Boulinier, T., Nichols, J.D., Pollock, K.H., Sauer, J.R. and Hines, J.E. (1996) On the use of closed models of capture-recapture to estimate bird species richness: a test with large scale data. Unpublished manuscript.

Bulmer, M. (1974) On fitting the Poisson lognormal distribution of species-abundance data. *Biometrics*, **30**, 101–10.

Burnham, K.P. and Overton, W.S. (1979) Robust estimation of population size when capture probabilities vary among animals. *Ecology*, **60**(5), 927–36.

Bystrak, D. (1981) The North American Breeding Bird Survey. *Studies in Avian Biology*, **6**, 34–41.

Dempster, A.P., Laird, N.M. and Rubin, D.B. (1977) Maximum likelihood estimation from incomplete data via the EM algorithm. *Journal of the Royal Statistical Society, Series B*, **39**, 1–38.

Efron, B. (1981) Non-parametric estimates of standard error: The jackknife, the bootstrap and other methods. *Biometrika*, **68**, 589–99.

Efron, B. and Thisted, R. (1976) Estimating the number of unseen species: how many words did Shakespeare know? *Biometrika*, **63**(3), 435–47.

Engen, S. (1978) *Stochastic Abundance Models*, Chapman and Hall, London.

Fisher, R.A., Corbet, A.S. and Williams, C.B. (1943) The relation between the number of species and the number of individuals in a random sample from an animal population. *Journal of Animal Ecology*, **12**, 42–58.

Kempton, R.A. and Taylor, L.R. (1974) Log-series and log-normal parameters as diversity discriminants for the Lepidoptera. *Journal of Animal Ecology*, **43**, 381–99.

Lee, S. and Chao, A. (1994) Estimating population size via sample coverage for closed capture-recapture models. *Biometrics*, **50**, 88–97.

Lindsay, B.G. and Roeder, K. (1992) Residual diagnostics for mixture models. *Journal of the American Statistical Association*, **87**, 785–94.

Ludwig, J.A. and Reynolds, J.F. (1988) *Statistical Ecology: A Primer on Methods and Computing*, John Wiley and Sons, New York.

Mehninick, E.F. (1964) A comparison of some species individuals diversity indices applied to samples of field insects. *Ecology*, **45**, 859–61.

Norris, J.L. and Pollock, K.P. (1996) Non-parametric MLE under two closed capture-recapture models with heterogeneity. *Biometrics*, **52**, 639–49.

Preston, F.W. (1948) The commonness and rarity of species, *Ecology*, **29**, 254–83.

Robbins, C.S., Bystrak, D. and Geissler, P.H. (1986) The breeding bird survey: its first fifteen years, 1965–1979. U.S. Fish and Wildlife Service, Resource Publication 157, Washington, D.C., USA.

Romano, J.P. (1988) A bootstrap revival of some non-parametric distance tests. *Journal of the American Statistical Association*, **83**, 698–708.

Shannon, C E. and Weaver, W. (1949) *The Mathematical Theory of Communication*, University Illinois Press, Urbana, Il.

Sichel, H. (1991) Modelling species-abundance frequencies and species-individual functions with the generalized inverse Gaussian-Poisson distribution law. Unpublished manuscript, University of the Eitwatersrand, South Africa, Department of Statistics and Actuarial Science.

Simpson, E.H. (1949) Measurement of diversity. *Nature*, **163**, 688.

Taylor, L.R., Kempton, R.A. and Woiwod, I.P. (1976) Diversity statistics and the log-series model. *Journal of Animal Ecology*, **45**, 255–72.

Titterington, D. M. (1991) Some recent research in the analysis of mixture distributions. *Statistics*, **21**, 619–41.

Titterington, D.M., Smith, A.F.M. and Makov, U.E. (1985) *Statistical Analysis of Finite Mixture Distributions*, John Wiley and Sons, Chichester, England.