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Analyzing Growth Studies of Four Mullidae Species Distributed in Mediterranean Sea and Black Sea.

Byline: Sedat Gundogdu and Makbule Baylan

ABSTRACT

This study aims to determine the factors affecting von Bertalanffy growth factors and to demonstrate the relationships between these factors. Accordingly, 65 sets of growth data belonging to 43 studies on the subject of the growth of four Mullidae species prevalent in the Mediterranean (Mullus barbatus, Mullus surmuletus, Upeneus pori and Upeneus moluccensis) and the Black Sea (M. barbatus, M. surmuletus). It was discovered that the growth parameters, theoretically affected by similar factors, are not affected by every factor at the same time. It was also discovered that the sample structure given in the studies also affects the biological validity of the parameter estimations.

Key words

Mullidae, goatfish, von Bertalanffy growth factor.

INTRODUCTION

Von Bertalanffy growth factors (VBGF) are parameters needed in stock estimate models, ecosystem models, maximum sustainable product estimations and the estimations of many biological parameters (Apostolidis and Stergiou, 2014; Beddington and Kirkwood, 2005; Cheung et al., 2005; Froese and Binohlan, 2000; Hilborn and Walters, 1992; Pauly et al., 2000). This model, based on a physiological perspective, is widely known and often used in the fisheries sciences (Pauly, 1980; von Bertalanffy, 1957). According to this physiological perspective based by von Bertalanffy on the hypothesis that net growth causes a change in mass as a result of the difference between anabolism and catabolism, a cubic function can demonstrate this metabolic process. This process might differ between species, or even between stocks. For this reason, it is necessary to perform a comparative analysis with different stocks of a given species when establishing the growth characteristics of a species.

Goatfishes are quite significant species for Turkish fisheries. Total fishing amount of these highly valuable goatfishes sum up to 4277 tons (TUIK, 2015) in 2013 based on statistics from Turkish Statistical Institute (TUIK). However, this amount gradually diminishes due to over fishing. For instance, TUIK reports 6557 tons of products for the previous year (TUIK, 2015). This decrease requires reassessment of this species in terms of fisheries management and regulation of the fishing. In addition, growth parameters must be well understood and studied comprehensively for fisheries management.

It is possible to access VBGP data for many species found in the Mediterranean and the Black Sea (Apostolidis and Stergiou, 2014). Most of this data is specifically on economically significant species such as the goatfishes. Goatfishes which are economically very lucrative, now are among the target species of trawl fishing and hence suffer from overfishing (Stergiou, 1990; Golani and Ritle, 1999; Tserpes et al., 2002; Cicek and Avsar, 2014). There have been many studies on the growth of goatfishes; but none of these were on evaluation of growth of different goatfish stocks. This study aims to cover the gap in this subject, and determine the regional differences and similarities between the growth parameters of four goatfish species. In addition an empirical equation that shows the relationship between maximum size (Lmax) and L[?] in directly related observations was intended to be demonstrated in this study. This relationship was investigated at a species and family level.

MATERIALS AND METHODS

In this study, 43 fish specimens of goatfish species prevalent in Mediterranean (M. barbatus barbatus (MB), M. surmuletus (MS), U. pori (UP) and U. moluccensis (UM)) and Black Sea (M. barbatus barbatus (MB), M. surmuletus (MS) were examined. Databases like Web of Science, Scopus, Google Scholar; technical reports and thesis papers were used for this purpose. Twenty one specimens from the total fishes studied were used for estimation of growth parameters separately for females (F) and males (M). Other fish samples were evaluated without distinguishing between genders (B). As a result, 65 growth sets were collected. All samples were classified according to five geographical sub-regions recommended by FAO for the Mediterranean/Black Sea water system as a fishing region (Fig. 1), viz., Western Mediterranean (WM), Central Mediterranean (CM), Aegean Sea (AS), Eastern Mediterranean (EM) and the Black Sea (BS).

The estimation methods in this study were classified as length-frequency analysis (LFD), otolith reading (OR), scale reading (SR) and undetermined (UN). UN however, were disregarded in analysis of impact of these factors. In LFD method t0 value was calculated using equation (1) as reported by Pauly (1980).

Log10(-t0)=-03922 - 0.2752Log10(L[?]) - 1.038Log10(K) (1)

The data of each variable was analyzed with reference to each specific region. In these cases regional differences were disregarded and species and family differences were focused. The effect of geographical region, sex and age determination method on the growth parameters (L[?],K, t0) and Lmax at the family level was analyzed using separate one way analysis of variance (ANOVA). One way ANOVA was used to determine the parameter differences between species, and to test if regions, sex and age determination methods were different for various parameters for each species. Tukey multiple comparison tests were used to determine the cause of differences discovered by variance analysis (Gundogdu, 2014). In cases where the number of studies were not sufficient for a multiple comparison, two sample t-tests were used. Pearson multiple correlation test was used to determine the correlation between L[?], K N (sample size), maximum size (Lmax) and t0.

The relationship between Lmax and L[?] was investigated proportionally as demonstrated by Froese and Binohlan (2000). An attempt was also made to determine the relationship between Lmax and L[?] on both species and family basis (Froese and Binohlan, 2000; Pauly, 1984). L[?] values reported by the studies were assessed based on the criteria determined by Froese and Binohlan (2000) and Pauly (1984b). The studies where L[?] value was outside the 30% limit of the Lmax value were classified as problematic. As all studies included all 4 seasons, effects caused by seasonal variations were assumed to be equal for all studies. Lmax values derived from observations were disregarded when examining the differences caused by age determination methods.

All statistical analysis was performed by IBM SPSS (version 20.0; IBM Corp, Armonk, NY, USA) package software. Significance level was determined as 0.05.

RESULTS

Table I shows data on fish specimens of the family Mullidae from five different regions of Mediterranean/Black Sea waters.

Table II shows descriptive statistics for various parameters of fish samples gathered from literature. The median values of L[?] for M. barbatus barbatus, M. surmuletus, U. moluccensis and U. pori for all regions were 247, 281.15, 247.05 and 205.2 mm, respectively; the median values of K were 0.23 year-1, 0.24 year-1, 0.13 year-1 and 0.26 year-1, respectively and the median values of t0 were found, -1.59 year, -2.15 year, -3.76 year and -1.31 year, respectively. Median values of Lmax were 207, 237.5, 178 and 162.5 mm, respectively. There were significant differences for all the three parameters of all fish species (pless than 0.05). But no significant difference was found with regards to the K parameter. When a species based von Bertalanffy equation was prepared using these values, following equations were derived (Fig. 2).

Table I.- Sources of information of four species of the family Mullidae in the mediterranean and Black Seas used in this analysis.

(TL, total length; FL, fork length; n.r., not reported; WM, Western Mediterranean; CM, Central Mediterranean; EM, Eastern Mediterranean;

AS, Aegean Sea; BS, Black Sea; B, both sex; L.T, length type, OR, otolith reading; LFA, length-frequency analysis; UN, unknown; SR, scale reading)

Code###Species###Area (Sub area)###Author###Sex###N###L.T.###Aging###L[?]###K###t0###Lmin###Lmax###Lmax/L[?]###L[?] -

###(mm)###(year-1)###(year)###(mm)###(mm)###Lmax

1###M. barbatus###WM###Spanish###Larrafleta and Roda (1956)###F###1634###TL###LFA###248.8###0.4###-0.2###100###177###0.71###71.8

###M###2147###TL###LFA###181.7###0.59###-0.12###105###226###1.24###-44.3

2###M. barbatus###EM###Eygptian Coast###Hashem (1973)###F###223###TL###UN###237###0.28###-0.33###41###240###1.01###-3

###M###180###U.###UN###195.2###0.33###-0.28###41###200###1.02###-4.8

3###M. surmuletus###CM###Tunusia###Gharbi and Ktari (1981)###B###202###TL###SR###215.1###0.5###-0.14###80###230###1.07###-14.9

4###M. surmuletus###WM###Tyrrhenian Sea###Andaloro (1982)###F###n.r.###TL###UN###301.2###0.24###-2.68###n.r.###n.r.###-

###M###n.r.###TL###UN###250.2###0.3###-2.39###n.r.###n.r.###-

5###M. surmuletus###WM###Catalan sea###Sanchez et al., (1983)###B###3339###TL###OR###325.2###0.11###-3.65###120###320###0.98###5.2

6###M. surmuletus###CM###Strait of sicily###Andaloro and Giarritta (1985)###F###n.r.###TL###UN###297.5###0.49###-0.31###n.r.###n.r.###-

###M###n.r.###TL###UN###262.5###0.41###-0.23###n.r.###n.r.###-

7###M. barbatus###BS###Central BS###Samsun (1990)###B###2116###TL###OR###295.8###0.1###-3.28###69###253###0.86###42.8

8###M. surmuletus###WM###Majorca Island###Morales-Nm (1991)###F###n.E.###TL###OR###297.6###0.24###-3.82###95###270###0.91###27.6

9###M. surmuletus###AS###Aegean Sea###Vassilopoulou and Papaconstantinou (1992)###F###336###FL###OR###413.3###0.1###-2.77###90###260###0.63###153.3

###M###451###FL###OR###380.1###0.1###-2.76###100###220###0.58###160.1

10###M. barbatus###CM###lonian Sea###Tursi et al. (1994)###B###19116###TL###OR###252###0.26###-1.71###68###236###0.94###16

11###M. surmuletus###WM###Majorca Island###Renones et al. (1995)###F###1771###TL###OR###319###0.21###-2.61###120###330###1.03###-11

###M###1342###TL###OR###255.4###0.27###-0.21###110###270###1.06###-14.6

12###M. barbatus###BS###Eastern BS###Sahin and Akbulut (1997)###F###1190###TL###OR###212.6###0.23###-1.94###80###207###0.97###5.6

###M###1428###TL###OR###210.2###0.2###-2.33###82###195###0.93###15.2

13###M. barbatus###CM###Adriatic###Jukic-Peladic and Vrgoc (1998)###B###15933###TL###UN###277.5###0.27###-0.62###55###265###0.95###12.5

14###M. surmuletus###BS###Marmara Sea###Moldur (1999)###B###1885###TL###OR###328.2###0.23###-2.13###90###235###0.72###93.2

15###U. moluccensis###EM###EM###Kaya et al. (1999)###F###535###FL###OR###262###0.11###-4.08###86###178###0.68###84

###M###176###FL###OR###238.6###0.12###-3.69###85###161###0.67###77.6

16###M. surmuletus###CM###Tunusia###Jabeur et al. (2000)###B###123###TL###OR###223###0.34###-0.79###50###230###1.03###-7

17###M. barbatus###AS###Edremit Bay###Celik and Torcu (2000)###B###474###FL###OR###260.8###0.13###-3.54###94.5###197###0.76###63.8

18###M. barbatus###AS###lznur Bay###Akyol et al. (2000)###F###110###FL###LFA###225###0.2###-2.3###86###183###0.81###42

###M###218###FL###LFD###270###0.17###-1.84###95###150###0.56###120

19###M. barbatus###AS###lzmir Bay###Kinacigil et al, (2001)###B###221###FL###OR###190.3###0.44###-0.78###81###161###0.85###29.3

20###M. barbatus###BS###BS###Genc et al. (2002)###B###747###TL###OR###242.2###0.22###-1.71###75###207###0.85###35.2

21###Upon###EM###EM###cicek et al. (2002)###F###461###TL###OR###200.2###0.16###-1.67###65###155###0.77###45.2

###M###534###TL###OR###220.5###0.17###-1.67###63###147###0.66###73.5

22###U. moluccensis###EM###Karatal Off###Kokcu (2004)###F###356###TL###OR###279.4###0.09###-4.71###70###180###0.64###99.4

###M###216###TL###OR###251.1###0.11###-4.04###60###160###0.63###91.1

23###M. barbatus###AS###Izmir bay###Ozbilgin et al. (2004)###B###110891###TL###LFD###242.6###0.57###-0.31###50###230###0.95###12.6

24###U. moluccesis###EM###Iskenderun Bay###Ismen (2005)###F###216###U.###OR###243###0.22###-0.92###70###205###0.84###38

###M###202###TL###OR###225###0.24###-0.92###70###178###0.79###47

25###M. barbatus###EM###Karatal Off###cicek (2006)###B###212###TL###OR###219.8###0.19###-1.17###69###157###0.71###62.8

25###U. pori###EM###Karatal Off###cicek (2006)###B###247###TL###OR###219.8###0.19###-1.17###63###155###0.71###64.8

26###U. pori###EM###Iskenderun Bay###Ilmen (2006)###F###324###TL###OR###185###0.42###-0.63###70###170###0.92###15

###M###292###TL###OR###179###0.37###-0.89###66###151###0.84###28

27###M. barbatus###BS###Central BS###Suer (2008)###F###449###TL###OR###393.6###0.08###-1.92###75###225###0.57###168.6

###M###736###TL###OR###252.5###0.15###-1.59###85###205###0.81###47.5

28###M. surmuletus###EM###Eygptian Coast###Mehanna (2009)###B###1385###TL###OR###317.4###0.47###-0.3###100###320###1.01###-2.6

29###M. surmuletus###AS###Gulf of lzmir###lihan et al. (2009)###B###192###TL###OR###278.5###0.19###-1.58###66###226###0.81###52.5

30###M. barbatus###EM###Mersin Bay###Atar and Mete (2009)###B###297###TL###OR###279###0.11###-3.47###105###185###0.66###94

31###U. moluccensis###EM###Antalya Bay###Ozvarol et al. (2010)###B###464###TL###OR###255.6###0.14###-3.83###80###211###0.83###44.6

32###M. surmuletus###AS###Edremit Bay###Ustun (2010)###B###520###TL###OR###250.9###0.14###-2.48###77###170###0.68###80.9

33###M. barbatus###WM###Castellammare###Sieli et al. (2011)###F###578###TL###OR###221.2###0.38###-0.94###90###245###1.11###-23.8

34###M. barbatus###BS###Central BS###Aksu et al. (2011)###B###699###TL###LFD###201.5###0.33###-0.28###73###187###0.93###14.5

35###M. barbatus###EM###NE Levant###Ok (2012)###B###18894###TL###LFD###260###0.56###-0.51###30###250###0.96###10

35###U. pori###EM###NE Levant###Ok (2012)###B###3577###TL###LFD###200###0.45###-0.67###50###190###0.95###10

###B###1208###TL###LFD###170###0.6###-0.52###70###160###0.94###10

36###M. barbatus###BS###BS###Aydin and Karadurmus (2013)###F###950###TL###LFD###254###0.14###-2.7###95###215###0.85###39

###M###485###TL###LFD###193###0.35###-0.75###64###170###0.88###23

37###M. surmuletus###AS###Saros Bay###Arslan and Ilmen (2013)###F###184###TL###OR###283.8###0.19###-2.16###110###268###0.94###15.8

###M###119###TL###OR###269.4###0.2###-2.34###118###198###0.73###71.4

38###U. pori###CM###Cost of Libya###El-Drawany (2013)###F###252###TL###OR###211.5###0.25###-1.71###70###175###0.83###36.5

###M###234###TL###OR###210.2###0.27###-1.44###70###175###0.83###35.2

39###M. barbatus###AS###Izmir Bay###Irmak (2013)###F###125###FL###OR###193.3###0.23###-2.6###50###153###0.79###40.3

40###M. barbatus###AS###Saros Bay###Arslan and Ilmen (2014)###F###2302###TL###OR###265.8###0.18###-1.75###92###236###0.89###29.8

###M###1308###TL###OR###283###0.14###-2.39###88###241###0.85###42

41###M. surinuletus###WM###Algerian Coast###Kherraz et al. (2014)###F###516###TL###LFD###247###0.37###-0.37###120###240###0.97###7

###M###322###TL###LFD###255.2###0.32###-0.71###125###235###0.92###20.2

42###nil. barbatus###EM###Iskenderun Bay###Gundogdu and Baylan (2014)###B###422###FL###OR###247###0.27###-0.33###62###275###1.11###-28

43###M. barbatus###WM###Algerian Coast###Chafika (2015)###B###1697###TL###LFD###288.8###0.59###-0.08###83###277###0.96###11.8

Table II.- Descriptive statistics of collected data (S.E.: Standard error of mean).

###Mullus barbatus barbatus###Mullus surmuletus###tlpeneus moluccenses###Upeneus pori

###MeanSEM###Range###Median###MeanSEM###Range###Median###MeanSEM###Range###Median###MeanSEM###Range###Median

L[?]###WM###235.1322.58 a###181.7-288.8###235###281.311.58 a###247-325.2###276.5

(mm)###CM###264.7512.75 a###252-277.5###264.75###249.519.06 a###215.1-297.5###242.75###210.850.65 a###210.2-211.5###210.85

###AS###241.3512.48 a###190.3-283###251.7###312.627.3 a###250.9-413.3###281.15

###EM###239.6712.1 a###195.2-279###242###317.40###317.4-317.4###317.4###240.5911.6###170-279.4###247.05###200.757.01 a###179-220.5###200.1

###BS###250.620.88 a###193-393.6###242.2###328.20###328.2-328.2###328.2

###Total###244.68.05 2*###181.7-393.6###247###288.511.08 3###215.1-413.3###281.15###240.611.6 2###170-279.4###247.05###203.35.39 1###179-220.5###205.2

K###WM###0.490.06 a###0.38-0.59###0.5###0.260.03 b###0.11-0.37###0.26

(year-1)###CM###0.270.01 b###0.26-0.27###0.27###0.440.04 c###0.34-0.5###0.45###0.260.01 a###0.25-0.27###0.26

###AS###0.260.06 b###0.13-0.57###0.19###0.150.02 a###0.1-0.2###0.17

###EM###0.290.06 b###0.11-0.56###0.28###0.470###0.47-0.47###0.47###0.20.06###0.09-0.6###0.13###0.290.05 a###0.16-0.45###0.28

###BS###0.20.03 b###0.08-0.35###0.2###0.230###0.23-0.23###0.23

###Total###0.280.03 1###0.08-0.59###0.23###0.270.03 1###0.1-0.5###0.24###0.20.06 1###0.09-0.6###0.13###0.290.04 1###0.16-0.45###0.26

t0###WM###-0.340.2 a###-0.86###-0.16###-2.060.51 b###-3.61###-2.5

(year)###CM###-1.170.55 c###-1.09###-1.17###-0.370.15 a###-0.65###-0.27###-1.580.14a###-0.27###-1.58

###AS###-1.940.36 b###-3.23###-2.07###-2.350.18 b###-1.19###-2.41

###EM###-1.020.51 c###-3.19###-0.42###-0.30###0###-0.3###-2.840.61###-4.19###-3.76###-1.120.19 a###-1.04###-1.03

###BS###-1.830.31 b###-3###-1.92###-2.130###0###-2.13

###Total###-1.44 1###-3.46###-1.59###-1.720.27 1###-3.68###-2.15###-2.840.61 2###-4.19###-3.76###-1.230.16 1###-1.08###-1.31

Lmax###WM###231.220.92 c###177-277###235.5###277.516.21 a###235-330###270

(mm)###CM###250.514.5 a###236-265###250.5###230 a###230-230###230###1750 a###175-175###175

###AS###193.813.43 b###150-241###190###223.615.1 a###170-268###223

###EM###217.818.16 c###157-275###220###3200###320-320###320###179.137.01###160-211###178###161.336.56 a###147-190###155

###BS###207.17.84 c###170-253###207###2350###235-235###235

###Total###2126.8 2###150-277###207###251.411.05 1###170-330###237.5###179.17.01 3###160-211###178###164.75.29 3###147-190###162.5

N###WM###1514332###578-2147###1666###1458540###322-3339###1342

###CM###175251592###15933-19116###17525###16340###123-202###163###2439###234-252###243

###AS###1445613779###110-110891###348###30066###119-520###264

###EM###33713105###180-18894###260###13850###1385-1385###1385###422122###176-1208###286###906536###247-3577###393

###BS###978177###449-2116###747###18850###1885-1885###1885

###Total###64063862###110-110891###736###846238###119-3339###451###422122###176-1208###286###740407###234-3577###308

M. barbatus barbatus: Lt= 247.9 (1 - e -0.23(t-1.59)) (2)

M. surmuletus: Lt = 281.15 (1 - e -0.24(t-2.15)) (3)

U. moluccenses: Lt = 247.05 (1 - e -0.13(t-3.76)) (4)

U. pori: Lt = 250.2 (1 - e -0.26(t-1.31)) (5)

When L[?], K, Lmax and t0 for the Mullidae family were calculated without differentiating between species and regions, median levels were found to be 250.9 mm, 0.23 year-1, 207 mm and -1.67 year, respectively. Based on this, the von Bertalanffy growth equation of the Mullidae family was empirically determined as;

Lt= 250.1 (1 - e -0.23(t-1.67)) (6)

The growth curves drawn using the equations (2), (3), (4), (5) and (6) are shown in Figure 2. As can be seen, the growth curve of the entire family is similar to M. barbatus barbatus. Since only M. barbatus barbatus and M. surmuletus were studied in all regions, only these two species were tested with regards to the regions using one way ANOVA.

M. barbatus barbatus

When all parameters (L[?], K Lmax and t0) were compared based on regions, a difference was discovered for all parameters except L[?] (pless than 0.05; Table II). When we excluded studies that did not contain any information about age determination method, the remaining two methods (LFD and OR) were compared and it was found that K and t0 displayed a variation between regions (pless than 0.05), but L[?] had no differences (p>0.05). When examined based on sex, none of the parameters had any significant variance (p>0.05). Regression equation between L[?] and Lmax and the r2 value was determined as;

ln(L[?]) = 3.238 + 0.421 ln (Lmax) (n=25, r2 = 0.197, s.e. = 0.156) (7)

The variance analysis result of equation (7) was determined to be significant (pless than 0.05). According to this, for M. barbatus equation (7) can be used for estimation of L[?] given Lma.

M. surmuletus

Since M. surmuletus had more than two values in three regions (WM, CM, AS) these were compared in these three regions. According to this, K and t0 parameters showed significant difference based on regions (pless than 0.05), however no differences were found for Lmax ve L[?] (p>0.05; Table II). When age determination methods were compared, no difference was discovered for any parameters other than the K parameter (p>0.05). For the K parameter, it was discovered that the studies using LFD and OR methods had the same K value, and those using the SR method had a different K value. No difference was found for any of the four parameters in comparisons based on sex (p>0.05). Regression equation between L[?] and Lmax and the r2 value was determined as;

ln(L[?]) = 3.587 + 0.376 ln (Lmax) (n=19, r2 = 01.36, s.e. = 0.173) (8)

The variance analysis of data obtained through equation (8) was not found significantly different (p>0.05). This means equation (8) can not be used for the estimation of L[?] when Lmax is given for M. surmuletus.

U. moluccensis

Since all studies on U. moluccensis were focused on the EM region, no regional comparisons were made (Table I). Since only LFD and OR methods were used for age determination, the differences between these methods were examined and it was discovered that t0 showed no difference (p>0.05) and that L[?] and K were different (pless than 0.05). Again it was checked whether there was any difference in estimates and Lmax between sexes and no difference was discovered (p>0.05). Regression equation between and Lmax and the r2 value was determined as;

ln(L[?]) = 2.511 + 0.572 ln (Lmax) (n=8, r2 =01.67, s.e. = 0.148) (9)

The variance analysis of data from equation (9) showed its significance (p>0.05). This means equation (9) cannot be used for the estimation of L[?] when Lmax is given for U. moluccensis.

U. pori

Since U. pori were focused only on EM and CM (Tables I, II) regions, these two regions were compared with regards to all parameters. None of the four parameters showed any regional differences (p>0.05; Table II). Likewise OR and LFD did not show any difference in all the three parameters (p>0.05). Regression equation between L[?] and Lmax and the r2 value was determined as;

ln (L[?])=5.579-0.052 ln(Lmax) (n=8, r2 =0.04, s.e. = 0.082) (10)

The variance analysis result of equation (10) was determined to be significant (p>0.05). This means equation (10) can not be used for the estimation of Lmax when L[?] is given for U. pori.

Mullidae

On an examination on a family level without differentiating between species and genus, it was determined that no parameters other than Lmax showed any difference (Table III). When age determination methods were examined, it was discovered that there was no difference in L[?] but there was a difference in K and t0 (Table III).

Regression equation between L[?] and Lmax and the r2 value with regards to the family was determined as;

ln(L[?]) = 2.607 + 0.544 ln (Lmax) (n=63, r2 =0345, s.e. = 0.154) (11)

The variance analysis result of equation (11) was determined to be significant (pless than 0.05). According to this, for Mullidae, equation (11) can be used to estimate of L[?] given Lmax.

When correlations between parameters and between the number of observations and Lmax were examined, a significant negative correlation between L[?] and K (-0.402) was determined. Along with this, a statistically significant positive correlation between L[?] and Lmax (0.576) was observed. Existences of positive and negative correlations between other parameter combinations were also found (Table IV, Fig. 3). When ratio Lmax/L[?] was examined, it was noted that all samples were between 0.5 and 1.5 as stated in Froese and Binohlan (2000) (Table I). Again when the difference between L[?] - Lmax was investigated, it was noted that 10 of the 61 growth sets had a negative (i.e. L[?] less than Lmax), and 51 had a positive (i.e. L[?] > Lmax) difference (as Lmax wasn't reported for 4 growth sets, these studies weren't included; Table I).

44 of the L[?] values that were estimated were within the 30% limit given in Pauly (1984) and Froese and Binohlan (2000). L[?] estimates of the remaining 17 samples were outside this limit.

DISCUSSION

The data used in this study coming only from four species of total of 85 species of Mullidae family should be considered insignificant, since it has been demonstrated that (Froese and Binohlan, 2000; Von Bertalanffy, 1957) species with similar size were distributed almost at similar places on the same regression line and moreover belonged to different species. The empirical equations and results reached by this study can be comfortably used for all Mullidae member species, which is the main claim of this study. The results of this study will, however, be discussed with reference to Mullidae family, if not for all fishes.

These four members of the Mullidae family are heavily studied species in the Mediterranean and the Black Sea. Most of these studies focus on growth. Usually either a single stock of a single species was examined or multiple stocks of a single species were studies comparatively (Table I). No studies that cover the Mediterranean in its entirety other than the study where Bianchini and Ragonese, (2011) gathered previous studies on M.barbatus barbatus were noted.

The inter-species differences between growth parameters are regulated by physiological, environmental, geographical, nutritional and similar factors (Jobling, 1997). Also, the methods used to estimate the growth parameters and the sampling methods can also cause differences within the species (Biro and Post, 2008; Pardo et al., 2013; Pilling et al., 2002; Taylor et al., 2005). This is primarily demonstrated by the limitation of size frequency distribution of sampled individuals by the use of size-selective fishing tools (Biro and Post, 2008; Taylor et al., 2005). This causes the differentiation of captured Lmax value. Again, size frequency distribution in a limited range affects the estimates that would be reached using the LFD analysis as a method (Pauly and David, 1981). It also causes differences to appear in age determination using otolith. Limited size frequency distribution means a limited age group was captured, and that affects the estimates of L[?], K and t0.

Froese, (2006) argues that a good and effective growth study would be achieved if a sampling method that has an equal chance of capturing all size groups. To understand this, examining Table I might be advisable. For example, Cicek (2006) worked in a very narrow size range like 69-157 mm and as a result reached an unrealistic t0 (-1.17) and as a result estimated a L[?] value that is outside the limit of 30% of Lmax (219.8 mm).

Sparre and Venema, (1998) state that t0 value must be close to zero and, L[?] value must be close to the Lmax value. However, this can be affected by different factors that can't be explained solely by a narrow sample structure. Again Froese and Binohlan (2000) stated that L[?] - Lmax of difference should be close to zero. The chief among these is the fishing pressure, and all four Mullidae members are under severe pressure of overfishing (Stergiou, 1990).

Table III.- Descriptive statistics of family level parameters with regards to age determination method and regions. (S.E.: Standard error of mean; Superscripted numbers indicate statistically significant differences both between parameters and aging methods, and study area)

###L###K###t0###Lmax

###Mean###Median###Mean###Median###Mean###Median###Mean###Median

Aging###LFD###231.39.6 a###244.8###0.410.04 a###0.38###-0.810.2 a###-0.51###206.410.1###202.5

###OR###259.18.2 a###252###0.210.01 b###0.19###-2.10.2 b###-1.92###211.57.4###205

###Total###252.36.7 a###250.9###0.250.02###0.22###-1.780.2###-1.71###210.36.1###205

Area###WM###263.914.1 a###255.3###0.350.05 a###0.34###-1.270.5 a###-0.54###25914.2 a###257.5

###CM###224.29.7 a###217.2###0.280.02 a###0.26###-1.410.3 a###-1.57###20416.8 b###202.5

###AS###271.916.3 a###267.6###0.210.03 a###0.18###-2.110.2 a###-2.32###206.610.5 a,b###209

###EM###234.38.7 a###238.6###0.260.04 a###0.19###-1.850.3 a###-1.17###188.810.6 b###178

###BS###258.420.2 a###247.3###0.210.03 a###0.21###-1.860.3 a###-1.93###209.97.5 a,b###207

###Total###252.36.7 a###250.9###0.250.02###0.22###-1.780.2 a###-1.71###210.36.1###205

Table IV.- Correlations between parameters.

###N###L###K###t0###Lmax

N###Pearson Correlation###1

###Sig. (2-tailed)

###N###60

L###Pearson Correlation###0.003###1

###Sig. (2-tailed)###0.980

###N###60###65

K###Pearson Correlation###0.328###-0.402###1

###Sig. (2-tailed)###0.01###0.001

###N###60###65###65

t0###Pearson Correlation###0.176###-0.383###0.771###1

###Sig. (2-tailed)###0.177###0.002###0.000

###N###60###63###65###65

Lmax###Pearson Correlation###0.129###0.576###0.112###0.076###1

###Sig. (2-tailed)###0.327###0.000###0.39###0.56

###N###60###61###61###61###61

It was argued by some authors that M. barbatus might demonstrate nanism specific to the Levantine region of the Mediterranean and the Lmax value estimated here might be smaller than the other regions (Azov, 1991; Bianchini and Ragonese, 2011; Maurin, 1970; Sonin et al., 2007). However, this study did not reveal any finding like that at least with regards to the reported studies. However, the existence of a significant difference between EM and WM with regards to Lmax should be discounted. While this does not provide sufficient evidence for nanism, different environmental factors might have an effect on this difference. (Jobling, 1997; Helser et al., 2007).

The estimated size-age graph shown in Figure 2 demonstrates that all four species have a similar growth trend. But the estimated size values for each age group demonstrated that M. surmuletus is one group, the entire family and M. barbatus are one group, and U. moluccensis and U. pori are one group. This is thought to be a result of the nutrition, anabolism, catabolism, breeding period etc. of the species involved. Also, the reason M. barbatus showing almost the same growth curve as the entire family is thought to be the highest number of studies among all on the family being on M. barbatus.

Situations where growth parameters vary by both regional and age determination methods are supported by literature as well. Apostolidis and Stergiou (2014) have stated that otolith misreading during age determination also affects growth parameters. Thus different age determination methods result in different growth parameter estimates. Helser et al. (2007) has posited that the geographical differences between growth parameters might be related to the bio-ecological characteristics of the ecosystem the stock is in. This situation is explained similarly by (Froese, 2006) as well.

The correlations between parameters have a negative inclination according to Beverton (1992), Helser et al. (2007), Pilling et al. (2002) and von Bertalanffy (1957). However, Pilling et al. (2002) state that these negative correlations are statistical, not biological. This means real populations are far from offering clear evidence on this subject. When Table III is examined, it can be seen that the correlations between parameters are low but statistically significant. For example, the -0.402 correlation between K and L[?] doesn't fit the strong negative correlation state posited in the theory. It must be noted that these correlation values were calculated together for all species. Otherwise, when considered for each species separately, the correlation values drop even lower.

The ratio between Lmax and L[?] appears to be on the 0.5 - 1.5 range for all studies. This means it is within the limits established by Froese and Binohlan, (2000). However, the regression relationship between Lmax and L[?] while statistically important, was not considered strong. For example, when all species are considered, only 34.5% of the change in L[?] can be explained by Lmax. This means there are more factors that must be explained. Considering the state established by Sparre and Venema, (1998) with regards to the difference between L[?] - Lmax when the differences between L[?] - Lmax are examined, it can be noted that the L[?] estimates derived from 10 growth sets are contrary to biological reality. Because these 10 growth sets imply that the stock worked on contains fishes that are larger than the size the fishes could have reached in infinity.

The 30% limit implied by Pauly (1984) and Froese and Binohlan (2000) was breached by 17 growth sets, marking these studies as problematic studies.

As a result, VBGP are affected by many factors. The examination of all these factors together is very difficult due to the limits of the data provided in the studies reported in literature. However, both multi-species and multi-stock analyses examining main involved factors like geographical region and age determination method would be very beneficial for the fishing management of the involved species. This study demonstrates that age determination, sample composition and regional differences somehow affects VBGP estimations. Pardo et al. (2013) states von Bertalanffy parameters are quite important for biomass estimation and that non-realistic estimates could affect biomass estimation and hence, stock estimations. Therefore, it is clear that conducting more of such studies is necessary considering the importance of stock estimation on preparing fishing method plan.

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