Design-Based Estimation of Animal Density and Abundance

Abstract

Conventional distance sampling may be thought of as an extension of plot sampling (Sect. 1.4), to allow imperfect detection of animals on the plots. Standard plot sampling is purely design-based: we use a randomized design to ensure that the density on plots, which we observe, can be taken as an estimate of density in the wider study area. By contrast, conventional distance sampling is a mix of design-based and model-based methods. Models are proposed for the detection function, and are fitted to the distance data using maximum likelihood methods. This component of estimation is therefore model-based. However, the likelihood maximized is not the full likelihood, but a conditional likelihood: the likelihood of the distances y from the line or point, conditional on the number n of animals detected. In Chap. 7, we will explore modelling both the distances y and the sample size n, using separate likelihoods in a two-stage model-based approach, and in Chap. 8, we will consider methods that use an integrated likelihood, allowing both components to be modelled simultaneously. Conceptually, we can think of a full likelihood approach for conventional distance sampling using the product L n × L y of likelihood components, where for line transect data, L y is as given in Eq. (5.13) (exact distances) or Eq. (5.26) (grouped distances). The equivalent likelihood components for point transect sampling are given by Eqs. (5.30) and (5.37). The other component, L n , is the likelihood corresponding to the count n of animals. If we ignore this component, then we use the design-based methods of this chapter to estimate abundance: we use properties of the design to extrapolate from the surveyed plots to estimate density and abundance for the whole study area. For MCDS, the full likelihood is given by L n × L z × L y|z where L z is the component of the likelihood corresponding to covariates z, and L y|z is the contribution to the likelihood of the distances y, given the covariates z of Eq. (5.42).