Inferring resource distributions from Atlantic bluefin tuna movements: An analysis based on net displacement and length of track

We use observed movement tracks of Atlantic bluefin tuna in the Gulf of Maine and mathematical modeling of this movement to identify possible resource patches. We infer bounds on the overall sizes and distribution of such patches, even though they are difficult to quantify by direct observation in situ. To do so, we segment individual fish tracks into intervals of distinct motion types based on the ratio of net displacement to length of track (Δ D / Δ L) over a time window Δ t. To find the best segmentation, we optimize the fit of a random-walk movement model to each motion type. We compare results from two distinct movement models: biased turning and biased speed, to check the model-dependence of our inferences, and find that uncertainty in choice of movement model dominates the uncertainties of our conclusions. We find that our data are best described using two motion types: "localized" (Δ D / Δ L small) and "long-ranged" (Δ D / Δ L large). The biased turning model leads to significantly better resolution of localized movement intervals than the biased speed model. We hypothesize that localized movement corresponds to exploitation of resource patches. Comparison with visual behavior observations made during tracking suggests that many inferred intervals of localized motion do indeed correspond to feeding activity. From our analysis, we estimate that, on average, bluefin tuna in the Gulf of Maine encounter a resource patch every 2 h, that those patches have an average radius of 0.7-1.2 km, and that, overall, there are at most 5-9 such patches per 100 km² in the region studied.