Continuous-Time Discrete-State Modeling for Deep Whale Dives

Abstract

Understanding unexposed/baseline behavior of marine mammals is required to assess the effects of increasing levels of anthropogenic noise exposure in the marine environment. However, quantifying variation in the baseline behavior of whales is challenging due to the fact that they spend much of their time at depth, and therefore, their diving behavior is not directly observable. Data collection employs tags as measurement devices to record vertical movement. We focus here on satellite tags, which have the advantage of collection over a time window of weeks. The type of data we analyze here suffers the disadvantage of being in the form of depths attached to an arbitrarily created set of depth bins and being sparse in time. We provide a multi-stage generative model for deep dives using a continuous-time discrete-space Markov chain. Then, we build a likelihood, incorporating dive-specific random effects, in order to fit this model to a set of satellite tag records, each consisting of a temporally misaligned collection of deep dives with sparse binned depths for each dive. Through simulation, we demonstrate the ability to recover true model parameters. With real satellite tag records, we validate the model out of sample and also provide inference regarding stage behavior, inter-tag record behavior, dive duration, and maximum dive depth. Supplementary materials accompanying this paper appear online.