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

between the other alternati ves Heincke' s autumn estimate ( Z = 1.1 ) should be preferred
since the method is more suitable for cases of discrete recruitment.
Assuming a maximum life span of6 years (Demestre and Lleonart, 1993), Alagaraya's
approximation produces an annua! natura! mortality coefficient M= O. 77, approximated to
M h= 0.8 for successive computations; the alternative M = 0.5 represents a more conser-
1
vative choice. The parameters used to compute the yield-per-recruit values are summarized
in T ab le 3; the resulting four curves, for the two mean ages of first capture (te= l; tz = 1.5)
and the two M values, are presented in Fig. 5. As expected, the shape of the curves suggests
a rapi d increase of Y l R for small increments of F, and thereafter the curves ftatten out,
without any evidence of a clear maximum.
For M h= 0.8, the yield-per-recruit could be substantially increased even by raising only
F ( i.e. the population is actually underexploited); o n the contrary, for M = 0.5, gains in
1
the Y l R could no t be obtained without changing the age of first capture too.

4. Discussion

Length-based methods are currently the only techniques available for the estimation of
growth and mortality parameters for deep-water shrimps, as hard parts are lost during
moulting, tagging is not feasible, and rearing experiences ( Sardà, 1986) for Aristeus anten-
natus are only in an embryonic phase. Despite the discontinuities in the growth process
(Dali et al., 1990), continuous asymptotic models, such as the VBGF, are considered a
reasonable approximation for shrimps (Pauly et al., 1984; Garcia, 1985).
T ab le 4 summarizes the VBGF estimates for other Mediterranean populations of Aristeus
antennatus ( see the introduction for references), which indicate asymptotic carapace lengths
ranging from 63 to 76 mm an d a relatively long l ife span ( up to 6 years); the annua! Brody's
coefficients fall in the range 0.3-0.9, with the exception of the Ligurian stock (K = 1.71;
Orsi-Re lini and Relini, 1985).
While ali growth values (MIX, 'fast' and 'slow' ELEFAN) for the population of the
Strait of Sicily fall inside the above ranges, the present analysis shows the need to take into
consideration the variability of parameters (mainly a sampling problem) on one side, and
the consistency of the MIX estimates on the other side.
The population of the Strait of Sicily shows a discrete recruitment, whereas a more or
less prolonged presence of juveniles is generally reported for the other populations ( Sardà,
1988).
T ab le 4
Summary of the VBGF estimates for the Mediterranean populations of Aristeus antennalus ( CL.x in mm; 1 0 in
year)

Area C Lx Kly lo Source
Catalan Sea 76 0.3 -0.07 Demestre and Lleonart ( 1993)
Algeria 63.5 0.33 Y ahiaoui (1990)
Ligurian Sea 63 1.71 0.44 Orsi-Relini and Relini ( 1985)
Southern Tyrrhenian 69.4 0.34 Arculeo et al. (1992)
lonian Sea 66.2 0.93 Matarrese et al. ( 1992)
Strait of Sicily 69.1 0.53 o Present paper