Hidden Markov models reveal complexity in the diving behaviour of short-finned pilot whales

Abstract

Diving behaviour of short-finned pilot whales is often described by two states; deep foraging and shallow, non-foraging dives. However, this simple classification system ignores much of the variation that occurs during subsurface periods. We used multi-state hidden Markov models (HMM) to characterize states of diving behaviour and the transitions between states in short-finned pilot whales. We used three parameters (number of buzzes, maximum dive depth and duration) measured in 259 dives by digital acoustic recording tags (DTAGs) deployed on 20 individual whales off Cape Hatteras, North Carolina, USA. The HMM identified a four-state model as the best descriptor of diving behaviour. The state-dependent distributions for the diving parameters showed variation between states, indicative of different diving behaviours. Transition probabilities were considerably higher for state persistence than state switching, indicating that dive types occurred in bouts. Our results indicate that subsurface behaviour in short-finned pilot whales is more complex than a simple dichotomy of deep and shallow diving states, and labelling all subsurface behaviour as deep dives or shallow dives discounts a significant amount of important variation. We discuss potential drivers of these patterns, including variation in foraging success, prey availability and selection, bathymetry, physiological constraints and socially mediated behaviour.

Figure 1. Dive allocation per state for all dives from all individuals.

Red = state 1, blue = state 2, green = state 3, purple = state 4.

Figure 2. State allocation per dive for each of the three observed variables.

Red filled circles represent state 1; blue triangles represent state 2; green crosses represent state 3 and purple open circles represent state 4. All dives for all individuals are shown sequentially in chronological order along the X-axis.

Figure 3. Box-plots for each of the three variables for all four states, showing median value, 25^th and 75^th percentiles, min-max range and outliers.

Figure 4. Fitted state dependent distributions and observed data for the best model.

Figure 5. Dive allocation per individual (a single tag record each).

Red = state 1, blue = state 2, green = state 3, purple = state 4. See Table 1 for individual information; First column, individuals 143a-151b; second column, individuals 185b-208a; third column, individuals 209a-149b; fourth column, individuals 150b-280a Note different x and y axis scales.

Figure 6. Time budgets for each individual whale.

Left panel shows proportion of time in state. Right panel shows actual time in state for each tag duration. Grey = surface (i.e. data not used in the analysis, including shallow dives classified at surface behaviour (max depth < 20 m)), red = state 1, blue = state 2, green = state 3, purple = state 4.

Figure 7. Dive profile data from three individuals (top: gm10_187b, middle: gm10_266a, bottom: gm10_267a) with the most likely state sequences mapped onto the dives.

Red lines indicate highest probability of being in state 1, blue lines indicate highest probability of being in state 2, green lines indicates highest probability of being in state 3 and purple lines highest probability of being in state 4. Grey lines indicate data not used in the analysis, including shallow dives classified at surface behaviour (max depth < 20 m), and incomplete dives or dives lacking acoustic records. Black asterisk identify individual buzzes, yellow moon on x axis indicates time of sunset (20:00) and yellow sun indicates time of sunrise (6:00). Note different x and y axis ranges.