SOllderdru,k .IllS Bd. 18 (1980), H. 1, S. 56-60

Meeresforsdlung . Reports on Marine Rcseard1Beridne der Deutsmen WissensmaA:limen Kommission fur Meeresforsmung

VERLAG PAUL PAREY . SPIl'ALERSTRASSE 12 . D-2000 HAMBURG 1Aile Rednc, ~uch die der Obersctzung, des Nadldru~s, dcr plu)1omcdl;mi)mcn Wiede(~;lbc und SpcidH'run~

in Datrnv('rarlu:itUug~3.nlat:c.'n. vorlwhaltcn. (0 tlJ!iQ \cd:\I; 1'::11111'3"'Y JL\lnbuq~ unJ Heflin

The use of a pseudo catch-curve for the estimation of mortality

rates in Leiognathus splendens (Pisces: Leiognathidae)in Western Indonesian Waters

By D. PAUI.Y

Institut fur Meereskunde an der Universitat Kiel

Ms. received 28 June 1979

Ms accepted 20 Sept. 1979

Abstract

The relationship betWeen fish length and fishing depth, and the relationship betWeen catch rate andfishing depth are used, together with the growth parameters of the v. Bertalanffy Growth Formula anda length-weight relationship to construct a pseudo catch-curve for little exploited Indonesian stocks ofLeiognathus splendens. An estimate of Z = 1.84 is obtained which corresponds to a value of M = 1.8.

Kurzfassung

Die Verwendung einer Pseudo-Fangkurve zur Ermittlung der Sterblichkeitsraten von Leiognathussplendens (Pisces: Lewgnathidae) in Gewassern des westlichen Indonesiens

Die Beziehung zwischen mittlerer Fischlange und Fangtiefe sowie die Beziehung zwischen Fangratenund Fangtiefe wurden verwendet, zusammen mit den Parametem der von Bertalanffy Wachstumsglei-chung und der Langen-Gewichtsbeziehung, um eine Pseudo-Fangkurve zu zeichnen, die die Sterb-lichkeit in westindonesischen Bestanden von Leiognathus splendens ausdriickt. Ein Schatzwert vonZ = 1.84 wurde erhalten, entsprechend M = 1.8.

The natural mortality of fish is generally quite difficult to estimate. In virgin or little-exploited stocks, however, total mortality (Z) corresponds to natural mortality (M), whichmakes estimates of Z in such stocks particularly valuable.

Total mortality (Z) may be expressed by

Nt = Noe-Zt 1)

where No is the number of fishes at a given time 0, and Nt is the number of remaining fishesat time t (BEVERTONand HOLT 1957).

Total mortality is commonly estimated by means of a catch-curve which consists of aplot of the natural logarithm of the number of fishes (of various ages) against theirrespective age.

The construction of catch-curves demands, however, that certain requirements be met.Among these, the first requirement is that the sample should not be biased against the sizeof certain age groups. This requirement is, however, the most difficult to meet in the case ofthose neritic fishes which migrate into deeper waters as they grow older and larger.

A simple method is presented here which allows for the construction of a 'pseudo catchcurve' from data sampled for purposes other than estimating mortality rates. The method isas follows:

u.s. Copyright ClearanceCenter Code Statement:0341-6836/80/2801/0056 $ 02.50/0Meeresforsch. 28 (1980), 56-60@ 1980 Verlag Paul Parey, Hamburg und BerlinISSN 0341-6836 / ASTM-Coden: MEERDW

- - ---

Use of pseudo catc!J-CIIrve for tl)(. ,'stimatiml of mortality rates ill L,'iognatIJIls spleud,'/lS 57

Step A A quantitative relationship between mean fish length and water depth is estab-lished.

Step B From this relationship, and reasonable estimates of the growth parameters L .., Kand to of the von Bertalanffy Growth Formula (VBGF), a mean age is calculatedfor each depth.

Step C The mean catch rate (weight of catch per unit effort) per depth mid-range isdivided by the mean fish wl'i~ht l"Orrcspondin~ \0 rhe mean len~th estinutl.d forthat depth in Step A in order to obtain the number of fish caught per unit effort.

Step D The natural logarithm of the estimate of fish number obtained in Step C is plottedagainst the age obtained in B. The slope of this plot - called here pseudo catchcurve - provides, with sign changed, an estimate of Z.

Example:Fig. 1, which is based on data in Table 1, gives the relationship between length and

water depth off southern Kalimantan (Borneo), Indonesia. The relationship may bedescribed by the equation

L = 7.36 + 0.106 m; r = 0.544" 2)

where L is the total length in cm, and m the depth in meters.PAULY(1978a) gives for L. sp/endens various estimates of L 00and K from which the

combination L 00 = 14.3cm and K = 1.04 appears to correspond best to the maximumsize of about 14 cm recorded by this author off southern Kalimantan. We thus have

Mean length in em.

12

10.

8.

6. .4.2

o6 10 20 30 40 Depth..m.

Fig. 1. Relationship between mean length of Leiognathus splendens and fishing depth, off SouthernKalimantan, 1976

Table 1. Leiognathus splendens: relationship of mean length to fishing dcpth, South Kalimantanl

--- -----

Stn Depth (m) LT(cm) s.d. N Stn Depth (m) LT(cm) s.d. N

12 11 8.3 n.a. n.a. 22 41 11.1 0.59 7313 15 10.0 1.95 27 58 38 10.2 0.60 14614 9 5.3 0.60 130 59 10 6.5 n.a. n.a.15 14 10.8 1.63 138 60 19 7.3 n.a. n.a.16 22 11.0 0.66 96 61 26 12.0 n.a. n.a.17 30 11.9 0.62 110 92 20 8.6 0.96 14720 24 8.7 0.32 6 93 14 9.3 0.94 9021 32 11.1 1.23 45 94 10 11.3 n.a. n.a.

n.a. = not availablc; N = sample sizc; s.d. = standard dcviation

I The data were obtained in 1976 as part of the Indonesian-German Demersal Fisheries Project onboard RN Mutiara IV. MARTOSUBROTOand PAULY(1976) and SAEGERet al. (1976) may beconsulted for exact station locations, mode of operation and RN Mutiara IV specifications.

58 D. Pauly

L, = 14.3 (I _ c.1.04(,+ 0.1~)

to (= - 0.19) having been estimated from the empirical relationship

log (-to) = - 0.3922- 0.2752log L 00 - 1.038 log K

3)

4)

given in PAULY(1979) and which allows for the derivation of approximate estimates of tofrom estimatesof L 00 and K. Fig. 2 shows the meandepth distribution of little-exploitedand virgin stocks of L. splendens from western Indonesia based on a large number ofexperimental trawl hauls (PAULY1977, Note: the growth parameters for L. splendens givenin this paper are erroneous). Fig. 2, however, gives estimates of catch-per-effort in terms ofweight. These may be converted to estimates of fish number by dividing the kg/h value bythe estimate of mean fish weight pertaining to each depth mid-range.

o, 10. 20. 30 Kg/h,

Depthin m.10

30

20

40

50

Fig. 2. Mean catch rates of Leiognathus splendens in little exploited stocks of Western IndonesianWaters. From PAULY(1977)

I based on equation 2. - 2 based on Equation 3. -} based on Equation 5. - 4 based on the data alsoused for drawing fig. 1.

The length corresponding to each of these depths is calculated by means of equation 3"(seetable 2). These length are then converted to weight estimates by means of the followingequation

W = 0.01122 L3.2166 5)

which is taken from PAULY(1977) and converts in L. splendens total length, in cm, to liveweight, in g. The mean weights and the estimates of fish number per depth mid-rangeobtained in this manner are given in table 2.

Finally, fig. 3 shows the pseudo catch-curve so obtained. The regression equation is

- -- ----

Table 2. Data for the construction of a pseudo catch-curve

Depth(m) LT(cm)' age(yJ' w (g)' kgIh' N() inN

15 8.95 0.755 12.9 18.01 1395 7.2425 10.0 0.965 18.5 31.0 1676 7.4235 11.1 1.25 25.8 14.9 578 6.3645 12.1 1.61 34.1 9.63 282 5.6455 13.2 2.28 45.1 4.97 110 4.70

Use of pseudo catch-curve for the estimation of mortality rates in Leiognathus splendens 59

In N = 8.80- 1.84y 6)

where y is the age in years. This allows for an estimate of Z = 1.84.As the stocksinquestion were, when sampledvery little exploited, we also have M "'"1.8.

inN8.0.

7.0

6.0.

5.0.

4.0~ r0.5

,1.0

,1.5

Fig. J. Pseudo catch-curve for Leiognatbus splendens in little exploited western Indonesian stocks

Discussion

The present method was developed mainly for the purpose of using for the estimation of Zdata which had been gathered and published for miscellaneous purposes and which couldnot be used directly for the construction of a real catch curve.

The present method may therefore be considered as a palliative to be used only as a lastresort. This point should be viewed especially in light of the fact that the biases of themethod are rather difficult to assess.

In the present case, the various equations happen to produce a value of M = 1.8,whichis astonishingly close to the value of M obtained from the relationship

log M = 0.1228-0.1912 log L 00 + 0.7485log K + 0.2391log T 7)

and which produces an estimateof M = 1.83when L 00 = 14.3,K = 1.04andT = 28°C(PAULY1978b).

Equation 7 was derived from a multiple regression of 122 independent estimates of M,plotted against their corresponding values of log L 00' log K and log T, the latter valueexpressing in °C the mean environmental temperature of the stock in question.

An exhaustive discussion of the links betWeen the growth of fishes and those aspects oftheir physiology which determine their longevity and mortality is given in PAULY(1979).

Equation 7 tends to produce very reliable estimates of M, and this confirmation of thevalue of M obtained by the pseudo catch-curve argues for the applicability of this method.

Zusammenfassung

1. Die Beziehung zwischen mittlerer Lange und Fangtiefe bei Leiognathus splendens wurde berech-net, wobei Daten von der $jjdkuste Borneos verwendet wurden.

2. Aus dieser Beziehung und der Uingen-Gewichtsbeziehung fjjr diese Art wurde das mittlercGewicht fUr 5 ausgcwahlte Ticfcnhorizontc bcrechnet.

60 D. Pauly

3. Dieses mitdere Gewicht wurde fLirj..-dcnTidcnhoriwm in dil' minll'fl' ran~ralc (in kl:/h) cinesjeden Ticfenhorizonls hineindividicrt, um su cincHSch;il~.wnl fur diL'millkrL' AII~..lhlYun Fisch"n,die pro Stunde in jedem Tiefenhorizont gefangen wurden, zu erhalten, Dic mittl.m:n Fangraten, diehier verwendet wurden, stammen aus einer friiheren Arbeit des Autors und gelten fiir das westlicheIndonesien insgesamt.

4. Aus den Wachstumsparametern yon L. splendens wurde das Alter berechnet, das der LangeentSpricht, die fiir jeden Tiefenhorizont berechnet wurde.

5. Der natiirliche Logarithmus der Anzahl von Fischen, wie in 3) berechnet, wurde gegen dasentsprechende Alter aufgetragen, das in 4) berechnet wurde. Es ergab sich eine Gerade, derenSteigung mit Zeichenwechsel den exponentiellen Koeffizienten der Gesamtsterblichkeit (Z) dar-stellt.

6. Dieser Wert fiir Z (1.8) stellt auch einen Schiitzwert fiir M, den exponenliellen Koeffizienten dernatiirlichen Sterblichkeit dar, weil der hier untersuchte Bestand 1976 nicht oder kaum befischtwurde. .

7. Dieser Wert fUr Mist gleich dem Wert fiir M, der fiir diesen Bestand mit einer anderenunabhangigen Methode berechnet wurde.

8. Die Methode sollte trotz der nachgewiesenen guten Obereinstimmung nur dann verwendetwerden, wenn Standardmethoden nicht verwendet werden konnen, weil die Empfindlichkeit einersolchen Pseudo-Fangkurve gegeniiber zuf:illigen Storungen und systematischen Fehlern nichtgetestet werden konnte.

Acknowledgements

I thank Prof. HEMPEL for reviewing the manuscript, and my brother GILBERT PAULYfor drawing thefigures.

References

BEVERTON,R. J. H.; HOLT, S. J., 1957: On the dynamics of exploited fish populations. U. K. Min.Agric. Fish. Invest. 19.

MARTOSUUKOTO,P.; PAULY,D., 1976: R/V "Mutiara" IV survey data. November 1974 to July 1976.Contrib. Demersal Fish. Project Mar. Fish. Res. Inst. Jakarta 2.

PAULY,D., 1977: The Leiognathidae (Teleostei): their species, stocks and fisheries in Indonesia, withnotes on the biology of Leiognathus splendens (Cuvier). Penelitian Laut Indones.lMar. Res.Indones. 19,73-93.

PAULY,D., 1978a: A preliminary compilation of fish length groWth parameters. Ber. InSt. Meeresk.Univ. Kiel 55.

PAULY,D., 1978b: A discussion of the potential use in population dynamics of the interrelationshipsbetween natural mortality, growth parameters and mean environmental temperature in 122 fishstocks. ICES CM 1978/G: 21.

PAULY,D., 1979: Gill size and temperature as governing factors in fish growth: a generalization of theyon Bertalanffy Growth Fonnula. Ber. Inst. Meeresk. Univ. Kiel 63, 156 pp. .

SAEGER,J.; MARTOSUBROTO,P.; PAULY,D., 1976: First report of the Indonesian-Gennan demersalfisheries project: results of a trawl survey in the Sunda Shelf area. Laporan Penelitian PerikananLaut/Mar. Fish. Res. Rep. Contrib. Demersal Fish. Project, Jakarta I, 1-46.

Author's address: Dr. D. PAULY, International Center for living Aquatic Resource Management, P.O.Box 1501 Makati, Metro Manila, Philippines