Kenneth P. Burnham

Mathematical models for nonparametric inferences from line transect data.

A general mathematical theory of line transects is develoepd which supplies a framework for nonparametric density estimation based on either right angle or sighting distances. The probability of observing a point given its right angle distance (y) from the line is generalized to an arbitrary function g(y). Given only that g(O) = 1, it is shown there are nonparametric approaches to density estimation using the observed right angle distances. The model is then generalized to include sighting distances (r). Let f(y/r) be the conditional distribution of right angle distance given sighting distance. It is shown that nonparametric estimation based only on sighting distances requires we know the transformation of r given by f(O/r).

Riparian Fencing, Grazing, and Trout Habitat Preference on Summit Creek, Idaho

Abstract In 1975, 3.2 km of Summit Creek, Idaho were fenced by the Bureau of Land Management to exclude livestock from the riparian area. Six stream sections were electrofished in 1979 to determine differences in trout abundance, size, and growth between grazed and ungrazed stream sections. Electrofishing stations were paired by habitat type. There were more trout in ungrazed sections than in grazed sections in all three habitat types sampled. With one exception, there were more catachable-sized (200 mm long or longer) rainbow trout (Salmo gairdneri) and brook trout (Salvelinus fontinalis) in the ungrazed area than in the grazed area. There was also evidence that the average size of the fish was less in grazed sections. Fish population data were not collected prior to fencing; therefore, it cannot be firmly concluded that the trout population increased within the livestock enclosure as a result of fencing the riparian area. However, the combined results of previous trout habitat improvements documented fo...

Assumptions and modelling philosophy

This section provides material for a deeper understanding of the assumptions required for the successful application of distance sampling theory. The validity of the assumptions allows the investigator assurance that valid inference can be made concerning the density of the population sampled. The existing theory covers a very broad application area and makes it difficult to present a simple list of all the assumptions that are generally true for all applications. Three primary assumptions are emphasized, but first two initial conditions are mentioned.

Study design and field methods

The analysis methods presented in Chapters 3-5 depend on proper field methods, a valid design, and adequate sample size. This chapter presents broad guidelines for the design of a distance sample survey and outlines appropriate field methods. In general, a statistician or quantitative person experienced in distance methods should be consulted during the initial planning and design of the study. Just as important is the need for a pilot study. Such a preliminary study will provide rough estimates of the encounter rate n/L (line transect sampling) or n/k (point transect sampling), and of variance components from which refined estimates of n and of L or k for the main study are obtained. Additionally, operational considerations can be reviewed and training of participants can occur. A pilot study is strongly recommended as it can provide insights into how best to meet the important assumptions.

Extensions and related work

In this chapter, we consider extensions to the theory described in Chapter 3, and we describe distance sampling methods that are closely related to line and point transect sampling. We also examine models that do not fit into the key + adjustment formulation of earlier chapters. The material on these other models is not exhaustive, but is biased towards recent work, and models that may see future use and further methodological development. Most of the older models not described here are discussed in Burnham et al. (1980). One of the purposes of this chapter is to stimulate further research by raising some of the issues that are not satisfactorily handled by existing theory.

Line transect estimation of population size:the exponential case with grouped data

Gates, Marshall, and Olson (1968) investigated the line transect method of estimating grouse population densities in the case where sighting probabilities are exponential. This work is followed by a simulation study in Gates (1969). A general overview of line transect analysis is presented by Burnham and Anderson (1976). These articles all deal with the ungrouped data case. In the present article, an analysis of line transect data is formulated under the Gates framework of exponential sighting probabilities and in the context of grouped data.