1.Protected and managed species, including harvested fishes, exhibit spatial and temporal variation in their distribution and productivity. Spatio‐temporal variation can arise from differences in habitat quality, human impacts (including harvest), density‐dependent changes in per capita productivity, as well as individual movement. Human impacts (e.g. direct harvest) also vary spatially and over time, and monitoring the overlap between impacts and population distribution is necessary to ensure that human impacts are sustainable and to prioritize research and management for populations that are heavily impacted. However, estimating spatio‐temporal variation in human impacts and population dynamics while accounting for individual movement has remained computationally challenging for decades.2.We developed a spatial population growth (also known as ‘surplus production’) model that is inspired by finite element analysis, which estimates spatio‐temporal population dynamics given density‐dependent population regulation, individual movement and spatially explicit harvest. We demonstrate the method using data for big skate Raja binoculata in the California Current from 2003 to 2013 and demonstrate that results can be processed to estimate an upper limit on sustainable harvest (an ‘overfishing limit’). We also conduct a simulation experiment to explore the small‐sample properties of parameter estimates. 3.A simulation experiment confirms that real‐world sample sizes are sufficient to estimate the sustainable harvest level within 20% of its actual value. However, sample sizes are likely insufficient to reliably estimate movement rates.4.The spatial population growth model estimates an overfishing limit of 740–890 metric tonnes for big skate from 2010 to 2013, compared with annual harvest <100 tonnes. This suggests that recent harvest of big skate is likely sustainable, and sensitivity analysis confirms that this conclusion is robust to different potential rates for individual movement.5.Synthesis and applications. We recommend that spatio‐temporal population models be used across systems and taxa to monitor the spatial overlap between species distribution and human impacts. For big skate, we recommend management rules triggering additional data collection and assessment effort if harvest rates substantially increase. We also recommend future research regarding spatial management regulations for emerging fisheries. |
