Page 3 - Ragonese_Bianchini_1996

S. Ragonese, M.L. Bianchini l Fisheries Research 26 ( 1996) 125-137 127

Preliminary estimates of CL~ an d K ( Ragonese an d Bianchini, 1992) were used as seed
values for the ELEFAN-1 procedure; the program was run on the sequence of four LFD
( after smoothing, to reduce sample noise), unti! the best index of goodness-of-fit (R 0 ),
compatible with the biologica! knowledge on the species, was found. The variance of the
estimates of CLL and Brody's coefficient (K) was evaluated by bootstrapping the sequence
of the LFD, and repeatedly applying the ELEFAN-1 procedure to obtain a set of paired
values.
'Bootstrap' or 'bootstrapping' is a relatively recent, computationally burdensome tech-
nique (Efron, 1981) suitable for evaluating the statistica! precision of estimates, even in
cases that are not tractable using classica! approaches, such as the parameters derived by
ELEFAN-I.
In fact, a series of new LFD was derived from the originai LFD, by repeatedly extracting,
with replacement, a new set of equa! size. A total of 98 bootstrappings of the originai
sequence ofLFD was derived by an ad hoc program (Bianchini et al., 1994). The ELEFAN-
1 procedure was applied on each of these new sequences and the resulting sets of growth
parameters were used to compute mean values, other descriptive statistics and to construct
the bi variate ellipse of confidence (95%). The bootstrap estimate ( Stuart and Ord, 1987)
of the sampling variance of each parameter was obtained by the classica! formulations.
The m od es in the LFD were preliminarily discriminated using Bhattacharya' s method in
the MPA procedure of the Compleat ELEFAN, and these estimates (number of groups,
moda! lengths and corresponding proportions an d standard deviations) w ere used as seed
values for the MIX program, which is based o n a maximum likelihood criterion (MacDonald
and Green, 1985).
MIX estimates were integrated, or 'stretched' (Caddy, 1986), on the assumption of a
'steady-state' condition. A moda! progression analysis was performed by a weighted non-
linear fitting ( least square methods, with Quasi-Newton and Simplex algorithms; SYSTAT,
1992) ofthe VBGF. The mean values of asymptotic length and Brody's coefficient, derived
by bootstrapping, represented the seed-values for the non-linear regression; the reciproca!
of the standard error of the estimated moda! length represented the weight factor.
Putative absolute ages ( year) w ere assigned according to the available information o n
the reproductive biology of the population, i.e. a single spawning peak in summer (Azouz,
1972); 3 months (i.e. 0.25 year) were assumed as the time interval between surveys.
Annua! total mortalities (Z) were estimated according to Heincke's method (Ricker,
1975); the use of a length-converted catch curve ( Pauly, 1987), based o n the pooled LFD,
allowed another estimate of Z.
As the annua! natura! mortality (M) is unknown, plausible values were derived from the
literature (M 1 ca. 0.5: Yahiaoui, 1990; Demestre and Lleonart, 1993), and by applying
Alagaraya's approximation (in Sparre et al., 1989): Mh=- (log" 0.01)/Tmax where Tmax
refers to the age at which about l% of one cohort would have survived in the absence of
the fishery ( the M h that resulted in the present case was about 0.8).
Length-weight relationships do not exist for Aristeus antennatus in the area studied, but
analogous data indicate a strong negative allometry (Demestre and Lleonart, 1993); con-
sequently, the incomplete beta function was used to compute Beverton and Holt's yield-
per-recruit curves (Paulik and Gales, 1964).