growth discontinuity in males of the deep-water giant red shrimp aristaeomorpha foliacea in the...

SHORT COMMUNICATION

Growth discontinuity in males of the deep-water giant redshrimp Aristaeomorpha foliacea in the Mediterranean SeaSergio Ragonese1, Sergio Vitale1, Mark Dimech2 & Alberto De Santi1

1 Institute for Marine and Coastal Environment, Italian National Research Council, IAMC-CNR, via L. Vaccara, Mazara del Vallo (TP), Italy

2 Malta Centre for Fisheries Science (MCFS), Fort San Lucjan Marsaxlokk, BBG, Malta

Introduction

Deep-water giant red shrimp Aristaeomorpha foliacea

(Risso, 1827) is a highly valuable resource in the

Mediterranean Sea (Bianchini & Ragonese 1994; Cau et al.

2002; Papaconstantinou & Kapiris 2003; Politou et al.

2004) and a potential resource in both the Atlantic and

Indo-Pacific Oceans (Bianchini & Ragonese 1994; Pezzuto

et al. 2006). In the Mediterranean, both well developed

fisheries (Cau et al. 2002) and lightly exploited stocks

(Papaconstantinou & Kapiris 2003; Politou et al. 2004)

exist, and there is evidence of increased overfishing of the

stocks in recent years (Sabatini et al. 2002; Bianchini et al.

2003; Arculeo et al. 2011).

A proper assessment of the giant red shrimp stocks is

complicated by the contrast between the few clearly dis-

tinguishable year classes in exploited stocks (3–4 years

and 4–5 years in males and females, respectively) and the

long life span (Tmax 7–9 year) and low natural mortality

(M � 0.4–0.7 year)1) reported in both exploited

Keywords

Aristaeomorpha foliacea; giant red shrimp;

growth discontinuity; Malta; Mediterranean

Sea; Sicily straits.

Correspondence

Sergio Vitale, Institute for Marine and Coastal

Environment, Italian National Research

Council, IAMC-CNR, via L. Vaccara, 61,

91026, Mazara del Vallo (TP) Italy.

E-mail: [email protected]

Accepted: 6 September 2011

doi:10.1111/j.1439-0485.2011.00492.x

Abstract

The deep-water giant red shrimp, Aristaeomorpha foliacea (Risso, 1827) (Deca-

poda, Aristeidae), represents a highly valuable resource for bottom trawling in

the Mediterranean Sea. Recent assessments have described both a worsening of

the status of the traditionally exploited stocks and low levels of annual-based

instantaneous natural mortality (M 0.4–0.7 year)1) in the unexploited stocks.

The mortality (M) figures, however, are in contrast with the longevity (Tmax)

of 3–4-year males and 4–5-year females, estimated from classical length

frequency distribution analysis. Reduced growth (after the onset of sexual

maturity) and pile-up of older individuals in the larger size classes have been

considered to be reasonable explanations for the contrast between M and Tmax.

We propose that a discontinuity of the growth models could address this con-

trast. Because a clear discontinuity in sexual maturity is evident only in males,

length frequency distribution data for different sets of males collected from the

South of Sicily and the Maltese Islands deep bottoms (400–800 m) were fitted

with both the classic (c) and double-phased (d) von Bertalanffy growth for-

mula (VBGF). According to the dVBGF, adult males sharply reduce their

growth rate after reaching an age between 1.2 and 1.5 year, which corresponds

to the estimates of age at sexual maturity (tm between 1 and 1.5 years). The

reduction in growth determines a higher Tmax (7.3–9.5 year) and lower M

(0.4–0.6 year)1) than previously derived on the basis of cVBGF estimates (Tmax

3–4 years and M 1.2 year)1). The dVBGF results suggest that sexual dimor-

phism and length–sex segregation in giant red shrimps reflect an alternative life

history strategy that is based mainly on growth reduction in adult males and it

might be adopted for implementing more conservative assessments.

Marine Ecology. ISSN 0173-9565

Marine Ecology (2011) 1–7 ª 2011 Blackwell Verlag GmbH 1

(Ragonese et al. 1994; Cau et al. 2002) and unexploited

stocks (Papaconstantinou & Kapiris 2003; Politou et al.

2004). This contrast might reflect reduced growth after

the onset of sexual maturity and a consequent pile-up of

individuals in the larger size classes (Pauly et al. 1984). In

bony and cartilaginous fish species, hard structures (e.g.

otoliths) allow accurate age determinations but this is not

possible for crustaceans. Thus, alternative direct tech-

niques, such as rearing in controlled conditions, tagging,

quantification of lipofuscin pigments (Hartnoll 2001),

should be used to determine age. For the giant red

shrimp, only length-based methods (Pauly et al. 1984) are

routinely used to derive the mean modal size per pseudo-

age class and their progression through time according to

the classic one-phase (herein cVBGF, or c) growth param-

eters (CL¥, k t0) of the von Bertalanffy growth formula

(VBGF; Kimura 1980; Pauly et al. 1984).

Table 1 summarises a selection of giant red shrimp

one-phase growth and biological parameters calculated

based on the life history invariant approach (Charnov

1993). According to these figures, males and females have

different life spans. One possible explanation for the

observed sexual dimorphism in life history is that males

sharply reduce their growth rate after the onset of sexual

maturity but continue to live for a life span that is almost

equal to that of females. The true difference between sexes

lies in the onset of sexual maturity, which occurs abruptly

and in a narrow size range in males (as evidenced by the

shortening of the rostrum) and more gradually in

females, as is true for many crustaceans (Somerton 1980).

Applying separate growth models for juvenile and adult

components of the population (Hartnoll 2001) could be a

way to test and explain the above hypothesis (Ragonese

et al. 1994; Bianchini & Ragonese 2002). Different discon-

tinuity growth models are available in the literature

(Pauly et al. 1984; Porch et al. 2002) but the double-

phased model (Craig 1999; Porch et al. 2002; Tracey &

Lyle 2005) seems to be the most suitable for giant red

shrimp males. The aim of this study was to explore the

suitability of the double-phased growth curve (herein

dVBGF, or d) to explain the growth of giant red shrimp

males, considering that slower growth rate and higher

longevity than previously estimated would led to more

conservative (risk averse) stock assessments.

Table 1. Synopsis of the classic von Bertalanffy growth formula (cVBGF) parameters estimated for Mediterranean deep-water giant red shrimp,

Aristaeomorpha foliacea. L¥, k and t0 denote the asymptotic carapace length (mm), the curvature coefficient (year)1) and the theoretical age

(year) at size 0. Life history invariants (size at maturity, longevity and mortality) are based on the average values.

Geographic area Sex L¥ k t0 Sex L¥ k t0 Source ⁄ remarks

Tyrrhenian F 72 0.40 0.0 M Cau et al. (2002)

Sardinia F 75 0.46 0.6 M Cau et al. (1994)

Sardinia F 51 0.62 0.0 M 51 0.63 )0.2 Mura et al. (1997)

Sardinia F 71 0.54 0.3 M Cau et al. (2002)

Central Tyrrhenian F 71 0.47 )0.3 M Spedicato et al. (1994)

Central Tyrrhenian F 76 0.45 0.0 M Spedicato et al. (1998)

Central Tyrrhenian F 73 0.62 0.2 M Leonardi & Ardizzone (1994)

South of Sicily F 66 0.67 0.0 M 42 0.96 )0.3 Ragonese et al. (1994)

South of Sicily F 60 0.63 M 40 1.08 Females: Bianchini & Ragonese

(2002); males: Bianchini (1999)

South of Sicily F 61 0.66 M 41 1.08 Females: Bianchini & Ragonese

(2002); males: Bianchini (1999)

W Ionian Sea F 70 0.45 )0.2 M 50 0.42 )0.3 D’Onghia et al. (1998)

E Ionian F 73 0.43 M 60 0.40 Anon (2001)

E Ionian F 62 0.60 )0.3 M Cau et al. (2002)

E Ionian F 64 0.46 )0.2 M 47 0.56 )0.1 Papaconstantinou & Kapiris (2003)

E Ionian F 67 0.37 )0.1 M 47 0.45 )0.4 Politou et al. (2004)

Average cVBGF parameters F 67 0.52 )0.01 M 47 0.70 )0.3

Standard deviation F 6.9 0.102 0.26 M 6.7 0.295 0.12

Coefficient of variation (%) F 10.2 19.6 > 100 M 14.1 42.3 46.9

Size at maturity (Lm) F 1.6 M 1.2 according to 0.82 ⁄ k; Charnov

(1993)

Life span (Tmax) F 5.7 M 4.0 Taylor’s proxy (3 ⁄ k)+t0; D’Incao &

Fonseca (2000)

Natural mortality (M) F 0.9 M 1.2 according to ln(M) = 0.5 +

0.95*ln(k); Charnov (1993)

Growth discontinuity in males of giant red shrimp Ragonese, Vitale, Dimech & De Santi

2 Marine Ecology (2011) 1–7 ª 2011 Blackwell Verlag GmbH

Material and Methods

Modal size (carapace length; CL, mm) at age (year)

of giant red shrimp males was estimated based on data

gathered within the waters off Sicily and Malta. Mean CL

at different ages was obtained either from the literature

(Ragonese et al. 1994; Bianchini 1999; Bianchini &

Ragonese 2002) or from length frequency distribution

(LFD) separation (Bhattacharya routine as implemented

in FISAT II; Gayanilo et al. 2005). In particular, the LFDs

were derived from data gathered in experimental bottom

trawl surveys conducted between 1994 and 2004 in

spring–summer MEDITS (MEDiterranean International

Trawl Survey; Bertrand et al. 2002) and autumn GRUND

(GRUppo Nazionale Demersali; Levi et al. 1998).

Overall, four case studies were considered based on the

area covered and time period (Table 2): (A) south of Sic-

ily and Maltese Islands grounds between 1985 and 1987

(original LFDs in Ragonese et al. 1994); (B) southeast of

Linosa Island in 1993; (C) northeast of Linosa Island in

1993 (original LFDs in Bianchini 1999; Bianchini & Rago-

nese 2002); and (D) south of Sicily and Maltese Islands

grounds between 1994 and 2004 (original LFDs available

from the authors).

Yearly age classes were assigned based on the spawning

and recruitment patterns (both peak in summer; Rago-

nese & Bianchini 1995) assuming a birth date of 31 July.

As ancillary information, the mean Lmax and its 95%

probability confidence limits (CI) were computed for the

longest series of data (case D) according to the theory of

extreme values (Formacion et al. 1992; as implemented in

FISAT II; Gayanilo et al. 2005).

Both cVBGF and dVBGF (Craig 1999; Porch et al.

2002; Tracey & Lyle 2005) were applied to the representa-

tive modal components (i.e. separation index >2; and

component relative consistency >0.05) by implementing

an iterative procedure using EXCEL (2003); this routine

integrates a systematic least-squared based search with the

Solver procedure already present within EXCEL. The

dVBGF, in particular, can be expressed as follows:

Lt ¼L1 � 1� e�ko

t�t0ð Þ� �with t<tq

L1 � 1� e�k1 t�t1ð Þ� �t � tq

(

and

tq ¼k1t1 � k0t0

k1 � k0

where Lt and L¥ are the expected length at age (CL; mm) at

a given age (t; year) and the ‘average’ asymptotic size

(according to a probabilistic distribution function of the

parameter), respectively, and k0 and k1 are the curvature

coefficients before and after the transitional age (tq) is

achieved. Seed values for the dVBGF fit were obtained after

exclusion of the juvenile component (Bianchini &

Ragonese 2002) by adopting a threshold of 30 mm CL. The

influence of local minima was investigated by re-starting

the routine using different seed values. The best fit among

the convergent and stable solutions was chosen according

to the mean square error. For the dVBGF, spurious or triv-

ial fits were limited by constraining the transitional age

(tq), which might be related to the onset of sexual maturity

(Somerton 1980), within the estimated age ranges within

the case’s components (0.5–4 years).

Based on a selection of life history invariant

approaches, the resultant growth parameters were related

to the size at maturity (tm; Charnov 1993), longevity

(Tmax; Taylor’s approximation; D’Incao & Fonseca 2000)

instantaneous coefficient of natural mortality (Charnov’s

Table 2. Case study (A,B,C,D), study area coverage, number ⁄ season of survey and corresponding reference ⁄ remarks of data related to Aristaeo-

morpha foliacea males in waters off Sicily and Malta reported in the present contribution. All individuals were gathered at between 400 and

800 m depth.

Case study Survey years and month ⁄ seasons Remarks ⁄ references

A – Off Sicily and Malta 1985–87; May, August, November,

February

n = 8 experimental bottom trawl surveys (GRUND

program); mean size at age retrieved from Table 1 in

Ragonese et al. (1994)

B – Southeast (SE) Linosa

Island grounds

1993; May, July n = 2 commercial surveys; mean size at age derived by

recovering and analysing length frequency distributions (LFD);

Bianchini & Ragonese (2002)

C – Northeast (NE) Linosa

Island grounds

1993; May, July n = 2 commercial surveys; mean size at age derived by

recovering and analysing LFD; Bianchini & Ragonese (2002)

D – Off Sicily and Malta 1994–2004; May–July (MEDITS) and

September-December (GRUND)

n = 21 experimental bottom trawl surveys realized within

MEDITS (11) and GRUND (10; 1999 not performed) program;

mean size at age derived by analysing LFD; present study

Ragonese, Vitale, Dimech & De Santi Growth discontinuity in males of giant red shrimp


approximation; Charnov 1993); see bottom rows in

Table 1 for the computational details. For the ancillary

analysis, the sex ratios (Sr = F ⁄ sexed individuals), both

overall and by size class (Wenner 1972), were estimated

for case D by considering the expected relationship

between Sr and growth pattern (Parker 1992).

Results

The number of representative modal components ranged

between a minimum of two and a maximum of four in

study area cases A and D, whereas four components

were found in study cases B and C. Table 3 provides

descriptive statistics of the size (CL, mm) at age classes

(year) for each case study. The mean size at the oldest

age class in the four case analyses (39.3–43.9 mm;

Table 3) is lower than the observed (50–52 mm) and

expected maximum size (50–52 mm; range 48.2–

54.9 mm), supporting the hypothesis of a pile-up effect

in the older classes (Pauly et al. 1984). The size at age

plots (Fig. 1A–D) suggest a sharp increase in length in

the first year of life (although data about early growth

generally are lacking); thereafter, the growth trajectory

reaches a plateau (cases A and D) or becomes nearly lin-

ear (B and C). A main discontinuity in the growth tra-

jectory occurs within 1–2 years, but in case D, a further

and anomalous discontinuity was detectable at the

rightmost end of the curve.

Table 4 and Fig. 1A–D show the results of the cVBGF

and dVBGF curve fits, with the corresponding statistics

and related invariants. The fit performance varied greatly

between the cVBGF and dVBGF. For the cVBGF, quick

and consistent convergence occurred in all case studies,

whereas weak convergence and the presence of local min-

ima occurred in all cases except case A when dVBGF was

applied. In particular for the dVBGF, CL¥ = 50 mm and

A B

C D

Fig. 1. Mean carapace length in mm at given

ages by case study (A,B,C,D) for

Aristaeomorpha foliacea males for both the

classic (solid line) and double-phased (dotted

line) VBGF.

Table 3. Basic statistics of Aristaeomorpha foliacea males related to mean carapace length (mm) at age class (year) by case study (all surveys

combined). N, mCL and CV represent the number of modal components (N), the overall mean of the carapace length (mCL) and the correspond-

ing coefficient of variation (s ⁄ mean) (CV). Case as in Table 2.

Age class (year)

Case

0.5–1.1 1.1–1.5 1.5–2.0 2.1–2.5 2.6–3.0 3.1–3.5 3.6–4.0 4.1–4.3

N mCL CV N mCL CV N mCL CV N mCL CV N mCL CV N mCL CV N mCL CV N mCL CV

A 2 25.0 11 2 31.6 4 2 34.3 2 2 37.5 0.1 2 38.2 <1 2 40.4 1 2 41.7 1 1 43.9 –

B 2 20.7 14 1 25.6 – 1 32.9 – 1 33.6 – 1 35.8 – 1 36.0 – 1 38.8 – 1 39.4 –

C 2 21.3 12 1 26.4 – 1 33.1 – 1 33.2 – 1 35.9 – 1 35.9 – 1 38.9 – 1 39.9 –

D 7 25.7 8 10 29.7 4 10 34.1 2 11 34.3 3 10 37.8 3 11 37.7 4 1 41.3 – 3 39.3 4



tq <3 year constraints were required to reach a stable

solution in the B and C (almost linear growth trajectory

in older classes) and D (anomalous discontinuity close to

the oldest age class) cases, respectively.

For the sex ratio analysis of case D, the figures by year

irregularly oscillated around the expected value of 0.5 (Cau

et al. 2002). Any significant temporal trend (linear coeffi-

cient of determination, R2 = 0.01) in both the MEDITS

and GRUND data resulted in overall average values of 0.52

and 0.51, respectively. The Sr by size class plot (Fig. 2)

shows an almost complete sex segregation in the adult

components, with males prevailing over females in the

middle (30–40 mm) size classes and females prevailing over

males in the large (40–50 mm) size classes.

Discussion

Giant red shrimps show a characteristic sexual dimor-

phism. Males mature earlier than females (28–35 versus

28–62 mm CL; 1 versus 1.5 year) and reach a smaller

maximum size compared to females (52 versus 72 mm

CL) (Ragonese et al. 1994, 1997; Ragonese & Bianchini

1995; Bianchini 1999). These features should reflect a ‘fit-

ness induced by alternative life history strategy’ (Hutch-

ings 2002) in which males have evolved towards smaller

size and early maturation compared to females when no

competition occurs (for example, no territoriality or ‘fight

for females’; Parker 1992).

In addition to the differences in the estimations of the

CL¥ among the investigated cases (likely reflecting size

structures ⁄ exploitation levels instead of methodological

differences), the supposed alternative life history in giant

red shrimp has been attributed traditionally to the CL¥–

mortality inverse relationships (Pauly et al. 1984). How-

ever, both females and males of the giant red shrimp are

considered to be top active feeders (with no sex-related

differentiation) with no cannibalism or systematic preda-

tors (except fishermen) (Cartes 1995; Bianchini 1999).

Moreover, neither depth nor spatial segregation, or con-

sistent overall predominance of one sex over the other

has been documented for Mediterranean stocks (Bianchi-

ni 1999; Cau et al. 2002), with the exception of those in

Greek waters, where a predominance of males has been

reported (Papaconstantinou & Kapiris 2003; Politou et al.

2004). Consequently, the biological evidence might sug-

gest that males do not conform to either the life history

invariant theory or the cVBGF. The present Sr analysis

results are in agreement with the general pattern of the

Table 4. Male Aristaeomorpha foliacea growth estimations according the classic (c) and double-phased (d) von Bertalanffy growth formula

(VBGF) by case study. C-j-excl., parameters obtained after the exclusion of juveniles (CL <30 mm); N, number of age groups used; 0, parameter

prefix related to the cVBGF or dVBGF before the transitional age; 1, parameter prefix related to the dVBGF; tq, transitional age; k0 and k1, the

curvature coefficients before and after the transitional age; MSE, mean square error. *Forced fit through CL¥ = 50 mm. The invariants tm, Tmax

and M (year)1) correspond to the age at maturity (0.82 ⁄ k), longevity [(3 ⁄ k)+t0] and instantaneous rate of natural mortality [ln(M) =

0.5 + 0.95*ln(k)]; see Table 1 for references.

Case Model N CL¥ k0 k1 t0 t1 tq MSE tm Tmax M

A Classic 15 43.9 0.73 )0.42 1.52 1.1 3.7 1.21

1985–87 C-j-exc 13 50.0 0.33 )1.89 0.40 7.3 0.57

Double 15 53.4 0.75 0.25 )0.05 )2.55 1.18 1.08 9.5 0.44

B Classic 9 39.6 0.90 )0.03 2.05 0.9 3.3 1.49

1993 C-j-exc 6 *50 0.21 )3.33 0.20 11.2 0.37

Double 9 43.7 0.90 0.37 0.10 )1.86 1.47 2.46 6.2 0.64

C Classic 9 40.1 0.82 )0.14 2.04 1.0 3.5 1.37

1993 C-j-exc 6 *50 0.22 )2.97 0.60 10.7 0.39

Double 9 47.9 0.70 0.26 )0.04 )2.56 1.45 2.08 9.0 0.46

D Classic 63 40.3 0.79 )0.44 1.55 1.0 3.4 1.31

1994–2004 C-j-exc 53 42.8 0.48 )1.35 1.40 4.9 0.82

Double 63 41.9 1.40 0.56 0.20 )0.99 1.00 1.43 4.4 0.95

Fig. 2. Aristaeomorpha foliacea sex ratio by size class (CL, mm).

Overall profile (all years combined) by survey season within the South

of Sicily and the Maltese Islands. Dotted and solid lines represent

MEDITS and GRUND interpolated values, respectively.



species and support the hypothesis that males and females

differ in growth rather than mortality rate.

Despite severe criticisms, the VBGF remains one of the

most used model in fishery science (cf. Kimura 1980),

also for non-fish species (cf. Lourdes et al. 2008); in

particular, the VBGF and its relatives (such as the sea-

sonalised version) have been applied in the less armoured

penaeid shrimps, which generally show moult asynchrony,

lack of terminal ecdysis and moderate growth even during

the intermoult period (Pauly et al. 1984; Company &

Sarda 2000; D’Incao & Fonseca 2000).

The dVBGF results and the corresponding new invari-

ants suggest a different interpretation of the giant red

shrimp alternative life history strategy that is more con-

servative. In fact, lower adult growth and mortality rates

are more coherent with the life history pattern (longevity,

>4 year, M, <1.0) expected in general for deep-water

nektobenthic demersal shrimps (Company & Sarda 2000;

D’Incao & Fonseca 2000) and in particular for the blue

and red shrimp Aristeus antennatus (Orsi Relini & Relini

1998).

The causes of the severe growth reduction in males are

unknown, but reduced food competition and enhanced

mating and reproductive success may have played a sig-

nificant role. At least in fish, there is evidence that the

pile-up of many year classes within the adult component

(i.e. higher longevity) might represent a buffer to recruit-

ment instability (Leaman & Beamish 1984). Finally, con-

sidering the available evidence of morphological changes

in crustaceans (Hartnoll 2001) as discontinuities (rarely)

in the length at age (cf. Crosnier et al. 1970) and

(mainly) in the allometric post–pre-moult plot (cf. Som-

erton 1980), the dVBGF might represent a useful way to

test growth, longevity, mortality estimations as an alterna-

tive to those obtained with the classic one-phase VBGF.

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growth discontinuity in males of the deep-water giant red shrimp aristaeomorpha foliacea in the...

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