growthmultifit: Fit a Multi-Group Growth Model

In fishmethods: Fishery Science Methods and Models

Fit a Multi-Group Growth Model

Description

Fits a von Bertalanffy, Gompertz or logistic growth curve to length and age for two or more groups.

Usage

growthmultifit(len=NULL,age=NULL,group=NULL,model=1,fixed=c(1,1,1),error=1,
        select=1,Linf=c(NULL),K=c(NULL),t0=c(NULL),plot=FALSE,
                control=list(maxiter=10000,minFactor=1/1024,tol=1e-5))

Arguments

len	the vector of lengths of individual fish.
age	the vector of ages associated with the length vector.
group	the vector of character names specifying group association. The first character in the name must be a letter.
model	which model to fit. 1= von Bertalanffy, 2= Gompertz, and 3 = logistic. Default=1.
fixed	arguments specifying that Linf, K or t0 should be fitted as a constant between groups or as separate parameters for each group. 1 = single parameter between groups, 2 = separate parameters for each group. The order of fixed is c(Linf,K,t0).
error	the error variance assumption. 1= constant variance for all lijs; 2= constant variance for all mean lengths at age; 3=var of lij varies with age. See methods a-c in Kimura (1980: pp. 766). The required statistics for each type of error are calculated from the individual length-age observations.
select	the selection of starting values of L-infinity, K, and t0. 1=automatic selection, 2=user-specified. If select=1, initial starting values of L-infinity, K, and t0 are calculated from Walford lines (Everhart et al. 1975), and ages represented as decimal values are truncated to the integer before linear regression is applied. If select=2, the user must specify values of L-infinity, K, and t0 for each group.
Linf	if select=2, the starting values for L-infinity of the von Bertalanffy equation, one for each group.
K	if select=2, the starting values for K of the von Bertalanffy equation, one for each group.
t0	if select=2, the starting value for t0 of the von Bertalanffy equation, one for each group.
plot	logical argument specifying whether observed versus predicted and residuals graphs should be plotted. Default is FALSE.
control	see function nls.

Details

A von Bertalanffy, Gompertz or logistic model is fitted to the length and age data of two or more groups using function nls (nonlinear least squares). Parameters can be estimated for each group or as constants across groups. Individual observations of lengths-at-age are required. If error variance assumptions 2 or 3, mean lengths and required statistics are calculated. The parameters are fitted using a model.matrix where the 1st column is a row of 1s representing the parameter estimate of the reference group (group with lowest alpha-numeric order) and the remaining group columns have 1 if group identifier is the current group and 0 otherwise. See function model.matrix. This is a companion function to function growthlrt. If errors arise using automatic selection, switch to select=2.

When separate parameters are estimated for each group, estimates for the the non-reference groups would be the reference-group estimated parameters (e.g., Linf1 or K1 or t01) plus the coefficent estimate for the nth group (e.g., group 2: Linf2 or K2, or t02) based on the alpha-numeric order. If the parameter is assumed constant across groups, then estimates of Linf1 or K1 or t01 is used as the parameter for each group. The von Bertalanffy equation is Lt=Linf*1-exp(-K*(age-t0)). The Gompertz equation is Lt=exp(-exp(-K*(age-t0))). The logistic equation is Lt=Linf/(1+exp(-K*(age-t0))).

Value

results	list element containing summary statistics of nls fit
residuals	list element with the residuals from the model.

Author(s)

Gary A. Nelson, Massachusetts Division of Marine Fisheries [e-mail]

References

Everhart, W. H., A. W. Eipper, and W. D. Youngs. 1975. Principles of Fishery Science. Cornell University Press.

Kimura, D. K. 1980. Likelihood methods for the von Bertalanffy growth curve. U. S. Fish. Bull. 77(4): 765-776.

See Also

growthlrt

Examples

data(Kimura)
growthmultifit(len=Kimura$length,age=Kimura$age,group=as.character(Kimura$sex),
model=1,fixed=c(2,1,1),
error=1,select=1,Linf=NULL,K=NULL,t0=NULL,plot=FALSE,control=list(maxiter=10000,
minFactor=1/1024,tol=1e-5))

fishmethods documentation built on April 27, 2023, 9:10 a.m.