Roles of spatial scale in quantifying stock-recruitment relationships for American lobsters in the inshore Gulf of Maine

It is well known in ecological studies that the choice of spatial scale can influence the possibility of detecting ecological patterns and the type of patterns observed. However, this has rarely been evaluated for fish stock-recruitment (SR) dynamics. Inappropriate scales may result in failure to identify possible SR relationships, especially for species with complicated life history and stock structure and locally generated recruitment. Using American lobster (Homarus americanus) in the Gulf of Maine (GOM) as an example, we tested the hypotheses that the SR relationship is detectable only at certain spatial scales and the functional SR relationships vary with spatial scales. We estimated the SR relationship separately for American lobster in the eastern and western GOM, which have strongly differing oceanographic conditions that may result in different suitable spatial scale and SR dynamics for lobster. We analyzed data of 11 different spatial scales using a Bayesian method. The model fit and performances in the posterior predictive assessment for the SR models were convexly related to the spatial scales. The functional SR relationships differed for different spatial scale. The SR parameter estimates are negatively or concavely related to the spatial scale. The best model was found at medium spatial scale for both the eastern and western GOM, and the scale differed between the eastern and western GOM, suggesting that optimal spatial scale might be process-related. We demonstrated that the choice of spatial scale directly affected the possibility of identifying the SR relationship, the estimation of SR parameters, the type of SR relationships, and the predictive abilities of the SR models.