Survival of the blacktip shark, Carcharhinus limbatus

Proportional survival (S) is a crucial life-history parameter in population dynamics, natural selection, and management of harvested stocks; variations in survival due to age, sex, or geographic region may have large effects on the success of managing fish stocks. The blacktip shark, Carcharhinus limbatus, is the most abundantly harvested shark species in American fisheries. Direct estimates of survival are preferred, but all current survival estimates for this species are either focused on young-of-the-year (YOY) or based on indirect methods. The objectives of this study were to determine whether age, sex, or geographic grouping affects survival and to generate direct survival estimates based on tag-recovery data. As a byproduct of this analysis, distribution maps and descriptive data summarizing captures were included. The U.S. National Marine Fisheries Service has been collecting tag-recovery data since 1962 through the Cooperative Shark Tagging Program (CSTP). Models were generated from this database with program MARK, ranked in order of parsimony according to Akaike’s Information Criterion, and tested for significance of effects with likelihood ratio tests. No movement has been observed to date between the west Gulf of Mexico, east Gulf of Mexico, and U.S. Atlantic, but 2 sharks tagged in the U.S. Virgin Islands were recaptured off Florida and Georgia (displacement= 1049 and 1183 n. mi., respectively). Survival did not differ significantly for males vs. females (P=0.761), east vs. west Gulf of Mexico (P=0.654), or U.S. Atlantic vs. Gulf of Mexico (P=0.243). However, significant differences were found for survival of YOY (0.580) and post-YOY (0.725) within the Gulf of Mexico (P=0.0003). These results demonstrate that survival can be modeled effectively for species in the CSTP with relatively small sample sizes. Future analyses may benefit from a length-based model, due to the difficulty in assigning life stages based on size.

. Variation in survival, fecundity, and growth rate can interact to influence adaptive fitness . Accurate estimates of survival are a key component of demographic analysis and stock assessment of marine species , and they determine which levels of exploitation are sustainable .  suggested that survival in fish stocks can vary due to a number of factors, including changing levels of fishing effort . Gear selectivity, predation pressure, or other factors may result in survival probabilities that vary with age . These variations in survival could also have large effects on the success of fisheries management . In either of the cases above, stock assessments that assume constant survival may greatly overestimate or underestimate a stock's capacity to handle intensive fishing pressure.
This lack of information may lead to fishing limits that are too high for sustainable harvest. In a broader sense, determining whether survival varies with time or age is the first step in understanding how anthropogenic causes may be affecting the lifehistory of a species.
Proportional survival over a finite interval is related to total instantaneous mortality rate (Z) by where Z is the sum of instantaneous natural mortality (M) and instantaneous fishing mortality (F) . Converting between instantaneous mortality and finite survival assumes that the instantaneous mortality rate is constant during the finite time interval. Many methods of estimating survival were described by  and . Direct methods of calculating survival (i.e., mark-recapture) are preferable over indirect methods that involve the use of life-history parameters . Recent advances in computer modeling technology allow powerful hypothesis testing related to variations in survival . New models allow the user to separate the effects of recovery probability from the probability of death using mark-recapture histories Cooch & White 1 ).
Elasmobranchs are slow-growing fish with late maturity and small litter size . This K-type strategy (sensu  represents a significant challenge for managing these populations . In addition, large predatory fishes like sharks may be much more sensitive to overexploitation (and ultimately, extinction) than previously anticipated . In order to assist stock assessment and management, more information about shark populations and biological variables is needed ICCAT 2 ). In particular, proportional survival is a critical factor in stock assessment and demographic analysis (Mollet & Calliet, 2002 most abundantly harvested shark species in American fisheries; investigations of survival are appropriate for such an ecologically and economically important species Cortés 3 ; NOAA/NMFS 4 ; NOAA/NMFS 5 ).
Blacktip sharks inhabit tropical, subtropical, and temperate waters throughout the world . This species has an annual migration cycle that corresponds with a biennial ovulation cycle .
Females either breed or give birth in May to June; post-parturition females are not able to mate again until the following spring. It is believed that the entire population migrates to more southern waters in the fall; in the following spring, the sharks return to their northern breeding and pupping grounds Killam 6 ;.
Indirect methods have provided survival probabilities for blacktip sharks that range from 0.66-0.88   Similarly, no one has tested for significant differences in survival based on time, age, sex, and location in blacktip sharks. Therefore, the primary objectives of this research were to estimate survival in blacktip sharks based on tag-recovery data and determine if significant differences in survival exist based on time, age, sex, and location.
Information on size, distribution, and movement were provided as a byproduct of this survival analysis. Blacktip sharks in the Gulf of Mexico (GOM) are currently managed by the National Marine Fisheries Service (NMFS) as a single stock, but the degree of exchange between the east GOM, west GOM, and U.S. Atlantic is unknown Kohler et al. 8 ; NOAA/NMFS 4 ). According to recent SEDAR stock assessment reports, there is a great need for conventional mark-recapture studies that describe the exchange (or lack thereof) of this stock between the East and West GOM (NOAA/NMFS 4 ; NOAA/NMFS 5 ). No exchange has been observed between these regions to date. Therefore, it is desirable to determine whether survival differs significantly among sharks from these 3 regions. Blacktip sharks were predominantly caught by rod and reel, longline, and gill net. The body length of some sharks was measured by biologists, but some were recorded as "estimates." The effect of this uncertainty was minimized by collapsing length data into life stage categories. This database was fishery-dependent, but the large sample size (n>9000 blacktip shark captures) presented a unique opportunity to map distribution and analyze survival in the geographic areas that are most important to fisheries. The CSTP database represented extensive spatial coverage of U.S.
waters, so spatial bias in distribution was minimized . For the purposes of this analysis, all shark landings were defined as "captures", including both tags and recaptures. Shark recaptures were "dead" recoveries; the sharks were not rereleased and recaptured after initial recapture.

MATERIALS AND METHODS
In the CSTP, length and weight were reported with varying units of measure.
Fork length was used whenever provided and converted to cm when applicable. Total length was converted to fork length using the formula: TL(cm)=(1.1955)FL(cm)+1.13 (NMFS SEFSC unpublished data).
When neither fork length nor total length was provided, weight in kilograms was converted to FL according to the formula: Weight (kg)=(1*10 -5 )FL(cm) 3.0549 (NMFS SEFSC unpublished data).
Sharks were categorized into life stages according to length. The boundary between young-of-the-year (YOY) and juveniles was set to 56.6 cm FL, the maximum embryo size plus 10% TL (cm) according to . Sharks measuring less than 56.6 cm FL were classified as YOY. Males and females in the Gulf of Mexico were considered mature when FL was greater than the median length at maturity, 103.4 cm and 117.3 cm, respectively . Males and females between 56.6 cm FL and the median length at maturity were considered to be juveniles for the purposes of this study. Sharks of unknown sex that were between 56.6 cm FL and 103.4 cm FL were categorized as juveniles. Sharks without a size estimate or sharks of unknown sex that were between 103.4 cm FL and 117.3 cm FL were categorized as "unknown maturity." Sharks of unknown sex that were larger than 117.3 cm FL were categorized as mature. Sharks were classified as embryos when they were taken from pregnant females. A similar methodology was used for Atlantic sharks, substituting 116.7 and 126.6 cm FL as the median length at maturity for males and females, respectively . Data were plotted as points for parameterization . In this parameterization, S was the probability that the fish survives the year, and r was the probability that the fish was recovered and reported ( Fig. A-1). Model names describe the parameters included in the model. For example, S(g*t) r(g+t) indicates that survival was modeled with an interaction between group and time, and recovery probability was modeled with group and time effects, but no interaction. A period (.) indicates that either group or time effects were not included in the model. Data were entered in the classic recovery (triangular) matrix format ( Fig. A-2). S and r were solved numerically for the maximum likelihood estimate, and the profile likelihood method generated confidence intervals. A parametric bootstrap procedure (Cooch and White 1 ) for the most general model (group-and time-dependent survival and recovery probabilities) assessed goodness of fit. The quasi-likelihood parameter, ĉ was estimated as the average of the mean ĉ and mean deviance estimates. Models were ranked according to the quasi-likelihood adjusted AIC .

Likelihood ratio tests (LRT) determined whether survival and recovery
probabilities were time-dependent, age-dependent, sex-dependent, regiondependent or constant.
In addition to the predictive variables of group and time, models were fit with an external index to account for changing levels of yearly fishing effort. It is known that

F=qf
where F=fishing mortality rate, q=catchability coefficient, and f=fishing effort . The catchability coefficient was assumed to be constant over time, so that F could be used as proxy for effort. Values of F were available specifically for Gulf of Mexico and U.S. Atlantic blacktip sharks from 1986-2004 from the SEDAR 11 Stock Assessment Report ( Fig. A-3). Therefore, the analysis was constrained to this time period. A more detailed explanation of survival analysis procedures is provided in Appendix II.

RESULTS
The first blacktip sharks in the CSTP were tagged in 1964, but the tagging rates remained below 100 sharks per year until 1988 in the GOM and 1999 in the U.S.  Table 1). The fate of these tagged sharks is displayed by region in Table 2. Notably, 1 shark tagged in U.S. waters of the Atlantic Ocean was recaptured in the International Atlantic, 3 sharks tagged in the International Atlantic were recaptured in the U.S. Atlantic, and 35 sharks tagged in the U.S. waters of the western GOM were recaptured in Mexican waters of the GOM. Tables 3-5.

Information on these captures by sex and life stage is provided in
Females were caught more often than males, resulting in a male to female sex ratio of 1:1.2 in the U.S. Atlantic, 1:1.8 in the GOM and 1:1.6 in the International Atlantic.
Juveniles were the most commonly caught life stage for both males and females.
Mean time at liberty ranged from 242.3 days in the eastern U.S. GOM to 506.9 days in the International Atlantic (Table 6). During the period of study, 35 blacktip sharks were recaptured in Mexican waters, but no blacktip sharks were tagged there.
For this reason, the final destination of sharks in the southern GOM was unknown.
Recapture statistics by sex are provided in Tables A-1-3 (excluding the 4 sharks that crossed between the U.S. Atlantic and the International Atlantic, as described in Table 7). In the U.S. Atlantic, 3959 sharks were tagged, and 81 of these tagged sharks were recaptured in the same region (2.0%), yielding a total of 4040 captures. The highest values for maximum displacement (616 n. mi.), maximum speed (15.3 n. mi./day), and maximum time at liberty (5.9 years) were from a male, female, and a shark of unknown sex, respectively. In the GOM, 4415 sharks were tagged, and 130 of these tagged sharks were recaptured (2.9%), yielding a total of 4545 blacktip shark captures. The highest values for maximum displacement (632 n. mi.), maximum speed (16.4 n. mi./day), and maximum time at liberty (7.8 years) were from female sharks. In the International Atlantic, 493 sharks were tagged, and 15 of these tagged sharks were recaptured in the same region (3.0%), yielding a total of 508 captures. The highest values for maximum displacement (215 n. mi.) and maximum speed (0.5 n. mi./day) were from females, but the maximum time at liberty (2.6 years) was from a male.
Distribution of recaptures by time at liberty, displacement, and speed is displayed in Figure  The CSTP database included a combination of effort from recreational fishermen, biologists, and commercial fishermen. Recreational landings were more common than those specifically identified as "commercial". Biologists also tagged many sharks in the GOM, but most of the tagging was done by recreational fishermen (Table A-

Survival
In analysis 1, survival models were constructed with an age effect, differentiating between YOY and post-YOY groups (designated by a "g" in the model structure). The most parsimonious model S(..) r(g+effort) had 2.38 times more weight than the next best model S(g.) r(g+effort) and 29.73 times more weight than S(g.) r(.effort) ( Table A-6). Likelihood ratio tests determined the significance of various effects in the GOM YOY vs. post-YOY analysis (Tables A-7-8). No tests were significant for the interaction of age group and time for recovery probability, r(g*t), or survival, S(g*t). However, 7 out of 14 possible tests were significant for S(g), 5 out of 14 for S(t), 8 out of 10 for r(effort), and 5 out of 10 for r(t). All LRT's were significant for r(g). The first comparison in each section of Tables A-7-8 displays the simplest model that contains the parameter of interest. These comparisons are particularly useful in hypothesis testing. By only considering the simplest LRT's, r(effort), r(g), and S(g) were significant effects. Therefore, survival and recovery probabilities were significantly different for YOY and post-YOY, and effort is a significant factor in recovery probability in this analysis.
In analysis 2, post-YOY data were modeled with male and female groups. The most parsimonious model S(..) r(.effort) had 2.64 times more weight than the next best model, S(g.) r(.effort) and 2.67 times more weight than S(..) r(g+effort) ( Table A-9).
The relevant likelihood ratio tests are given in Tables A-10-11. No tests were significant for S(g), S(g*t), r(t) and r(g*t). However, 1 out of 14 tests was significant for S(t), 7 out of 10 for r(effort), and 4 out of 15 for r(g). By only considering the simplest LRT's, only r(effort) was a significant effect. Therefore, survival was not significantly different for male vs. female sharks, and effort is a significant factor in recovery probability in this analysis.
In analysis 3, post-YOY data were modeled with groups representing the west GOM and east GOM. The most parsimonious model S(..) r(.effort) had 2.64 times more weight than the next best model S(g.) r(.effort) and 2.67 times more weight than

S(..) r(g+effort) (Table A-12). The relevant likelihood ratio tests are shown in Tables
A-13-14. No tests were significant for S(g), S(g*t), r(t), or r(g*t). However, 3 out of 14 tests were significant for S(t), 8 out of 10 tests were significant for r(effort), 6 out of 15 tests were significant for r(g). By only considering the simplest LRT's, only r(effort) was a significant effect. Therefore, survival was not significantly different for post-YOY sharks from the west GOM vs. those from the west GOM. Effort was a significant factor in recovery probability in this analysis.
In analysis 4, post-YOY data were then modeled with groups in the Atlantic for S(t), 1 out of 6 for S(g*t), 4 out of 5 for r(effort), 3 out of 10 for r(g), 4 out of 10 for r(t), and 1 out of 5 for r(g*t). By only considering the simplest LRT's, S(g*t), r(effort), and r(t) were significant effects. Therefore, there was no evidence that survival was significantly different for post-YOY sharks from the GOM vs. those from the U.S. Atlantic. However, effort and time significantly affected recovery probability in this analysis. The interaction between group and time on survival is significant, but it cannot be easily interpreted.
The average ĉ values generated from the deviance ĉ and mean ĉ are provided in Table 8. All average ĉ values were less than 3, indicating that the models fit the data adequately. Recovery probability ranges for the most parsimonious models are also given in Table 8.

DISCUSSION
The extensive spatial and temporal span of data in the CSTP provides a unique opportunity to describe the biology and ecology of the species within the program.
Specifically, the data gathered provide unique insights into size, spatial distribution, movement, and changes in fishing industry and gear over time. Of course, one of the most substantial contributions of this database is its ability to provide direct estimates of survival.

Size
With the large sample size of the CSTP, it was possible to observe a wide range of size estimates. In the GOM, 2.4% of males and 1.2% of females in the CSTP were larger than the largest sharks observed by .
Similarly, in the U.S. Atlantic, 4.2% of males and 3.8% of females in the CSTP were larger than the largest sharks observed by . Excluding the 7 sharks specifically listed as embryos, 40 of the YOY tagged in the CSTP were smaller than the smallest neonate size observed by  and Castillo-Géniz et al.
(1998) (range: 32-37.5 cm FL). These 40 YOY were evenly distributed throughout the east and west Gulf coasts, and 22 of these 40 (including the smallest) were "measured," not "estimated" lengths. These authors sampled sharks with the same types of gear (gillnet, longline, and rod and reel) as the CSTP. We are therefore encouraged to expand the perceived size range of this species.

Spatial Distribution
Some have reported the presence of blacktip sharks in water over 800 m deep . However, the Gulf of Mexico blacktip sharks in the CSTP seemed to remain strictly within the 200 m depth contour (Figs. 5-6). There was extensive fishing effort from the CSTP in deeper waters; other species were commonly reported in mid-Gulf waters in the CSTP . It is therefore likely that blacktip sharks rarely venture into water deeper than 200m.
Accounts of blacktip shark in water deeper than 800m seem to be the exception, not the rule, to their behavior.
The location of YOY and pregnant females can be useful for the identification of nurseries. In the CSTP, YOY were almost exclusively found close to shore (Figs. A-27-35). These data further support the idea that blacktip shark juveniles spend the first few months of their lives in nurseries close to shore . While pregnant and embryo blacktip sharks were generally found close to shore, there were also exceptions to this behavior. A mother of 3 embryos (each measuring 41 cm FL) off Louisiana was caught very close to the 200 m depth contour (Fig. A-32). The date of capture for this event was January 3 rd , several months before the expected time of parturition.
Similarly, 2 YOY were found very close to the 200 m depth contour off the Florida Keys (Fig. A-31). However, these YOY were still relatively close (<15 nautical miles) to land.

Movement
For the purposes of effective population management, it is desirable to determine the extent of exchange within and among water bodies in the northwest Atlantic. Genetic work by  implied that the U.S. Atlantic waters and the Gulf of Mexico represented 2 distinct populations, while Ryburn 9 suggested that sharks from the 2 areas interbreed. None of the Gulf of Mexico blacktip sharks migrated out of the Gulf to the Caribbean or Atlantic (Figs. 11-12). By comparison, CSTP data indicated that other sharks have well-established exchange patterns between Gulf and Atlantic waters . However, the CSTP data currently suggest that the Gulf blacktip sharks do not mix with those from the Atlantic.
This data set continues to support the decision to manage the Gulf of Mexico and Atlantic blacktip sharks as 2 separate stocks (NOAA/NMFS 4 ).
Exchange was also not observed between the west and east Gulf of Mexico in the CSTP. Limited genetic data suggest that the east and west Gulf of Mexico are 2 separate populations of blacktip sharks, although they are currently managed as 1 population ; NOAA/NMFS 4 ). If the Gulf truly contains 2 stocks, the CSTP data suggest that eastern Louisiana (approximately 89°W longitude) may be the location of this natural boundary; no recaptures have been observed across this line.
An exchange of blacktip sharks was observed between Mexican and U.S.
waters within the Gulf of Mexico (Fig. 12) While exchange between the GOM and Atlantic was not observed, 4 sharks crossed the U.S. EEZ between U.S. and International waters of the Atlantic Ocean (Table 7). Two of these sharks were recaptured over 1000 nautical miles away from their tagging location (Fig. 13). These recaptures are the first documented evidence that blacktip sharks can travel this far, and that exchange exists for blacktip sharks between the U.S. coastal waters and those of the Caribbean. A NMFS biologist identified the 2 males as blacktip sharks, ensuring positive identification.

Migration Research Integration and Synthesis
On the eastern U.S. coast, blacktip sharks spend the winter in the waters of southern Florida, migrate to the Carolinas and Georgia in the spring to breed and give birth, and return to their wintering grounds in the fall . The seasonal movement of blacktip sharks within the GOM, however, is not fully understood.
Sharks in the western and eastern GOM may have separate yearly north-south migration cycles, similar to those in the U.S. Atlantic waters Killam 6 ;. Genetic work suggests that females are philopatric for their natal nurseries, but it is possible that males contribute to genetic exchange between regions .
The migration cycle in the western GOM is especially interesting because the CSTP provides strong evidence of exchange with Mexican waters. It is believed that blacktip sharks in the western GOM spend the spring and summer months in the northern coastal waters for mating and breeding (Branstetter 10  Campeche. This hypothesis is consistent with the observation that blacktip sharks are generally rare in Tamaulipas, but very common in Veracruz   (Tyminski et al. 11 ).
This may further suggest that western Gulf blacktip sharks stay in the western Gulf, instead of crossing into eastern waters.
This analysis of Gulf of Mexico blacktip sharks is not without limitations.
Movement data are only based on 2 points of reference (i.e., mark and recapture). were more common in the 1990s, whereas biologist captures were the most substantial contributor in the early 2000s (Fig. A-12).
During the period of study, fishing mortality rate was much lower in the Atlantic (average F=0.003) compared with that in the GOM (average F=0.047). In the GOM, F was highest in the 1990s, but never reached F MSY of 0.084 (Fig. A-3). Effort and catches decreased through the early 2000s, so that F current is 0.03-0.04 (NOAA/NMFS 5 ). As of 2006, only about 8-23% of the virgin stock size was depleted in the GOM (NOAA/NMFS 4 ). The SEDAR SAR concluded on the basis of these data that neither the Atlantic nor GOM stock was overfished (NOAA/NMFS 4 ).

Survival
The 4 assumptions of the Seber parameterization are: (1) all marked animals present at time (i) have the same probability of surviving to time (i+1) and the same recapture probability, (2) sampling is an instantaneous processes, relative to the time interval between occasions (i) and (i+1), (3) tagged cohorts are thoroughly mixed, and (4) tags are not lost or missed. If there were a difference in survival probability or recapture probability due to age (assumption 1), this difference needed to be addressed . Therefore, the data were first modeled with YOY vs.
post-YOY groups, to determine if such a difference existed.
Assumption 3 (mixing of cohorts) was investigated because genetic work has suggested that the east GOM, west GOM, and U.S. Atlantic may represent distinct populations of blacktip sharks . No exchange of blacktip sharks has been observed to date between these 3 areas.
Recaptures in these 3 regions were analyzed for nonmixing with a χ 2 contingency table . This test did not require evidence of exchange between geographic areas; it simply determined if the number of recaptures in each region differed significantly from what would be expected if cohorts were thoroughly mixed.
However, the final test (2005-2009) was marginally significant (P=0.05), indicating some evidence for a lack of mixing in those years. The number of recaptures was small (n<20) for every combination of region and cohort, so these results may be affected by the sparseness of the data.
Regardless of χ 2 test results, it is possible to determine post-facto whether survival in these geographic areas is significantly different. According to the simplest likelihood ratio tests, geographic grouping had no effect on either survival or recovery probability (Table 9). Satellite tags would be necessary to definitively determine if tagged cohorts are thoroughly mixed. Nevertheless, the CSTP data demonstrate that the survival is not significantly different among the east GOM, west Gulf of Mexico, and U.S. Atlantic.
In order to correct for assumption (4) Table 10.
This survival analysis provided two useful types of information: tests of significance for various effects on survival and recovery, and direct estimates of survival. Likelihood ratio tests supported the conclusion that YOY and post-YOY have different survival probabilities (Table 9). There was no evidence for significant differences in survival based on sex or geographic region within the GOM. These findings were encouraging, because they were consistent with current NMFS policy to manage the entire GOM as 1 stock (NOAA/NMFS 4 ; NOAA/NMFS 5 ). However, genetic work suggested that the Atlantic and GOM are 2 distinct populations . Therefore, it was interesting that there was no significant difference in survival between the Atlantic and GOM. It is possible that the small sample size of recaptures only permits the detection of large differences in survival.
Likelihood ratio tests were also used to investigate the significance of different effects on recovery probability (Table 9). Recovery probability was different for YOY vs. post-YOY, but not significantly affected by other grouping schemes. In every analysis, recovery probability was significantly affected by fishing effort. These results underscore the need to account for changes in fishing effort in any future studies in the CSTP.
True survival estimates were generated after correcting for tag-shedding rate (Table 8). In analysis 1 (YOY vs. post-YOY), the model S(..) r(g+effort) was the most parsimonious model with a corrected age-constant survival of 0.711. Likelihood ratio tests determined that there was a significant age effect on survival and recovery probability in this analysis, and that fishing effort had a significant effect on recovery probability (Table 9). Therefore, the second most parsimonious model S(g.) r(g+effort) was also found to be valuable for management purposes. In this model,  (Table 8). Differences between these estimates were caused by differences in data input. Analysis 2 did not include any sharks of unknown sex, resulting in a slightly different estimate of survival. Analyses 3 and 4 only included sharks that were tagged as post-YOY, and they both yielded the same estimate.
Analysis 1 included YOY that were assumed to mature into post-YOY after 1 year; this additional source of data resulted in the narrowest of the 4 confidence intervals.
For this reason, 0.725 is the preferred estimate of post-YOY survival.
Several authors have suggested that survival is lowest in the first year of life for fish in general, and elasmobranchs specifically .  provided an empirical estimate of YOY survival as low as 0.36 to 0.55 for lemon sharks in Bimini, Bahamas. Why does survival appear to be so low for YOY? It is possible that inexperienced young sharks are more vulnerable to predation or less effective at foraging . Alternatively, survival of YOY may appear to be low due to emigration from the studied area. If juvenile sharks are dispersing from the Gulf of Mexico, it would be impossible to determine whether those sharks died or emigrated.
Survival estimates can only take values from 0 to 1. Confidence intervals for all original survival estimates fell within these limits. However, when confidence intervals were corrected for tag-shedding rate, some values were inflated to impossibly high values (≥1). It is possible that the true tag-shedding rate in blacktip sharks is lower than the proxy value of 0.259 (Table 10). A larger sample size would also ensure that confidence interval boundaries were between 0 and 1.
The effects of sex and geographic location were intentionally tested for post-YOY only. Combining YOY and post-YOY in these analyses would have confounded the effects that were being investigated. Because direct estimates of YOY survival have already been conducted with robust methods , it was more appropriate to test these group differences in post-YOY sharks. This experimental design allowed a more definitive investigation of the significance of group effects through LRT.
The corrected survival estimates provided were consistent with those already published. The survival for age 0 blacktip sharks used in management is 0.52, based on the direct estimate by  (NOAA/NMFS 4 ). The YOY survival estimate from analysis 1 (0.580) was slightly higher than this value.
Whereas the CSTP included a full size range of YOY,  studied a narrower subset of smaller "neonate" sharks (i.e., those with an open umbilical scar and a mean TL of 62 cm). This difference in data source likely caused the small apparent discrepancy between these 2 estimates.
Prior to this paper, the only estimates of adult survival for blacktip sharks have been from indirect methods based on life history parameters.   In 2006, NMFS tentatively accepted the average mortalities from  and  weight-based indirect methods as developed by and  and . To ensure that calculated M values allowed for positive population growth, the minimum of these 4 estimates was used.
Total instantaneous mortality (Z) is the sum of natural mortality (M) and fishing mortality (F). Proportional survival is related to Z by S=e -z   (Dodrill 13 ). It is likely, therefore, that predation continues to contribute to natural mortality into older age.
Recent studies have investigated the evolutionary impact of size-selective fisheries Olsen et al., 2004;Heino and Dieckmann 14  These changes often resulted in decreasing length at maturity; evidence has suggested that this phenomenon has also occurred in elasmobranchs ).  suggested that size at maturity has decreased for blacktip sharks in the Gulf of Mexico in a span of 11-14 years . If there was a real decrease in size-atmaturity in blacktip sharks, some juvenile sharks from the early years of the program were categorized as "mature" according to the modern size at maturity. If future survival analyses differentiate between juvenile and mature sharks, this potential life history change may negatively affect the results. Because specific data on the magnitude of these changes is limited, it would be beneficial to analyze survival based on length, instead of life stage.
The usefulness of this survival analysis is limited by the broad categorization of sharks into groups such as "YOY" and "post-YOY." Unfortunately, it is not possible to further refine post-YOY estimates into juvenile vs. mature groups, due to ambiguity in the coding of juvenile shark parameters. It was assumed that YOY became post-YOY after 1 year's time, but juvenile sharks may take 1-4 years to become mature . Because of the inherent variation in size and maturity at age (and because estimates of age in the CSTP are originally based on length measurements), a length-based model may be more appropriate for future work.
Program MARK has already been used to calculate survival directly in some elasmobranchs . Despite the relatively low sample size for blacktip sharks, it was possible to effectively model survival. As a result, survival estimates for YOY and post-YOY blacktip sharks were calculated from direct methods, and likelihood ratio tests determined that there is a significant effect of age group on survival and recovery probability.

Reduced (Seber) Parameterization
Survival was modeled with the reduced (Seber) parameterization . Animals are tagged once, released, and recovered once; they are not re-released alive after recovery. In this model, S is the probability that the fish survives a time interval, and r is the probability that a dead fish is recovered and reported (Fig. A-1). If the number of animals released and recovered during each occasion is known, one can calculate estimates of these parameters based on the probability associated with each specific fate (Fig. A-1).
The simplicity of the reduced parameterization is advantageous for the calculation of parameters. The disadvantage of the reduced parameterization is that S does not consider the source of mortality (natural vs. hunting/fishing). As a result, a fish that avoids natural mortalitybut is caught and reportedhas the probability (1-S)r. Therefore, survival from the Seber parameterization represents survival from all sources of mortality, including natural and fishing mortality.
The probabilities S and r can be used to calculate expressions for the expected number of fish recovered in a given occasion. In the sample diagram in Figure A-43, three rows represent three years of marking, and three columns represent three years of recovery. In this diagram, N i is the number of individuals tagged in year i (i=1,2,…, I), r i is the recovery probability in year i, and S i is the survival probability in year i.
Estimates of S and r can also be modeled separately for young-of-the-year (YOY) and post-YOY. When investigating models with an age effect, S and r represent the post-YOY survival and recovery probability, respectively, while S * and r * represent YOY survival and recovery probability, respectively. An animal that is marked and released as YOY is assumed to acquire the post-YOY parameters by the second year of its life. Therefore, probability expressions for sharks tagged as YOY include both YOY and post-YOY parameters (Fig. A-44).
The triangular matrix of probability expressions corresponds to a triangular matrix of fish recovered in each element of that matrix. Recovery data are entered into program MARK using this classic recovery matrix format (Fig. A-2). In this format, n represents the number of fish recaptured, rows represent years of tagging (up to I years), and columns represent years of recovery (up to J years). A sample input file that was used in the analysis is shown in Figure A-45.
Models were also fit with an external index of effort. It is known that F=qf, where F=fishing mortality rate, q=catchability coefficient, and f=fishing effort. If the catchability coefficient is assumed to be constant over time, fishing mortality rate (F) can be used as proxy for effort. Values of F are available specifically for Gulf of Mexico and U.S. Atlantic blacktip sharks from 1986-2004 from the SEDAR 11 Stock Assessment Report (Fig. A-3). Therefore, the analysis was constrained to this time period. From 1986 to 2004, 3240 blacktip sharks were tagged in the CSTP in the GOM, and 96 of these were recaptured (2.96%). During the same time period, 1589 sharks were tagged in the U.S. Atlantic, and 38 were recaptured (2.39%).

Calculation of Parameters
To calculate parameter estimates, the observed recovery matrix is compared to matrix of probability expressions. Program MARK solves for the maximum likelihood estimates of S and r numerically (not algebraically). In maximum likelihood methods, the true value of the parameter is unknown. However, there is a likelihood (probability) distribution for the value of the true parameter, given the observed data (Fig. A-46). Program MARK solves for the maximum likelihood, and its corresponding parameter value. The maximum likelihood estimate (MLE) of the parameter is the point where the likelihood distribution's first derivative is 0.
The variance associated with a given parameter depends on the shape of the likelihood distribution. For example, two likelihood distributions may have the same MLE of survival, but different variances (Fig. A-46). A greater spread in the likelihood function implies greater variance. The profile likelihood method generates confidence intervals that are 0,1 bounded. In this method, possible parameter values are plotted on the x axis, and log-likelihood is plotted on the y axis. When α = 5%, the χ 2 value with 1 degree of freedom is 3.84. With the profile likelihood approach, a y value is calculated by adding 1.92 (half of 3.84) to the log-likelihood at the maximum of the log-likelihood distribution (Fig. A-47). This y value intersects with the loglikelihood function at two points, and the x values at these intersections represent the 95% CI. The confidence interval in this method is not symmetrical around the MLE for the parameter, but it is always 0,1 bounded.

Goodness of Fit (GOF)
Models can only be successfully analyzed if they adequately fit the data. factor or quasi-likelihood parameter, ĉ (Cooch and White, 2004). Perfect fit is achieved when ĉ=1, whereas overdispersion or lack of fit occurs when ĉ>1. A parametric bootstrap approach can be used to estimate ĉ. In this method, the most general model is used to simulate data (capture histories) that fit all the assumptions of model. The model is then fit to each set of simulated data, and the model deviance and ĉ are calculated for each simulation.
There are two ways to use bootstrap simulations to estimate ĉ. One method of calculating ĉ is based on deviance. The mean of all the simulated deviances represents the expected deviance when no assumptions are violated (and fit is perfect).
Therefore, the estimate of ĉ is the ratio of the observed model deviance over the mean of all the simulated deviances. A ratio higher than 1.0 suggests a certain amount of overdispersion. Figure  The mean of all the simulated ĉ represents the expected value of ĉ when fit is perfect.
Therefore, the ratio of the observed model ĉ over the mean of all the simulated ĉ provides a similar measurement of overdispersion. Estimates from both methods were averaged to calculate the final value of ĉ in the analysis. The model fits the data adequately if ĉ≤3 .

Ranking
Various models can be ranked using Akaike's Information Criterion, AIC. This metric is used for determining relative parsimony of a model, balancing overall fit with the number of parameters involved (Akaike, 1973). AIC is defined by: AIC= -2ln(L) +2K, where K is the number of parameters and L is the likelihood of the model, given the data. High likelihood results in a lower AIC; more parameters results in a higher AIC. As a result, a more parsimonious model has a lower AIC.
AIC c is a variation of AIC that corrects for sample size (Sugiura, 1978;Hurvich & Tsai, 1989). AIC c is defined by where n is sample size The extra term in this definition creates a higher penalty for small sample size. QAIC c is another variation, known as the quasi-likelihood adjusted AIC . QAIC c is defined by: If ĉ >1, the contribution of the model likelihood term decreases, and the K penalty is relatively more powerful. Therefore, when ĉ >1, simpler models with fewer parameters become more favored. All models in the candidate set are ranked by QAIC c to identify the most parsimonious model.
Any two models can be directly compared through ΔQAIC c , the difference in QAIC c between two models. If ΔQAIC c >7, there is strong support for a difference in the two models. If 2<ΔQAIC c <7, there is moderate support for a difference in the two models. If ΔQAIC c <2, there is very little support for a difference in the two models (Anderson and Burnham, 1999). The normalized Akaike weights are used to quantify and standardize the difference in support between two models. By definition, w i =(e -ΔAIC(2)^-1 )(Σe -ΔAIC(2)^-1 ) -1 , where w i is the normalized Akaike weight (Buckland et al. 1997). The ratio of two normalized Akaike weights shows the relative support of one model over another. For example, if model A has a weight of 0.6 and model B has a weight of 0.2, model A is 3 times more supported than model B. Program MARK also provides an index called "model likelihood," which is simply the weight of a model divided by weight of most parsimonious model.

Likelihood Ratio Tests
QAIC is one useful method of comparing two models, but it also possible to use classic statistical hypothesis testing between nested models using the likelihood ratio test (LRT). Two models are nested if one (known as the general model) can be transformed into the other (known as the reduced model) by a linear restriction (Cooch and White, 2004). In other words, the two models differ only by the presence or absence of a term. In most cases, the general model contains a certain parameter (e.g.,

S(t))
, whereas the reduced model does not (e.g., S(.)) ( Fig. A-49). The difference in deviance between nested models is approximately Chi-square distributed, and the difference in the number of parameters is the degrees of freedom. The Chi-square statistic is calculated as: χ 2 =Dev r -Dev g where χ 2 is the Chi-square statistic, Dev r is the reduced model deviance, and Dev g is the general model deviance. Equivalently, LRT is determined by comparing -2 ln(L r /L f ) with a χ 2 distribution, where L f is the likelihood of the full model, and L r is the likelihood of the reduced model.
In a LRT, a significant difference (probability<0.05) means that there is a significant increase in deviance with the reduction in the number of parameters. In other words, there is a significant increase in deviance when you remove the parameter of interest; the model that includes the added parameter fits the data significantly better. A non-significant difference (probability>0.05) means that the two models both fit the data equally well, but the reduced model is preferred, since it has fewer parameters. The deviance is not statistically different between the two models, but the reduced model is more parsimonious. If probability>0.05, there is not a significant difference between the models; adding the parameter (e.g., timedependency in survival) does not significantly improve the model fit.