Wells et al Age validation of |uvemle Isurus oxynnchus tagged off southern California 
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Length-frequency analysis 
Length-frequency distributions of juvenile Shortfin 
Mako were analyzed to estimate size at age of the first 
3 age classes and to compare to vertebrae readings. The 
MULTIFAN model (Fournier et al., 1990) was one of 2 
techniques used to analyze length-frequency data on 
the basis of size distributions. This model simultane- 
ously analyzes multiple length-frequency distributions 
using a maximum likelihood method to estimate the 
number of age classes and proportions of fish at age. 
Tests for significance (best-fit growth parameters) were 
made through the use of likelihood ratio tests. First, a 
systematic search was performed to estimate the num- 
ber of age classes and to hold the standard deviations 
of length constant across all age classes. Next, stan- 
dard deviations of length were allowed to vary across 
age classes. The MIXDIST package (MacDonald and 
Pitcher, 1979) in R, vers. 2.8.0 (R Development Core 
Team, 2008) was the second length-frequency analysis 
used. This analysis uses a maximum likelihood method 
to estimate proportions of fish at age with the added 
benefit of fitting non-normally distributed data. 
Data for both techniques were analyzed annually 
and came from 2 sources: 1) fishery-dependent data 
from the California drift gillnet fishery (1981-2009), 
which operates between May and January, and 2) fish- 
ery-independent data from longline research surveys of 
juvenile Shortfin Mako conducted by the NOAA South- 
west Fisheries Science Center (1993-2009) between 
June and August of each year. A mixture of length 
measurements taken across study years: TL, FL and 
alternate length (AL, straight line distance between 
the origins of the first and second dorsal fins) were 
standardized into FL for this study to allow for com- 
parison of our results with the results of other studies. 
The following length conversions were obtained from 
the 2 sources and used to standardize data for subse- 
quent length-frequency analyses: 
FL = 0.913 x (TL) - 0.397, coefficient of 
determination (r 2 ) = 0.986 (zz =2 177) 
FL = 2.402 x (AL) + 9.996, r 2 = 0.957 (n=3250). 
Size data were combined between sexes because no 
significant difference existed (P=0.769), and size bins of 
5 cm, ranging from 55 to 265 cm FL, were used. 
Growth of tagged and recaptured mako sharks 
Growth rates were calculated for 1) recaptured, 
OTC-marked sharks and 2) angler- and research-re- 
leased, unlabeled sharks for which reliable length es- 
timates were available (n=6 2 of 317 returns) (Fig. 1A). 
Growth was estimated with the tag-recapture growth 
model GROTAG (Francis 1988a, 1988b) on the basis of 
length and time-at-liberty. This model was chosen be- 
cause age-based and length-based growth models often 
differ, and it is a useful alternative for comparison of 
growth rates at particular sizes (Francis, 1988a; Na- 
tanson et al., 2006; Claisse et al., 2009). We used a 
maximum likelihood approach with this model to esti- 
mate growth rates (g a and g^) at 2 selected lengths (a 
and /?), a CV of growth variability, mean measurement 
error and standard deviation, and outlier probability. 
Therefore, estimated growth of a Shortfin Mako, i, was 
calculated with the following equation: 
AL , = uPe a - agp) / P a - gp ) - l,) / (i - a + (g a -g p ) 
/ a -pF Tl ), 
where L ( = length at release; and 
A T, = the tag deployment time. 
Results 
Tagging and recapturing oxytetracycline-marked sharks 
Off southern California from 1996 to 2010, 940 OTC- 
injected Shortfin Mako were tagged and released (Fig. 
1, A and B). Of the subset of released sharks for which 
sexes were determined, 67% were males and 33% were 
females. Average size at release was 110 cm FL (±0.80 
SE). Of the released OTC-marked sharks, 35 were re- 
captured from 2000 to 2010. Of these 35 sharks, 29 fish 
were selected for this study because they had been at 
liberty for >4 months and OTC marks in the vertebrae 
fluoresced (Table 1, Fig. IB). Five samples were ex- 
cluded from analysis because of a short time-at-liberty 
(within a range from 24 to 60 days), provided no infor- 
mation on band-pair progression, and in the case of 1 
shark, the vertebrae did not fluoresce. 
For the 29 fish used in this study, average time-at- 
liberty was 522 days (±71.0 SE), within a range from 
145 to 1594 days, and average size was 109 cm FL 
(±2.9 SE) at tagging and 148 cm FL (±5.0 SE) at re- 
capture (Table 1). The average displacement distance 
(great-circle distance from tagging to recapture loca- 
tion) for the 29 OTC-marked Shortfin Mako was 902 
km (±291 km SE), within a range from 2 to 5295 km 
(Fig. IB). According to results from analyses with lin- 
ear regressions, no significant effects of time-at-liberty 
or size-at-tagging existed in relation to total displace- 
ment distance (P>0.05). 
Age validation results 
Results from readings of the OTC-marked vertebrae 
indicated that 2 band pairs are deposited each year 
in samples analyzed in this study. The observed slope 
of the relationship between the number of band pairs 
each year and years-at-liberty significantly differed 
from the 1:1 relationship (P<0.01). Specifically, the av- 
erage number of band pairs predicted each year was 
modeled with the following linear regression: average 
number of band pairs = 1.988 x (number of years-at- 
large) - 0.136, r 2 =0.942 (P<0.05) (Fig. 2). 
