Abstract
Simple classical approaches to mathematical analysis of fisheries are inherently limited. Increased use of more realistic population models, in the form of age- or size-specific, density-dependent models based on physiological energetics, is proposed here. Recent, fishery-related results using models of this type illuminate such issues as cyclic behavior of populations, multiple equilibrium levels, and optimal policy. Specific results include: size-selective fishing can lead to unstable cycles, an increase in individual growth rate can maintain depressed equilibrium levels, optimal policy for size-specific, density-dependent models may involve pulse-fishing, and more realistic models of multispecies problems in the Antarctic may alter conclusions reached through simpler models.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Allen, R.L. and Basasibwaki, P. 1974. Properties of age structure models for fish populations. J. Fish. Res. Board Can. 30, 1936–1947
Allen, K.R. and Kirkwood, G. 1977. A sperm whale population model based on cohorts (SPCOH). Rep. Int. Waling Comm. (no. 27), 268–271
Beddington, J.R. and Taylor, D.B. 1973. Optimum age specific harvesting of a population. Biometrics 29, 801–809
Beverton, R.J.H. and Holt, S.H. 1957. On the dynamics of exploited fish populations. Fish. Invest. London, Ser. 2, 19
Botsford, L.W. 1978. Modeling, stability and optimization of aquatic production systems. Ph.D. Thesis, University of California, Davis
Botsford, L.W. 1980a. The effects of increased individual growth rates on depressed population size. American Naturalist. In press
Botsford, L.W. 1980b. Optimal fishery policy for size-specific, density-dependent population models. Ms. submitted for publication
Botsford, L.W. and Wickham, D.E. 1978. Behavior of age-specific, density-dependent models and the northern California Dungeness crab fishery. J. Fish. Res. Board Can., 35, 833–845
Brodie, P.F. 1977. Form, function and energetics of Cetacea: a discussion. In Functional Anatomy of Marine Mammals vol. 2, R.J. Harrison, ed. Academic Press, London
Clark, C. 1976. Mathematical Bioeconomics: The Optimal Management of Renewable Resources. John Wiley and Sons, Inc.
Clark, C., Edwards, G., and Friedlander, M. 1973. Beverton-Holt model of a commercial fishery: optimal dynamics. J. Fish. Res. Board Can., 30, 1629–1640
Getz, W.M. 1979. Optimal harvesting of structured populations. Math. Biosci. 44, 269–291
Graham, M. 1935. Modern theory of exploiting a fishery, and application to North Sea trawling. J. Cons. Expl. Mer, 10, 264–274
Guckenheimer, J., Oster, G. and Ipaktchi, A. 1977. The dynamics of density-dependent population models. J. Math. Biol. 4/2, 8–147
Gulland, J. 1977. The analysis of data and the development of models. In Fish Population Dynamics J. Gulland, ed. John Wiley and Sons
Hannesson, R. 1975. Fishery dynamics: a North Atlantic cod fishery. Can. J. Econ. VIII (2), 151–173
Holling, C.S. 1973. Resilience and stability of ecological systems. Ann. Rev. Ecol. Syst. 4, 1–23
Hutchinson, G.E. 1978. An Introduction to Population Ecology. Yale University Press, New Haven and London, 260 pp.
Ivlev, V.S. 1961. Experimental Ecology of the Feeding of Fishes. Yale University Press, New Haven
Keyfitz, N. 1978. Introduction to the Mathematics of Populations. Addison-Wesley, Reading, 450 pp.
Laws, R.M. 1977. The significance of vertebrates in the Antarctic marine ecosystem. In Adaptations Within Antarctic Ecosystems G.A. Llano, ed.
Leslie, P.H. 1945. On the use of matrices in certain population mathematics. Biometrika 33 (Pt. 3), 183–212
Levin, S.A. and Goodyear, C.P. 1980.. Analysis of an age-structured fishery model. J. Math. Biology 9(3):245–274.
Lockyer, C.H. 1972. A Review of the Weights of Cetaceans with Estimates of the Growth and Energy Budgets of the Large Whales. M.Phil. thesis, University of London, London
Schaefer, M.B. and Beverton, R.J.H. 1963. Fishery dynamics–their analysis and interpretation. In The Sea, M.N. Hill, ed., 2, 464–483, Wiley, New York, N.Y.
Lockyer, C.H. 1974. Investigation of the ear plug of the southern sei whale, Balaenoptera borealis as a valid means of determining age. J. Cons. int. Explor. Mer, 36 (1), 71–81
Lotka, A.J. 1925. Elements of Physical Biology. Williams and Wilkins, Baltimore. Republished by Dover Publications, 1956, as Elements of Mathematical Biology
MacFadyen, A. 1973. Some thoughts on the behavior of ecologists. J. Anim. Ecol., 44, 351–363
MacKintosh, N.A. 1973. Distribution of postlarval krill in the Antarctic. Discovery Rep. 36, 95–156
May, R.M., Beddington, J.R., Horwood, J.W. and Shepherd, J.G. 1978. Exploiting natural populations in an uncertain world. Math. Biosci. 42, 219–252
May, R.M., Beddington, J.R., Clark, C.W., Holt, S.J. and Laws, R.M. 1979. Management of multispecies fisheries. Science 205 (4403), 267–277
Mendelssohn, R. 1976. Optimization problems associated with a Leslie matrix. The Amer. Natur. 110(973), 339–349
Menshutkin, V.V. 1964. Pbpulation dynamics studied by representing the population as a cybernetic system. (In Russian) Vopr. Ikhtiol. 4, 23–33
Murphy, G.I. 1968. Pattern in life history and the environment. The Amer. Natur. 102(927), 391–403
Paloheimo, J.E. and Dickie, L.M. 1965. Food and growth of fishes. I. A growth curve derived from experimental data. J. Fish. Res. Board Can. 22, 521–542
Pope, J.G. 1973. An investigation into the effects of variable rates of the exploitation of fishery resources. In The Mathematical Theory of the Dynamics of the Dynamics of Biological Populations M.S. Bartlett and R.W. Hiorns, eds., Academic Press
Reed, W.J. In press. Optimum age-specific harvesting in a non-linear population model. Biometrics
Ricker, W.E.“ 1954. Stock and recruitment. J. Fish. Res. Board Can., 11, 559–623
Ricker, W.E. 1977. The historical development. In Fish Population Dynamics J.A. Gulland, ed., John Wiley and Sons, New York, N.Y.
Rorres, C. 1976b. Optimal sustainable yields of a renewable resource. Biometrics 32, 945–948
Rorres, C. and Fair, W. 1975. Optimal harvesting policy for an age-specific population. Math. Biosci. 24, 31–47
Rothschild, B.J. and Suda, A. 1977. Population dynamics of tuna. In Fish Population Dynamics J.A. Gulland, ed., John Wiley and Sons, London, 372 pp.
Salmon, W.C. 1973. Logic. Prentice-Hall, Inc., Englewood Cliffs, N.J., 150 pp.
Schaefer, M.B. 1954. Some aspects of the dynamics of populations important to the management of the commercial marine fisheries. Bull. Inter-Amer. Trop Tuna Comm., 1, 26–56
Sinko, J.W. and Streifer, W.E. 1967. A new model for age, size structure of a population. Ecology 48 (6), 910–918
Sinko, J.W. and Streifer, W.E. 1969. Applying models incorporating age-size-structure of a population of Daphnia. Ecology 50, 608–615
Von Foerster, H. 1959. Cell Proliferation F.
Walters, C.J. 1969. A studies. Trans. Amer.
Some remarks on changing populations. In The Kinetics of Stohlman, ed., 382–407, Grune and Stratton, New York generalized computer simulation model for fish population Fish. Soc. 98, 505–512
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Botsford, L.W. (1981). More Realistic Fishery Models: Cycles Collapse and Optimal Policy. In: Vincent, T.L., Skowronski, J.M. (eds) Renewable Resource Management. Lecture Notes in Biomathematics, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46436-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-46436-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10566-4
Online ISBN: 978-3-642-46436-2
eBook Packages: Springer Book Archive