fishmethods (version 1.3-0)

grotag: Maximum likelihood estimation of growth and growth variability from tagging data - Francis (1988)

Description

This function estimates parameters of Francis (1988)'s growth model using tagging data. The data are fitted using a constrained maximum likelihood optimization performed by optim using the "L-BFGS-B" method.

Usage

grotag(L1 = NULL, L2 = NULL, T1 = NULL, T2 = NULL, alpha = NULL, beta = NULL, 
       design = list(nu = 0, m = 0, p = 0, sea = 0), 
       stvalue = list(sigma = 0.9, nu = 0.4, m = -1, p = 0.01, u = 0.4, w = 0.4), 
       upper = list(sigma = 5, nu = 1, m = 2, p = 1, u = 1, w = 1), 
       lower = list(sigma = 0, nu = 0, m = -2, p = 0, u = 0, w = 0), gestimate = TRUE, 
       st.ga = NULL, st.gb = NULL, st.galow = NULL, st.gaup = NULL, st.gblow = NULL,
       st.gbup = NULL, control = list(maxit = 10000))

Arguments

L1

Vector of length at release of tagged fish

L2

Vector of length at recovery of tagged fish

T1

Vector of time at release of tagged fish

T2

Vector of time at recovery of tagged fish

alpha

Numeric value giving an arbitrary length alpha

beta

Numeric value giving an arbitrary length beta (beta > alpha)

design

List specifying the design of the model to estimate. Use 1 to designate whether a parameter(s) should be estimated. Type of parameters are: nu=growth variability (1 parameter), m=bias parameter of measurement error (1 parameter), p=outli

stvalue

Starting values of sigma (s) and depending on the design argument, nu, m, p, u, and w used as input in the nonlinear estimation (function optim) routine.

upper

Upper limit of the model parameters' (nu, m, p, u, and w) region to be investigated.

lower

Lower limit of the model parameters' (nu, m, p, u, and w) region to be investigated.

gestimate

Logical specifying whether starting values of ga and gb (growth increments of alpha and beta) should be estimated automatically. Default = TRUE.

st.ga

If gestimate=FALSE, user-specified starting value for ga.

st.gb

If gestimate=FALSE, user-specified starting value for gb.

st.galow

If gestimate=FALSE, user-specified lower limit for st.ga used in optimization.

st.gaup

If gestimate=FALSE, user-specified upper limit for st.ga used in optimization.

st.gblow

If gestimate=FALSE, user-specified lower limit for st.gb used in optimization.

st.gbup

If gestimate=FALSE, user-specified upper limit for st.gb used in optimization.

control

Additional controls passed to the optimization function optim.

Value

• table
  list element containing the model output similar to Table 3 of Francis (1988). The Akaike's Information Criterion (AIC) is also added to the output.
• VBparms
  list element containing the conventional paramaters of the von Bertalanffy model (Linf and K).
• correlation
  list element containing the parameter correlation matrix.
• predicted
  list element containing the predicted values from the model.
• residuals
  list element containing the residuals of the model fit.

Details

The methods of Francis (1988) are used on tagging data to the estimate of growth and growth variability. The estimation of all models discussed is allowed. The growth variability defined by equation 5 in the reference is used throughout.

References

Francis, R.I.C.C., 1988. Maximum likelihood estimation of growth and growth variability from tagging data. New Zealand Journal of Marine and Freshwater Research, 22, p.42-51.

Examples

data(bonito)

#Model 4 of Francis (1988)
with(bonito,
 grotag(L1=L1, L2=L2, T1=T1, T2=T2,alpha=35,beta=55,
 	design=list(nu=1,m=1,p=1,sea=1),
 	stvalue=list(sigma=0.9,nu=0.4,m=-1,p=0,u=0.4,w=0.4),
 	upper=list(sigma=5,nu=1,m=2,p=0.5,u=1,w=1),
 	lower=list(sigma=0,nu=0,m=-2,p=0,u=0,w=0),control=list(maxit=1e4)))