980 



Fishery Bulletin 97(4), 1999 



separately. Mortality for each sex was calculated as 

 the negative value of the slope of the regression line 

 for points to the right of, and including, the peak In 

 N value. Ricker (1975) used only points to the right 

 of the peak In N value to calculate mortality; how- 

 ever, the small number of age classes in R. taylori 

 meant that including the peak value would increase 

 the reliability of the estimate. To confirm that the 

 peak hi A/^ value should be included in the regression 

 calculations, linear and quadratic functions were fit- 

 ted to the data. If the quadratic function provided a 

 significantly improved fit as judged by an F test, then 

 it was assumed that the inclusion of the peak In N 

 value introduced significant curvature into the data 

 set and so violated the assumption of catch curve 

 calculations that mortality is constant across all age 

 classes. In this situation the peak In N value was 

 not used in the calculation. As with the Hoenig ( 1983 ) 

 method, the estimate of mortality from the catch 

 cui-ves was taken to be natural mortality because 

 there was little or no fishing pressure on the stock 

 from which the age data were collected. 



Demographic analysis 



Demographic analysis ofRhizoprionodon taylori was 

 undertaken with standard life history table meth- 

 ods (e.g. Krebs, 1985). The parameters estimated 

 from the life history table were net reproductive rate 

 (/?(,), generation time (G), intrinsic rate of popula- 

 tion increase (r), and population doubling time (^y, '■ 

 Positive values of /• indicate that a population is able 

 to replace itself and thus will not decline, whereas 

 negative values of r indicate that the population is 

 unable to replace itself and will decline. Values of ;• 

 were calculated by solving the Euler equation (Krebs 

 1985): 



Lm, 



1 



x=(i 



where .V 



age; 



maximum age; 



the proportion of animals surviving to 



the beginning of a given age class; and 



age-specific natality. 



Age and growth data for the demographic analy- 

 sis were taken from Simpfendorfer ( 1993 ). Maximum 

 age was taken as 6 years for males and 7 years for 

 females, and age at maturity'for males and females 

 was taken to be one year. Because Simpfendorfer 

 (1993) was not able to validate age estimates (but 

 did have supporting marginal increment and length- 

 frequency data), sensitivity tests were run to inves- 



tigate the influence of the uncertainty of age esti- 

 mates (maximum age 10 years, age at maturity 2 

 years). 



Reproductive data were taken from Simpfendorfer 

 (1992). Litter size varied significantly with mater- 

 nal length (Fig. 1; /--=0.33, P<0.05). Because obser- 

 vations of litter size were made throughout the year, 

 the litter size for each age class was calculated from 

 the size of females at the midpoint of the age class. 

 Mature females produce a litter each year. The sex 

 ratio of the embryos was not significantly different 

 from 1:1; therefore the litter size for each age class 

 was halved to give the number of female pups per 

 female. Although R. taylori matures at the age of one, 

 the first litter is not produced until the end of the 

 second year. Thus only females that survive to the 

 end of that age class produce young. To accommo- 

 date this in the life history table, age-specific natal- 

 ity was calculated from the number of animals sur- 

 viving to the end of a given age class (i.e. the num- 

 ber at the start of the next age class). Similarly, the 

 age-specific natality of the final age class was set to 

 zero because it was assumed that no animals sur- 

 vived to the end of the last age class. To assess the 

 difference in results between calculating age-specific 

 natality from the number present at the beginning 

 and end of an age class, separate life history tables 

 were constructed and the results compared. 



A life history table was constructed for each of the 

 values for natural mortality, calculated as described 

 above, to investigate the sensitivity of demographic 

 parameters to different values. To simulate increased 

 mortality of the youngest age class, a number of other 

 authors have doubled the normal value of M for the 

 first age class (e.g. Hoenig and Gruber, 1990; Smith 

 and Abramson, 1990; Cailliet, 1992; Sminkey and 

 Musick, 1996). A life history table was constructed 

 with double the normal value of M for the first R. 

 taylori age class to test the sensitivity of outcomes to 

 this approach. 



Fishing mortality (F) was incorporated into the 

 survivorship function of the life history table such 

 that total mortality was the sum of M and F. The 

 critical value of F, at which /• equaled zero (i.e. the 

 level of fishing beyond which the population could 

 not replace itself, F,,), was calculated for each life 

 table. For the calculation of F^., fishing mortality was 

 assumed to be equal for each age class. Negative 

 values of F, occurred when the population was de- 

 clining without fishing and indicated that the popu- 

 lation could sustain no fishing. The main source of 

 fishing mortality on R. taylori in northern Australia 

 is gill nets, which do not normally catch animals until 

 they are at least one year of age. To investigate the 

 effect of the age at which F begins (age at first cap- 



