parameter values were [L.sub.[infinity]] = 150.0 mm TL, K = 1.64 annual and [t.sub.0] = -0.11 year[s.sup.-1] for S.
6) after fitting the VBGM
to the length-at-age data, whereas Morro Bay and Catalina Island had the lowest values of [L.sub.inf] (Fig.
where conditional probability P(l/a) of being in a discrete length l given age a follows a normal distribution around the predicted length-at-age ([L.sub.a]) based on the VBGM
showed the higher growth constant of all the studied models ([0.028.week.sup.-1]).
This equation was fitted for males and females separately, and an analysis of the residual sum of squares (ARSS) was used to compare VBGM
's by sex (Ratkowsky 1983; Chen et al.
where k = instantaneous growth coefficient obtained with VBGM
. The Electronic Length Frequency Analysis (ELEFAN II) method was used to estimate the recruitment pattern (Pauly & David, 1981; Pauly, 1987), which projects the samples of frequency length presented in the catches back on the time axis.
Special cases 1 and 2 of the Schnute model were the same as the VBGM
and Logistic models, respectively.
We fitted the VBGM
and obtained estimates of growth model parameters, using a nonlinear regression in R, vers.
where [L.sub.a,i] is the predicted length of individuals i at age a; [mu] [L .sub.[infinity]] is the mean VBGM
asymptotic length parameter, and [L .sub.[infinity],i] is the deviation from [mu] [L .sub.[infinity]], of the asymptotic length for individual I; [mu] k is the mean VBGM
growth parameter, [k.sub.i], is the deviation from [mu] k of the growth parameter for individual i; [t.sub.a,i] is the size at hatch of individuals i at age a [[mu]t.sub.0] is the mean VBGM
age-at-hatch parameter, and [t.sub.0,i] is deviation from [[mu]t.sub.0] of the age-at-hatch for individual.
One of the approximations widely used during the past two decades to estimate the VBGM
parameters ([L.sub.[infinity]] and k) are the so called length-based methods (LBM's) or indirect methods (IM).
Another significant result shown in Table 4 is the Delta value ([DELTA]i) for each model; the [DELTA]i values were higher than 10 for the Case 2 (equivalent to Gompertz model) and special case 1 (equivalent to VBGM
model) models, that is, there were not supported by the data.
Age data for both species were fitted to the von Bertalanffy growth model (VBGM