UW Aquatic & Fishery Sciences Quantitative Seminar

**Noble Hendrix**

QEDA Consulting and University of Washington

**Estimating the probability of whale-strike events in Glacier Bay, Alaska using Extreme Value Theory**

## Abstract

"One of the greatest challenges to the risk manager is to implement risk management models which allow for rare but damaging events, and permit the measurement of their consequences." — Alexander McNeil

Understanding the nature of extreme events, generally defined as having low probability but high consequence, is a fundamental goal in a number of disciplines. For example, finance managers seek to minimize exposure to large changes in asset prices, meteorologists seek to understand the frequency and magnitude of hurricanes, engineers seek to design coastal facilities that can withstand extreme tidal and wave height events (e.g., tsunamis), and hydrologists seek to predict the frequency of extreme flooding events. Such extreme events can also be important in conservation biology. For example, collisions between ships and whales are a global conservation and management concern. Although the number of collisions may be small relative to the volume of shipping traffic, these collisions can adversely impact population dynamics of whales either locally or range-wide. Furthermore, managers may have significant difficulties in estimating the probability of collisions because ship pilots may not detect ship strikes when they occur or may not report the event even if detected. To estimate the probability of whale-strikes, we developed models from Extreme Value Theory (EVT), a well-developed theory from other disciplines but rarely used in ecology or conservation biology. We utilized data from an 8-year study that quantified the frequency at which endangered humpback whales surfaced near cruise ships in the waters surrounding Glacier Bay National Park, Alaska. In this seminar, we will present the basic underpinnings of EVT and show how we implemented EVT in both maximum likelihood and Bayesian frameworks. An important outcome of our work is that maximum likelihood estimates may significantly underestimate risk, and we found that Bayesian estimates were approximately 10 times higher than maximum likelihood estimates of whale-strike events.