fishmethods (version 1.12-1)

grotagplus: Flexible maximum likelihood estimation of growth from multiple tagging datasets.

Description

This is an extension of fishmethods function grotag to allow a wider variety of growth models and also the simultaneous analysis of multiple tagging datasets with parameter sharing between datasets (see Details).

As in grotag, the data are fitted using a constrained maximum likelihood optimization performed by optim using the "L-BFGS-B" method. Estimated parameters can include galpha, gbeta (mean annual growth at reference lengths alpha and beta); b (a curvature parameter for the Schnute models); Lstar (a transitional length for the asymptotic model); m, s (mean and s.d. of the measurement error for length increment); nu, t (growth variability); p (outlier probability); u, w (magnitude and phase of seasonal growth).

Usage

grotagplus(tagdata, dataID=NULL,alpha, beta = NULL,
 model=list(mean="Francis",var="linear",seas="sinusoid"),
 design, stvalue, upper, lower,fixvalue=NULL,
 traj.Linit=c(alpha,beta),control = list(maxit = 10000), debug = FALSE)

Value

parest

Parameter estimates and their s.e.s.

parfix

Parameter values, if any, fixed by user.

correlations

Correlations between parameter estimates. When there are multiple estimates of a parameter these are numbered by their ordering in argument design, so in example given above galpha1 would apply to Area1, and galpha2 to Area2 and Area3.

stats

Negative log-likelihood and AIC statistic.

model

The three components of the grotagplus argument model.

datasetnames

The dataset names, if there are multiple datasets.

pred

Dataframe of various predicted quantities need for residual plots - one row per data record.

Linf.k

Values of parameters Linf and k as calculated between equations (1) and (2) of Francis (1988) (but not possible for the Schnute model). These are provided for computational convenience only; they are not comparable with Linf and k estimated from age-length data. Comparisons of growth estimates from tagging and age-length data are better done using output meananngrowth.

meananngrowth

Data for plot of mean annual growth vs length, as in Fig. 8 of Francis and Francis (1992).

traj

Data for plots of growth trajectories like Fig. 2 of Francis (1988).

Arguments

tagdata

Dataframe with components L1, L2 (lengths at release and recovery of tagged fish), T1, T2 (julian times (y) at release and recovery), and (optionally), a numeric or character vector (named by argument dataID) identifying which dataset each data record belongs to (with n datasets this must include n unique values). Other components are ignored, as are any records with missing values in the required components.

dataID

Name of optional component of tagdata identifying separate datasets within tagdata. The default dataID=NULL means there is no such component (so there is only one dataset).

alpha

Numeric value giving an arbitrary length alpha.

beta

Numeric value giving an arbitrary length beta (must have beta > alpha).

model

List with components mean, var, seas, specifying which model equations to use for the mean (or expected) growth, individual variability in growth, and seasonal variation in growth (see Details for valid values). The default is that of model 4 in Francis (1988).

design

List specifying the design of the estimation: which parameters are estimated, and whether multiple values are estimated. There should be one component for each parameter of the model specified by model. Each component must be either 0 (not estimated), 1 (same parameter value estimated for all data), or, when there are multiple datasets, a list in which each component is a sub-vector of unique(tagdata[[dataID]]) and all members of unique(tagdata[[dataID]]) occur in one and only one component of the list (e.g., galpha=list("Area2",c("Area1", "Area3") ) means that two values of galpha are to be estimated: one applying to the dataset Area2, and the other to datasets Area1 and Area3).

stvalue

List containing starting values of estimated parameters, used as input in the nonlinear estimation (function optim) routine. There should be one component for each estimated parameter (except, optionally, galpha and gbeta). Each component should be either a single number or a vector whose length is the number of separate values of that parameter (as specified in design). In the latter case, the order of the parameter values should correspond to that in design (e.g., if design$galpha is as above and stvalue$galpha=c(10,15) then 10 will apply to Area2 and 15 to Area1 & Area3). If galpha or gbeta are omitted from stvalue then their starting values are calculated from the data.

lower

Lists containing lower limits for each parameter, with structure as for stvalue. galpha and/or gbeta may be omitted if they don"t appear in stvalue.

upper

Lists containing upper limits for each parameter, with structure as for stvalue. galpha and/or gbeta may be omitted if they don"t appear in stvalue.

fixvalue

Optional list containing fixed values for parameters that are needed (according to model) but are not being estimated (according to design) and do not have default values (the only default parameter values are nu = 0, m = 0, p = 0). The list should have one named component for each fixed parameter. Usually, each component will be a single number. See example below for the required format when a fixed parameter takes different values for different datasets.

traj.Linit

Vector of initial length(s) for output growth trajectories. Default is c(alpha,beta).

control

Additional controls passed to the optimization function optim.

debug

output debugging information.

Author

Chris Francis

Marco Kienzle

Gary A. Nelson, Massachusetts Division of Marine Fisheries

Details

Valid values of model$mean are "Francis" as in Francis (1988). "Schnute" as in Francis (1995). "Schnute.aeq0" special case of Schnute - see equns (5.3), (5.4) of Francis (1995). "asymptotic" as in Cranfield et al. (1996).

Valid values of model$var are "linear" as used in the example in Francis(1988) - see equn (5). "capped" as in equn (6) of Francis(1988). "exponential" as in equn (7) of Francis(1988).

"asymptotic" as in equn (8) of Francis(1988). "least-squares" ignore individual variability and fit data by least-squares, as in Model 1 of Francis(1988).

Valid values of model$seas are "sinusoid" as in model 4 of Francis(1988). "switched" as in Francis & Winstanley (1989). "none" as in all but model 4 of Francis(1988).

The option of multiple data sets with parameter sharing is intended to allow for the situation where we wish to estimate different mean growth for two or more datasets but can reasonably assume that other parameters (e.g., for growth variability, measurement error, outlier contamination) are the same for all datasets. This should produces stronger estimates of these other parameters. For example, Francis & Francis (1992) allow growth to differ by sex, and in Francis & Winstanley (1989) it differs by stock and/or habitat.

grotagplus may fail if parameter starting values are too distant from their true value, or if parameter bounds are too wide. Try changing these values. Sometimes reasonable starting values can be found by fitting the model with other parameters fixed at plausible values.

References

1 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.

2 Cranfield, H.J., Michael, K.P., and Francis, R.I.C.C. 1996. Growth rates of five species of subtidal clam on a beach in the South Island, New Zealand. Marine and Freshwater Research 47: 773-784.

3 Francis, R.I.C.C. 1995. An alternative mark-recapture analogue of Schnute"s growth model. Fisheries Research 23: 95-111.

4 Francis, R.I.C.C. and Winstanley, R.H. 1989. Differences in growth rates between habitats of southeast Australian snapper (Chrysophrys auratus). Australian Journal of Marine & Freshwater Research 40: 703-710.

5 Francis, M.P. and Francis, R.I.C.C. 1992. Growth rate estimates for New Zealand rig (Mustelus lenticulatus). Australian Journal of Marine and Freshwater Research 43: 1157-1176.

See Also

plot.grotagplus print.grotagplus

Examples

#Model 4 of Francis (1988)
data(bonito)
grotagplus(bonito,alpha=35,beta=55,
               design=list(galpha=1,gbeta=1,s=1,nu=1,m=1,p=1,u=1,w=1),
               stvalue=list(s=0.81,nu=0.3,m=0,p=0.01,u=0.5,w=0.5),
               upper=list(s=3,nu=1,m=2,p=0.1,u=1,w=1),
               lower=list(s=0.1,nu=0.1,m=-2,p=0,u=0,w=0))

#Model 1 of Francis (1988), using least-squares fit
grotagplus(bonito,alpha=35,beta=55,
               model=list(mean="Francis",var="least-squares",seas="none"),
               design=list(galpha=1,gbeta=1,s=1,p=0),
               stvalue=list(s=1.8),upper=list(s=3),lower=list(s=1))

#Paphies donacina model in Table 4 of Cranfield et al (1996) with
#asymptotic model
data(P.donacina)
grotagplus(P.donacina,alpha=50,beta=80,
       model=list(mean="asymptotic",var="linear",seas="none"),
       design=list(galpha=1,gbeta=1,Lstar=0,s=1,nu=0,m=0,p=0),
       stvalue=list(galpha=10,gbeta=1.5,s=2),
       upper=list(galpha=15,gbeta=2.7,s=4),
       lower=list(galpha=7,gbeta=0.2,s=0.5),
       fixvalue=list(Lstar=80))

#Paphies donacina model in Table 4 of Cranfield et al (1996) with
#asymptotic model
data(P.donacina)
grotagplus(P.donacina,alpha=50,beta=80,
       model=list(mean="asymptotic",var="linear",seas="none"),
       design=list(galpha=1,gbeta=1,Lstar=0,s=1,nu=0,m=0,p=0),
       stvalue=list(galpha=10,gbeta=1.5,s=2),
       upper=list(galpha=15,gbeta=2.7,s=4),
       lower=list(galpha=7,gbeta=0.2,s=0.5),
       fixvalue=list(Lstar=80))

# Model 4 fit from Francis and Francis (1992) with different growth by sex
data(rig)
grotagplus(rig,dataID="Sex",alpha=70,beta=100,
           model=list(mean="Francis",var="linear",seas="none"),
          design=list(galpha=list("F","M"),gbeta=list("F","M"),s=1,nu=1,m=0,p=0),
          stvalue=list(galpha=c(5,4),gbeta=c(3,2),s=2,nu=0.5),
          upper=list(galpha=c(8,6),gbeta=c(5,4),s=4,nu=1),
          lower=list(galpha=c(3,2),gbeta=c(1.5,1),s=0.5,nu=0.2))

#Example where all parameters are fixed 
# to the values estimated values for model 4 of Francis and Francis (1992)]
grotagplus(rig,dataID="Sex",alpha=70,beta=100,
          model=list(mean="Francis",var="linear",seas="none"),
          design=list(galpha=0,gbeta=0,s=0,nu=0,m=0,p=0),
          stvalue=list(),upper=list(),lower=list(),
          fixvalue=list(galpha=list(design=list("F","M"),value=c(5.87,3.67)),
          gbeta=list(design=list("F","M"),value=c(2.52,1.73)),s=1.57,nu=0.58))