Demographic analysis of gummy shark (Mustelus antarcticus) and school shark (Galeorhinus galeus) off southern Australia by applying a generalized Lotka equation and its dual equation

Canadian Journal of Fisheries and Aquatic Sciences

Volumn 57, Issue 1, 2000, Pages 214-222

  Xiao, Yongshun ^a   Walker, Terence I ^b  

^a SOUTH AUSTRALIAN RESEARCH AND DEVELOPMENT INSTITUTE   (Australia)

^b Marine and Freshwater Resour Inst   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

AGE; AUSTRALIA; MATHEMATICAL ANALYSIS; MODEL; MORTALITY; POPULATION; POPULATION DYNAMICS; SHARK;

DEMOGRAPHY; POPULATION GROWTH; SHARK;

(SOUTH); AUSTRALIA;

GALEORHINUS GALEUS; MUSTELUS ANTARCTICUS;

EID: 0034028885     PISSN: 0706652X     EISSN: None     Source Type: Journal    
DOI: 10.1139/f99-224     Document Type: Article

References (36)

1. Au, D.W., and Smith, S.E. 1997. A demographic method with population density compensation for estimating productivity and yield per recruit. Can. J. Fish. Aquat. Sci. 54: 415-420.
2. Cailliet, G.M. 1992. Demography of the central California population of the leopard shark (Triakis semifasciata). Aust. J. Mar. Freshwater Res. 43: 183-193.
3. Cailliet, G.M., Mollet, H.F., Pittenger, G.G., Bedford, D., and Natanson, L.J. 1992. Growth and demography of the Pacific angel shark (Squatina californica), based upon tag returns off California. Aust. J. Mar. Freshwater Res. 43: 1313-1330.
4. Cortés, E. 1995. Demographic-analysis of the Atlantic sharpnose shark, Rhizoprionodon terraenovae, in the Gulf of Mexico. Fish. Bull. U.S. 93: 57-66.
5. Cortés, E. 1998. Demographic analysis as an aid in shark stock assessment and management. Fish. Res. 39: 199-208.
6. Cortés, E. 1999. A stochastic stage-based population model of the sandbar shark in the western North Altantic. Trans. Am. Fish. Soc. In press.
7. Cortés, E., and Parsons, G.R. 1996. Comparative demography of two populations of the bonnethead shark (Sphyrna tiburo). Can. J. Fish. Aquat. Sci. 53: 709-718.
8. Grant, C.J., Sandland, R.L., and Olsen, A.M. 1979. Estimation of growth, mortality and yield per recruit of the Australian school shark, Galeorhinus australis (Macleay), from tag recoveries. Aust. J. Mar. Freshwater Res. 30: 625-637.
9. Gunderson, D.R. 1980. Using r-K selection theory to predict natural mortality. Can. J. Fish. Aquat. Sci. 37: 2266-2271.
10. Hoenig, J.M., and Gruber, S.H. 1990. Life-history patterns in the elasmobranchs: implications for fisheries management. In Elasmobranchs as living resources: advances in the biology, ecology, systematics, and the status of the fisheries. Edited by H.L. Pratt, Jr., S.H. Gruber, and T. Taniuchi. NOAA Tech. Rep. NMFS No. 90. pp. 1-16.
11. Hoff, T.B., and Musick, J.A. 1990. Western North Atlantic shark-fishery management problems and informational requirements. In Elasmobranchs as living resources: advances in the biology, ecology, systematics, and the status of the fisheries. Edited by H.L. Pratt, Jr., S.H. Gruber, and T. Taniuchi. NOAA Tech. Rep. NMFS No. 90. pp. 455-472.
12. Hoppensteadt, F. 1975. Mathematical theories of populations: demographics, genetics and epidemics. Society for Industrial and Applied Mathematics, Philadelphia, PA 19103, U.S.A.
13. Jones, B.C., and Geen, G.H. 1977. Reproduction and embryonic development of spiny dogfish (Squalus acanthias) in the Strait of Georgia, British Columbia. J. Fish. Res. Board Can. 34: 1286-1292.
14. Kermack, W.O., and McKendrick, A.G. 1927. Contributions to the mathematical theory of epidemics. II. The problem of endemicity. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 115: 55-83.
15. Kermack, W.O., and McKendrick, A.G. 1932. Contributions to the mathematical theory of epidemics. III. Further studies of the problem of endemicity. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 138: 94-122.
16. Last, P.R., and Stevens, J.D. 1994. Sharks and rays of Australia. CSIRO Australia.
17. Lotka, A.J. 1922. The stability of the normal age distribution. Proc. Nat. Acad. Sci. U.S.A. 8: 339-345.
18. Lotka, A.J. 1924. Elements of physical biology. Reprinted in 1956 as "Elements of mathematical biology." Dover Publications, Inc., New York.
19. Márquez-Farias, J.F., and Castillo-Géniz, J.L. 1998. Fishery biology and demography of the Atlantic sharpnose shark, Rhizoprionodon terraenovae, in the southern Gulf of Mexico. Fish. Res. 39: 183-198.
20. Márquez-Farias, J.F., Castillo-Géniz, J.L., and Rodríguez de la Cruz, M.C. 1998. Demography of the bonnethead shark, Sphyrna tiburo (Linneaus, 1758), in the southeastern Gulf of Mexico. Cienc. Mar. 24: 13-34.
21. McKendrick, A.G. 1926. Applications of mathematics to medical problems. Proc. Edinb. Math. Soc. 44: 98-130.
22. Moulton, P.M., Walker, T.I., and Saddlier, S.R. 1992. Age and growth studies of gummy shark, Mustelus antarcticus Günther, and school shark, Galeorhinus galeus (Linnaeus), from southern-Australian waters. Aust. J. Mar. Freshwater Res. 43: 1241-1267.
23. Ohsumi, S. 1979. Interspecies relationships among some biological parameters in cetaceans and estimation of the natural mortality coefficient of the Southern Hemisphere minke whale. Rep. Int. Whaling Comm. 29: 397-406.
24. Pauly, D. 1980. On the relationship between natural mortality, growth parameters, and mean environmental temperature in 175 fish stocks. J. Cons. Cons. Int. Explor. Mer, 3: 175-192.
25. Pielou, E.C. 1984. The interpretation of ecological data: a primer on classification and ordination. John Wiley & Sons, Chichester, U.K.
26. Roff, D.A. 1981. Reproductive uncertainty and the evolution of iteroparity: why don't flatfish put all their eggs in one basket? Can. J. Fish. Aquat. Sci. 38: 968-977.
27. Smirkey, T.R., and Musick, J.A. 1996. Demographic analysis of the sandbar shark, Carcharhinus plumbeus, on the western North Atlantic. Fish. Bull. U.S. 94: 341-347.
28. Smith, S.E., Au, D.W., and Show, C. 1998. Intrinsic rebound potentials of 26 species of Pacific sharks. Mar. Freshwater Res. 49: 663-678.
29. Walker, T.I. 1992. A fishery simulation model for sharks applied to the gummy shark, Mustelus antarcticus Günther, from southern Australian waters. Aust. J. Mar. Freshwater Res. 43: 195-212.
30. Walker, T.I. 1994. Fishery model of gummy shark, Mustelus antarcticus, for Bass Strait. In New opportunities: best practice. Edited by I. Bishop. Resource Technology '94 Conference Proceedings, Melbourne, 26-30 September 1994. Centre for Geographic Information Systems and Modelling, University of Melbourne, Melbourne, Australia, pp. 422-438.
31. Walker, T.I. 1998. Can shark resources be harvested sustainably? A question revisited with a review of shark fisheries. Mar. Freshwater Res. 49: 553-572.
32. Walker, T.I., Stone, T., Brown, D., and McLoughlin, K. 1997. Fisheries assessment report: the southern shark fishery 1996. Australian Fisheries Management Authority, Canberra, Australia.
33. Wolfram, S. 1991. Mathematica: a system for doing mathematics by computer. 2nd ed. Addison-Wesley Publishing Company, Inc., Reading, Mass.
34. Woodley, T.H., and Read, A.J. 1991. Potential rates of increase of a harbour porpoise (Phocoena phocoena) population subjected to incidental mortality in commercial fisheries. Can. J. Fish. Aquat. Sci. 48: 2429-2435.
35. Xiao, Y. 1997. Subtleties in, and practical problems with, the use of production models in fish stock assessment. Fish. Res. 33: 17-36.
36. Xiao, Y. 1999. Formulae for calculating the instantaneous rate of natural mortality of animals from its surrogates. Math. Comput. Model. In press.