A kernel estimate for the density of a biological population by using line transect sampling

Motivated by line transect aerial surveys of Southern Bluefin Tuna in the sea, a nonparametric kernel method is explored for estimating the density D = N/A of a biological population where N is the unknown population size and A is the area occupied by the population. The kernel estimator is based on explicitly modelling the probability density function of the perpendicular sighting distances without any assumptions on the form of a detection function. The kernel estimates are shown to be asymptotically unbiased and robust estimates for D, satisfying the robustness criteria suggested by Burnham and co-workers. A new kernel-type confidence interval for D is also proposed. A simulation study shows that the kernel confidence intervals have better coverage than those of the Fourier series method. A tuna data set is analysed; the kernel method yields reasonable estimates of abundance and is robust against the changing detection function during a line transect survey.