S. Afr. J. mar. Sci. 18: 11-18 1997 11 MORTALITY ESTIMATES FOR JUVENILE DUSKY SHARKS CARCHARHINUS OBSCURUS IN SOUTH AFRICA USING MARK-RECAPTURE DATA A. GOVENDER* and S. L. BIRNIE* A maximum likelihood model is developed, using mark-recapure daa, o esimae oal and fishing moraliy raes for he dusky shark Carcharhinus obscurus in Souh Africa. The model accouns for ag-shedding, nonreporing of recapured ags, he muliple release and single recapure naure of he sudy and he usage of wo differen ypes of ags (sheep-ear and ORI ags). Tag shedding was quanified as ags washed up on beaches and fouling of ags in proecive shark nes, which amouned o 17% of all ags recovered beween 1986 and 1993. The ORI ag had a higher ag-shedding rae han he sheep-ear ag. Assuming a 75% reporing rae for recapured dusky sharks, an insananeous fishing moraliy rae was esimaed o be 0.27. year 1, wih a 95% confidence level ranging beween 0.19 and 0.44. year 1. In KwaZulu-Naal, elasmobranch research was iniiaed by he Oceanographic Research Insiue (ORI) in 1959, wih various sudies invesigaing he axonomy, disribuion and biology of sharks being underaken (Bass e al. 1973). In 1964, a agging programme aimed a gaining insigh ino he growh and migraions of sharks was iniiaed (Davies and Jouber 1966). In ha sudy, 726 dusky sharks Carcharhinus obscurus, mos of which were <1 m long, were agged and released off Durban. Of ha oal, 322 (44%) were recapured. Davies and Jouber (1966) speculaed ha he high rae of recapure was parially as a resul of a reward sysem for reurned ags, which encouraged anglers o arge dusky sharks, and parially because many sharks were recapured before hey were able o move away from he area of agging (mean ime-a-libery = 26 days). Bass e al. (1973) coninued he sudy by agging and releasing a furher 2 316 dusky sharks, of which 97 (4.2%) were recapured. Tag reurns from ha sudy showed a disinc geographical segregaion of dusky sharks in erms of sex and size, and he souhern KwaZulu-Naal coas was idenified as a primary nursery area for juvenile dusky sharks. Van der Els (1979) invesigaed claims from recreaional anglers ha a proliferaion of small sharks (including dusky sharks) in he nearshore zone was having a negaive effec on he eleos composiion of heir caches. The analysis from ha sudy showed an increase in he number of small sharks caugh during shore-angling compeiions, wih a simulaneous reducion in he number of eleoss caugh per ouing. In 1984, ORI iniiaed anoher agging programme (wih commercial and conservaionis sponsorship) o obain fisheries-relaed parameers such as growh and moraliy of finfish, sharks and baoids. Recreaional anglers paricipae in his agging programme and deails are oulined in Van der Els (1990). From 1986 o 1993, a oal of 3 629 dusky sharks was marked and released along he KwaZulu- Naal and Easern Cape coass. Sharks were mainly marked by members of he agging programme, bu ag recoveries were repored by personnel servicing shark nes (Cliff and Dudley 1992), anglers and he general public. In all, 345 (9.5%) ags were recovered. These included ags ha were washed up on he shore and hose recovered from shark nes. Recapures of agged sharks alone amouned o 7.7%, which is nearly double he recapure rae repored by Bass e al. (1973). In he curren sudy, oal and fishing moraliy raes for he dusky shark are esimaed from informaion based on he agging programme mark-recapure daa. A model ha considers he naure of muliple releases (marking of sharks found hroughou he sudy) and single recapure of dusky sharks (recapured agged sharks are usually no again released) is developed. Aspecs such as he fouling of ags on shark gill nes, wash-up of ags on he shore, non-reporing of recapures and he fac ha wo differen ypes of ags were used in he sudy are incorporaed ino he model. These moraliy esimaes are required for assessmen of he saus of he sock of dusky sharks. Moraliy model MATERIAL AND METHODS The model developed is similar o Hilborn s (1990) general movemen model. The model esimaes raes of fishing and oal moraliy from mark-recapure * Oceanographic Research Insiue, P.O. Box 10712, Marine Parade 4056, Durban, Souh Africa. E-mail: seaworld@nepune.lia.ac.za Manuscrip received: April 1996
12 Souh African Journal of Marine Science 18 1997 Table I: Tagging programme mark-recapure daa for Carcharhinus obscurus agged off he Easern Cape and KwaZulu-Naal 0 coass during he period 19861993 Year 1986 1987 1988 1989 1990 1991 1992 1993 Number agged 470 481 299 246 085 066 7 073 Sheep-ear ags ORI ags Recoveries Number agged Recoveries Wash-ups + ne fouling Recapures Toal Wash-ups + ne fouling Recapures Toal * Includes one ag found in he somach of a predaory shark Includes one ag from a dead specimen 5 6 4 2 0 3 0 1 41 38 55 22 12 09 47* 45* 59* 25 12* 06* * 10* 0 0 0 055 253 299 517 758 12 13 10 18 18 25 36 * * * * 30* 20* 38* 48* daa. Iniially, he model is developed for a single ag ype and is hen exended o include anoher ag ype. Each model has hree main componens: ii(i) a populaion dynamics componen ha describes how agged individuals survive over ime; i(ii) an observaion componen ha describes he capure of marked individuals; and (iii) a componen specifying he likelihood of recoveries. Mark-recapure daa for C. obscurus beween 1986 and 1993 are summarized in Table I. The model is based on he following assumpions and equaions. I is assumed ha dusky sharks are marked in he middle of each year, whereas recapures occur a he end of each year. Assuming ha N dusky sharks (which were marked in he previous ime inerval) survive o he end of ime, and if a furher T animals are marked and released during ime inerval (+1), hen he number of sharks surviving o he end of his inerval can be expressed as N +1 = N e Z + T +1 e Z/2, (1) where Z is he insananeous oal loss rae for dusky sharks and is assumed o be consan for he sudy period. Equaion 1 describes he number of marked dusky sharks alive a he end of ime +1 as dependen on hose surviving from he previous ime inerval and he number of newly agged sharks. In his model, aginduced moraliy is considered negligible. In a ank sudy of marked C. obscurus, Davies and Jouber (1966) repored ha no dusky sharks suffered moraliy ha could be aribued o he presence of a ag. From 1986 o 1993, only five ags were recovered ha could possibly be considered as ag-induced moraliies (Table I). The following equaions model he recapure of marked dusky sharks (observaion model). Using he Baranov cach equaion (Ricker 1975), he number of marked dusky sharks recaugh (r) a he end of ime inerval is expressed as r = N 1 F Z (1e Z )+T F Z (1e Z/2 ), (2) where F is he insananeous rae of fishing moraliy and is assumed o be consan for he sudy period. However, no all recapures are repored. A consan fracion ß is assumed o be repored, herefore, R = βr, (3) where R is he repored number of recapures. Similarly, i can be shown ha he number of washups (W), which includes ags ha have been washed ashore as well as hose fouled in he shark nes, in inerval can be expressed as W = N 1 βk Z (1 e Z ) + T βk Z (1 e Z/2 ), (4) where K is he insananeous ag-loss rae. For Equaions 1 4, Z = F + K + O, where O is he sum of he insananeous raes of naural moraliy and emigraion. The hird model componen specifies he likelihood (L) of he number of recoveries being repored if he populaion dynamics and observaion model are rue. Hilborn (1990) has shown ha he sampling disribuion of he ag recoveries can be approximaed by a Poisson disribuion. The likelihood of he expeced number of recoveries Rˆ and Ŵ, given he observed number of ag recoveries R and W are
1997 Govender & Birnie: Esimaes of Moraliy for Juvenile Carcharhinus obscurus 13 and respecively. e Rˆ Rˆ R L (R /Rˆ ) = (5) R! e Ŵ Ŵ W L (W /Ŵ ) = (6) W! The oal likelihood of observing all R and W recoveries, given he corresponding Rˆ and Ŵ values, are he producs of he individual likelihoods: and so ha L (R/Rˆ) = Π (e Rˆ Rˆ R /R!) (7) L (W/Ŵ ) = Π (e Ŵ Ŵ W /W!), (8) L (R,W /Rˆ,Ŵ) = L (R/Rˆ) L (W/Ŵ) = Π (e Rˆ Rˆ R /R!) Π (e Ŵ W Ŵ /W!). (9) For compuaional convenience, he negaive of he log-likelihoods was calculaed and forms he quaniy o be minimized: ln(l (R/Rˆ))ln(L (W/Ŵ)) = Rˆ R ln(rˆ )+[ R!] + Ŵ W ln(ŵ )+[ W!]. (10) Noe ha he erms wihin square brackes are ignored when esimaing he model parameers, because hey are consans and independen of he model parameers. Tag ype During he firs year of he agging sudy by Davies and Jouber (1966), large sheep-ear ags were used on juvenile dusky sharks. Noe ha he ag was a larger version of he sheep-ear ag ha was commonly used hen o ag small livesock (Davies and Jouber 1966). However, based on resuls of ag-evaluaion experimens sared a ORI in 1962 (Davies and Jouber 1966), use of he large sheep-ear ags was disconinued afer he firs year of he agging sudy in favour of specially designed ORI ags. The difference beween he ags is in heir shape; he large sheep-ear ag is elongaed, whereas he ORI ag is round. The shape of he ORI ag is believed o reduce verical movemen in he waer and supposedly increases ag reenion ime (Van der Els 1990). The agging programme issued members wih large sheep-ear ags for agging sharks up unil 1989. Subsequenly, only ORI ags have been issued for he purpose, bu members who sill possessed sheep-ear ags coninue o use hem. Some anglers also incorrecly use ags ha have been designed for use on oher fish, bu hese incorrecly marked dusky sharks were excluded from he presen analysis. However, because of he change in ags, here has been a marked increase in he number of wash-ups and of ags recovered from he shark nes (Table I). In his sudy, he hypohesis ha he shedding rae of ORI and large sheep-ear ags is he same was esed. I is defensible o assume ha sharks agged wih eiher of he ag ypes are harvesed a he same rae, i.e. F is he same for each ag ype. For his case (Model 1), he objecive funcion o be minimized is he sum of he negaive log-likelihoods (Equaion 10) for each ag ype, wih F and β being consan for each ag ype, i.e. ln(l (R s /Rˆ s))ln(l (W s /Ŵ s )) ln(l (R o /Rˆ o))ln(l (W o /Ŵ o )), (11) where he superscrips s and o index he sheep-ear and ORI ags respecively. In his model, here are five parameers o be esimaed (F, K s, K o, β and O). In he following analysis (Model 2), he assumpion ha he rae of ag loss is he same for each ag ype, i.e. he insananeous rae of ag loss is assumed o be he same for sheep-ear and ORI ags (K s = K o ), is examined. This reduces he number of parameers o be esimaed o four (F, K, β and O ). Noe ha Model 2 is a special case (nesed wihin) of Model 1. All models were implemened on a spreadshee, which was programmed wih a funcion-opimizaion rouine. Given he number of sharks marked and he ag reurns repored in each ime inerval, esimaes of he parameers can be obained by use of a non-linear minimizaion rouine ha finds opimum parameer esimaes ha saisfy he required minimizaion crieria. Model selecion The likelihood-raio es was used o es wheher a model fi is improved by he inclusion of an exra free parameer. When Model 1 has one more parameer han Model 2 and Model 2 is nesed wihin Model 1, he crierion is 2(ln(Pˆ 2)) 2(ln(Pˆ 1)) 3.84, (12)
14 Souh African Journal of Marine Science 18 1997 Fig. 1: The mark-recapure daa (1986-1993) of Carcharhinus obscurus agged off he Easern Cape and KwaZulu-Naal coass, showing he locaion of (a) he number agged and (b) he number recapured relaive o disance (km) from he border beween Moçambique and Souh Africa
1997 Govender & Birnie: Esimaes of Moraliy for Juvenile Carcharhinus obscurus 15 Table II: Esimaes of model parameers for fixed values of β (reporing rae) and he 95% confidence inervals (CI ) for β = 0.75 0 and model negaive log-likelihood values (ln L). Numbers in square brackes indicae annual raes Parameer Value lnl = 689.856 lnl = 689.999 lnl = 690.290 β = 1 β = 0.75 (C1) β = 0.5 F (. year 1 ) K s (. year 1 ) K o (. year 1 ) O (. year 1 ) 0.210 0.9 0.060 2.220 Model 1 0.27 (0.190.44) 0.9 (0.190.072)[4%] 0.080 (0.0510.135)[8%] 2.14 (1.453.58) 0.410 0.058 0.120 1.990 F (. year 1 ) K (. year 1 ) O (. year 1 ) 0.220 0.047 2.390 Model 2 0.29 (0.20.48) 0.062 (0.040.106)[6%] 2.30 (1.543.96) 0.470 0.093 2.120 where ln(pˆj) is he negaive log-likelihood of he vecor Pˆj of bes parameer esimaes of model j and 3.84 is he value of he χ 2 disribuion, wih 1df a he 95% confidence level. If Equaion 12 is rue, Model 2 is rejeced in favour of Model 1. Likelihood profile mehod Confidence bounds for he parameers of he moraliy model were deermined by he likelihood profile mehod (Schnue 1989, Lebreon e al. 1992). The 95% confidence inerval for a parameer P i of vecor P (i = 1,2,..., k) is deermined by minimizing he negaive log-likelihood for a range of values of P i, wih he remaining (k1) parameers being free. The 95% confidence poin values of P i are equal o he upper and lower boundary values of he range of P i ha saisfies he inequaliy 2(ln L (Pˆ))2(ln (L (Pˆbes)) 3.84 (13) where ln L (Pˆbes) is he negaive log-likelihood of he bes esimae of P, wih all k parameers free, and ln L (Pˆ) is he negaive log-likelihood of he bes esimae of P, wih k1 parameers free and parameer P i fixed. RESULTS The number of dusky sharks agged and released along he easern and souh-easern coass of Souh Africa are shown in Figure 1. The majoriy of sharks were agged and recapured in KwaZulu-Naal, especially near Durban, approximaely 4 km souh of he Moçambican border. Times-a-libery ranged beween 0 and 521 days, wih a mean value of 65 days (SD = ± 83). Esimaion of he model parameers was difficul. Despie he global minimum being aained, unique values for F, β, K o and K s could no be obained, because some of he parameers (e.g. F and β) are confounded in he models. In oher words, alhough an esimae of he produc of he parameers (e.g. Fβ) was obainable, here was insufficien informaion in he daa o obain separae and unique parameer values for he produc coefficiens. As β is confounded wih hree parameers (F, K o and K s ), i was fixed for a range of values which reduced he number of free parameers by one in each model. Esimaes of he parameers, heir 95% confidence inervals and he negaive log-likelihoods for each model are given in Table II. Based on he likelihood- raio es, Model 1 (K s no equal o K o ) bes describes he daa. In Table III, he observed and prediced numbers of recapures and wash-ups and heir associaed residuals are given. Figure 2 shows he fi of Model 1 o he observed daa (wih β = 0.75). DISCUSSION The fac ha mos dusky sharks agged and released along he KwaZulu-Naal coas were juveniles is no surprising, because he area has been idenified as a nursery area for ha species (Bass e al. 1973). Mos recapures occurred wihin he area of agging, which is probably a resul of he shor ime of wo monhs beween agging and recapure. The bes fi o he observed daa was obained by Model 1, i.e. ag reenion is no he same for ORI and
16 Souh African Journal of Marine Science 18 1997 Table III: Observed and Model 1 predicions of recapures of Carcharhinus obscurus and wash-ups for sheep-ears and ORI 0 0ags. The non-reporing rae for recapures and wash-ups was assumed o be 25% (β = 0.75) Year Sheep-ear ags ORI ags Observed Prediced Residual Observed Prediced Residual 1986 1987 1988 1989 1990 1991 1992 1993 41 38 55 22 12 09 28 39 29 22 11 06 05 Recapures 13.211 0.958 25.656 0.236 0.810 3.333-0.282 3.935 18 18 25 36 16 23 37 56 3.225 1.974 5.104 12.244 20.204 1986 1987 1988 1989 1990 1991 1992 1993 05 06 04 04 06 04 Wash-ups 1.057 0.473 0.163 1.155 1.588 2.1 0.466 0.281 12 13 10 05 07 11 16 0.782 7.298 4.780 2.072 6.492 sheep-ear ags. Wih β = 0.75, he overall fi of Model 1 o he observed recapures is reasonable, as depiced by he small residual values, excep for he years 1986, 1988, 1992 and 1993 (Table III, Fig. 2a). However, he parameers K s,k o, O and F (for β = 0.75) have fairly wide confidence bounds (Table II). A possible reason for he poor esimae of F is ha he assumpion of consan fishing moraliy during he sudy was violaed. The assumpion of a consan fishing moraliy could have been relaxed if effor daa for he dusky shark fishery were available. Such effor daa only exis for he shark-ne fishery. For he recreaional dusky shark fishery, only effor indices in KwaZulu-Naal are available, bu hese are regarded as unreliable. Furhermore, he shark-ne effor daa are no direcly comparable o effor indices of he recreaional fishery because he laer is a hook-andline fishery, whereas he former is a ne fishery. The esimaes of raes of fishing moraliy and agshedding are very sensiive o he choice of reporing rae (Table II) and are a resul of he confounding of parameers in he model. In his agging sudy, a preliminary reporing rae of 75% for recapured sharks and finfish, based on angler surveys (ORI unpublished daa), has been assumed. Based on compeiion angler surveys, Van der Els (1979) found a nonreporing rae of only 3%, bu his rae is considered here o be oo low for applicaion o he enire specrum of anglers who migh capure a agged animal. The reporing rae in his sudy, however, excludes an unknown percenage of recapured dusky sharks ha are no idenified as agged individuals by anglers. Tag recogniion by anglers is ofen reduced as a resul of heavy algal growh on he ag and he pracical difficulies of handling a live shark. If he number of overlooked ags is negligible, and assuming a nonreporing rae of 25%, an insananeous fishing moraliy (F) rae of approximaely 0.27. year 1 for dusky sharks is obained (Table II). Off KwaZulu-Naal, dusky sharks are caugh by boh spor anglers and by shark-neing operaions (Van der Els 1979), whereas off he Easern Cape hey are mainly fished by spor anglers (Smale 1991). All hese fishing operaions paricipaed in he mark-recapure sudy, and herefore esimaes of fishing moraliy represen a combined assessmen. Because he agging programme relies on he paricipaion of he general public and field idenificaion of sharks can be difficul (Bass e al, 1973), here is a poenial for misidenificaion of sharks. Juvenile C. obscurus can be confused wih he milkshark Rhizoprionodon acuus, bu he percenage of anglers misidenifying hose sharks is likely o be small. Van der Els (1979) repored ha only 4.3% of R. acuus capured during fishing compeiions were misidenified as C. obscurus. The same auhor also showed ha he mass frequency disribuions of anglers caches of C. obscurus and R. acuus closely resembled hose described by Bass e al. (1973), subsaniaing he anglers abiliy o disinguish beween he species.
1997 Govender & Birnie: Esimaes of Moraliy for Juvenile Carcharhinus obscurus 17 Fig. 2: Fi of Model 1 (wih = 0.75), showing he rends in (a) he number of agged Carcharhinus obscurus recapured and (b) he number of ag wash-ups for he sheep-ear and ORI ags In his sudy, 1.7% of marked dusky sharks (17% of all ags recovered) had heir ags ripped from heir dorsal fins, washed up on beaches or fouled in he shark nes. Because mos agged dusky sharks were <1 m long and shark nes are no designed o cach sharks <1.5 m (Cliff and Dudley 1992), small, agged dusky sharks are able o pass hrough he nes, increasing he chance of ag fouling. Reporing on he firs year of heir agging programme using sheep-ear ags, Davies and Jouber (1966) esimaed ha 4% of agged dusky sharks shed heir ags as a resul of fouling in shark nes. The same proporion of sheep-ear ags was shed per year in he presen sudy. Davies and Jouber (1966) considered ha, as a resul of fin growh, i was unlikely ha he ags would be shed wihin he firs hree years of agging. However, i is no cerain if ag shedding is only a resul of ineracion wih shark nes. Tag-induced moraliy was considered o be negligible and was no accouned for in he model. Over he sudy period, five ags were recovered by mehods oher han recapured animals, fouling in shark nes or wash-ups (Table I). Of hese, hree were recovered from he somachs of predaory sharks, and were considered as naural moraliy, and wo were recovered from dead agged specimens ha were a libery for 2 and 81 days. Even if boh moraliies are assumed o have been ag-induced, his facor is negligible considering he number of dusky sharks ha were agged and released annually. Noe ha an assumpion of Equaions 14 is ha he reporing raes of ags recovered from recapured sharks, wash-ups and hose from shark nes are he same. This is probably unlikely, because he reporing rae of ags fouled and from agged sharks recapured in he nes is probably higher han hose from agged sharks recapured by anglers or wash-ups. This is because personnel servicing he nes are more aware of he agging programme and are more likely o repor all ags recovered in shark nes. The magniude of his difference in reporing rae is unknown. The ORI ags have a shedding rae double ha of he sheep-ear ags (Table II). From 1989, he use of sheep-ear ags was changed in favour of he ORI ag, in he belief ha he ORI ag was reained longer in sharks (Van der Els 1990). However, he presen resuls show ha he annual mean ag-shedding rae has increased by 4% since he inroducion of he ORI ag. I is suggesed ha he sheep-ear ags be reained in combinaion wih he ORI ags, because fuure sudies may explain he mechanism by which ag reenion is improved wih a change in ag shape. Naanson e al. (1995) repored an age-a-mauriy of 21 years for female dusky sharks. Subsiuing his value in he Rikher and Efanov (1977) moraliy equaion indicaes a naural moraliy rae (M) of 0.5. year 1. This value is much smaller han he curren esimae for F of 0.27. year 1. I is he general belief ha overfishing occurs a fishing raes where F»M. Subsiuion of lower age-a-mauriy for dusky sharks of 11 years, according o Van der Els (1979), resuls in an M value of 0.116. year 1, which is sill smaller han he curren value of F. The fac ha F»M, coupled wih he relaively low fecundiy of dusky sharks (614 pups, Bass e al. 1973) and he lae agea-mauriy (Naanson e al. 1995, Van der Els 1979), is cause for concern and fuure research should be direced a addressing his issue. Cliff and Dudley (1992) repored ha beween 1981 and 1990 an average annual oal of 283 dusky sharks was capured in shark nes off he KwaZulu- Naal coas. A leas 10% of hese were found alive in he nes and were usually agged and released. The cach by spor anglers is unknown. However, use of daa of compeiion spor anglers Van der Els (1979) showed ha he cach raes of dusky sharks (mosly juveniles) increased sharply beween 1956 and 1976. Mos of hose sharks were killed because hey were regarded as pess by anglers. However, here has been a move recenly owards promoing he release
18 Souh African Journal of Marine Science 18 1997 of sharks alive (and agged if possible), which is he resul of an increase in conservaion awareness among anglers. This conservaion pracice could augur well for he fuure of he fishery. ACKNOWLEDGEMENTS We hank our colleagues Ms E. Bullen for diligenly mainaining he agging daabase and Mr N. Kisnasamy who provided many answers o our persisen queries on early dusky shark research a ORI. Drs L. E. Beckley (ORI), K. L. Cochrane (F. A. O., Rome) and A. E. Pun (CSIRO, Ausralia) and Mr S. T. Fennessy (ORI) commened on an early draf of he manuscrip. Equaions 14 were developed from suggesions by Drs Pun and Cochrane and Mr B. Wareham is hanked for his informaion on recreaional fishing for dusky sharks. This work was underaken under he auspices of a special programme on modelling of KwaZulu-Naal fisheries and funded by he Souh African Foundaion for Research Developmen. Parial funding was also obained from he Universiy of Naal Research Fund. Mr J. A. A. de Oliveira of he Sea Fisheries Research Insiue and an anonymous reviewer are hanked for heir commens, which enhanced his paper considerably. LITERATURE CITED BASS, A. J., D AUBREY, J. D. and N. KISTNASAMY 1973 Sharks of he eas coas of souhern Africa. 1. The genus Carcharhinus (Carcharhinidae). Invesl Rep. oceanogr. Res. Ins. S. Afr. 33: 168 pp. CLIFF, G. and S. F. J. DUDLEY 1992 Proecion agains shark aack in Souh Africa, 195290. Aus. J. mar. Freshwa. Res. 43: 263-272. DAVIES, D. H. and L. S. JOUBERT 1966 Tag evaluaion and shark agging in Souh African waers. Inves. Rep. oceanogr. Res. Ins. S. Afr. 12: 36 pp. HILBORN, R. 1990 Deerminaion of fish movemen paerns from ag recoveries using maximum likelihood esimaors. Can. J. Fish. aqua. Sci. 47: 635643. LEBRETON, J-D., BURNHAM, K. P., CLOBERT, J. and D. R. ANDERSON 1992 Modeling survival and esing biological hypoheses using marked animals: a unified approach wih case sudies. Ecol. Monogr. 62(1): 67118. NATANSON, L. J., CASEY, J. G. and N. E. KOHLER 1995 Age and growh esimaes for he dusky shark Carcharhinus obscurus in he wesern norh Alanic Ocean. Fishery Bull., Wash. 93:116126. RICKER, W. E. 1975 Compuaion and inerpreaion of biological saisics of fish populaions. Bull. Fish. Res. Bd Can. 191: 382 pp. RIKHTER, V. A. and V. M. EFANOV 1977 On one of he approaches o esimaing naural moraliy of fish populaions. Trudy AlanNIRO 73: 77-85 (in Russian). SCHNUTE, J. [T.] 1989 The influence of saisical effor on sock assessmen: illusraions from Schaefer s model. In Effecs of Ocean Variabiliy on Recruimen and an Evaluaion of Parameers in Sock Assessmen Models. Beamish, R. J. and G. A. McFarlane (Eds). Can. spec. Publ. Fish. aqua. Sci. 108: 1109. SMALE, M. J. 1991 Occurrence and feeding of hree shark species, Carcharhinus brachyurus, C. obscurus and Sphyrna zygaena, on he Easern Cape coas of Souh Africa. S. Afr. J. mar. Sci. 11: 3142. VAN DER ELST, R. P. 1979 A proliferaion of small sharks in he shore-based Naal spor fishery. Environ. Biol. Fishes 4(4): 349362. VAN DER ELST, R.P. 1990 Marine fish agging in Souh Africa. In Fish-Marking Techniques. Parker, N. C., Giogi, A. E., Heidinger, R. C., Jeser, D. B., Prince, E. D. and G. A. Winans. (Eds). Behesda; American Fisheries Sociey: 854862 Am. Fish. Soc. Symp. 7.