978 Abstract.–Natural mortality was es- Mortality estimates and demographic analysis timated for Rhizoprionodon taylori by using seven indirect methods based on for the Australian sharpnose shark, relationships between mortality and life history parameters and one direct Rhizoprionodon taylori, method, catch curve analysis. Esti- mated values from indirect methods from northern Australia were 0.60 to 1.65, whereas catch curves produced values of 0.56 for females and 0.70 for males. Demographic analysis Colin A. Simpfendorfer was undertaken by using standard life Western Australian Marine Research Laboratories history table techniques. Life history P.O. Box 20 tables where each of the seven indirect North Beach, Western Australia estimates of natural mortality for R. 6020 Australia taylori produced intrinsic rates of natu- Present address: Center for Shark Research ral increase from –1.297 to 0.212 for an Mote Marine Laboratory unfished population, and only two of 1600 Ken Thompson Parkway the seven produced positive population Sarasota, Florida 34236 growth. The implications of these re- E-mail address: [email protected] sults are discussed in relation to the accuracy of indirect methods for esti- mating natural mortality for R. taylori and other species of shark. The catch curve method was considered the best estimate of natural mortality and gave In a paper entitled “Problems in the traits and as such represents a bi- an intrinsic rate of increase of 0.27 and rational exploitation of elasmo- ased set of data on which to base a doubling time of 2.55 years. The re- sults of life history table analysis with branch populations and some sug- conclusions about sustainability of the estimate of natural mortality from gested solutions,” Holden (1974, p. elasmobranch stocks. In particular, the catch curve analysis indicated that 137) concluded that “elasmobranch the examples lack representatives a R. taylori population could sustain stocks offer very limited opportuni- from tropical areas, especially fishing mortality up to 0.18 if applied ties for long-term exploitation.” short-lived, rapidly growing, early evenly over all age classes, or 0.67 if age at first capture was two years. The Holden’s conclusion was based on maturing species. With adequate implications of this study are discussed the fact that elasmobranch life his- information on species with a wide in relation to sustainability of elasmo- tory traits, such as slow growth, range of life histories, a more accu- branch stocks, particularly short-lived, long lifespan, late age at maturity, rate assessment of the ability of fast growing, early maturing species. and low fecundity, make popula- elasmobranch stocks to sustain fish- tions very susceptible to recruit- ing pressure should be possible. ment overfishing. Holden’s hypoth- In recent years the use of demo- esis has been supported by evidence graphic analysis (i.e. life history from a number of shark stocks that tables) has become popular in the have been rapidly overfished. These assessment of elasmobranch popu- stocks include the spiny dogfish off lations and their ability to be sus- Scotland and Norway (Squalus tainably fished (e.g. Hoenig and acanthias; Holden, 1968, 1977), the Gruber, 1990; Cailliet, 1992; Cailliet soupfin shark off California (Galeo- et al., 1992; Cortes, 1995; Cortes rhinus galeus; Ripley, 1946), the and Parsons, 1996; Sminkey and basking shark of the Irish Sea (Ceto- Musick, 1996; Au and Smith, 1997; rhinus maximus; Parker and Stott, Cortes, 1998). This style of analysis 1965), the porbeagle of the western requires only knowledge of the life Atlantic (Lamna nasus; Casey et al., history traits of a species. Because 1978), and the sandbar and dusky demographic models are static rep- sharks of the western North Atlan- resentations of populations with a tic (Musick et al., 1993). The ma- stable age structure, they have limi- jority of these examples are long- tations in respect to density-depen- lived, slow growing, late maturing, dent responses (e.g. density-depen- temperate-water species. This dent natural mortality) and dynamic group of commonly cited examples processes (e.g. fishing and variable Manuscript accepted 5 October 1998. does not, however, represent the full recruitment) that can be included in Fish. Bull. 97: 978–986 (1999). range of elasmobranch life history dynamic models. The latter types of Simpfendorfer: Demographic analysis of Rhizoprionodon taylori 979 Table 1 Methods used to estimate mortality for Rhizoprionodon taylori from life history parameter relationships. GSI = gonadosomatic index; K = von Bertalanffy growth parameter; L∞ = von Bertalanffy growth parameter; M = natural mortality; T = average water temperature; tmax = maximum age; xm = age at maturity; Z = total mortality. Method Relationships Hoenig (1983) ln(Z) = 1.46 – 1.01 ln (tmax) Pauly (1980) ln(M) = –0.0066 – 0.279 log (Lx) + 0.6543 log (K) + 0.4634 log (T) Gunderson (1980) M = 4.64 GSI – 0.370 Gunderson and Dygert (1988) M = 0.03 + 1.68 GSI = 165. Jensen (1996) (age) M xm Jensen (1996) (growth) M = 1.5K (theoretical) Jensen (1996) (Pauly) M = 1.6K models require abundance data (e.g. CPUE time-se- tween life history parameters and natural mortality ries data or fishery-independent surveys) that are not (M) or total mortality (Z) from the literature. Seven available for many elasmobranch populations. In cases relationships were chosen (Table 1) to investigate where abundance data are not available, demographic variability in their results. All seven were based models may represent the best available technique for heavily on data from teleost fish, although most in- the analysis of stock dynamics. cluded some data from elasmobranchs. The most The Australian sharpnose shark, Rhizoprionodon widely used relationship in elasmobranch studies is taylori, is an ideal example of a small, short-lived, that of Hoenig (1983), which uses a linear function fast growing, early maturing tropical species (Simpf- to estimate total mortality from maximum age. Al- endorfer, 1992, 1993). It is endemic in the inner con- though this method estimates total mortality, it was tinental shelf waters of northern Australia between the assumed to represent natural mortality for R. taylori Northwest Shelf and southern Queensland (Last and because there was little or no fishing for this species Stevens, 1994). It is captured throughout much of its in the study area (Simpfendorfer, unpubl. data). The range as bycatch in commercial fishing operations, method of Pauly (1980) uses two parameters of the including gillnet fisheries for barramundi, mackerel, von Bertalanffy growth curve (L∞ and K) and aver- and shark, and prawn trawl fisheries (Simpfendorfer age temperature to estimate natural mortality. and Milward, 1993; Last and Stevens, 1994). This Jensen (1996) reanalyzed Pauly’s (1980) data and paper reports the results of mortality estimation and found that natural mortality could be estimated with demographic analysis for R. taylori. Mortality was the same level of accuracy based only on the value of estimated in two ways. First, a number of relations K. In the same paper Jensen (1996) also gave two between mortality and life history parameters from other relationships for estimating natural mortality the literature were used to evaluate the appropri- based on life history theory, one based on K and the ateness of these methods for estimating natural other on age at maturity. The final two relationships mortality in sharks. Second, catch curve analysis was selected used maximum female gonadosomatic in- conducted to produce a direct estimate of mortality. dex (GSI) as an indicator of reproductive effort to The results of the demographic analyses are used to estimate natural mortality. The method of Gunderson comment on the probable sustainability of short- (1980) was based on only 10 species; Gunderson and lived, fast growing, early maturing, tropical elasmo- Dygert (1988) expanded this to 20 species. Data for branch populations. calculation of M were taken from Simpfendorfer (1992; GSI) and Simpfendorfer (1993; von Bertalanffy param- eters, maximum age, and age at maturity). Materials and methods The second approach to the estimation of mortal- ity was catch curve analysis (e.g. Ricker, 1975; Vetter, Estimation of mortality 1987). Age data for the catch curves were taken from Simpfendorfer (1993). Ages were converted to whole Two approaches were taken to estimate mortality in years and the natural log of the number of individuals R. taylori. The first was to employ relationships be- (ln N) was plotted against age for males and females 980 Fishery Bulletin 97(4), 1999 separately. Mortality for each sex was calculated as tigate the influence of the uncertainty of age esti- the negative value of the slope of the regression line mates (maximum age 10 years, age at maturity 2 for points to the right of, and including, the peak ln years). N value. Ricker (1975) used only points to the right Reproductive data were taken from Simpfendorfer of the peak ln N value to calculate mortality; how- (1992). Litter size varied significantly with mater- ever, the small number of age classes in R. taylori nal length (Fig. 1; r2=0.33, P<0.05). Because obser- meant that including the peak value would increase vations of litter size were made throughout the year, the reliability of the estimate. To confirm that the the litter size for each age class was calculated from peak ln N value should be included in the regression the size of females at the midpoint of the age class. calculations, linear and quadratic functions were fit- Mature females produce a litter each year. The sex ted to the data. If the quadratic function provided a ratio of the embryos was not significantly different significantly improved fit as judged by an F test, then from 1:1; therefore the litter size for each age class it was assumed that the inclusion of the peak ln N was halved to give the number of female pups per value introduced significant curvature into the data female.