Biologically Important Areas for bowhead whales (Balaena mysticetus): Optimal site selection with integer programming

Place-based approaches to marine conservation identify areas that are crucial to the success of populations, species, communities, or ecosystems, and that may be candidates for special management actions. In the United States, the National Oceanic and Atmospheric Administration defined Biologically Important Areas (BIAs) for cetaceans (whales, dolphins, and porpoises) as areas and periods that individual populations or species are known to preferentially use for certain activities or where small resident populations occur. The activities considered to be biologically important are feeding, migrating, and activities associated with reproduction. We present an approach using spatial optimization to refine the BIA delineation process to be more objective and reproducible for conservation planners and decision makers who wish to use various spatial criteria to address conservation or management objectives. We present a case study concerning feeding bowhead whales (Balaena mysticetus) and bowhead whale calves in the western Beaufort Sea to illustrate the mechanics and benefits of our optimization model. In the case study, we incorporate spatial information about whales' relative density and optimally delineate BIAs under different thresholds for minimum patch (cluster) size and total area encompassed within the BIA network. Results from our case study showed three consistent patterns related to minimum cluster size (contiguity) and maximum area threshold for both BIA types and all months: (1) cells with the highest whale density were selected when contiguity or maximum area thresholds were small; (2) for a given area threshold, the number of whales inside BIAs was inversely proportional to cluster size; and (3) the number of whales inside BIAs initially increased rapidly as the area threshold increased, but eventually approached an asymptote. Additionally, information on temporal variability in a BIA may influence the development of conservation, management, monitoring, or mitigation methods. To provide additional insight into the ecological characteristics of the BIAs selected during the optimization step, we quantified inter-annual variability in whale occurrence and density within individual BIAs using statistical techniques. The bowhead whale BIAs and associated information that we present can be incorporated with other relevant information (e.g., objectives, stressors, costs, acceptable risk, legal constraints) into conservation and management decision-making processes.