Scientific Reports of theHokkiudo Salmon Hatchery
No 50 113-116, November 1996

Allometric Back-Calculation of Individual Growthfor Chum Salmon Otolith During Early Life
Masa-aki Fukuwaka
Research Division, Hokkaido Salmon Hatchery, Fisheries Agency of Japan,
2-2Nakanoshima, Toyohira-ku, Sapporo 062, Japan
Abstract. - Otolith growth and rate of increment formation in juvenile chum salmon were e x m iried to determine whether otoliths could be used to back-calculate body sizes at various juvenile life
history stages. Sagittal otoliths were firstly observed in newly hatched chum alevines. At that time, thefish had an average total length of 19.5 mm and their sagittae were approximately 0.312 m long. As
the fish grew, the relationship between body length ( L in mm) and sagitta length (0 in mm) was allometric and equaled: 0 = 0.312 + 0.0359 . ( L - 19.5)0.7w.
Increment periodicity was found to occur on adaily basis and was ascertained by performing a fluorescent marlung experiment. The results of thiswork show that individual growth in juvenile chum salmon can be estimated by features readily detected in their otoliths.

Introduction
In many instances it is important to estimate thesize of fish as they enter new environments or modesof life. In the past, many investigators have relied onscales to back-calculate fish size. For example, size
selective mortality in salmonids was observed incoho (Oncorhynchus kisutch) and steelhead ( 0 .
mykiss) by back-calculating fish size from scaleparameters (Ward et al., 1989; Holtby et al., 1990).
Healey (1982) also used circulus spacing patterns onchum salmon (0.keta) scales to estimate when size
selective mortality occurred.
However, in many instances juvenile chumsalmon enter nearshore areas before scale formation.
Additionally, it i s often difficult to interpret the scalepatterns induced during early marine life in thisspecies. For these reason, investigators have recently
begun to look at extracting early life history information from otoliths which are the first calcified structures to appear during early ontogeny in salmonids(Campana and Neilson, 1985).
To back-calculate fish growth, it is necessary toknow the periodicity of increment formation and toestablish the relationship between otolith size andfish size (Campana and Neilson, 1985). The formation of increments in otoliths has been found to occur
on a daily basis in many teleosts. The relationship
Contribution A No. 356 from the Hokkaido Salmon Hatchery

between otolith size and body size has proven to be
more difficult to establish. Generally, these relationships can only be elucidated by examining many
individuals from the same population (Francis, 1995).
In this paper, I evaluated whether otolith increments occurred on a daily basis in juvenile chumsalmon. I also examined the relationship between
otolith size and body size. Both were done to ascertain whether otoliths could be used to back-calculate
body size in juvenile chum salmon.

Materials and Methods
On October 25, 1993, chum salmon eggs werestriped and fertilized and then incubated in 8°C
water. Twenty embryos, alevins, or fry were collected at 0, 10, 20, 30, 60, 90, 120, and 150 days afterfertilization. The fish were fixed in 10% buffered formalin for one day and then stained with alizarin red S
so that their otoliths could be easily observed. For theotolith growth of successive stages, chum salmon
juveniles were also collected off Yamagata, Japan
Sea in March 22, April 7, and 21, 1994. These fish
were fixed in 10% buffered formalin for 3 or 4 days
and then preserved in 70% ethanol. Total or fork
lengths taken o n the fish were in millimeters.
Saggitae were dissected from all specimens under astereo microscope. The long axis of each sagitta wasmeasured in millimeters.
I used three models to examine the relationshipbetween sagitta length and juvenile length, one was- 113 -S I f . S-#-A>tF%
SCI. REP. HOKKAIDO SALMON HATCHERY, NO. 50, 1996

Table 1. Parameters and residual sum of squares of log-transformed variable ( S s ) of a linear and two allometric models fitting the relationship between sagitta length and body length in alevin and juvenile chum salmon.

Model 1Model 2Model 3Model
a0.1320= a +b'L0.0326
O=a.Lb
O = O , + U . ( L - L J ~ * 0.0359bssn0.0140

0.654

129

0.830

0.594

129

0.790

0.543

129

* 0,is 0.312 mm (sagitta length at hatching) and Lois 19.5 mm (body length at hatching).
linear (model 1) while models 2 and 3 were allometric:
O=a+b.Lmodel 1
O=a.Lbmodel 20 = 0, + a . ( L - Lo) b
model 3A

E 1.5-1
W

Where 0 is sagitta length (mm); L is body length(mm); 0,, is sagitta length at hatching; Lo is bodylength at hatching; a and b are constants of a given
model. Models were fit for alevins and juveniles
except for alevins at hatching by the least-squares
method assuming the log-normal distribution of theerror. The resulting models were analyzed by using
the residual sum of squares of log-transformed values
which compared how well the data fit each model.
The model with the minimum sum of squares wasselected as having the best fit.
To investigate increment periodicity, a mark wasinduced on the otoliths of 40 juvenile chum salmon
by immersing the fish in 10 ppm alizarin complexone(ALC) for one day on May 17, 1994 (Tsukamoto,1988). Each fish was also marked a second time, tenwere marked 7 days after receiving their first exposure to ALC, other sets of ten fish were marked at 14,21, and 28 days. Seven days after the fish had beenmarked for the second time they were sacrificed, andfixed in 70% ethanol. The sagittae from each fish
were ground and polished to produce thin sections for
microscopic observation. A fluorescent microscope
was used to count the number of growth increments
between the two ALC marks.

Resultsa.acnY0E,

1010050Body length (mm)Fig. 1. The relationship between body length ( L in mm) andsagitta length (0 in mm) of alevin and juvenile chumsalmon. Line indicates the allometric equation: 0 = 0.3 12+ 0.0359 . ( L - 19.5y'w.

cEE!

0 20-c.
I

rc

0I'

O I L -= oSagittae were first observed in alevin chumsalmon at hatching (60 days after fertilization). At
this time the mean total body length was 19.5 mm(0.75 SD) and the sagitta had a mean longitudinallength of 0.312 mm (0.0256 SD). The residual sum ofsquare revealed that model 3, which equaled:

I03020Time (days)
10Fig. 2. The relationship between time in days (T) and increment number (IN) in chum salmon otolith. The regression
equation is described by: IN = 0.962 * T + 0.0556; r =0.932, n = 40.

0 = 0.312 + 0.0359 ( L - 19.5)0.7vo- 114 -FUKUWAKA - BACK-CALCULATION FOR CHUM SALMON OTOLITH

provided the best fit (Table 1) for the relationshipbetween body length and sagitta length (Fig. 1).
A regression analysis on increment number (IN)and time in days (T) between ALC marking episodes
produced the following equation (Fig. 2):
NI = 0.962 . T + 0.0556
The correlation coefficient ( I ) for this equation
equaled 0.932 and n was 40. A t-test (0.2 < P < 0.5)
disclosed that the regression coefficient was not different than unity, and thus growth increments wereproduced in the sagittae on a daily basis.

Discussion
My evaluation of increment periodicity was performed in freshwater under laboratory conditions.
Volk et al. (1984) also observed daily increment production i n chum salmon juveniles when they were
held in sea water tanks. However, non-daily increment production was observed in juvenile pinksalmon that had been freely migrating and feeding inan Alaskan estuary (Vok et al.,1995). Consequently,
when studies are undertaken to evaluate early marine
growth of chum salmon or other juvenile salmonids itwill be necessary to conduct field evaluations ofincrement production by using tagginglstaining andrecapture methods.
The relationship between otolith length and fish
length was found to be allometric during alevin andjuvenile stages in chum salmon. Hence it is not possible to simply use a proportional back-calculation
method to predict fish size based on otolith size.
Generally, morphological change with development
are often expressed by allometric relationshipbetween body parts or tissues in fishes (Weatherleyand Gill, 1987). The relationship between otolith sizeand fish size has also described allometric equation(Fitzhugh and Rice, 199.5). Other non-linear relationships between otolith length and fish length are oftenobserved during early life in many fishes. For example, otolith - fish size relationship have been
described by using polynomial equation (Mugiya andTanaka, 1992). Moreover, this relationship appears tochange with ontogenetic stages in early life (Hare andCowen, 1995). In their review, for instance, Campanaand Neilson (1 985) state that a curvilinear relationship is characteristic during larval phases and thisusually changes into a linear one during later juvenilestages.

Here I was able to describe the relationshipbetween otolith length and fish length for bothalevins and juveniles by using an allometric equation.
The logarithmic form of allometric relationship is linear. Graynoth (1987), however, feels that the slopesof such allometric relationships will vary among individuals and this will have to be considered whenback-calculation are made. In addition, Secor and
Dean (1992) point out that the otolith length - fish
length relationship will vary with somatic growth.
Back-calculation methods designed to assess individual growth such as the Fraser-Lee and biologicalintercept methods have taken this phenomenon intoaccount by using individual growth trajectories(Campana, 1990).
I used otolith size and fish size at hatching as acommon point in biological intercept method ofback-calculation. Sometimes this common point isdetermined mathematically whereas in other cases it
is empirically determined (see Francis, 1990). In
either case it is often difficult to decide which backcalculation method should be used. Whatever method
is chosen should be validated by comparing individual growth trajectories with back-calculated ones. In
this study, the allometric equation which included
otolith length and fish length at hatching provided thebest fit between otolith size and fish length. Theseresults indicated that individual growth could be estimated by using allometric back-calculations based onotolith characteristics.

Acknowledgments
I am thankful to A. W. Newton and P. Wright(Marine Laboratory, Agriculture and Fisheries
Department, Scottish Office), S. L. Schroder and E.
C. Volk (Washington Department of Fish andWildlife), and T. Akamine (National ResearchInstitute of Fisheries Science, Fisheries Agency ofJapan) for reading and comments on the manuscript.

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サケ初期生活期における 耳石のアロメ トリー関係を用いたパック カル キュレーション
福若雅章

sur‑

サケ幼稚魚、の 個成長推定のため，耳石を用いたバッvival Or coho salmon (Oncorhynchuskisutch).
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Otolith to somatic growth rates fn larval and juve‑
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ク ・カルキュレーションが可能か否かを判定するため，耳石の成長とその輪紋形成を調べた．扁平石はふ化時から観察されるようになった． ふ化時の平均全長と耳石長は ，それぞれ1<@． Rmmと 312mmであった． 仔魚期から幼魚期の間は，体長 仕， mm) と 耳石長 (0,mm) の関係は

アロ851.

メトリー式で表された: (? 二 0 ． 312+0.0359

・(L‑19.5) 。 '。。．蛍光物質を用いた標識実験から，耳石の輪紋

Secor, D. H., and J. M. Dean (1992): COmparison 0f
otolith‑based back‑calculation methods to deter‑mine individual growth histories 0f larval striped
bass, MOrone saxatilis.Can. J. Fish. Aquat. Sci.,・，サケ形成はl 日に I本であることが示された．結果から．
幼魚の個成長は耳石形質から計算できることがわかった

116