In the open ocean, movements of migratory fish populations are typically surveyed using tagging methods that are subject to low sample sizes for archive tags, except for a few notable examples, and poor temporal resolution for conventional tags. Alternatively, one can infer patterns of movement of migratory fish by tracking movements of their predators, i.e., fishing vessels, whose navigational systems (e.g., GPS) provide accurate and frequent VMS (vessel monitoring system) records of movement in pursuit of prey. In this paper, we develop a state-space model that infers the foraging activities of fishing vessels from their tracks. Second, we link foraging activities to probabilities of tuna presence. Finally, using multivariate geostatistical interpolation (cokriging) we map the probability of tuna presence together with their estimation variances and produce a time series of indices of abundance. While the segmentation of the trajectories is validated by observers' data, the present VMS-index is compared to catch rate and proved to be useful for management perspectives. The approach reported in this manuscript extends beyond the case study considered. It can be applied to any foragers that engage in an attempt of capture when they see prey and for whom this attempt is linked to a tractable change in behavior.