Cortes: Demographic analysis of Rhizoprionodon terraenovae 



59 



mographic parameter of interest relative to the best 

 case scenario. In the case of ^ x2 , sensitivity was assessed 

 by calculating a multiplication factor that measures 

 the number of times the population doubling time 

 changes relative to the best case scenario (example: if 

 ^=15.7 in the best case scenario and 4.1 in the altered 

 state, then the multiplication factor [mf]=15. 7/4. 1=3.8, 

 i.e. t^ has been shortened 3.8 times in the altered state). 

 Based on the results from the initial set of analy- 

 ses (scenarios 1 through 3), the existing knowledge 

 of life history traits in R. terraenovae, and the re- 

 sults from the FMP (e r =1.91), input parameter val- 

 ues were manipulated in the direction that would be 

 favorable to population increase and should thus be 

 regarded as optimistic scenarios. The following varia- 

 tions, relative to the best case scenario, were applied: 

 doubling m x (m x =2; scenario 4); reducing t nmt by 1 

 year (t mat =3; scenario 5) and by 2 years (t mat =2; sce- 

 nario 6); reducing t mat by 1 year and doubling m x 

 (t mat =3, m x =2; scenario 7); reducing t mat by 2 years 

 and doubling m x (t mat -2, m x =2; scenario 8); increas- 

 ing S by 10% (S o =0.723; scenario 9) and by up to 

 50% (°S o =0.985; scenario 10); increasing S by 10% 

 (S=0.72°3; scenario 11) and by up to 50% (S=0.985; 

 scenario 12); doubling t fuax (t max =20 [note that S and 

 S will also vary, since they depend on t max \; scenario 

 13); and an extreme manipulation that was under- 

 taken to approximate the FMP value of e r =1.91 

 (equivalent to an r of 0.647), where t mat was reduced 

 by 1 year, m x was doubled, and S and S o set at 95% 

 (t ,=3, m =2, S=S =0.95; scenario 14). 



mat ' x ' o ' 



A third set of simulations was run incorporating 

 the estimated mean instantaneous fishing mortal- 



ity rate from 1986 to 1989 (F=0A28), as used in the 

 stock assessment of small coastal species (Parrack 2 ) 

 on which the FMP for sharks of the Atlantic Ocean 

 is based, to demonstrate the effect of exploitation and 

 various age-at-first-entry scenarios. Fishing mortal- 

 ity (F) was added to natural mortality (M) in the 

 survivorship function l x = N Q (e~ [M+F]x ), with F initially 

 starting at age 0, then sequentially up to age 9. A rep , 

 the minimum age at which individuals can first enter 

 the fishery and still allow the population to replace it- 

 self (r>0) was calculated by noting the age at which the 

 intrinsic rate of increase (r) becomes zero or positive. 

 These simulations were run first under scenarios 1 

 through 3, and then under scenarios 4 through 14. 



Results 



The initial set of life history tables yielded net re- 

 productive rates per generation (R ), ranging from 

 0.844 to 1.284, a generation length (G) of 5.8 years, 

 and intrinsic rates of population change (r), ranging 

 from -0.029 to 0.044 (Table 1 ) depending on the value 

 of first year survivorship (S ) used. In scenario 1 

 (S =0.432), the results indicated that the population 

 would decrease at a rate of 2.9% per year and would 

 halve about every 24 years. Halving times are indi- 

 cated by negative values in the t x2 column. In sce- 

 nario 2 (S =0.512), r is equal to by definition. Un- 

 der the best case scenario (scenario 3; S =0.657), the 



2 Parrack, M. L. 1990. A preliminary study of shark exploi- 

 tation during 1986-1989 in the U.S. FCZ. Contrib. MIA- 

 90-493, NOAA, NMFS, SEFC, Miami, FL 33149, 23 p. 



Table 1 



Simulations of the Gulf of Mexico population of the Atlantic sharpnose shark, Rhizoprionodon terraenovae, under three scenarios 

 that use input parameter values representing the best biological information available. Only natural mortality is included in 

 these analyses. First year survival rates (S ) were obtained as follows: S o =0.432 (scenario 1 ) was obtained by doubling the natural 

 mortality value computed from Hoenig's ( 1983) relationship between mortality rate and maximum age; S o =0.512 (scenario 2) was 

 computed from the Leslie matrix algorithm (see text) assuming an equilibrium population (Vaughan and Saila, 1976). The third 

 line (in italics) represents the best case scenario (scenario 3; S o =S=0.657). 



Input parameter values' 



Computed parameter values 2 



1 'ma; =a e e at maturity; f mal =maximum age; m .^age-specific natality; S=survivorship after the first year of life; S o =survivorship 

 for the first year of life. 



2 fl =net reproductive rate per generation; G=generation length, in years; r=intrinsic rate of population change refined through 

 the Euler equation (see text); e r =finite rate of population change; ^^theoretical doubling (positive values) or halving ( negative 

 values) time in years assuming a stable age distribution. 



3 "1" indicates baseline age-specific natality. 



