Wang and Heino: Growth and maturation of Trichiurus japonicus in the subtropical Pacific Ocean 
1 75 
half distance from the core to the edge (Suppl. Fig.) 
(online only). Two readers counted otolith annuli under a 
microscope at 2QQ-400x magnification, examining each 
otolith independently. The otolith age estimates were 
inspected to determine whether the differences in age 
estimates between readers were >2 years. We excluded 
47 otoliths because of otolith breaks or discrepancies 
>2 years between the 2 readings. After these otoliths 
were excluded, the rate of agreement in age estimates 
between the 2 readers was 85.5% (i.e., the 2 readings 
were the same for 501 of 586 otoliths). For subsequent 
analyses, we used the average values of the 2 age read¬ 
ings. However, because T. japonicus spawn year-round 
in the waters off Taiwan, the true age can vary among 
fish for an age estimate. 
Data analysis 
Growth We compared growth of T. japonicus between 
the areas on the basis of length-at-age data and by fit¬ 
ting a growth model. For the length-at-age compari¬ 
son, we accounted for the effects of sex and stages of 
maturation on lengths. Therefore, we compared lengths 
at a given age for immature fish, males, and females 
between the areas by using a 2-sample Atest. 
Given the prolonged, year-round spawning season 
of T. japonicus (Shih et al., 2011), months of birth for 
these fish could vary between the areas, resulting in 
bias for our comparison of growth. To account for such 
bias, we estimated daily ages, using otoliths for age- 
0 fish and compared their average daily growth rates 
between the 2 areas (number of fish sampled [n }=24 
for Kengfang and n =20 for Tsukuan). One experienced 
reader assessed these otoliths 3 times independently, 
and the data were averaged after discrepant estimates 
between readings were excluded (e.g., difference >10 
d). Because daily growth increments for fish of ages 
>1 year were too dense to be counted correctly, we 
could not estimate daily growth rates for older fish. 
We calculated individual average daily growth rates as 
the ratio of pre-anal lengths over average daily ages. 
For comparison, we derived another estimate of daily 
growth rates by fitting a linear regression of pre-anal 
lengths (y axis) in relation to daily ages (x axis) with 
a constant intercept of 5.5 mm for each area (i.e., cor¬ 
responding to the length at hatching of T. japonicus ; 
Kiang 5 ). The regression slopes indicate the average 
daily growth rates. We evaluated differences in daily 
growth rates between the 2 areas by comparing the ex¬ 
plained variance of pre-anal lengths of these 2 models: 
the model with both area and daily ages as predictors 
compared with the model with daily ages as the sole 
predictor. 
To describe ontogenetic growth, we used the von 
Bertalanffy growth model (von Bertalanffy, 1938). Be¬ 
cause of apparent size dimorphism of the sexes, we 
fitted this model separately for males and females in 
5 Kiang, Y.-K. 2017. Unpubl. data. National Taiwan Univ., 
No. 1, Sec. 4, Roosevelt Rd., Taipei, Taiwan 10617. 
each area; immature fish were incorporated into sam¬ 
ples of either sex for fitting sex-specific growth models. 
The von Bertalanffy growth model in terms of length is 
typically expressed as 
L t = LJl-e~ K(t ~ to) ), 
where t - age, L t is length at age t; and 
L„ - asymptotic length; 
K - the Brody growth coefficient; and 
t 0 = the intercept at the horizontal axis (i.e., the 
hypothetical age at length 0). 
Because of the lack of a biological meaning for t 0 , it is 
common to replace it with L 0 , the theoretical length at 
age 0. This leads to an alternative model form: L t =L,„- 
(L^-Lole -1 ^. This formulation is commonly applied to 
describe growth trajectories of elasmobranchs, given 
that their relatively large sizes at hatching can pro¬ 
vide an adequate estimate of L 0 (Pardo et al., 2013). 
However, size at hatching is too small to be estimat¬ 
ed accurately for many teleosts, including cutlassfish. 
Therefore, we substituted L 0 with L min , the minimum 
length at catch. Accordingly, we offset all ages by < min , 
the age corresponding with L min , in the model: 
L t = - (L„ - L min ) e ~ Ku ~ tmin) . (1) 
The length-at-age data derived from length-strati¬ 
fied sampling may deviate from the true length-at-age 
distribution of a population. To avoid such bias and 
because measuring length is relatively precise and es¬ 
timating age may not be, we estimated the von Ber¬ 
talanffy growth parameters by using the inverse von 
Bertalanffy growth model, i.e., estimating age as a 
function of length (Vainikka et al., 2009; Mollet et al., 
2013). The inverse function of Equation 1 is 
The minimum lengths at catch (i.e., pre-anal lengths) 
of T. japonicus were 48 and 75 mm at Kengfang and 
Tsukuan (Table 1). By counting daily increments of 
these otoliths with 3 replicates, we estimated the mean 
of t min to be 34 d (standard deviation [SD] 2.6) or 0.09 
year and 51 d (SD 1.0) or 0.14 year at Kengfang and 
Tsukuan, respectively. Because a fish of length equal 
to L min is immature and there is no reason to expect 
differential growth between sexes well before maturity, 
we assumed the same L min and £ min for males and fe¬ 
males. Inserting L min and £ mm into Equation 2, we used 
the nonlinear least squares method to estimate L x and 
K for each sex and area. For comparison and compat¬ 
ibility with earlier studies, we also fitted Equation 1 to 
the length-at-age data. 
We derived 95% confidence intervals (CIs) for the 
and K estimates, using a bootstrap method (Manly, 
1997). Specifically, we randomly sampled the length- 
at-age data with replacement to generate 1000 boot¬ 
strapped data sets, each with an equal sample size of 
the original data set, and then fitted Equations 1 and 
2 to the bootstrapped samples. The lower and upper 
