Evidence of a relationship between age andotolith weight in the Chilean jack mackerel,Trachurus symmetricus murphyi (Nichols)$

Miguel Arayaa, Luis A. Cubillosb,*, Margarita GuzmaÂna,Jessica PenÄaililloa, Aquiles SepuÂlvedab

aDepartamento de Ciencias del Mar, Universidad Arturo Prat, Casilla 121, Iquique, ChilebInstituto de InvestigacioÂn Pesquera, Casilla 350, Talcahuano, Chile

Received 30 March 1999; received in revised form 27 September 1999; accepted 13 July 2000

Abstract

The relationship between age and otolith weight was examined in the Chilean jack mackerel, Trachurus symmetricus

murphyi (Nichols). The purpose was to present evidence for the relationship in order to obtain a rapid and inexpensive method

of ageing individuals of T. s. murphyi. The evidence of the otolith age±weight relationship is presented according to: (a) the

persistence and progression of modes in otolith weight frequency distributions of ®shery-caught individuals during 1996, and

(b) establishing a direct relationship between the otolith weight and age. The ®sh were aged using the density of daily growth

increments, while the number of modes in the otolith weight frequency data (OWFD) were analyzed using MIX and

MULTIFAN computer software. According to MIX, there were between 8 and 10 modes in the OWFD and the average otolith

mass growth rate (mg yrÿ1) was 8.256 mg yrÿ1, under the assumption that modes in the data represent year classes. Using

MULTIFAN, the best ®t was a 10 age-class model and the otolith mass growth rate ranged between 7.22 mg yrÿ1 in the ®rst

two age classes and 7.07 mg yrÿ1 in the last age classes. The estimated ages of 52 ®sh ranged between 1.4 and 12.7 yr, and the

relationship between otolith weight and age was linear and statistically signi®cant (r2 � 0:42, n � 44, P < 0:05). The inverse

relationship, using the otolith weight as the independent variable, was also linear, but the intercept was statistically equal to

zero. The slope of a regression forced to pass through the origin was 0.119 yr mgÿ1 with a 95% con®dence interval between

0.104 and 0.134 yr mgÿ1. We concluded that the results support the idea that otolith weight is related with the age of jack

mackerel and that it may be a useful tool of rapidly estimating the age of individuals and probably the age structure of jack

mackerel. However, alternative methods of ageing should be applied because real ages of jack mackerel are far of clear.

# 2001 Elsevier Science B.V. All rights reserved.

Keywords: Otolith weight; Age; Central-southern Chile; Jack mackerel; Trachurus symmetricus murphyi

1. Introduction

Determination of age in some species of the Genus

Trachurus can be dif®cult using conventional methods

of otolith reading (FarinÄa Perez, 1983; Morales-Nin,

1987; Arruda, 1987; Kerstan, 1995). This seems to be

Fisheries Research 51 (2001) 17±26

$ This work was presented in the Second International

Symposium on Fish Otolith Research and Application, Bergen,

Norway, 20±25 June 1998.* Corresponding author. Tel.: �56-41-584820;

fax: �56-41-583939.

E-mail addresses: maraya@cec.unap.cl (M. Araya),

inpesca@arauco.reuna.cl (L.A. Cubillos).

0165-7836/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved.

PII: S 0 1 6 5 - 7 8 3 6 ( 0 0 ) 0 0 2 3 3 - 2

the case with the Chilean jack mackerel, Trachurus

symmetricus murphyi (Nichols), because there are

notable differences in age and growth studies (Kaiser,

1973; Pavez and Saa, 1978; Abramov and Kotlyar,

1980; Castillo and Arrizaga, 1987; Nekrasov, 1982,

1987; Kochkin, 1994; Cubillos and Grechina, 1998).

Systematic errors and differences in the interpretation

of age produce differences in estimates of growth rate,

von Bertalanffy growth parameters, and the index of

growth performance of the jack mackerel (Cubillos

and Arancibia, 1995).

Fish otoliths are employed as indicators of age,

but are useful only when age determination can be

precise and accurate. Conventional methods of age

determination are based on examination of growth

increments in ®sh otolith structure and correct

determination of age supposes that annuli in otoliths

can be identi®ed and counted. In otoliths of T. s.

murphyi however, the sequence of a single opaque

ring followed by a single hyaline ring is not alway-

sclear, but may contain double or multiple rings.

This problem has also been observed in Trachurus

trachurus trachurus of the North Atlantic (FarinÄa

Perez, 1983; Arruda, 1987) and Trachurus trachurus

capensis of Namibia and South Africa (Hatanaka

and Kawahara, 1985; Shcherbich, 1992; Kerstan,

1995).

The objective of the present study is to look for

alternative methods of determining the age of jack

mackerel. Recent research indicates that there is a

direct relationship between ®sh otolith weight and age

(Pawson, 1990; Radtke and Hourigan, 1990; Fletcher,

1991, 1995; Worthington et al., 1995a,b). This rela-

tionship has great potential for estimating age and age

structure in ®sh (Worthington et al., 1995a). It is a

faster and inexpensive method and would be prefer-

able when the ages of a great number of individuals are

required, e.g. the age composition of jack mackerel

catches.

In this paper we present evidence for the relation-

ship between age and otolith weight for T. s. murphyi,

in accordance with the following objectives: (1) to

investigate the persistence and modal progression

in the otolith weight frequency distributions of ®sh-

ery-caught individuals, and (2) to analyze the relation-

ship between otolith weight and age of some

individuals.

2. Materials and methods

2.1. Sampling

Between January and December 1996, specimens

of T. s. murphyi were collected from catches of the

purse-seine ¯eet operating in the central-southern area

off Chile (33±398S). Length±frequency data were

obtained as daily random samples from the catches

of vessels at the main places of landing and weekly

samples were analyzed to obtain biological data, i.e.

®sh weight, ovary weight, maturity and otoliths. A

total of 10 pairs of otoliths were collected for each

1 cm length class, cleaned, and stored dry in paper

envelopes. Body size was measured as fork length

(FL) to the nearest centimeter.

2.2. Otolith weight frequency

Sagittal otoliths of each ®sh were washed with

distilled water and dried over 12 h in an oven at

608C to constant weight. Undamaged otoliths were

then weighed individually to the nearest 0.0001 g. No

signi®cant difference was found (two-tailed tests)

between right and left otolith weight (t2;a�0:01;d:f:�32

� 2:724, tobserved � 1:490), nor between readers

(t2;a�0:01;d:f:�32 � 2:724, tobserved � ÿ0:457), nor

between wet and dry otolith weight

(t2;a�0:01;d:f:�32 � 2:724, tobserved � 1:325); therefore,

wet weights were used in subsequent analyzes. The

otolith weight data were compiled into quarterly

weight±frequency histograms (n � 1497), from which

the number of modes was analyzed using the MIX

(MacDonald and Pitcher, 1979; MacDonald and

Green, 1988) and MULTIFAN (Fournier et al.,

1990) computer programs, on the assumption that

the modes in the data represent year classes. These

programs, especially MULTIFAN, are designed to

help in discriminating between modes in length±fre-

quency data, but we used them to solve the number of

modes in the otolith weights. The data were summar-

ized within quarterly time series so that the ®rst

quarter is de®ned as the trimester from January to

March (designated as month 1), the second from April

to June (month 4), the third from July to August

(month 7), and the fourth from September to Decem-

ber (month 10).

18 M. Araya et al. / Fisheries Research 51 (2001) 17±26

2.3. Otolith weight versus age

In establishing the relationship between age and

otolith weight, a total of 60 otoliths from ®sh in the

range between 20 and 60 cm FL (otolith radius range:

2933±5500 mm) was selected at random to determine

age using the density of the daily growth increments

(Ralston and Miyamoto, 1983; Ralston and Williams,

1989). Otolith radius and weight were recorded before

the otolith was prepared for reading. Daily growth

increments were read and measured from thin sections

according to the recommendations by Brothers et al.

(1976) and Campana and Neilson (1985). It must be

mentioned that the deposition of daily growth incre-

ments in otolith sagittae of T. s. murphyi was validated

using oxytetracycline for marking the otoliths of ®sh

between 25 and 35 cm FL (unpublished results).

Because daily growth increments are daily, the appli-

cation of the method of density of daily growth

increments is justi®ed fully.

The thin sections were analyzed under a compound

microscope using transmitted light at 1000 times

magni®cation. To determine ages individually, an

adequate number of segments in which daily growth

increments were suf®ciently clear and interpretable

along the axis of growth were used. Readings of

segments were obtained trying to cover all the distance

between the nucleus and the postrostral border. Seg-

ment size and the number of daily growth increments

contained in each were used to determine the instan-

taneous otolith growth rate according to

Dx

Dincrements� Dx

Dt� dx

dt(1)

where Dx is the size of the segment (mm) at a certain

distance from the nucleus and Dt the number of

microincrements (days). There were n data pairs

(x, Dx/Dt) for each fish along the axis of growth

(x), i.e. from the nucleus to the postrostral border of

the otolith. In this way, it was possible to fit a

mathematical model describing the instantaneous oto-

lith growth rate (Dx/Dt) as a function of the growth

axis (x), i.e. distance from the nucleus. We used the

following mathematical model, which was fitted for

each fish using non-linear regression:

dx

dt� f �x� � ax�1ÿ bcx�1=c

(2)

where a, b, and c are constants to be estimated. This

model is very flexible since its shape depends on the

value of c. It was described by Deriso (1980) for

analysis of the stock±recruitment relationship in the

dynamics of a fish population. The model described by

Eq. (2) was selected because it is adequate for the

entire data sets (see Fig. 6). The age of each fish was

estimated by solving for dt in Eq. (2), and treating it as

a definite integral between the nucleus (x � 0) and the

otolith radius (x � R), i.e.

T �Z t�T

t�0

dt �Z x�R

x�0

f �x�ÿ1dx (3)

where T is the age in days. The definite integral was

evaluated using MTOOL of Maher (1988), which uses

Simpson's rule (Whittaker and Robinson, 1929) for

numeric integration.

Once age of individual were estimated by Eq. (3),

the relationship between otolith weight (OW) and age

(T) for T. s. murphyi was described using linear

regression with OW as the dependent variable and

age the independent variable. Results were tested for

signi®cance and log-transformed if required. To

obtain a predictive tool, analysis of regression was

also used to investigate the inverse relationship, with

age of individuals as the dependent variable and OW

the independent variable.

3. Results

3.1. Otolith dimensions

The relationships between otolith dimension and

®sh length are showed in Fig. 1. Otolith thickness

increased linearly with ®sh length, whereas for otolith

length and width, the line of best ®t was slightly

curved, and the increase in OW with ®sh length

was described by a power function (Fig. 1). It is clear

from these relationships that a notable change in

otolith width, thickness and weight occurred in ®sh

larger than 40 cm FL, particularly in otolith thickness

and weight. Although there is no notable change in

otolith length, results for the other measurements

suggest that there is a signi®cant change in the thick-

ness and weight of otoliths. It is probable that those

patterns can be due to differences in age of older

M. Araya et al. / Fisheries Research 51 (2001) 17±26 19

individuals with similar otolith size. If the weight of

otoliths is directly related with age of jack mackerel,

then the changes observed in otolith width, thickness

and weight for individuals larger than 40 cm FL would

be due to different ages from individuals with equal

length.

3.2. Otolith mass growth rate

3.2.1. Otolith weight frequency distribution

A series of modes can be separated in the quarterly

OW frequency distributions of the jack mackerel using

the MIX software (Fig. 2). It seems that the mean OW

of each mode represents a series of age classes. Also, it

can be seen that the mean OW of each age class

increases linearly with time, at least for the ®rst seven

classes, which are the most evident and easily sepa-

rated from the MIX (Fig. 3). Although the otolith mass

growth rate ¯uctuates between 0.435 and 0.929 mg

per month between age classes, the average annual

mass growth rate is estimated as 8.256 mg yrÿ1

(Table 1).

A more robust analysis for the analysis of OW

frequency can be carried out using MULTIFAN, on

the assumption that the modes represent age classes.

MULTIFAN was developed for analysis of ®sh

length±frequency data, where the original approach

assumes that the mean length of ®sh follow a von

Bertalanffy growth curve. In this case, the assumption

applies to the mean OW. However, in order to relax the

assumption of a von Bertalanffy function and to obtain

an approximately linear curve, we apply MULTIFAN

using very low initial values for the K parameter of the

von Bertalanffy growth function (0:01 � K � 0:1). In

Fig. 1. Otolith dimensions as a function of size of T. s. murphyi.

Fig. 2. Quarterly OW frequency distributions of T. s. murphyi

during 1996, showing the age classes identified by MIX.

Fig. 3. Progression of mean OW of T. s. murphyi identified in

Fig. 2. The slopes of these lines are an estimation of the otolith

mass growth rate (see Table 1).

20 M. Araya et al. / Fisheries Research 51 (2001) 17±26

this way, a model with 10 age classes was the only

model producing a signi®cant increment in the log-

likelihood function (Table 2, Fig. 4). The parameters

of the model are shown in Table 3. It can be seen that

the otolith mass growth rate diminishes from 7.22 to

7.07 mg yrÿ1 between the ®rst two age classes and the

last two (age classes 10 and 11). The otolith increment

weight as a function of the age is described by

OWt � 2808�1ÿ exp�ÿ0:003t�� (4)

where OWt is the otolith weight at age t (yr).

3.2.2. Otolith weight versus age

The model describing the microincrement width as

a function of the radius (distance from the nucleus)

was ®tted to 52 individuals from 60 because thin

sections of eight otoliths were defective. The number

of data pairs (x,Dx/D) available among the nucleus and

the postrostral border of otoliths ¯uctuated between 11

and 49 for the individuals analyzed and the coef®cient

of determination (r2) ¯uctuated between 0.413 and

0.913. An example of such modeling is presented in

Fig. 5 for four individuals, in which it can be observed

that the otolith growth rate attain a maximum at

distances between 400 and 800 mm from the nucleus.

This is also true for the entire data sets, where the

Deriso model was ®tted to the observed data

(r2 � 0:610, n � 1630, P < 0:05, Fig. 6).

Table 1

Otolith mass growth rate based on the modal progression of the

OW of T. s. murphyi (see Figs. 2 and 3)

No. of

modal group

Intercept

(mg)

Slope

(mg per month)

r2

2 16.0 0.435 0.899

3 21.3 0.673 0.896

4 28.2 0.783 0.957

5 33.4 0.929 0.923

6 42.6 0.762 0.805

7 50.7 0.734 0.845

8 61.1 0.504 0.402

Mean monthly rate: 0.688 mg per month

Mean annual rate: 8.256 mg yrÿ1

Table 2

Two times the log-likelihood values for the number age classes present in the OW frequency distribution of T. s. murphyi in 1996. The overall

best fit corresponds to the selection of number of age classes that generated a statistically significant increase in the log-likelihood

No. of age classes

5 6 7 8 9 10 11 12

2L 2334.99 2366.54 2425.18 2464.21 2497.47 2550.20 2539.82 2538.72

No. of parameter 20 24 28 32 36 40 44 48

Table 3

Estimated parameters from MULTIFAN analysis of the OW frequency data of T. s. murphyi. The standard error is indicated between

parenthesis

Parameter Estimated value Relative agea (yr) Mean OWa (mg)

Asymptotic OW (OW1, mg) 2808.0 (453.28) 2.19 15.88

Growth coefficient (K, yrÿ1) 0.003 (0.0004) 3.19 23.10

Age of first age class (yr) 2.19 (0.0110) 4.19 30.30

Mean S.D. 2.46 (0.2271) 5.19 37.48

Ratio of first to last S.D. 1 6.19 44.64

Mean weight at first age class (mg) 15.88 (0.211) 7.19 51.78

Mean weight at last age class (mg) 80.16 (0.193) 8.19 58.90

9.19 66.01

10.19 73.09

11.19 80.16

a Relative age and mean OW estimated by MULTIFAN for month 1 (first quarter).

M. Araya et al. / Fisheries Research 51 (2001) 17±26 21

Fig. 4. MULTIFAN results for the quarterly OW frequency distributions of T. s. murphyi during 1996. The dashed vertical lines represent the

estimated mean OW-at-age in each sample. The inner smooth curves are the estimated numbers at age class and the outer smooth curve is the

estimated frequency distribution.

22 M. Araya et al. / Fisheries Research 51 (2001) 17±26

The individual age ¯uctuated between 1.4 and

12.7 yr and the OW was directly related to the esti-

mated age (Fig. 7). The relationship between OW and

age was established with 44 individuals, discarding

eight because otoliths were broken at the time of

weighing, a situation that was only evident after

preparing the otoliths for reading. The linear relation-

ship is signi®cant for n � 44 (P < 0:05) and the slope

and the constant of the regression were different

from zero at the 95% con®dence level. Regressions

based on log-transformed variables were also signi®-

cant, but the coef®cient of determination was lower

(Table 4).

It must be mentioned that when establishing the

inverse relationship, using the OW as the independent

variable, it was found that the constant of regression

was not different from zero at the 95% con®dence

level (Table 4). Furthermore, variance increases with

Fig. 5. Some examples of the fitted model to explain the otolith

growth rate of four individuals of T. s. murphyi as a function of the

distance from the nucleus.

Fig. 6. Otolith growth rate as a function of the distance from the

nucleus of all individuals of T. s. murphyi. Observed data are

showed in the upper panel and the fitted model to all data is showed

in the lower panel.

Fig. 7. Relationship between OW and the age of T. s. murphyi, (a)

original values of variables and (b) values of variables transformed

to logarithms.

Table 4

The regression formulas for the analysis of the relationship between OW and T in T. s. murphyi. Lower and upper limits at the 95% of

confidence are showed between parenthesis for the constant and the coefficient of regression

Regression formula Constant Slope r2 P-value

OW � a� bT 16.260 (9.346, 23.173) 4.117 (2.621, 5.613) 0.424 <0.05

T � A� B OW 0.642 (ÿ0.698, 1.982) 0.103 (0.066, 0.140) 0.424 <0.05

ln�OW� � a0 � b0 ln�OW� 2.627 (2.318, 2.935) 0.603 (0.375, 0.831) 0.404 <0.05

ln�T� � A0 � B0 ln�OW� ÿ1.010 (ÿ1.876, ÿ0.144) 0.670 (0.417, 0.924) 0.404 <0.05

T � b OW ± ± 0.119 (0.104, 0.134) 0.411 <0.05

M. Araya et al. / Fisheries Research 51 (2001) 17±26 23

the independent variable (Fig. 8), suggesting that a

regression without intercept should better in describe

the relationship of age on OW. The slope of this

last regression indicates that otoliths of the jack

mackerel present an increment of 0.119 mg yrÿ1,

IC � f0:104; 0:134�. In other words, the inverse of

this slope (1/b) suggests that the otolith mass growth

rate is approximately 8.385 mg yrÿ1. This result is

consistent with the analysis of OW frequency data.

4. Discussion

This study provides evidence of a relationship

between age and OW in T. s. murphyi. This relation-

ship could provide a rapid and economic method to

determine age in this species, a suggestion that has

been made in previous studies for other species (Boeh-

lert, 1985; Pawson, 1990; Fletcher, 1991, 1995;

Worthington et al., 1995a). These studies include both

tropical and temperate ®sh, and found that OW

explained between 70 and 90% of variability in ®sh

age.

In this study, the relationship between OW and age

estimated by the density of the daily growth incre-

ments indicates that OW explains 42% of the variation

in the age of T. s. murphyi. This is a good result

because the individual age estimated in this form can

contain many sources of error, such as: (a) high

individual variability in the otolith growth rate; (b)

error of measurements, which are associated with the

resolution of the optic microscope; (c) error in the

model used to describe the instantaneous otolith

growth rate and (d) error of estimation of the para-

meters of the model. In this context, the relationship of

age on OW is preferred because in the OW data only

error of measurements are present.

Nevertheless, this study demonstrated that the den-

sity of daily growth increments can be applied to

estimate the individual age of ®sh, over a wide range

of ages (1.4±12.7 yr). However, it is desirable to use

new application in analyzing the growth patterns in the

otolith of older jack mackerel, may be through a

scanning electronic microscope. Indeed, the curved

growth of the otolith of jack mackerel with age makes

it very dif®cult to obtain a section where the complete

sequence of the individual's growth can be observed.

Also, when the growth rate diminishes it is possible

that the width of daily growth increments could be

under the resolution of the optic microscope, affecting

the estimation of ages (Morales-Nin and Ralston,

1990).

The indirect evidence presented here through the

analysis of the modal progression in the OW fre-

quency, suggests two questions in connection with

the otolith mass growth rate of T. s. murphyi. The ®rst

is related to the variability of the otolith mass growth

rate of jack mackerel. Indeed, the analysis based on

MIX suggests that the otolith mass growth rate would

be variable among year classes and that this rate could

¯uctuate between 5.22 and 11.15 mg yrÿ1 (Table 1).

This point requires special attention, since it could

affect the estimates of age using the OW data. How-

ever, it should also be kept in mind the limitations of

the analysis based on MIX, since modes (normal

groups) in larger otoliths can be dif®cult to separate,

affecting the otolith mass growth rates in the older

year classes.

The second question arises from the indirect ana-

lysis which assumes that the mean OW follows the von

Bertalanffy growth model just as it come from the

results based on the MULTIFAN analysis (Eq. (4)).

However, using this approach the otolith mass growth

rate diminishes with age, the asymptotic weight of the

otolith is very large and the coef®cient K is very small,

suggesting that the relationship is linear.

These questions should be considered in future

studies. Indeed, if the OW is related directly to ®sh

age, through a constant otolith mass growth rate, then

the modes in the OW frequency should be distributed

approximately equidistant.

Despite these considerations, we conclude from

the presented evidence that OW could be useful in

providing quick and economical estimates of the

age and of age structure of T. s. murphyi. However,

Fig. 8. Relationship between age and OW of T. s. murphyi.

24 M. Araya et al. / Fisheries Research 51 (2001) 17±26

experimental studies using ®sh of known age (Reznick

et al., 1989; Secor and Dean, 1989) have shown that

the relationship between otolith size and ®sh size is

strongly in¯uenced by the growth rate of the ®sh, and

suggest that otolith growth is not synchronous with the

growth of the ®sh itself, but has an additional time-

dependent rate which results in slow-growing indivi-

duals having relatively heavy otoliths for their body

size. Pawson (1990) concluded that although appro-

priate models based on otolith±®sh size relationship

can predict age for groups of ®sh in which growth rates

are known or can be assumed to be consistent, such

techniques have a limited application in ageing ®sh

from wild populations with highly variable growth

rates. In this context due to potential variation in the

relationship between the OW and age, the relationship

should be calibrated for each new sample of ®sh. To

maximize the bene®ts of using OW, the calibration

would require precise and exact estimates of the age of

only a relatively small number of ®sh that cover the

whole range of OWs and ages present in the samples.

It must be mentioned, however that the real ages of

jack mackerel are far of clear because otoliths are

dif®cult to read, and the interpretation of annual rings

on otoliths by several authors is generating confusion

about growth rates. Thus, alternative methods of age-

ing should be applied to validate the indirect evidence

presented in this study for the relationship between

OW and age of jack mackerel.

Acknowledgements

We are grateful to Paul Taylor of NIWA, New

Zealand, Dr. Vidar Wespestad and Dr. Daniel Kimura,

AFSC, Seattle, for the comments, advice and review

of an early version of the paper. This research was

®nanced by FIP No. 95-10. Also, we wish to thank to

the Council of the Chilean Fisheries Research Fund by

facilitating the publication of the results.

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