Optimizing removals to control a metapopulation: application to the yellow legged herring gull ( Larus cachinnans)

Abstract

The standard one-site harvest maximization problem is extended to consider minimizing the cost associated with removing individuals from an annually increasing ‘nuisance’ or ‘pest’ population exhibiting spatial structure (i.e. a metapopulation). We investigate the problem using a linear, deterministic, multi-site matrix. A new approach for estimating the optimal harvest strategy based on sensitivity analysis, rather than linear programming is presented. We show that the optimum stage class(es) to harvest can be determined from stage/site specific reproductive values (i.e. the components of the left eigenvector), weighted by stage/site specific harvest costs. The amount of harvest that should be directed at the determined stage(s) can be estimated from sensitivities. This method is illustrated for a Mediterranean gull, the Yellow Legged Herring Gull ( Larus cachinnans). Results obtained from the sensitivity analysis method (both a ‘one-step’ approximation and an iterative Newton-Raphson algorithm) are compared with linear programming solutions. As expected, the iterative sensitivity method yields the same solutions as linear programming, while the ‘one-step’ approximation underestimates the level of harvest. Several constrained optimizations are investigated to address spatial limitations and difficulties associated with age-determination.