  Distance sampling is a widely used method for estimating wildlife population
abundance. The fact that conventional distance sampling methods are partly
design-based constrains the spatial resolution at which animal density can be
estimated using these methods. Estimates are usually obtained at survey stratum
level. For an endangered species such as the blue whale, it is desirable to
estimate density and abundance at a finer spatial scale than stratum. Temporal
variation in the spatial structure is also important. We formulate the process
generating distance sampling data as a thinned spatial point process and
propose model-based inference using a spatial log-Gaussian Cox process. The
method adopts a flexible stochastic partial differential equation (SPDE)
approach to model spatial structure in density that is not accounted for by
explanatory variables, and integrated nested Laplace approximation (INLA) for
Bayesian inference. It allows simultaneous fitting of detection and density
models and permits prediction of density at an arbitrarily fine scale. We
estimate blue whale density in the Eastern Tropical Pacific Ocean from thirteen
shipboard surveys conducted over 22 years. We find that higher blue whale
density is associated with colder sea surface temperatures in space, and
although there is some positive association between density and mean annual
temperature, our estimates are consitent with no trend in density across years.
Our analysis also indicates that there is substantial spatially structured
variation in density that is not explained by available covariates.
