×

The ultimate-sustainable-yield problem in nonlinear age-structured populations. (English) Zbl 0426.92013


MSC:

92D25 Population dynamics (general)
92D40 Ecology
90C05 Linear programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Beddington, J. R.; Taylor, D. B., Optimum age specific harvesting of a population, Biometrics, 29, 801-809 (1973)
[2] Beverton, R. J.; Holt, S. J., On the Dynamics of Exploited Fish Populations, (Fisheries Investigation Series II, Vol. 19 (1957), Ministry of Agriculture, Fisheries and Food: Ministry of Agriculture, Fisheries and Food London)
[3] Clark, C. W., Mathematical Bioeconomics (1976), Wiley-Interscience: Wiley-Interscience New York · Zbl 0364.90002
[4] Doubleday, W. G., Harvesting in matrix populations, Biometrics, 31, 189-200 (1975) · Zbl 0311.92022
[5] Dunkel, G. M., Maximum sustainable yields, SIAM J. Appl. Math., 19, 1629-1640 (1970) · Zbl 0205.49603
[6] Getz, W. M., Optimal harvesting of structured populations, Math. Biosci., 44, 269-291 (1979) · Zbl 0402.92028
[7] Getz, W. M., A modified Leslie matrix harvesting model and the ultimate sustainable yield problem, (Technical Report TWISK 64 (1979), National Research Institute for Mathematical Sciences, CSIR: National Research Institute for Mathematical Sciences, CSIR Pretoria, South Africa) · Zbl 0405.92012
[8] Getz, W. M., Harvesting models and stock-recruitment curves in fisheries management, (Getz, W. M., Pretoria Symposium on Mathematical Modelling in Biology (1980), Springer-Verlag: Springer-Verlag Heidelberg) · Zbl 0421.92021
[9] Getz, W. M.; Price, R., Sustainable yield strategies from an age-structured two-season Beverton-Holt type model, (Jorgensen, S. E., State-of-the-Art of Ecological Modelling (1979), Pergamon: Pergamon New York)
[10] Lefkovitch, L. P., A theoretical evaluation of population growth after removing individuals from some age groups, Bull. Ent. Res., 57, 437-445 (1966)
[11] Leslie, P. H., On the use of matrices in certain population mathematics, Biometrika, 33, 183-212 (1945) · Zbl 0060.31803
[12] Leslie, P. H., Some further notes on the use of matrices in population mathematics, Biometrika, 35, 213-245 (1948) · Zbl 0034.23303
[13] Luenberger, D. G., Introduction to Linear and Nonlinear Programming (1973), Addison-Wesley: Addison-Wesley Reading, Mass. · Zbl 0241.90052
[14] Mendelsohn, R., Optimization problems associated with a Leslie matrix, Amer. Natur., 110, 339-349 (1976)
[16] Rorres, C., A linear programming approach to the optimal sustainable harvesting of a forest, J. Environ. Manage., 6, 245-254 (1978)
[17] Rorres, C.; Fair, W., Optimal harvesting policy for an age specific population, Math. Biosci., 24, 31-47 (1975) · Zbl 0304.92018
[18] Usher, M. B., Extensions to models used in renewable resource management which incorporate an arbitrary structure, J. Environ. Manage., 4, 123-140 (1976)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.