Examination and extension of statistical methodology for estimating animal abundance
The main objective of this thesis is to improve and extend some of the existing methodology for estimating animal abundance. The choice of topics was largely dictated by problems encountered during consultancy work; the opinions I express in the introduction (chapter 1) reflect my experiences in working with both statisticians and zoologists. In chapter 2, I look at confidence interval estimation. Estimates of population size are of little value if their, accuracy is. uncertain. Standard errors are helpful, but are often difficult to interpret. Many people mentally calculate an approximate confidence interval by taking say two standard errors above and below the corresponding estimate. Chapter 2 suggests another approach that provides more reliable intervals. It is conceptually simple, but may require a computer, and sophisticated programs in some circumstances, so that it may be implemented. Some aspects of capture-recapture experiments are investigated in the next two chapters. In chapter 3, an extension to the Jolly-Seber model that incorporates tag returns from dead animals is presented. An approach to adjust out-of-range Jolly-Seber estimates is also suggested. Chapter 4 advances from the modified Jolly-Seber model, to provide a survival analysis based on capture-recapture and tag return data. Populations of three species of bird are used to illustrate the analysis. The final three chapters are on line transect sampling. In chapter 5, which contains joint work with Mr R J Hayes, radial distance models for the line transect method are critically examined. A firmer theoretical base is proposed for such models which throws considerable doubt on those currently in use. The Fourier series perpendicular distance model seems more promising. However, confidence interval coverage for the model is poor; solutions are proposed in chapter 6. The final chapter compares the Fourier series model with other perpendicular distance models, and concludes that two have potentially useful advantages over the Fourier series. One of these is based on the hazard-rate work, and the second uses Hermite polynomials in place of the Fourier series.