Sminkey and Musick Demographic analysis of Carcharhinus plumbeus 



343 



0.20, 0.15, 0.10, and 0.05. F = 0.25 was the approxi- 

 mate level of mortality on large coastal sharks in the 

 fishery from 1986 to 1991 and is the recommended F 

 for maximum sustainable yield (Anonymous 1 ). The 

 mean carcass size of all large coastal sharks in the 

 1986-91 fishery was approximately 24 lb (Anony- 

 mous 1 ), but the mean carcass size landed for sand- 

 bar sharks only was approximately 40 lb (Bran- 

 stetter 3 ). Based on two sandbar shark growth mod- 

 els, 24 and 40 lb correspond to ages 8 and 12 years, 

 respectively (Sminkey and Musick, 1995; Musick, 

 unpubl. data) or 15 and 24 years, respectively (Casey 

 and Natanson, 1992). Considering that a mean is a 

 measure of central tendency, then nearly 50% of the 

 catch was younger than these ages. Therefore, fish- 

 ing mortality was simulated to begin at 8, 10, 15, 20, 

 and 29 years, which are conservative estimates based 

 on mean carcass sizes. 



Annual survival including natural mortality was 

 estimated to be only 0.90 (max. age=30) and 0.93 

 (max. age=60) following the method of Hoenig( 1983), 

 which related maximum age attained to instanta- 

 neous total mortality rate (Z). If the maximum age 

 attained was estimated from unexploited or lightly 

 exploited stocks, Z approximates the instantaneous 

 natural mortality rate (M). However, it has been sug- 

 gested that survival of young-of-year sandbar sharks 

 may be lower (Hoff, 1990). Increased mortality on 

 neonate and age-1 sharks would primarily result 

 from predation by larger sharks (Springer, 1960; 

 Branstetter, 1990). Therefore, natural mortality dur- 

 ing the first two years of life was varied in the life 

 history tables. But, the population of large preda- 

 tory sharks in coastal Virginia waters has been se- 

 verely depleted (Musick et al., 1993), potentially re- 

 ducing the mortality rate on juvenile sandbar sharks. 

 Following Hoff ( 1990), a best-case life history table 

 was constructed with survival equal to 0.95 (one-half 

 of estimated mortality rate). 



The net reproductive rate (i? ), the generation time 

 (G), and the intrinsic rate of increase of the popula- 

 tion (r) were calculated (Krebs, 1985) for each trial. 



The effects of exploitation can be assessed from 

 the value and sign of the intrinsic rate of increase. 

 Based upon the outcome, an appropriate minimum 

 size (age) and fishing mortality level (F) for sandbar 

 sharks may be recommended to maintain a viable, 

 reproducing population. 



Results 



Using the growth model for sandbar sharks calcu- 

 lated by Sminkey and Musick (1995) and the best 

 estimate of annual survival rate (0.90) with no in- 



creased juvenile mortality, the population will in- 

 crease at 6.4% per year (Table 1). If natural mortal- 

 ity were lower ("best-case" scenario, survival=0.95), 

 the population could increase at a rate of nearly 12%/ 

 yr (Table 2). If there was increased mortality of neo- 

 nates and age-1 sharks, the population increase rate 

 would range from 2.1%/yr to 7.2% /yr (Table 2). These 

 rates all suggest healthy and increasing populations 

 without fishing. Population replacement (r=0.0) was 

 attained with annual survival rates of 0.70 for neo- 

 nates and 0.85 for age 0+ fish, and 0.50, 0.70, and 

 0.88 for ages 0, 1, and 1+, respectively (Table 2). Any 

 greater mortality would lead to population declines. 



If age at maturity and maximum age are set at 29 

 and 60 years, respectively, and annual survival is 

 0.93, the population increase rate will be 3.5%/yr 

 (Table 2). If natural mortality is 0.1 for all ages (an- 

 nual survival=0.9), the population will decrease at 

 0.1%/yr (Table 2). With decreased juvenile survival 

 (0.70 for age 0, and 0.50 and 0.70 for ages and 1), 

 the population increase rates are only 2.7% and 

 1.1%/yr, respectively (Table 2). With similar juvenile 

 mortality rates, population equilibrium is obtained 

 when postjuvenile survival is 0.91 and 0.92 (Table 2). 



When fishing mortality is added at the recom- 

 mended level for maximum sustainable yield [MSY] 

 (F=0. 25; Anonymous 1 ), age of maturity is fixed at 15 

 years, and age at first capture is set at 8 years, the 

 population would decrease by >7%7yr (Table 3). As- 

 suming these ages of first maturity and first cap- 

 ture, we conclude that fishing mortality would have 

 to be reduced to F=0.10 to maintain a growing popu- 

 lation (Table 3). If a minimum-size limit equivalent 

 to a 15-year-old sandbar shark (135 cm precaudal 

 length, 148 cm fork length, or 178 cm total length) 

 were imposed, fishing mortality could remain at 

 F=0.25 and still support an increasing population 

 (Table 3). However, population doubling time 

 (= ln(2)/r) would be about 33 years. 



Under an age of maturity of 29 years and a maxi- 

 mum age of 60 years, the population increases at all 

 levels off up to 0.25, if fishing does not begin until 

 age 29. Population doubling time, however, would 

 increase dramatically as F increased, ranging from 

 27.7 years if F=0.05 to 693 years if F=0.25. If fishing 

 begins before age 29, the population could increase only 

 at very low fishing mortality rates (Table 3). The gen- 

 eration time (G) is the period between the birth of the 

 parents and the birth of the offspring. When offspring 

 are produced over a period of time, G is the mean pe- 

 riod between the parent's birth and the birth of each 

 offspring. As fishing mortality increases, survival oi 

 parents decreases, leading to fewer offspring later in 

 life, therefore G decreases. This result does not sug- 

 gest more rapid population replacement. 



