growth_length_age {TropFishR}

Estimation of growth parameter using length-at-age data

Description

This function estimates growth parameters from length-at-age data. It allows to perform different methods: Gulland and Holt, Ford Walford plot, Chapman's method, Bertalanffy plot, or non linear least squares method (LSM).

Usage

growth_length_age(
  param,
  method,
  Linf_est = NA,
  Linf_init = 10,
  K_init = 0.1,
  t0_init = 0,
  CI = FALSE,
  ci.level = 0.95,
  age_plot = NULL,
  do.sim = FALSE,
  nsim = 10000
)

Arguments

param

a list consisting of following parameters:

• age: age measurements,

• length: corresponding lengths in cm.

method

indicating which of following methods should be applied: "GullandHolt", "FordWalford", "Chapman", "BertalanffyPlot", or "LSM"

Linf_est

BertalanffyPlot requires an estimate for Linf to derive K and t0 (for more information see Details).

Linf_init

initital parameter of Linf for non-linear sqaures fitting (default 10)

K_init

initital parameter of K for non-linear sqaures fitting (default 0.1)

t0_init

initital parameter of t0 for non-linear sqaures fitting (default 0)

CI

logical; Should confidence intervals be calculated? This option only works for the LSM method. Default is FALSE.

ci.level

required confidence level (for LSM method only)

age_plot

sequence with ages used for plotting (LSM method only). By default age_plot = seq(min(param$age),max(param$age),0.1)

do.sim

logical. Should Monte Carlo simulation be applied? Default = FALSE

nsim

the number of Monte Carlo simulations to be performed, minimum is 10000 (default).

Details

Gulland and Holt plot assumes infinitestimal delta t (only reasonable approximation of growth parameters if delta t is small). Ford Walford plot and Chapman assume constant time intervals between ages (delta t). The Bertalanffy plot is a robust method, however it requires an estimate of Linf. As long as this estimate is reasonable the resulting estimate of K is reasonable. For a first estimate of Linf the Powell Wetherall method powell_wetherall can be used. Otherwise, the largest fish or the average of the ten largest fish can be used for a small or large sample, respectively. All lengths have to be smaller than Linf as otherwise the logarithm is not defined. Oldest fish (if larger than Linf) have to be omitted. Non-linear least squares fitting is the preferred method to estimate growth parameters according to Sparre and Venema (1998). If CI = TRUE the confidence interval of parameters is calculated and plotted. For plotting the confidence interval the predictNLS from the propagate package is applied.

Value

A list with the input parameters and following parameters:

• x: independent variable used for regression analysis,

• y: dependent variable used for regression analysis,

• mod: (non) linear model,

• Linf: infinite length for investigated species in cm [cm],

• K: growth coefficent for investigated species per year [1/year],

• t0: theoretical time zero, at which individuals of this species hatch (only for Bertalanffy plot and LSM method).

• estimates: dataframe with growth parameters and confidence intervals (only if LSM method was applied).

References

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

# synthetical length at age data
dat <- list(age = rep(1:7,each = 5),
   length = c(rnorm(5,25.7,0.9),rnorm(5,36,1.2),rnorm(5,42.9,1.5),rnorm(5,47.5,2),
   rnorm(5,50.7,0.4),rnorm(5,52.8,0.5),rnorm(5,54.2,0.7)))
growth_length_age(dat, method = "GullandHolt")

# Bertalaffy plot
growth_length_age(dat, method = "BertalanffyPlot", Linf_est = 50)

# non linear least squares method

output <- growth_length_age(param = dat, method = "LSM",
     Linf_init = 30, CI = TRUE, age_plot=NULL)
summary(output$mod)