gcm_objfun(par, data)

Value

The gcm function returns a TMB model object, produced by MakeADFun.

The gcm_curve function returns a numeric vector of predicted length at age.

The gcm_objfun function returns the negative log-likelihood as a single number, describing the goodness of fit of par to the data.

Arguments

par

a parameter list.

data

a data list.

silent

passed to MakeADFun.

...

passed to MakeADFun.

t

age (vector).

L0

predicted length at age 0.

rmax

shape parameter that determines the initial slope.

k

shape parameter that determines how quickly the growth curve reaches the asymptotic maximum.

t50

shape parameter that determines the logistic function midpoint.

Details

The main function gcm creates a model object, ready for parameter estimation. The auxiliary functions gcm_curve and gcm_objfun are called by the main function to calculate the regression curve and objective function value. The user can also call the auxiliary functions directly for plotting and model exploration.

The par list contains the following elements:

• L0, predicted length at age 0

• log_rmax, shape parameter that determines the initial slope

• log_k, shape parameter that determines how quickly the growth curve reaches the asymptotic maximum

• t50, shape parameter that determines the logistic function midpoint

• log_sigma_min, growth variability at the shortest observed length in the data

• log_sigma_max (*), growth variability at the longest observed length in the data

• log_age (*), age at release of tagged individuals (vector)

*: The parameter log_sigma_max can be omitted to estimate growth variability that does not vary with length. The parameter vector log_age can be omitted to fit to otoliths only.

The data list contains the following elements:

• Aoto (*), age from otoliths (vector)

• Loto (*), length from otoliths (vector)

• Lrel (*), length at release of tagged individuals (vector)

• Lrec (*), length at recapture of tagged individuals (vector)

• liberty (*), time at liberty of tagged individuals in years (vector)

*: The data vectors Aoto and Loto can be omitted to fit to tagging data only. The data vectors Lrel, Lrec, and liberty can be omitted to fit to otoliths only.

References

Maunder, M.N., Deriso, R.B., Schaefer, K.M., Fuller, D.W., Aires-da-Silva, A.M., Minte-Vera, C.V., and Campana, S.E. (2018). The growth cessation model: a growth model for species showing a near cessation in growth with application to bigeye tuna (Thunnus obesus). Marine Biology, 165, 76. tools:::Rd_expr_doi("10.1007/s00227-018-3336-9").

The fishgrowth-package help page includes references describing the parameter estimation method.

See Also

gcm, gompertz, gompertzo, richards, richardso, schnute3, vonbert, and vonberto are alternative growth models.

pred_band calculates a prediction band for a fitted growth model.

otoliths_had, otoliths_skj, and tags_skj are example datasets.

fishgrowth-package gives an overview of the package.

Examples

# Model 1: Fit to haddock otoliths

# Explore initial parameter values
plot(len~age, otoliths_had, xlim=c(0,18), ylim=c(0,105), pch=16,
     col="#0080a010")
x <- seq(1, 18, 0.1)
lines(x, gcm_curve(x, L0=5, rmax=20, k=0.15, t50=0), lty=3)

# Prepare parameters and data
init <- list(L0=5, log_rmax=log(20), log_k=log(0.15), t50=-1,
             log_sigma_min=log(3), log_sigma_max=log(3))
dat <- list(Aoto=otoliths_had$age, Loto=otoliths_had$len)
gcm_objfun(init, dat)

# Fit model
model <- gcm(init, dat)
fit <- nlminb(model$par, model$fn, model$gr,
              control=list(eval.max=1e4, iter.max=1e4))
report <- model$report()
sdreport <- sdreport(model)

# Plot results
Lhat <- with(report, gcm_curve(x, L0, rmax, k, t50))
lines(x, Lhat, lwd=2, col=2)
legend("bottomright", c("initial curve","model fit"), col=c(1,2), lty=c(3,1),
       lwd=c(1,2), bty="n", inset=0.02, y.intersp=1.25)

# Model summary
report[c("L0", "rmax", "k", "t50", "sigma_min", "sigma_max")]
fit[-1]
summary(sdreport)

# Plot 95% prediction band
band <- pred_band(x, model)
areaplot::confplot(cbind(lower,upper)~age, band, xlim=c(0,18), ylim=c(0,100),
         ylab="len", col="mistyrose")
points(len~age, otoliths_had, xlim=c(0,18), ylim=c(0,100),
       pch=16, col="#0080a010")
lines(x, Lhat, lwd=2, col=2)
lines(lower~age, band, lty=1, lwd=0.5, col=2)
lines(upper~age, band, lty=1, lwd=0.5, col=2)

#############################################################################

# Model 2: Fit to skipjack otoliths and tags

# Explore initial parameter values
plot(len~age, otoliths_skj, xlim=c(0,4), ylim=c(0,100))
x <- seq(0, 4, 0.1)
points(lenRel~I(lenRel/60), tags_skj, col=4)
points(lenRec~I(lenRel/60+liberty), tags_skj, col=3)
lines(x, gcm_curve(x, L0=20, rmax=120, k=2, t50=0), lty=2)
legend("bottomright", c("otoliths","tag releases","tac recaptures",
       "initial curve"), col=c(1,4,3,1), pch=c(1,1,1,NA), lty=c(0,0,0,2),
       lwd=c(1.2,1.2,1.2,1), bty="n", inset=0.02, y.intersp=1.25)

# Prepare parameters and data
init <- list(L0=20, log_rmax=log(120), log_k=log(4), t50=0,
             log_sigma_min=log(3), log_sigma_max=log(3),
             log_age=log(tags_skj$lenRel/60))
dat <- list(Aoto=otoliths_skj$age, Loto=otoliths_skj$len,
            Lrel=tags_skj$lenRel, Lrec=tags_skj$lenRec,
            liberty=tags_skj$liberty)
gcm_objfun(init, dat)

# Fit model
model <- gcm(init, dat)
fit <- nlminb(model$par, model$fn, model$gr,
              control=list(eval.max=1e4, iter.max=1e4))
report <- model$report()
sdreport <- sdreport(model)

# Plot results
plot(len~age, otoliths_skj, xlim=c(0,4), ylim=c(0,100))
points(report$age, report$Lrel, col=4)
points(report$age+report$liberty, report$Lrec, col=3)
Lhat <- with(report, gcm_curve(x, L0, rmax, k, t50))
lines(x, Lhat, lwd=2)
legend("bottomright", c("otoliths","tag releases","tac recaptures",
       "model fit"), col=c(1,4,3,1), pch=c(1,1,1,NA), lty=c(0,0,0,1),
       lwd=c(1.2,1.2,1.2,2), bty="n", inset=0.02, y.intersp=1.25)

# Model summary
report[c("L0", "rmax", "k", "t50", "sigma_min", "sigma_max")]
fit[-1]
head(summary(sdreport), 6)

#############################################################################

# Model 3: Stepwise estimation procedure, described by Maunder et al. (2018)
# - estimate L0 and rmax using linear regression on younger fish
# - estimate k and t50 using GCM and all data, keeping L0 and rmax fixed

# Estimate L0 and rmax
plot(otoliths_skj, xlim=c(0,4), ylim=c(0,100))
fm <- lm(len~age, otoliths_skj)
abline(fm)
L0 <- coef(fm)[[1]]
rmax <- coef(fm)[[2]]

# Explore initial parameter values (k, t50, age)
t <- seq(0, 4, by=0.1)
points(t, gcm_curve(t, L0, rmax, k=3, t50=2), col="gray")
points(lenRel~I(lenRel/50), tags_skj, col=4)
points(lenRec~I(lenRel/50+liberty), tags_skj, col=3)
legend("bottomright", c("otoliths","tag releases","tac recaptures",
       "linear regression (otoliths)"), col=c(1,4,3,1), pch=c(1,1,1,NA),
       lty=c(0,0,0,1), lwd=c(1.2,1.2,1.2,2), bty="n", inset=0.02,
       y.intersp=1.25)

# Prepare parameters
init <- list(L0=L0, log_rmax=log(rmax), log_k=log(3), t50=2,
             log_sigma_min=log(3), log_sigma_max=log(3),
             log_age=log(tags_skj$lenRel/50))

# Fit model
map <- list(L0=factor(NA), log_rmax=factor(NA))  # fix L0 and rmax
model <- gcm(init, dat, map=map)
fit <- nlminb(model$par, model$fn, model$gr,
              control=list(eval.max=1e4,iter.max=1e4))
report <- model$report()
sdreport <- sdreport(model)

# Plot results
plot(len~age, otoliths_skj, xlim=c(0,4), ylim=c(0,100))
points(report$age, report$Lrel, col=4)
points(report$age+report$liberty, report$Lrec, col=3)
Lhat <- with(report, gcm_curve(x, L0, rmax, k, t50))
lines(x, Lhat, lwd=2)
legend("bottomright", c("otoliths","tag releases","tac recaptures",
       "model fit"), col=c(1,4,3,1), pch=c(1,1,1,NA), lty=c(0,0,0,1),
       lwd=c(1.2,1.2,1.2,2), bty="n", inset=0.02, y.intersp=1.25)

# Model summary
report[c("L0", "rmax", "k", "t50", "sigma_min", "sigma_max")]
fit[-1]
head(summary(sdreport), 6)