58 



Fishery Bulletin 93(1), 1995 



This study was prompted by the existence of vali- 

 dated age and growth data (Branstetter and 

 McEachran, 1986) and reproductive information 

 (Parsons, 1983) on R. terraenovae, which provided 

 several important parameters needed for construc- 

 tion of a life history table, i.e. lifespan, fecundity, and 

 age at maturity. 



The purpose of this study was 1) to produce, using 

 the life history table approach and the best biologi- 

 cal information available, reliable estimates of de- 

 mographic parameters fori?, terraenovae in the Gulf 

 of Mexico, 2) to assess the sensitivity of the computed 

 demographic parameters of the population to a vari- 

 ety of biological (input) parameter manipulations and 

 harvest scenarios, and 3) to compare the resultant 

 rates of population increase with that calculated for 

 the "small coastal" shark group in the FMP for sharks 

 of the Atlantic Ocean and to evaluate the biological 

 basis of the stock assessment on which present man- 

 agement measures are based. 



The instantaneous natural mortality rate (M) was 

 calculated from Hoenig's (1983) equation relating 

 maximum age to total mortality rate, derived from 

 data pertaining to unexploited or lightly exploited 

 stocks. A value of 0.42 for Z (instantaneous total 

 mortality rate) was derived from the regression equa- 

 tion ln(Z) = 1.46 - 1.01 in(t max ), where t max is longev- 

 ity in years. Assuming that maximum age was de- 

 termined from a time when there was no fishing di- 

 rected at this species, Z can be approximated to M. 

 The proportion of survivors at the start of each age 

 interval (x) was l x = N (e~ Mx ), where 7V o is the num- 

 ber of individuals at time 0. 



Demographic parameters were computed follow- 

 ing methodology by Krebs ( 1985 ) and included R o (net 

 reproductive rate per generation), G (generation 

 length in years), and r (intrinsic rate of population 

 change). All the values of r reported in this study 

 were refined by using the Euler equation (Wilson and 

 Bossert, 1971; Krebs, 1985): 



l r m r 



= 1. 



Materials and methods 



Life history tables incorporating the best biological 

 information available on R. terraenovae in the Gulf 

 of Mexico were constructed. Maximum age (lifespan 

 or longevity; t max ) has been estimated to be 8 to 10 

 years (Branstetter, 1987), and age at maturity (t .) 

 for females has been estimated at 4 years (Bran- 

 stetter, 1987), and from 2.4 to 3.9 years (Parsons, 

 1985). For this study, it was assumed that all females 

 reproduced after reaching maturity. Parsons (1983) 

 reported that parturition was annual, gestation pe- 

 riod was 10 to 11 months, and sex ratios at birth 

 were 1:1. He also found a significant relationship 

 between total length of gravid females and number 

 of offspring produced. Fecundity at size was calcu- 

 lated from the regression equation Y = -8.4109 + 

 0.1396X (r=0.50,P<0.001,n=78; Parsons 1 ), where X 

 is female total length and Y is number of offspring. 

 Female length at age was obtained from the von 

 Bertalanffy growth function for both sexes combined 

 derived by Branstetter ( 1987): L t =Lj 1-e -*«-*>>), where 

 #=0.359, L x =108, and f o =-0.985. Number of offspring 

 was further divided by two, because the natality func- 

 tion (m x ) at age represents the number of female off- 

 spring per female parent and sex ratios at birth are 1:1 

 and parturition is annual (Parsons, 1983). Reports of 

 unusually large litter sizes in tropical populations of 

 R. terraenovae were also incorporated in some of the 

 analyses that follow by doubling fecundity at age (m ). 



*=o 



The finite or annual rate of change (e r ) was then 

 calculated from the refined values of r. In addition, 

 the theoretical population doubling or halving time in 

 years « x2 ) assuming a stable age distribution was com- 

 puted as (In 2)/r or (In 0.5)/r, respectively (Krebs, 1985). 



The initial set of analyses, consisting of three differ- 

 ent scenarios, was run by using the most reliable input 

 biological parameters: t =10, t mat =A, m r =baseline age- 

 specific natality, and S=0.657. In scenario 1, first year 

 natural mortality was arbitrarily doubled (M=0.42 x 

 2=0.84) or S o =0.432. In scenario 2, a value of S o =0.512 

 was obtained from the Leslie matrix algorithm by as- 

 suming an equilibrium (or stationary) population 

 (Vaughan and Saila, 1976). Thus, the following equa- 

 tion was solved for S o after assuming r=0: 



i-i 



i=i 



("•*!«■*) ll S J 



7 = 1 



1 Parsons, G. Univ. Mississippi, MI 38677. Personal commun.. 

 1993. 



where m is fecundity at age, I is the oldest age group 

 in the population ( 10 years), and S ; is survival from 

 age j to y+l. In scenario 3, (referred to as the best 

 case scenario), S was assumed to be equal to survivor- 

 ship in the following years (S o =S=0.657=e-° 42 ). For this 

 best case scenario, the stable age distribution (C^) was 

 calculated according to Krebs ( 1985) and plotted. 



In a second set of analyses, the input biological or 

 life history parameters (t .,t ,m,S,S) were var- 



J r mat 1 max 1 x 1 ' o 



ied to test the sensitivity of the resultant demographic 

 parameters (R , G, r, and t K2 ). These sensitivity analy- 

 ses measured the percentage change of the output de- 



