ELSEVIER Fisheries Research 26 (1996) 125-137

Growth, mortality and yield-per-recruit of the deep-water shrimp Aristeus antennatus

(Crustacea-Aristeidae) of the Strait of Sicily (Mediterranean Sea)

Sergio Ragonese **a, Marco L. Bianchini b ” Iytituto di Tecnolog$ct dellu Pescc~ e de1 Pescuto, CNR, Viu L. Vuccara. 61, Mazaru del Vallo, Italy

’ P.F. RAISA, CNR. Rome, Italv

Accepted 2 I February 1995

Abstract

The MIX and Compleat ELEFAN methods were used to analyse length-frequency distributions of females of the deep-water shrimp Aristeus untennatus in order to estimate growth, mortality and yield- per-recruit. Length data were gathered in four seasonal experimental trawl surveys made in the Strait of Sicily (Mediterranean Sea). Up to four annual cohorts were distinguishable. Modal lengths were integrated and the parameters of the von Bertalanffy growth function estimated by a weighted non- linear regression, yielding an asymptotic carapace length of 69.1 mm and an annual Brody’s coefficient K= 0.532. with a location parameter to=0 (line through the origin). The consistency of these estimates was evaluated by comparison with the corresponding parameters obtained applying ELE- FAN-I and producing a confidence interval by bootstrap resampling; this last procedure revealed the

presence of two possible solutions corresponding to a ‘slow’ and a ‘fast’ growth hypothesis. The growth estimates derived from the modal progression analysis in any case fall inside the confidence ellipse of the bivariate plot of the asymptotic lengths and growth coefficients derived from the

bootstrapped data sets. The total annual mortality was estimated as Z= 1.1, following Heincke’s approximation; two values of annual natural mortality, M, = 0.5 and M,, = 0.8, were used afterwards. As a negative allometric length-weight relationship (h < 3) does exist, the incomplete beta function was applied to compute the yield-per-recruit values. Analysis of the Y/R curves suggests that the current Y/R scan be improved by a moderate increase, from 1 to 1.5 years, in the age of first capture; this could be obtained by increasing the mesh size of the cod-end from the present 18 mm to 28 mm, without any economic loss, even short term.

~‘UIL~OQ/.Y. An,tc’u.$ mtcmwtus; Red shrimps; Mediterranean Sea; Yield-per-recruit; Growth-fish

*- Corresponding author: Tel. + 39 923 948723, Fax. + 39 923 906634.

016%7836/96/$15.00 0 1996 Elsevier Science B.V. All rights reserved

.SSD/Ol65-7836(95)00394-O

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

1. Introduction

The blue-and-red shrimp, Aristeus antennatus Risso 1816, represents an important tra- ditional resource for the Mediterranean deep-water trawl fisheries (Relini and Orsi-Relini, 1987; Yahiaoui, 1990; Arculeo et al., 1992; Matarrese et al., 1992; Mura et al., 1992; Demestre and Lleonart, 1993; Demestre and Martin, 1993), especially for those operating in the Western basin (Sarda, 1988). The spatial distribution of this shrimp is quite complex

(Sarda et al., 1993)) but normally the species shoals in deep waters of the upper and middle slope (400-800 m) and it is caught by trawling on muddy bottoms, near to submarine trenches and canyons.

In the Strait of Sicily, Aristeus antennatus is generally less abundant than its companion species, Aristaeomorphu foliuceu Risso 1827 (Ragonese and Bianchini, 1992; Ragonese et al., 1994b); nevertheless, the blue-and-red shrimp represents a valuable resource even for Sicilian fishermen (Arena, 1985). More than 1000 tons of red shrimps (both Aristeus and Aristueomorphu) , worth about 16 million US$, were landed during 199 1 in Mazara (Anony- mous, 1992), a harbour in southern Sicily which hosts the largest trawl fleet in Italy.

Despite the large quantity of biological and dynamics information available for the

Western Mediterranean stocks of Aristeus untennutus (Demestre and Lleonart, 1993; Demestre and Martin, 1993), only scanty data exist on the biology and dynamics of the blue-and-red shrimp population in the Strait of Sicily (Azouz, 1972; Arena and Li Greci, 1973; Arena, 1985; Ragonese and Bianchini, 1992). Unfortunately, there are no series of catches and effort records available, and attempts to assess this resource are based only on length data gathered in multispecies trawl surveys (Levi, 1991).

In this paper, growth, mortality and yield-per-recruit of the female population of Aristeus

antennatus in the Strait of Sicily are investigated to indicate the exploitation level sustained

by this stock.

2. Materials and methods

Length-frequency distributions (LFD) were derived from four seasonal random stratified experimental trawl surveys carried out in the Strait of Sicily by the Institute of Fisheries (ITPP-CNR) of Mazara between spring 1986 and winter 1987.

Hauls were limited to 1 h in daylight; an ‘Italian’ bottom trawl with 18 mm mesh side in the cod-end, towed at about 2.7 knots, was used; sampling periods lasted for 15-20 days according to the meteorological conditions (Levi, 1991, for a description of the general programme).

Middle dorsal oblique carapace lengths (CL, mm) were measured on board on fresh specimens; the LFD of females, by 2 mm class sizes, were compiled for each survey (spring, summer and autumn 1986, and winter 1987), but male shrimps were not further considered as they are poorly represented in the fishable population.

The LFD were investigated using the Compleat ELEFAN software (Pauly, 1987; Gay- anilo et al., 1989) following the sequential population analysis approach (Caddy, 1986). The classical von Bertalanffy growth function (VBGF) was chosen as the elective growth model (Ricker, 1975).

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

Preliminary estimates of CL,, and K (Ragonese and Bianchini, 1992) were used as seed

values for the ELEFAN-I procedure; the program was run on the sequence of four LFD

(after smoothing, to reduce sample noise), until the best index of goodness-of-fit (R,),

compatible with the biological knowledge on the species, was found. The variance of the estimates of CL, and Brody’s coefficient (K) was evaluated by bootstrapping the sequence of the LFD, and repeatedly applying the ELEFAN-I procedure to obtain a set of paired

values.

‘Bootstrap’ or ‘bootstrapping’ is a relatively recent, computationally burdensome tech-

nique (Efron. 198 1) suitable for evaluating the statistical precision of estimates, even in

cases that iare not tractable using classical approaches, such as the parameters derived by

ELEFAN-K.

In fact, a series of new LFD was derived from the original LFD, by repeatedly extracting.

with replacement, a new set of equal size. A total of 98 bootstrappings of the original

sequence of LFD was derived by an ad hoc program (Bianchini et al., 1994). The ELEFAN-

I 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 bivariale ellipse of confidence (95%). The bootstrap estimate (Stuart and Ord, 1987)

of the sampling variance of each parameter was obtained by the classical formulations. The modes in the LFD were preliminarily discriminated using Bhattacharya’s method in

the MPA procedure of the Compleat ELEFAN, and these estimates (number of groups,

modal lengths and corresponding proportions and standard deviations) were used as seed

values for the MIX program, which is based on 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 modal progression analysis was performed by a weighted non-

linear fitting (least square methods, with Quasi-Newton and Simplex algorithms; SYSTAT,

1992) of the VBGF. The mean values of asymptotic length and Brody’s coefficient, derived by bootstrapping, represented the seed-values for the non-linear regression; the reciprocal of the standard error of the estimated modal length represented the weight factor.

Putative iabsolute ages (year) were assigned according to the available information on

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.

Annual total mortalities (Z) were estimated according to Heincke’s method (Ricker.

1975) ; the use of a length-converted catch curve (Pauly, 1987), based on the pooled LFD,

allowed another estimate of Z. As the annual natural mortality (M) is unknown. plausible values were derived from the

literature (n4, ca. 0.5: Yahiaoui, 1990; Demestre and Lleonart, 1993), and by applying Alagaraya’s approximation (in Sparre et al., 1989) : M, = - (log, 0.01 >lT,,;,, where T,,,., x refers to the age at which about 1% of one cohort would have survived in the absence of

the fishery ( the Mh 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).

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

The yield-per-recruit (Y/R) formulation according to the incomplete beta function can be written as follows:

Y/R= F/K W, e-z(‘c-‘O) &x,(u,u)

where F and Z represent the instantaneous fishing and total mortality, K is the Brody’s coefficient, W, is the asymptotic weight, t, is the mean age at first capture, f, is the location parameter of the VBGF model,

PXX,(40) =I:’ t”-’ (1-t)“-‘dt

is the incomplete beta function, u and u being its parameters, i.e., u = Z/K, u, the estimated allometric coefficient plus one (specific case u = 3.5), and the integration limits: x=

e -K(r,-ro) and X, = e-K(fr -10) (with t, = maximum age of contribution to the fishery). The tables of Wilimovsky and Wicklund ( 1963) were used to compute the discrete Y/R

values for different levels of F and two values of M (0.5; 0.8) and t, ( 1; 1.5 year); the curves were constructed after smoothing (LOWESS procedure, SYSTAT, 1992).

As a rule, mathematical and statistical computations were performed using the SYSTAT

( 1992) package.

3. Results

Aristeus antennatus is caught between depths of 500 m and 820 m, the latter representing the lowest explored and exploited boundary. The distribution area of the blue-and-red shrimp, according to trawl surveys data, is presented in Fig. 1, but it is abundant only in the north-western sector, around the Egadi Islands; in any case mean yields are generally lower

lOa E 15O E

Fig. 1. Delimitation of the Strait of Sicily and of the investigated area with, evidenced, the distribution of Aristeus

crntennatus.

S. Ragonese, M.L. Binnchini / Fisheries Research 26 (I 996) 125-137 129

0.15

0.10

0.06

0.15

0.10

0.05

Spring ‘86; N=156

LO 42

Summer ‘86; NH29

- 42

f r e n

q u e C

i e s

0.25 1 Autumn ‘86; N=280

0.20

0.1s j

0.10

i

0.05 r

0.20 -1 Winter ‘87; N=233

0.15

0.10

0.05

20 42 64

Carapace length (mm)

Fig. 7. Length frequency distributions for female of Aristeus nnrennafu.s. The asterisks on the abscissa denote the

modal length estimated by MIX.

130 S. Rqonese. M.L. Bianchini / Fisheries Research 26 (1996) 125-137

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Brody’s cwfticient (K/y)

I.(

Fig. 3. Scatterplot of asymptotic length and Brody’s coefficient resulting from bootstrapping the LFD under the

ELEFAN-I routine with the corresponding bivariate confidence ellipsoid (95%). for Arisreus anfemms. The

asterisk denotes the location of the estimates derived by MIX.

than 5 kg h-- ’ (Ragonese and Bianchini, 1992)) with the catch dominated by females (sex ratio 6 : 1) . Incidentally, the captures of Aristeus antennatus are not correlated with the

abundance or scarcity of Aristaeomorpha foliacea.

A total of 798 females were measured, i.e. 156, 129,280 and 233 for the spring, summer, autumn and winter survey, respectively. The smallest length is 22 mm CL, and the largest

66 mm CL. The mean length of the pooled sample is 41.3 mm CL (with an SD of 8.7 mm); most of the sample (98%)) falls in the range 26-61 mm CL. Males are smaller, averaging only 29.7 mm CL.

Length frequency distributions (Fig. 2) show at least two clear modes. The start of recruitment is observed in summer, but the young-of-the-year appear to be fully recruited

only in autumn when the cohort is well represented and discriminated from the adult stock.

Table I Descriptive statistics for asymptotic length (CL,; mm), Brody’s coefficient (K/y), and index of goodness of fit

CR,, ) derived after bootstrapping (II = 99) the LFD under the ELEFAN-I routine, for Arisfeus anfennatus

Statistics Fast

CL. K/?: R,,

Slow

CL, wy R,,

Combined

CL, K/Y R,,

Minimum 55.0 0.67 0.43 61.0 0.38 0.35 55.0 0.38 0.35

Maximum 67.0 0.79 0.78 87.0 0.5 I 0.84 87.0 0.79 0.84

Mean 61.0 0.74 0.57 74.5 0.45 0.54 67.7 0.59 0.56

SE 0. I 0.0 I 0.0 1 0.3 0.0 I 0.01 0.5 0.0 I 0.01

Skewness 0.2 - 0.8 I 0.00 0.6 -0.26 0.0 I 0.2 -0.01 0.00

Median 61.0 0.74 0.57 74.0 0.45 0.54 67.0 0.53 0.55

S. Rngonese, M.L. Bianchini / Fisheries Research 26 (1996) 125-137 131

Table 2

Resolution of the length frequency distributions according the MIX method, forAri.veus nnfennatus

SeaSOIl Group MIX

Carapace length f mm)

MPA

Carapace length

(mm)

Mean SE ,$ df P ?TO Mean

Spring I986 I 0.4 I 43.0 1.2 0.47 43.5

II 0.58 S3.8 I .o 0.52 54.2

3.2 9 0.96

Summer I 0.36 29.3 0.5 0.3.5 29.2

I986 II 0.46 44.4 0.5 0.47 44.6

III 0.13 5.5.8 I.3 0.15 56.3

IV 0.05 62.9 I .6 0.02 64.3

11.x I4 0.62

Autumn 1986 I 0.67 33. I 0.2 0.68 33.1

II 0.22 45.3 I .9 0.25 46.4

III 0.1 I 53.3 2.7 0 07 54.4

7.1 9 0.62

Winter I987 I 0.78 38.9 0.4 0.82 39.4

II 0.22 SO.8 I .4 0.17 5 I .7

111 0.01 58.7

14.2 14 0.43

TO. Group proportion in numbers; SE, standard error of the mean; ,$, chi-square statistic; df, degree of freedom:

P. probability level.

The application of the ELEFAN-I results in two satisfactory (both R, above 0.5) and plausible scenarios (Fig. 3): ‘fast’ growth, with CL, =61 mm and K=0.74. and ‘slow’ growth. with CL, = 74 mm and K= 0.45 (other descriptive statistics and those correspond-

0.5 1.5 2.5 3.5

Putative absolute age (y)

4.5

Fig. 4. Integrated modal lengths versus putative age with, overimposed, the fitted VBGF (CL = 69. I mm;

K/Y = 0.532: I(, = O), for Arr.steu.s mrenm~tus. Vertical bars denote the standard errors of the estimated means.

132 S. Rqonese, M.L. Bianchini/ Fisheries Research 26 (1996) 125-137

Table 3 List of the parameters used for the computation of the yield-per-recruit values for Arisfeus antennam

Parameters

Comments

cr, K

to

G t; Z

M,

MI,

F,

F,> t,,;, x ‘A W.<

mm 69.1

Y -I 0.532

Y 0

Y I Y 1.5

Y -I I.1

Y -I 0.5

Y -I 0.8

Y -I 0.6

Y -I 0.3

Y 6

Y 4

g 66

Asymptotic length derived from modal length analysis

Brody’s coefficient

VBGF location parameter (the line passes through the origin)

Mean age at first capture

Assumed new age at first capture

Total mortality rate according to Heincke’s method

Natural mortality rate from literature

Natural mortality rate according to Alagaraya’s approximation

Fishing mortality according to Z- M, Fishing mortality according to Z - Mh Theoretical life span

Maximum age of actual contribution to the fishery

Asymptotic weight according to the estimated VBGF and the

length-weight relationship from literature

ing to combined data are summarized in Table 1). ‘Fast’ estimates fit slightly better than

‘slow’ estimates with the exception of the skewness in the Brody’s coefficient. It is worth

noting that despite the large range of the combined data, the estimates can be considered

quite satisfactory, given the resulting standard errors and the index of skewness (‘fast’

standard errors: 0.52 for CL, and 0.007 for K; ‘slow’ standard errors: 0.56 for CL, and

0.030 for K) . As expected, a strong (negative) correlation exists between the two growth

parameters when data are considered together (? = 0.856).

The MIX program leads to the identification of a minimum of two (spring and winter

surveys) and a maximum of four (summer survey) well discriminated modal groups, which

should reflect different annual cohorts, because of the discrete recruitment observed; the

results of the MIX analysis (number of groups, proportions, modal length and standard

error, comparison test) are summarized in Table 2. Significant differences (PcO.05)

between estimated and observed LFD were never detected.

Table 2 also reports the results of the MPA procedure (proportions and modal length) ; both methods produce practically the same results.

The MIX estimated modal lengths range from 29.3 mm to 62.9 mm CL (summer survey),

and generally the standard errors appear to be quite satisfactory, notwithstanding the limited

sample sizes. An absolute age of 1 year from hatching was assigned to the youngest modal

group (29.3 mm CL), according to the hypothesis that the recruits derive from the spawn of the previous summer (Azouz, 1972).

The ‘integration’ of the modal lengths (Fig. 4) suggests an asymptotic pattern of growth.

A preliminary fitting of the data revealed that the parameter to was not significantly different from zero and consequently data wererefitted with two parameters only. Both Quasi-Newton

and Simplex algorithms converge quickly on the estimates CL, = 69.1 mm (SE = 2.32) and K = 0.532 (SE = 0.028)) independently from the initial seeds values, ‘fast’ or ‘slow’, used.

S Ragonese. M.L. Bianchini / Fisheries Research 26 (1996) 125-137 133

20.0

15.0

B .g

b 10.0 t i

f S .‘y k

5.0

0.0

ilj:: /----- / / / /

‘M=O.S 1

20.0

5.0

0.a

0.0 0.3 0.6 0.9 1.2 1.5 1.8

b)

_ _ -~ - -

0.0 0.3 0.6 0.9 1.2 IS 1.8

Fishing mortality (F/year)

Fig. 5. Yield-per-recruit curves for M,, = 0.8 (above) or M, = 0.5 (below) with f, = 1 year and I,* = 1.5 year, for

Arisreu.v untemutu.s. The asterisk denotes the current level of exploitation according to the growth and mortality

estimates.

As a matter of fact, the curve fits the data quite well and it is worth noting that the MIX- integrated growth estimates fall inside the bivariate ellipse of confidence of the ELEFAN- I bootstrapped estimates (Fig. 3).

Concerning the annual total mortality (Z), Heincke’s method gives values of 0.4 and I. 1 for the summer and autumn survey respectively, whereas the length-converted catch curve yields a higherrange of values ( 1.3-I S) . The spring value (Z= 0.4) seems too low, whereas

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

between the other alternatives 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 of 6 years (Demestre and Lleonart, 1993)) Alagaraya’s approximation produces an annual natural mortality coefficient M = 0.77, approximated to Mh = 0.8 for successive computations; the alternative Ml = 0.5 represents a more conser- vative choice. The parameters used to compute the yield-per-recruit values are summarized

in Table 3; the resulting four curves, for the two mean ages of first capture (t, = 1; t,* = 1.5) and the two M values, are presented in Fig. 5. As expected, the shape of the curves suggests a rapid increase of Y/R for small increments of F, and thereafter the curves flatten out,

without any evidence of a clear maximum. For M,, = 0.8, the yield-per-recruit could be substantially increased even by raising only

F (i.e. the population is actually underexploited) ; on the contrary, for Ml = 0.5, gains in

the Y/R could not 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 (Sardh, 1986) for Aristeus anten-

natus are only in an embryonic phase. Despite the discontinuities in the growth process

(Dal1 et al., 1990), continuous asymptotic models, such as the VBGF, are considered a reasonable approximation for shrimps (Pauly et al., 1984; Garcia, 1985).

Table 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 and a relatively long life span (up to 6 years) ; the annual Brody’s coefficients fall in the range 0.3-0.9, with the exception of the Ligurian stock (K= 1.71; Orsi-Relini and Relini, 1985).

While all 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 (Sarda, 1988).

Table 4

Summary of the VBGF estimates for the Mediterranean populations of Aristeus antennatus (CL, in mm; to in

year)

Area CL, Source

Catalan Sea 16 0.3

Algeria 63.5 0.33

Ligurian Sea 63 1.71 Southern Tyrrhenian 69.4 0.34 tonian Sea 66.2 0.93

Strait of Sicily 69.1 0.53

- 0.07 Demestre and Lleonart (1993)

Yahiaoui (1990)

0.44 Orsi-Relini and Relini (1985)

Arculeo et al. ( 1992)

Matarrese et al. (1992) 0 Present paper

S. Rqonese, M.L. Bianchini / Fisheries Research 26 (1996) 125-137 135

Concerning the mortality estimates, the steady-state assumption of Heincke’s approach

can be accepted, given the relative stability, in both recruitment and fishing pattern, reported

for the Sicilian fishery in the last decade (Arena, 1985) and more generally also in the Catalan Sea (Demestre and Martin, 1993).

Determining a natural mortality value is a critical and always difficult choice (Vetter, 1988)) particularly for deep-water shrimps.

The situation is further complicated by the possibility that F is age- or size-dependent, as female,s of Aristeus antennatus could be more vulnerable when aggregated to spawn (Demestre and Lleonart, 1993).

Moreover, an inverse relationship between F and M has been suspected for short-living

highly predated animals (Cobb and Caddy, 1989); according to this hypothesis, over a wide range of exploitation regimes, as F increases, M would decrease, resulting in a constant value of Z. However, deep-water red shrimps should not be considered highly-predated

animals (Demestre and Martin, 1993). Notwithstanding the different approach, the shape of the Y/R curves (Fig. 5) obtained

for the Sicilian population resembles that of Demestre and Lleonart ( 1993) off the Catalan

coasts. Aristeu:; antennatus populations are generally considered resilient to exploitation, mainly

because only the upper fraction of the stock is available to the trawl (Demestre and Lleonart, 1993; Demestre and Martin, 1993; SardB et al., 1993).

Considering the high fishing pressure exerted on the demersal resources of the Mediter- ranean Sea (Anonymous, 1989), a condition of underexploitation (e.g. M,=O.8 and Z= 1.1) is unlikely, making the Y/R curves based on M, = 0.5 more realistic. The compar-

ison between the two curves in Fig. 5b suggests a condition of growth-overfishing, and yield-per-recruit should increase substantially by delaying the age at first capture to 1.5

years (corresponding to CL = 38 mm). The possibility of achieving this result by concentrating the 45 days of the annual fishing

ban in summer (Levi, 1991) does not seem to be practicable because the fishing activity peaks in season. As the mesh size presently in use ( 16-18 mm, side) is not selective, the only feasible management tool would be an increase in the cod-end mesh size.

Moreover, recent selectivity studies suggest that a mesh size up to 28 mm side can be employed to reduce the juveniles in the catch without any substantial loss of adult (and more prized ) animals (Ragonese et al., 1994a).

In conclusion, under any scenario, a delay of 6 months in the age at first capture would result in an increase of the yield-per-recruit, without any economic harm, even short-term.

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