Skip to main content

Maximum Sustainable Yields and the Self-Renewal of Exploited Populations with Age-Dependent Vital Rates

  • Conference paper
Size-Structured Populations

Abstract

This paper examines the relationship between two problems in the theory of harvesting self-renewing populations with age-dependent vital rates. The first problem is to find a method of harvesting such that the yield sustainable from a population is maximized. Because of the obvious practical importance of this problem, it has been the subject of many investigations (e.g., Beverton and Holt 1957; Beddington and Taylor 1973; Doubleday 1975; Reed 1980; Botsford 1981; Horwood and Whittle 1986). The second problem is to find a method of harvesting which will maximize the capacity of a population to renew itself, given that a certain minimum crop must be taken. At first sight this problem looks relatively unimportant, and it is perhaps understandable that it has received relatively little attention.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Beddington JR, Taylor DB (1973) Optimum age-specific harvesting of a population. Biometrics 29:801–809.

    Article  Google Scholar 

  • Beverton RJH, Holt SJ (1957) On the dynamics of exploited fish populations. Fish Invest London Ser II 19:1–533.

    Google Scholar 

  • Borisov VM (1978) The selective effect of fishing on the population structure of species with a long life cycle. J Ichthyol 18:896–904.

    Google Scholar 

  • Botsford LW (1981) Optimal fishery policy for size-specific, density-dependent population models. J Math Biol 12:265–293.

    Article  Google Scholar 

  • Charlesworth B (1980) Evolution in age-structured populations. Univ Press, Cambridge.

    Google Scholar 

  • Cushing DH (1966) The arctic cod. Pergamon, Oxford New York.

    Google Scholar 

  • Cushing DH, Horwood JW (1977) Development of a model of stock and recruitment. In: Steele JH (ed) Fisheries Mathematics. Academic Press, New York London, pp 21–35.

    Google Scholar 

  • Doubleday WG (1975) Harvesting in matrix population models. Biometrics 31:189–200.

    Article  Google Scholar 

  • Garrod DJ (1967) Population dynamics of the Arcto-Norwegian cod. J Fish Res Board Can 24:145–190.

    Article  Google Scholar 

  • Garrod DJ (1977) The North Atlantic cod. In: Gulland JA (ed) Fish population dynamics. John Wiley & Sons, New York London, pp 216–242.

    Google Scholar 

  • Garrod DJ, Jones BW (1974) Stock and recruitment relationship in the Northwest Arctic cod stock. J Con Perm Int Explor Mer 36:35–41.

    Google Scholar 

  • Gass SI (1969) Linear programming methods and applications. McGraw-Hill, New York.

    Google Scholar 

  • Goodman D (1980) Demographic intervention for closely managed populations. In: Soulé ME, Wilcox BA (eds) Conservation biology. Sinauer, Sunderland, Mass, pp 171–195.

    Google Scholar 

  • Grey DR (1984) Non-negative matrices, dynamic programming and a harvesting problem. J Appl. Probab 21:685–694.

    Article  Google Scholar 

  • Grey DR, Law R (1987) Reproductive values and maximum yields. Funct Ecol 1:327–330.

    Article  Google Scholar 

  • Horwood JW, Whittle P (1986) The optimal harvest from a multicohort stock. IMA J Math Appl Med Biol 3:143–155.

    Article  Google Scholar 

  • Law R (1979) Harvest optimization in populations with age distributions. Am Nat 114:250–259.

    Article  Google Scholar 

  • MacArthur RH (1960) On the relation between reproductive value and optimal predation. Proc Natl Acad Sci USA 46:143–145.

    Article  CAS  Google Scholar 

  • Reed WJ (1980) Optimum age-specific harvesting in a nonlinear population model. Biometrics 36:579–593.

    Article  Google Scholar 

  • Ricker WE (1954) Stock and recruitment. J Fish Res Board Can 11:559–623.

    Article  Google Scholar 

  • Rollefsen G (1953) Observations on the cod and cod fisheries of Lofoten. Rapp P V Reun Cons Perm Int Explor Mer 136:40–47.

    Google Scholar 

  • Rorres C, Fair W (1975) Optimal harvesting policy for an age-specific population. Math Biosci 24:31–47.

    Article  Google Scholar 

  • Slobodkin LB (1968) How to be a predator. Am Zool 8:43–51.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Law, R., Grey, D.R. (1988). Maximum Sustainable Yields and the Self-Renewal of Exploited Populations with Age-Dependent Vital Rates. In: Ebenman, B., Persson, L. (eds) Size-Structured Populations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-74001-5_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-74001-5_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-74003-9

  • Online ISBN: 978-3-642-74001-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics