Effects of density-dependence and sea surface temperature on interannual variation in length-at-age of chub mackerel (Scomber japonicus) in the Kuroshio-Oyashio area during 1970-1997.

Abstract--Annual mean fork length (FL) of the Pacific stock of chub mackerel (Scomber japonicus) was examined for the period of 1970-97. Fork length at age 0 (6 mouths old) was negatively correlated with year-class strength which fluctuated between 0.2 and 14 billion in number for age-0 fish. Total stock biomass was correlated with FL at age but was not a significant factor. Sea surface temperature (SST) between 38-40[degrees]N and 141-143[degrees]E during April-June was also negatively correlated with FL at age 0. A modified von Bertalanffy growth model that incorporated the effects of population density and SST on growth was well fitted to the observed FL at ages. The relative FL at age 0 for any given year class was maintained throughout the life span. The variability in size at age in the Pacific stock of chub mackerel is largely attributable to growth during the first six mouths after hatching.

**********

Variability in growth of marine fishes has been attributed to the effects of density-dependence or environmental factors such as water temperature, or to the effects of both factors (e.g. Moyle and Cech, 2002). Size-at-age data are crucial because they are necessary for stock assessment methods such as virtual population analysis, yield per recruit, and spawning-per-recruit analyses (Pauly, 1987; Mace and Sissenwine, 1993; Haddon, 2001) and are possibly useful for detecting regime shifts as well (Yatsu and Kidoroko, 2002). Around Japan, the effects of population density and sea water temperature on fish growth have been shown for the Pacific stock of chub mackerel (Scomber japonicus) (Iizuka, 1974), Japanese Spanish mackerel (Scomberomorus niphonius) (Kishida, 1990), the Pacific and Tsushima Current stocks of Japanese sardine (Sardinops melanostictus) (Hiyama et al., 1995; Wada et al., 1995), and Japanese common squid (Todarodes pacificus) (Kidokoro, 2001).

The Pacific stock of chub mackerel is one of the most important commercially exploited fish populations in Japan and has been managed by the total allowable catch (TAC) system in Japan since 1997. Chub mackerel seasonally migrate along the Pacific coast of Japan from Kyushu to Hokkaido. They spawn in the coastal waters around Izu Islands and off southwestern Japan between February and June (Fig. 1, Watanabe, 1970; Usami, 1973; Murayama et al., 1995; Watanabe et al., 1999). Adult fish (after spawning) and their offspring migrate eastward along the Pacific coast with the Kuroshio Current. Juvenile mackerel of about 6 months old usually recruit to the purse-seine and set-net fisheries off the coast of northeastern Japan at the end of summer (Fig. 1, Odate, 1961; Kawasaki, 1966; Watanabe, 1970; Iizuka, 1974). The total catch of the Pacific stock of chub mackerel increased during the 1960s and 1970s, peaked at 1.5 million metric tons in 1978, and then declined to 2.3 thousand tons in 1990 (Fig. 2). The estimated total biomass increased in the 1970s from 2.8 million tons in 1970 to 5.9 million tons in 1977, and the consecutive occurrences of large year classes exceeded 7 billion age-0 (6-month-old) fish in the early and mid 1970s. In 1990, the biomass was reduced to a minimum of 9.2 million tons in 1990 (Table 1, Fig. 2; Yatsu et al. (1)). Relatively large year classes occurred in 1992 (2.8 billion fish) and 1996 (4.5 billion fish), and the total biomass increased in the mid 1990s, but it remained at about 10% of the level attained in the mid 1970s (Yatsu et al. (1)).

[FIGURES 1-2 OMITTED]

On the basis of year-class strength and variations in fork length (FL) at ages 0-2 for the 11 year classes present from 1963 to 1973, Iizuka (1974) suggested an effect of density-dependent growth on young chub mackerels. In this study we describe the variation in FL at age of the Pacific stock of chub mackerel in the Kuroshio-Oyashio area, using data from 1970 to 1997 when the stock biomass fluctuated between 0.2 and 5.9 million metric tons. We use these data to evaluate the effects of population density and sea surface temperature on FL at age.

Materials and methods

Biological data

Biological data have been compiled since 1964 for purse-seine, set-net, dip-net catches, and other catches by national fisheries research institutes and local government fisheries experimental stations in Japan. Fork length (FL) was measured for one thousand to 100 thousand fish per year and body weight (BW) and gonad weight were measured for 10-100% of these fish. The monthly FL compositions and the relationships of FL to BW were established for each year with this data set. Year-specific age-length keys from 1970 to 1994 were adopted from the reports of cooperative research on Pacific mackerel by local government agencies in Chiba, Kanagawa, Shizuoka, and Tokyo. (2) Between 1995 and 1997, age-length keys were developed by national fisheries research institutes and local government fisheries experimental stations.

For calculating the mean FL for ages 0, 1,2, 3, 4, 5, and 6 years and older, we used data from the purse-seine fishery of northeastern Japan during September-December for 28 years, from 1970 to 1997. The catch of this fishery, in these four months constituted 26-80% (the 28-year mean is about 63%) of the total annual catch of the Pacific stock of chub mackerel. Catch in number at FL class i (cm) of each month were calculated by

(1) [n.sub.a,i] = [C.sub.a][d.sub.a,i]/[50.summation over k=1][d.sub.a,k][w.sub.a,k],

where [n.sub.a,i] = catch in number at FL class i (cm) {= 1, ..., k, .. 50} of month a {= Sep., Oct., Nov., Dec.};

[d.sub.a,i] = frequency at FL class i of month a;

[w.sub.a,i] = a mean weight of each FL class derived from the FL-BW relationship; and

[C.sub.a] = a total catch of month a.

We then summed [n.sub.a,i] of 4 months to derive the annual catch in number at FL class i:

(2) [n.sub.i] = [Dec..summation over a=Sep][n.sub.a,i],

where [n.sub.i,j] = the annual catch in number at FL class i.

Using the age-length key, we converted [n.sub.i] to catch at FL class i at age j:

(3) [n.sub.i,j] = [n.sub.i] x [r.sub.i,j],

where [n.sub.i,j] = the annual catch in number at FL class i at age j; and

[r.sub.i,j] = the proportion of age j at FL class i ([r.sub.i,0] + [r.sub.i,1] + .... + [r.sub.i,k = 1).

From [n.sub.i,j], we calculated the mean and variance of FL at age j:

(4) [l.sub.j] = [k.summation over i=1][n.sub.i,j][l.sub.i,j]/[k.summation over i=1][n.sub.i,j]

and

(5) Var([l.sub.j]) = [k.summation over i=1][n.sub.i,j][([l.sub.i,j] - [l.sub.j])].sup.2]/([k.summation over i=1]) - 1,

where [l.sub.j] = mean FL at age j; and

[l.sub.i,j] = mean FL at FL class i at age j.

Sea surface temperature

Time-series data for sea surface temperature (SST, temperatures averaged over 10 days for 1[degrees] latitude x 1[degrees] longitude blocks over the northwestern North Pacific between 0-53[degrees]N and 110-180[degrees]E since 1950) were provided by the Oceanographical Division of the Japan Meteorological Agency. The SST data for each block was averaged for periods of three months (i.e. January-March, April-June, July September, and October-December). The relationship between the SST of each block and FL at age 0 were examined from 1970 to 1997.

Autocorrelation 

For correlation analysis, effective sample sizes ([n.sup.*]) were calculated for all time series data to take autocorrelation into account, n* was computed by the formula (Pyper and Peterman, 1998):

(6) 1/[n.sup.*] = 1/n + 2/n [n/5.summation over j=1] [r.sub.XX](j)[r.sub.YY](j),

where [r.sub.XX](j) and [r.sub.YY](j) are the autocorrelations of X and Y at lag j, defined here with the additional weighting factor proposed by Pyper and Peterman (1998):

(7) [r.sub.XX](j) = n/n - j [n-j.summation over t=1] (X.sub.t] - [bar.X])([X.sub.t+j] - [bar.X]/[n.summation over t=1][([X.sub.t] - [bar.X]).sup.2].

Growth model

We used the modified yon Bertalanffy growth model to incorporate the effects of population density and sea surface temperature according to Millar and Myers, (3) who nvestigated three formulations of the modified yon Bertalanffy equations: 1) a reversible effect on the growth constant k; 2) a reversible effect on the asymptotic length [L.sub.[infinity]]; and 3) an irreversible effect on [L.sub.[infinity]] or k. We tested two of the models, 1 and 2, to investigate the effect of population density and SST. We did not test model 3 because we did not consider that the environmental effects on growth were permanent. Mean length at age i of year-class y was estimated with the following formulas:

Model 1: reversible environmental effect on k

(8) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

(10)[k.sub.i,y] = k + [[beta].sub.1][T.sub.i+y] + [[beta].sub.2][D.sub.i,y].

Model 2: reversible environmental effect on [L.sub.[infinity]]

(11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

(12) [L.sub.i,y] = [L.sub.i-1,y] + ([L.sub.[infinity]i,y] - [L.sub.i-1,y])([1.sup.-e-k])

(13) [L[infinity].sub.i,y] = [L.sub.[infinity]] + [[beta].sub.1][T.sub.i+y] + [[beta].sub.2][D.sub.i,y],

where [t.sub.0] = the age at length 0 (year);

[L.sub.[infinity]] = the asymptotic length; and

k = the growth coefficient;

[L.sub.[infinity]i,y] = [L.sub.[infinity]] at age i of year-classy;

[k.sub.i,y] = k at age i of year-classy;

[T.sub.i+y] = the sea surface temperature in year i+y; and

[D.sub.i,y] = a population density presented by the number of stock at age i of year-class y.

These variables were z-score standardized. The model parameters [[alpha].sub.1] and [[beta].sub.2] were estimated to represent the effects of T+y and [D.sub.i,y] on k or [L.sub.[infinity]].

The parameters were estimated by maximizing the likelihood function which is represented by

(14) L(i,y) = [L.sub.i,y] + [[epsilon].sub.i],

(15) [[epsilon].sub.i] ~ N(0,[[sigma].sup.2.sub.i]),

and

(16) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].

We ran the models with all possible combinations of explanatory variables (T, D, T, and D), and compared AIC with that obtained with the base parameters ([L.sub.[infinity]], [t.sub.0], k).

Results

Fork length at age

Mean FL at age 0 varied substantially over the time series examined. For example, it ranged from 16.9 (Sd [+ or -] 3.0) cm in 1975 to 25.9 (Sd [+ or -] 1.0) cm in 1989. The mean FL for the 28 years period was 21.7 ([+ or -] 2.1) cm (coefficient of variation: CV=9.8%, Table 1, Fig. 3). The FL-at-age-0 values were smaller than the 28-year mean FL for the 1970s, varied around the mean in the early and mid 19803, reached a maximum in 1989, and were at about 22-24 cm in the 1990s (Fig. 3).

[FIGURE 3 OMITTED]

Mean FL at age 1 was similarly variable; it ranged from 24.3 ([+ or -] 1.9) cm in 1976 to 31.6 ([+ or -] 1.4) cm in 1995. The 28-year mean FL was 27.7 ([+ or -] 1.6) cm (CV=5.6%, Table 1). The trend in interannual variability was similar to that in age 0, i.e. it was smaller in the 1970s and larger in the 1990s (Fig. 3). In age-2 fish the 28-year minimum FL of 29.1 ([+ or -] 1.8) cm was observed in 1986 and the maximum of 34.5 ([+ or -] 1.3) cm was observed in 1990 (the 28-year mean FL=31.1 ([+ or -] 1.5) cm, CV=4.7%, Table 1, Fig. 3).

In fish age 3 and older, mean FL varied year-to-year in a manner similar to that found in the younger ages (Table 1). Annual mean FLs for 3-, 4-, and 5-year-olds were 33.7 ([+ or -] 1.3) cm (3.8%), 36.2 (CI [+ or -] 1.4) cm (CV=4.0%), and 38.5 (CI [+ or -] 1.5) cm (CV=3.8%), respectively (Table 1). The mean FLs for ages 0 5 of each year were significantly different among different years (one-way ANOVA, P<0.01).

Mean growth increments I of each year class from age 0 (6 months old) to ages 1-5 ([I.sub.0-i]) showed significantly negative correlations (Table 2). Correlations between the two variables tended to increase with age: 0.69 for [I.sub.0-1], -0.71 for [I.sub.0-2], -0.80 for [I.sub.0-3], and -0.77 for [I.sub.0-4].

The relative FL at age 0 for any given year class was maintained throughout the life span. A correlation between the mean FL at age 0 and age 1 within each year class (1970 to 1996 year class) was positive and statistically significant (P<0.05, Fig. 4). Similarly, the positive correlations between the mean FL at age 0 and age 3 (1970 to 1994 year class, P<0.01, Fig. 4), and age 0 and age 4 (1970 to 1993 year class, P<0.05, Fig. 4) were significant (P<0.05, Fig. 4).

[FIGURE 4 OMITTED]

Correlation between FL and population density

Population densities represented by stock in number at age 0 and total biomass were negatively correlated to FL at age. Negative correlations between the logarithm of abundance of age 0 (ln[N.sub.0]) and FL at ages were relatively high in age 0 to 3 (-0.69 to -0.83, Table 3) and low in age 4 and 5 (-0.63 and -0.64, Table 3). Correlations were statistically significant for ages 0, 2, and 3 (Table 3). Negative correlations between the logarithm of total biomass and FL at ages were relatively high at ages 0 to 2 (0.73 to -0.75) and moderate for age 3 to 5 (0.50 to 0.52, Table 4). However; the relationships were not statistically significant for all ages (Table 4).

Correlation between FL and SST

Growth in the first six months of life was correlated with SST. We detected significant negative correlation between FL-at-age 0 and SST between April and June in the waters bounded by 38-40[degrees]N and 141-143[degrees]E (r=-0.45, [r.sup.2]=0.20, n=28, [n.sup.*]=27, df=25, P<0.05, Fig. 5). The SST between July and September of this area was also negatively correlated with FL at age 0 although the correlation coefficient was not significant at 5% level.

[FIGURE 5 OMITTED]

Growth analysis

Model 1 that incorporated SST (T) and population density (D) gave a minimum Akaike's information criterion (AIC) of 457.68 (Table 5) and the model was expressed by

(17) [L.sub.i,y] = 43.98 {1 - exp(-2.585)exp(-[5.summation over i=0][k.sub.i,y])}

(18) [k.sub.i,y] =0.271 - 0.008[T.sub.i+y] - 0.21[D.sub.i,y].

This model estimated the FL at ages 0-5 well (Fig. 6). The AIC of model 1 incorporating T and D was smaller than the AIC of model 2; therefore the environmental factors had an affect on k rather than [L.sub.[infinity]].

[FIGURE 6 OMITTED]

To investigate the effect of T and D, we calculated the total effect on k for year-class y according to Sinclair et al. (2002):

[5.summation over i=0][[beta].sub.1][T.sub.i+y]/6 for T, and [5.summation over i=0][[beta].sub.2][D.sub.i,y]/6 for D.

Discussion

Estimated population abundance of age-0 fish and total biomass may explain density-dependent growth. FL at age 0, 2, and 3 of the Pacific stock of chub mackerel were negatively correlated with the number of age-0 recruits. Correlations between biomass and FL at ages 0-5 were low and not significant. Therefore, year-class strength is indicated to have a greater negative influence on the growth of the Pacific stock of chub mackerel than total biomass, as reported for the Atlantic mackerel (Scomber scombrus) (Agnalt, 1989; Overholtz, 1989; Neja, 1995) and Atlantic herring (Clupea harengus) (Toresen, 1990).

Density-dependent growth in fish populations seems to be a common phenomenon for pelagic fishes found in the temperate waters of Japan. The FL at age 0 of the 1963-69 year classes ranged from 16 to 20 cm, and were smaller than those of the 1970s, possibly indicating density-dependent growth (Iizuka, 1974). According to Honma et al. (1987), the stock abundance of the Pacific stock of chub mackerel from 1963 to 1969 was larger than it was in the 1970s. Wada et al. (1995) and Hiyama et al. (1995) found negative relationships between total biomass and body length in the Pacific and Tsushima Current stock of the Japanese sardine (Sardinops melanostictus). Kishida (1990) demonstrated a density-dependent relationship between the growth and total stock density (CPUE) of Japanese Spanish mackerel (Scomberomorus niphonius).

Our results do not agree with the positive effect of sea water temperature on somatic growth that has been shown for several species, including Japanese common squid (Kidokoro, 2001), Atlantic herring (Moores and Winters, 1981; Toresen, 1990), and Atlantic cod (Gadus morhua) (Brander, 1995; Dutilet al., 1999; Ratz et al. 1999; Otterson et al., 2002).

There was a positive correlation between FL at age 0 and 1[degrees]x1[degrees] block SST in the waters of 32-34[degrees] N and 144-149[degrees]E, located south of the Kuroshio Extension flowing eastward at the latitude of 35-37[degrees]N from April to June (Figs. 1 and 5A). But the correlation coefficient was not significant, and this area was not considered to be inhabited by juvenile mackerel (Watanabe, 1970). Thus, we considered that the SST in the waters of 32-34[degrees]N and 144-149[degrees]E was not a significant factor on the variation of FL at age 0.

The low SST in the waters bounded by 38-40[degrees]N and 141-143[degrees]E is indicative of a large inflow of Oyashio Current waters (Hirai and Yasuda, 1988), which is a cold water current and has high productivity (Odate, 1994), into the Kuroshio-Oyashio transition zone, where is one of the main feeding grounds of mackerels (Odate, 1961; Watanabe, 1970; Watanabe and Nishida, 2002; Fig. 1). Thus, we hypothesized that the large inflow of Oyashio current waters into the Kuroshio-Oyashio transition zone improved the feeding condition and accelerated the growth of juvenile mackerel. Jobling (1988) suggested a parabolic relationship between water temperature and fish growth. The range of SST in this area, which was negatively correlated with FL at age 0 of mackerel, was 9-13[degrees]C (Table 1). This temperature range is near the lowest nonstressful temperatures for mackerel (10-12[degrees]C, Schaefer, 1986). Thus, we do not consider that the negative relationship between growth and SST was the result of suppressed growth by the high ambient temperature.

In mackerel, maximum egg production appears to have shifted to later in spring during the 1990s, as compared to the late 1970s and 1980s, resulting in a shorter period of growth and thus smaller fish (Fig. 8, Mori et al. (4); Kikuchi and Konishi (5); Ishida and Kikuchi (6); Zenitani et al. (7); Kubota et al. (8)). In the early 1970s, the main spawning period was also in April (Kuroda (9)). Delayed spawning in the 1990s should have resulted in a reduction in the mean FL at ages during September-December in the 1990s compared to the 1970s and 1980s; however the present study showed the opposite result (Table 1). We hypothesize that the effect of the shift of spawning period on the FL at ages may have been overwhelmed by the effect of population density (Fig. 7).

[FIGURES 7-8 OMITTED]

The estimated FL at age from our growth model, with the use of AIC, fitted well to the observed FL at age (Fig. 6). Mean growth increments I of each year class from age 0 (6 months old) to ages 1-5 ([I.sub.0-i]) were significant and negatively correlated with FL at age 0 (Table 2), indicating that the growth rate of mackerel had changed from year to year for a given year class. This negative correlation indicated that the effects of population density and SST was temporal, and influenced k rather than [L.sub.[infinity]]. The negative correlation between FL at age 0 and growth increments also suggested that the FL at age of mackerel approximated the asymptotic length. Thus, mackerel growth was best fitted to the modified von Bertalanffy growth model with the temporal environmental effect on k (Table 5).

The effect of population density on growth of mackerel was higher than the effect of SST (Fig. 7, Table 6). Our result agreed with the results for Japanese sardine (Wada et al., 1995) and Atlantic cod (Sinclair et al., 2002). Particularly, the effect of population density was significant in the late 1980s, which resulted in a remarkable increase in FL at age 0 (Figs. 3 and 7).

The relative size at age 0 was carried over to older ages (Fig. 4), indicating that the cohorts that were small at age 0 could not compensate for this early small size. Iizuka (1974) reported that the trend of growth established at age 0 for chub mackerel was maintained until age 2 for the 1963-73 year classes. Toresen (1990) demonstrated from length data that a trend in rate of growth for a given year class of Norwegian herring was determined at the immature stage and was consistent after maturation. Total length of Hokkaido-Sakhalin herrings (Clupea pallasii) at age 5 and older was positively correlated with the length at age 4 (Watanabe et al., 2002). Because fish first mature at age 4, this implied that the trend in total length of each year class was determined by the age at maturity. From these results we hypothesize that the variability in size at age in the Pacific stock of chub mackerel is largely attributable to growth before maturity, especially during the first 6 months after hatching.

Table 1

Total biomass, year class strength (stock number at age 0; Yatsu,
et al. (1)), SST, and mean fork length (FL) of Scomber japonicus
from 1970 to 1997. Blanks show the lack of data.

            Total              Stock number
           Biomass               at age 0                  SST
Year   ([10.sup.3] t)    ([10.sup.6] individuals)   ([degrees]C) (1)

1970        2833                  10,199                  11.5
1971        3781                  14,138                  10.9
1972        4860                    8342                  13.2
1973        4650                    7154                  11.1
1974        4048                    7854                  10.5
1975        3558                  10,353                  12.3
1976        3896                  14,402                  11.5
1977        5868                  11,701                  10.9
1978        5285                    6249                  10.0
1979        3250                    2931                  12.3
1980        1898                    2952                  11.3
1981        1683                    3374                   9.4
1982        1567                    2883                  10.8
1983        1516                    3175                  11.5
1984        1759                    3605                   9.3
1985        1565                    4998                  11.4
1986        1373                    1833                   9.7
1987         812                     583                  10.9
1988         555                     236                  11.4
1989         289                     219                   9.8
1990         185                     356                  11.7
1991         338                    1017                  12.2
1992         724                    2839                   9.7
1993         685                     589                  10.7
1994         343                     547                  11.3
1995         351                    1183                  11.3
1996         726                    4452                   9.9
1997         682                     529                   9.9
28-year mean of FLs at ages

                                         Mean FL (SD) cm

Year                               0            1            2

1970                           19.2 (2.6)   26.3 (1.8)   30.5 (2.4)
1971                           20.2 (2.3)   26.8 (1.9)   31.4 (1.5)
1972                           19.3 (1.0)   27.2 (1.4)   31.1 (1.6)
1973                           22.2 (1.4)   27.9 (1.5)   29.4 (1.6)
1974                           19.7 (1.4)   27.7 (2.5)   30.4 (1.4)
1975                           16.9 (3.0)   25.4 (1.8)   30.3 (2.6)
1976                           19.7 (2.0)   24.3 (1.9)   29.4 (2.4)
1977                           21.4 (1.3)   26.2 (1.8)   30.1 (2.8)
1978                           21.5 (1.1)   28.5 (1.7)   29.8 (1.6)
1979                           19.5 (1.1)   27.1 (2.0)   30.2 (2.0)
1980                           20.7 (1.1)   25.8 (2.6)   30.3 (2.2)
1981                           22.7 (1.3)   27.2 (1.7)   30.5 (1.5)
1982                           22.5 (1.8)   27.9 (1.6)   29.3 (1.8)
1983                           19.6 (1.2)   26.7 (2.2)   30.8 (1.6)
1984                           22.7 (1.3)   27.0 (2.4)   31.0 (1.8)
1985                           20.1 (2.2)   27.3 (2.1)   30.9 (1.9)
1986                           21.5 (1.7)   26.4 (1.4)   29.1 (1.8)
1987                           20.5 (2.1)   27.6 (1.7)   30.2 (1.3)
1988                           24.9 (1.4)   28.1 (1.5)   30.5 (1.4)
1989                           25.9 (1.0)   29.7 (2.3)   32.2 (1.4)
1990                           24.4 (1.3)   30.3 (2.6)   34.5 (1.3)
1991                           24.1 (1.6)   28.9 (1.8)   33.5 (1.9)
1992                           24.0 (1.6)   29.0 (1.7)   32.1 (1.4)
1993                           23.9 (0.9)   29.3 (1.3)   31.7 (1.1)
1994                           23.7 (1.7)   28.8 (2.5)   32.8 (1.0)
1995                           22.0 (1.3)   31.6 (1.4)   32.9 (1.8)
1996                           22.5 (1.1)   28.7 (2.5)   34.1 (1.2)
1997                           23.6 (1.4)   29.0 (1.5)   33.0 (1.3)
28-year mean of FLs at ages    21.7 (2.1)   27.7 (1.6)   31.1 (1.5)

                                         Mean FL (SD) cm

Year                               3            4            5

1970                           34.2 (1.7)   37.7 (1.6)   40.5 (1.4)
1971                           34.3 (1.6)   37.7 (1.6)   40.4 (1.3)
1972                           34.3 (1.5)   37.3 (1.7)   40.0 (1.5)
1973                           31.2 (1.8)   33.1 (2.0)   36.1 (1.9)
1974                           31.9 (1.7)   33.9 (1.8)   37.6 (1.7)
1975                           32.7 (1.6)   33.8 (1.6)   35.5 (1.7)
1976                           33.7 (1.9)   35.3 (1.8)   38.1 (1.8)
1977                           33.5 (2.2)   35.7 (1.7)   37.4 (1.4)
1978                           32.1 (2.3)   34.5 (2.1)   36.1 (1.9)
1979                           33.0 (1.7)   35.2 (1.6)   37.2 (1.3)
1980                           32.4 (1.8)   33.9 (1.8)   35.6 (1.6)
1981                           33.1 (2.1)   36.5 (1.8)   38.0 (1.5)
1982                           33.6 (2.2)   36.6 (1.6)   38.3 (1.4)
1983                           33.6 (1.5)   35.5 (2.0)   37.8 (1.2)
1984                           34.8 (1.9)   36.6 (1.8)   38.2 (2.0)
1985                           33.3 (1.9)   37.4 (1.7)   39.0 (1.8)
1986                           32.5 (2.4)   35.9 (2.1)   38.9 (1.9)
1987                           32.8 (1.6)   36.4 (2.3)   39.2 (0.8)
1988                           32.8 (1.7)   36.8 (1.6)   40.1 (1.2)
1989                           34.6 (1.5)   35.7 (1.5)   39.2 (1.5)
1990                           35.8 (1.5)   38.2 (1.1)   39.7 (0.8)
1991                           35.5 (1.2)   36.7 (1.9)   39.0 (1.8)
1992                           34.1 (1.5)   37.5 (1.6)   40.5 (1.6)
1993                           33.2 (0.5)
1994                           34.6 (0.8)   35.9 (0.7)   39.1 (1.0)
1995                           35.5 (1.8)   38.0 (1.3)   39.2 (0.8)
1996                           36.1 (1.1)   37.8 (0.9)   39.7 (0.7)
1997                           35.4 (1.7)   37.6 (0.7)   38.6 (0.5)
28-year mean of FLs at ages    33.7 (1.3)   36.2 (1.4)   38.5 (1.5)

(1) SST during April-June in the waters bounded by 38-40[degrees]N
and 141-143[degrees]E.

Table 2

Correlation of FL at age 0 and growth increment after age
0. n = actual sample size. [n.sup.*] and degree of freedom (df)
show the effective n and df when the data were corrected
for autocorrelation (Pyper and Peterman, 1998). Significance
level: **, P<0.01.

Growth increment       r       [r.sup.2]   n    [n.sup.*]   df

Ages                -0.69 **     0.48      27      21       19
Ages                -0.71 **     0.51      26      25       23
Ages                -0.80 **     0.64      25      23       21
Ages                -0.77 **     0.59      23      24       22
Ages                -0.78 **     0.61      22      22       20

Table 3

Correlation between the natural logarithm of the abundance
of age 0 and mean FL for each age. n = actual sample
number. [n.sup.*] and degree of freedom (df) show the significant
n and df when autocorrelation was considered (Pyper and
Peterman, 1998). Significance levels: *, P < 0.05.

Age                   r       [r.sup.2]   n    [n.sup.*]   df

0                   -0.75 *      0.57      28       8       6
1                   -0.69        0.48      27       7       5
2                   -0.83 *      0.69      26       6       4
3                   -0.71 *      0.51      25       9       7
4                   -0.63        0.40      23       8       6
5                   -0.64        0.40      22       6       4

Table 4

Correlation between natural logarithm of total biomass
and mean FL for each age. n = actual sample size. [n.sup.*] and
dgree of freedom (df) show the effective n and df when the
data were corrected for autocorrelation (Pyper and Peterman,
1998). No correlations were significant (P>0.05).

Age                    r       [r.sup.2]   n    [n.sup.*]   df

0                    -0.74       0.38      27       6        4
1                    -0.73       0.32      27       6        4
2                    -0.75       0.36      27       5        3
3                    -0.52       0.26      27      11        9
4                    -0.51       0.26      26       9        7
5                    -0.50       0.22      26       7        5

Table 5

Summary of statistics from the estimation of growth for
chub mackerel (Scomber japoraicus). AIC = Akaike's information
criterion.

                                           No. of       Log
                                          unknown     likeli-
Model             Variables              parameters    hood      AIC

1       [L.sub.[infinity]], k,
          [t.sub.0], [[sigma].sub.1]
          ... [[sigma].sub.5]                 9       -280.20   578.40
        [L.sub.[infinity]], k,
          [t.sub.0], [[sigma].sub.1]
          ... [[sigma].sub.5],
          [[beta].sub.1]                     10       -270.10   560.20
        [L.sub.[infinity]], k,
          [t.sub.0], [[sigma].sub.1]
          ... [[sigma].sub.5],
          [[beta].sub.2]                     10       -222.38   464.77
        [L.sub.[infinity]], k,
          [t.sub.0], [[sigma].sub.1]
          ... [[sigma].sub.5],
          [[beta].sub.1],
          [[beta].sub.2]                     11       -217.84   457.68
2       [L.sub.[infinity]], k,
          [t.sub.0], [[sigma].sub.1]
          ... [[sigma].sub.5]                 9       -280.20   578.40
        [L.sub.[infinity]], k,
          [t.sub.0], [[sigma].sub.1]
          ... [[sigma].sub.5],
          [[beta].sub.1]                     10       -268.63   557.25
        [L.sub.[infinity]], k,
          [t.sub.0], [[sigma].sub.1]
          ... [[sigma].sub.5],
          [[beta].sub.2]                     10       -224.01   468.02
        [L.sub.[infinity]], k,
          [t.sub.0], [[sigma].sub.1]
          ... [[sigma].sub.5],
          [[beta].sub.1],
          [[beta].sub.2]                     11       -220.81   463.62

Acknowledgments

We would like to thank K. Meguro of Chiba Prefecture Governmental Office and K. Kobayashi of Shizuoka Prefecture Governmental Office for providing insights into chub mackerel's growth and into age determination. We also thank T. Akamine, M. Suda, and N. Yamashita of the National Research Institute of Fisheries Science for advice on the statistical analysis. We also thank Y. Watanabe and C. B. Clarke of the Ocean Research Institute, University of Tokyo, for their constructive comments on this manuscript.

(1) Yatsu, A., C. Watanabe, and H. Nishida. 2001. Stock assessment of the Pacific stock of chub mackerel in fiscal 2000 year. In Stock assessment report, p. 64-87. [In Japanese. Available from Fisheries Research Agency, 2-12-4 Fukuura, Kanazawa, Yokohama 236-8648, Japan.]

(2) Age-length keys. In Kanto Kinkai no Masaba ni tuite, Appendix 1, vol. 30, 30 p. [In Japanese. Available from Kanagawa Prefectual Fisheries Research Institute, Jyogashima, Misaki, Miura, Kanagawa 238 0237, Japan.]

(3) Millar, R. B., and R. A. Myers. 1990. Modeling environmentally induced change in growth for Atlantic Canada cod stock. ICES CM 1990/G:24.

(4) Mori, K., K. Kuroda, and Y. Konishi. 1988. Monthly egg production of the Japanese sardine, anchovy, and mackerels off the southern coast of Japan by egg censuses. Datum Collect. Tokai Reg. Fish. Res. Lab. 12:1-321. [In Japanese. Available from National Research Institute of Fisheries Science, 2-12-4 Fukuura, Kanazawa, Yokohama 236-8648, Japan.]

(5) Kikuchi, H., and Y. Konishi. 1990. Monthly egg production of the Japanese sardine, anchovy, and mackerels off the southern coast of Japan by egg censuses: January, 1987 through December, 1988, 72 p. National Research Institute of Fisheries Science, Tokyo. [In Japanese. Available from National Research Institute of Fisheries Science, 2 12-4 Fukuura, Kanazawa, Yokohama 236-8648, Japan.]

(6) Ishida, M. and H Kikuchi. 1992. Monthly egg production of the Japanese sardine, anchovy, and mackerels off the southern coast of Japan by egg censuses: ,January, 1989 through December, 1990, 86 p. National Research Institute of Fisheries Science, Tokyo. [In Japanese. Available from National Research Institute of Fisheries Science, 2-12-4 Fukuura, Kanazawa, Yokohama 236-8648, Japan.].

(7) Zenitani, H., M. Ishida, Y. Konishi, T. Goto, Y. Watanabe, and R. Kimura. 1995. Distributions of eggs and larvae of Japanese sardine, Japanese anchovy, mackerels, round herring, jack mackerel and Japanese common squid in the waters around Japan, 1991 through 1993. Resources Management Research Report Series A-2, 368 p. National Research Institute, Japan Fisheries Agency, Tokyo. [In Japanese. Available from National Research Institute of Fisheries Science, 2-12-4 Fukuura, Kanazawa, Yokohama, 236-8648 Japan.]

(8) Kubota, H., Y. Oozeki, M. Ishida, Y. Konishi, T. Goto, H. Zenitani, and R. Kimura. 1999. Distributions of eggs and larvae of Japanese sardine, Japanese anchovy, mackerels, round herring, jack mackerel and Japanese common squid in the waters around Japan, 1994 through 1996, 352 p. Resources Management Research Report Series A-2., National Research Institute, Japan Fisheries Agency, Tokyo. [In Japanese. Available from National Research Institute of Fisheries Science, 2-12-4 Fukuura, Kanazawa, Yokohama 236-8648, Japan.]

(9) Kuroda, K. 2002. Personal commun. 1-1-3-406, Kasumi, Narashino, Chiba 275-0022, Japan.

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Chikako Watanabe

Akihiko Yatsu

National Research Institute of Fisheries Science Fisheries Research Agency

2-12-4 Fukuura, Kanazawa Yokohama 236-8648, Japan

E-mail address (for C. Watanabe/: [e-mail]

Manuscript approved for publication 22 September 2003 by Scientific Editor.

Manuscript received 20 October 2003 at NMFS Scientific Publications Office.