Analysis of lethal and sublethal impacts of environmental disasters on sperm whales using stochastic modeling

Seasonal movements of Gulf of Mexico sperm whales following the Deepwater Horizon oil spill and the limitations of impact assessments

As part of the Deepwater Horizon Oil Spill Natural Resource Damage Assessment in the Gulf of Mexico, we conducted a large passive acoustic survey across the eastern Gulf continental shelf edge to assess impacts to sperm whale population. In the months immediately after the spill, sperm whale occurrence was significantly higher in areas closest to the spill. Over the following seasons in 2010-2011, we documented cyclical patterns of decreased and increased occurrence suggesting that this population exhibits a seasonal occurrence pattern in the region, with seasonal movements to other regions, and not likely directly influenced by the oil spill. Unfortunately, a lack of adequately scaled, pre-spill data on sperm whales, along with limitations on the survey duration constrain our ability to infer spill-related changes in sperm whale occurrence. However, our study establishes post-disaster baseline data for continued monitoring, and an expanded study design could provide a model for continued monitoring.

Examining the effect of reoccurring disturbances on population persistence with application to marine mammals

We develop a two-state Markov chain to describe the effect of reoccurring disturbances on a population that is modeled by discrete-time matrix model. The environment is described by three parameters that define the magnitude of impact of a disturbance, the average duration of impact of a disturbance, and the average time between disturbances. We derive an approximation for the stochastic growth rate in order to examine how these three parameters affect population growth. From this approximation, we calculate the sensitivity and elasticity of the growth rate with respect to the environmental parameters. We show that the average duration of impact of a disturbance and the average time between disturbances contribute equally to the stochastic growth rate. We also show that the elasticity of the stochastic growth rate is more sensitive to changes in the magnitude of impact than to changes in either the average duration of impact of a disturbance or the average time between disturbances. These conclusions hold irrespective of the population under consideration. We then provide an application of the model formulation to examine how disturbances, such as oil spills, may affect a sperm whale population. The model results suggest that, in oder to mitigate the impact of disturbances, management strategies should focus on reducing the magnitude of impact. Meanwhile, if it is more feasible to reduce either the duration of impact or the time between impacts, managers should focus on whichever is easier to obtain. In addition, when applied to a sperm whale population, our model shows that the probability of extinction can dramatically increase when disturbance frequency increases but is not greatly impacted by the assumption that all disturbances have the same magnitude.