Abstract
The management of Pacific sardine off the California coast is used to motivate a number of problems associated with egg or larvae sampling. The use of the negative binomial distribution as a model for the spatial distribution of eggs is discussed and inference for the negative binomial by classical and Bayesian methods is introduced, A particular problem, that of presence-absence sampling when not all sampling sites are habitats, is analyzed in detail. The paper closes with a number of open questions, ranging from improvements in the modeling, to prescriptive problems associated with survey design.
Dedicated to the memory of Philip Morse: An extraordinary man and scientist who pioneered bringing the approach of basic science to operational problems
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References
Anscombe, F.J. 1950. Sampling theory of negative binomial and logarithmic series distributions. Biometrika, Vol. 34, pp. 358–382.
Bissell, A.F. 1972. A negative binomial model with varying element sizes. Biometrika, Vol. 59, pp. 435–441.
Bliss, C.I. 1958. The analysis of insect counts as negative binomial distributions. Proc. Tenth Intl. Cong. Entom., pp. 1015–1032.
Box, G.E.P. and G.C. Tiao. 1973. Bayesian Inference in Statistical Analysis. Addison Wesley, Reading., MA, 588 pp.
DeGroot, M. 1970. Optimal Statistical Decisions. McGraw-Hill, NY, 489 pp.
Dennis, B. and G.P. Patil. 1984. The gamma distribution and weighted multimodal gamma distributions as models of population abundance. Mathematical Biosciences, Vol. 68, pp. 187–212.
Downing, U.A. 1979. Aggregation, transformation and the design of benthos sampling programs. J. Fisheries Res. Board of Can., Vol. 36, pp. 1454–1463.
Feller, W. 1968. An Introduction to Probability Theory and its Applications, Vol. 1, John Wiley, NY, 509 pp.
Gerard, G. and P. Berthet. 1971. Sampling strategy in censusing patchy populations. In G.P. Patil, E.C. Pielou and W.E. Waters (eds.), Statistical Ecology, Vol. 1, pp. 59–68, Pennsylvania State University Press, University Park, PA.
Gunderson, D.R., G.L. Thomas, P. Cullenberg, D.M. Eggers and R.F. Thorne. 1980. Rockfish investigations off the coast of Washington. Report FRI-UW-8021, Fisheries Research Institute, University of Washington, Seattle.
Hewitt, R. 1976. Sonar mapping in the California Current area: A review of recent developments. Cal. COFI Report, Vol. 18, pp. 149–154.
Hewitt, R. 1981. The value of pattern in the distribution of young fish. Rapp. P-v. Reun. Cons. Int. Explor. Mer., Vol. 178, pp. 229–236.
Hewitt, R. 1984. 1984 Spawning biomass of Northern Anchovy. Administrative Report LJ-84–18, Southwest Fisheries Center, National Marine Fisheries Service, La Jolla, CA.
Hewitt, R. and P. Smith. 1979. Seasonal distributions of epipelagic fish schools and fish biomass over portions of the California Current region. Cal. COFI Report, Vol. 20, pp. 102–110.
Hewitt, R., P.E. Smith, and J.C. Brown. 1976. Development and use of sonar mapping for pelagic stock assessment in the California Current area. Fish Bull. US, Vol. 74, pp. 281–300.
Hewitt, R. and P.E. Smith. 1982. Sonar mapping of the California Current area: Some considerations of sampling strategy. Report, Southwest Fisheries Center.
Johnson, N. and S. Kotz. 1969. Discrete Distributions in Statistics. Wiley, NY.
Leaman, B.M. 1981. A brief review of survey methodology with regard to groundfish stock assessment. Can. Spec. Pub. Fish. Aq. Sci., Vol. 58, pp. 113–123.
Lloyd, M. 1967. Mean crowding. J. Anim. Ecol., Vol. 36, pp. 1–30.
Ludwig, D. 1975. Persistence of dynamical systems under random perturbations. SIAM Review, Vol. 17, pp. 605–640.
MacCall, A.D. (ed.) 1984a. Report on a NMFS-CDFG workshop on estimating pelagic fish abundance. Administrative Report LJ-84–40, Southwest Fisheries Center, P0B 271, La Jolla, CA 92038.
MacCall, A.D. (ed.) 1984b. Management information document for California coastal pelagic fishes. Southwest Fisheries Center Administrative Report LJ-84–39. Southwest Fisheries Center, P0B 271, La Jolla, CA 92038.
Mangel, M. 1985a. Decision and Control in Uncertain Resource Systems. Academic Press, NY.
Mangel, M. 1985b. Search models in fisheries and agriculture. In M. Mangel, (ed.), Proc. of the Ralf Yorque Workshop on Resource Management, Springer Verlag, NY.
Mangel, M. and P.E. Smith. 1987. Presence-absence plankton sampling for fisheries management. Can. J. Fish. Aq. Sci., to appear.
Martz, H. and R. Waller. 1982. Bayesian Reliability Analysis. John Wiley and Sons, NY. 745 pp.
Pennington, M. 1983. Efficient estimators of abundance, for fish and plankton surveys. Biometrics, Vol. 39, pp. 281–286.
Pennington, M. and P. Berrien. 1984. Measuring the precision of estimates of total egg production based on plankton surveys. J. Plankton Res., Vol. 6, No. 5, pp. 869–880.
Pielou, E.C. 1977. Mathematical Ecology. Wiley, NY. 385 pp.
Resh, V.H. 1979. Sampling variability and life history features: Basic considerations in the design of aquatic insect studies. J. Fish. Res. Board Can., Vol. 36, pp. 290–311.
Schuss, Z. 1980. Theory and Application of Stochastic Differential Equations. Wiley, NY.
Smith, P.E. 1978. Biological effects of ocean variability: Time and space scales of biological response. Rapp. P-v. Reun. Cons. Int. Explor. Mer., Vol. 173, pp. 117–127.
Smith, P.E. and S.L. Richardson. 1977. Standard techniques for pelagic fish egg and larva surveys. FAO Fisheries Technical Paper 175, Food and Agriculture Organization of the United Nations, Rome, Italy.
Taylor, C.C. 1953. Nature of variability in trawl catches. Fish. Bull. 83, U.S. Department of the Interior, Vol. 54, pp. 145–166.
Taylor, L.R. 1971. Aggregation as a species characteristic. In G.P. Patil, E.C. Pielou and W.E. Waters (eds.), Statistical Ecology, Vol. 1, pp. 357–377, Pennsylvania State University Press, University Park, PA.
Wald, A. 1947. Sequential Analysis. Dover, NY. 121 pp.
Wolf, P. 1985. Status of the spawning biomass of the Pacific Sardine, 1984–85. Marine Resources Report to the Legislature, California Department of Fish and Game.
Wolf, P. and P.E. Smith. 1985. An inverse egg production method for determining the relative magnitude of Pacific sardine spawning biomass off California. Cal. COFI Report, Vol. 26, pp. 130–138.
Zweifel, J.R. and P.E. Smith. 1981. Estimates of abundance and mortality of larval anchovies (1951–75): Application of a new method. Rapp. P-v. Cons. Int. Explor. Mer., Vol. 178, pp. 248–259.
Elliott, J.M. 1977. Some methods for the statistical analysis of samples of benthic invertebrates. Sci. Publ. No. 25, Freshwater Biological Association, Ambleside Cumbria: 160 pp.
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Mangel, M. (1987). Sampling Highly Aggregated Populations with Application to California Sardine Managenent. In: Vincent, T.L., Cohen, Y., Grantham, W.J., Kirkwood, G.P., Skowronski, J.M. (eds) Modeling and Management of Resources under Uncertainty. Lecture Notes in Biomathematics, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93365-3_19
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DOI: https://doi.org/10.1007/978-3-642-93365-3_19
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