Marine Biology

, Volume 95, Issue 2, pp 201–208 | Cite as

Use made in marine ecology of methods for estimating demographic parameters from size/frequency data

  • A. Grant
  • P. J. Morgan
  • P. J. W. Olive


Macdonald and Pitcher's method of decomposing a sizefrequency histogram into cohorts (mathematical optimization of the fit of the distribution function to the histogram) has been used to estimate the composition of random samples drawn from populations with known cohort structure. The large-sample behaviour of the method is in accordance with the results of asymptotic theory. With sample sizes typical of those used in many ecological studies, good estimates often could not be obtained without imposing constraints upon the estimation procedure, even when the number of age classes in the population was known. If the number of age classes was not known, it was frequently difficult to determine from small samples. When unconstrained solutions were obtainable, confidence limits about estimates were often very wide. Our results and information in the theoretical literature indicate that if the Petersen method (whereby several modes on a size-frequency histogram are taken to represent single age classes and all age classes to be present) does not work, accurate estimates of demographic parameters are unlikely to be obtainable using more rigorous methods. In view of these difficulties, we recommend that an iptimization method, such as that described by Macdonald and Pitcher, be used to estimate demographic parameters. Standard errors of estimates should be reported. Optimization methods give an indication when the data is inadequate to obtain accurate parameter estimates, either by failing to converge or by placing large standard errors about the estimates. Graphical methods do not give a clear warning of this, and should be avoided except where the modes on the size-frequency histogram are very well separated and sample sizes are large. Often, assumptions must be made about population parameters to enable their estimation. This may involve constraining some parameters to particular values, assuming a fixed relationship between cohort mean sizes and their standard deviations, or by assuming that individuals grow according to a von Bertalanffy curve. Any such assumptions need detailed justification in each case.


Asymptotic Theory Demographic Parameter Theoretical Literature Fixed Relationship Mathematical Optimization 
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Literature cited

  1. Abramson, N. J.: Computer programs for fish stock assessment. F.A.O. Fish. techn. Pap. Pag. var. (1971)Google Scholar
  2. Bhattacharya, C. G.: A simple method of resolution of a distribution into Gaussian components. Biometrics 23, 115–135 (1967)PubMedGoogle Scholar
  3. Breen, P. A. and D. A. Fournier: A user's guide to estimating total mortality rates from length frequency data with the method of Fournier and Breen. Tech. Rep. Fish. aquat. Sciences, Can. 1239, 1–63 (1984)Google Scholar
  4. Buchanan, J. B.: Dispersion and demography of some infaunal echinoderm populations. Symp. zool. Soc. Lond. 20, 1–11 (1967)Google Scholar
  5. Butler, A. J. and F. J. Brewster: Size distribution of the fan-shell Pinna bicolor Gmelin (Mollusca: Eulamellibranchia) in South Australia. Aust. J. mar. Freshwat. Res. 30, 25–39 (1979)Google Scholar
  6. Cassie, R. M.: Some uses of probability paper in the analysis of size frequency distributions. Aust. J. mar. Freshwat. Res. 5, 513–522 (1954)Google Scholar
  7. Cerrato, R. M.: Demographic analysis of bivalve populations. In: Skeletal growth of aquatic animals. pp 417–465. Ed. by D. C. Rhoads and R. A. Lutz. New York: Plenum Press 1979Google Scholar
  8. Cohen, A. C.: “Estimation of parameters for a mixture of normal distributions” by Victor Hasselblad. Technometrics 8, 445–446 (1966)Google Scholar
  9. Dapson, R. W.: Guidelines for statistical usage in age-estimation technics. J. Wildl. Mgmt 44, 541–548 (1980)Google Scholar
  10. Ebert, T. A.: Longevity, life history, and relative body wall size in sea urchins. Ecol. Monogr. 52, 353–394 (1982)Google Scholar
  11. Fournier, D. A. and P. A. Breen: Estimation of abalone mortality rates with growth analysis. Trans Am. Fish. Soc. 112, 403–411 (1983)CrossRefGoogle Scholar
  12. Gage, J. D.: The analysis of population dynamics in deep-sea benthos. Proc. 19th Eur. mar. Biol. Symp. 201–212 (1985). (Ed. by P. E. Gibbs, Cambridge: Cambridge University Press)Google Scholar
  13. Gage, J. D. and P. A. Tyler: Growth and reproduction of the deepsea brittle star Ophiomusium lymani Wyville Thomson. Oceanol. Acta 5, 73–83 (1982)Google Scholar
  14. Harding, J. P.: The use of probability paper for the graphical analysis of polymodal frequency distributions. J. mar. biol. Ass. U.K. 28, 141–153 (1949)Google Scholar
  15. Hasselblad, V.: Estimation of parameters for a mixture of normal distributions. Technometrics 8, 431–444 (1966)Google Scholar
  16. Hosmer, D. W.: A comparison of iterative maximum likelihood estimates of the parameters of a mixture of normal distributions under three different types of sample. Biometrics 29, 761–770 (1973)Google Scholar
  17. Knutson, S. W., R. W. Buddemeier and S. V. Smith: Coral chronometers. Seasonal growth bands in reef corals, Science, N.Y. 177, 270–272 (1972)Google Scholar
  18. Lutz, R. A. and D. C. Rhoads: Growth patterns within the molluscan shell. In: Skeletal growth of aquatic animals, pp 203–254. Ed. by D. C. Rhoads and R. A. Lutz. New York: Plenum Press 1979Google Scholar
  19. Macdonald, P. D. M.: FORTRAN programs for statistical estimation of distribution mixtures: some techniques for statistical analysis of length-frequency data. Tech. Rep. Fish. Res. Bd Can. 129, 1–45 (1969)Google Scholar
  20. Macdonald, P. D. M.: A FORTRAN program for analysing distribution mixtures, 74 pp. Hamilton, Ontario, Canada: McMaster University (1980) (Statistics Technical Report 80-ST-1, Department of Mathematical Sciences)Google Scholar
  21. Macdonald, P. D. M. and T. J. Pitcher: Age-groups from size-frequency data: a versatile and efficient method of analysing distribution mixtures. J. Fish. Res. Bd Can. 36, 987–1001 (1979)Google Scholar
  22. McNew, R. W. and R. C. Summerfelt: Evaluation of a maximumlikelihood estimator for analysis of length-frequency distributions. Trans. Am. Fish. Soc. 107, 730–736 (1978)Google Scholar
  23. Morgan, P. J.: Ecological investigations of the British intertidal Nephtidae (Annelida: Polychaeta), 141 pp. Ph.D. thesis, University of Newcastle upon Tyne 1984Google Scholar
  24. Nichols, D., A. A. T. Sime and G. M. Bishop: Growth in populations of the sea-urchin Echinus esculentus L. (Echinodermata: Echinoidea) from the English Channel and Firth of Clyde. J. exp. mar. Biol. Ecol. 86, 219–228 (1985)CrossRefGoogle Scholar
  25. Olive, P. J. W.: Polychaete jaws. In: Skeletal growth of aquatic animals, pp 501–592. Ed. by D. C. Rhoads and R. A. Lutz. New York: Plenum Press 1979Google Scholar
  26. Petersen, C. G. J.: Eine Methode zur Bestimmung des Alters und Wuchses der Fische. Mitt. dt. Seefisch Ver. 11, 226–235 (1891)Google Scholar
  27. Purdom, C. E.: Variation in fish. In: Sea fisheries research, pp 347–355. Ed. by F. R. Harden Jones London: Elek Science 1974Google Scholar
  28. Ropes, J. W., D. S. Jones, S. A. Murawski, F. M. Serchuk and A. Jeald. Documentation of annual growth lines in ocean quahogs, Arctica islandica Linne. Fish. Bull. U.S. 82, 1–19 (1984)Google Scholar
  29. Ropes, J. W. and A. S. Merrill: Marking surf clams. Proc. natn. Shellfish. Ass. 60, 99–106 (1970)Google Scholar
  30. Schnute, J. and D. A. Fournier: A new approach to length-frequency analysis: growth structure. Can. J. Fish. aquat Sciences 37, 1337–1351 (1980)Google Scholar
  31. Titterington, D. M., A. F. M. Smith and U. E. Makov: Statistical analysis of finite mixture distributions, 243 pp. Chichester: John Wiley & Sons 1985Google Scholar
  32. Williamson, P. and M. A. Kendall: Population age structure and growth of the trochid Monodonta lineata determined from shell rings. J. mar. biol. Ass. U.K. 61, 1011–1026 (1981)Google Scholar
  33. Yakowitz, S. J. and J. D. Spragins: On the identifiability of finite mixtures. Ann. math. Statist. 39, 209–214 (1968)Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • A. Grant
    • 1
  • P. J. Morgan
    • 1
  • P. J. W. Olive
    • 1
  1. 1.Dove Marine LaboratoryTyne and WearEngland

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