Markov-modulated nonhomogeneous Poisson processes for modeling detections in surveys of marine mammal abundance

We consider Markov-modulated nonhomogeneous Poisson processes for modeling sightings of marine mammals in shipboard or aerial surveys. In such surveys detection of an animal is possible only when it surfaces, and with some species a substantial proportion of animals is missed because they are diving and thus not available for detection. This needs to be adequately accounted for in order to avoid biased abundance estimates. The tendency of surfacing events of marine mammals to occur in clusters motivates consideration of the flexible class of Markov-modulated Poisson processes in this context. We embed these models in distance sampling models, introducing nonhomogeneity in the process to account for the fact that the observer's probability of detecting an animal decreases with increasing distance to the animal. We derive approximate expressions for the likelihood of Markov-modulated nonhomogeneous Poisson processes that enable us to estimate the model parameters through numerical maximum likelihood. The performance of the approach is investigated in an extensive simulation study, and applications to pilot and beaked whale tag data as well as to minke whale tag and survey data demonstrate its relevance in abundance estimation.