Optimal escapement in stage-structured fisheries with environmental stochasticity

Stage-structured population models are commonly used to understand fish population dynamics and additionally for stock assessment. Unfortunately, there is little theory on the optimal harvest of stage-structured populations, especially in the presence of stochastic fluctuations. In this paper, we find closed form optimal equilibrium escapement policies for a three-dimensional, discrete-time, stage-structured population model with linear growth, post-harvest nonlinear recruitment, and stage-specific pricing and extend the analytic results to structured populations with environmental stochasticity. When only fishing reproductive adults, stochasticity does not affect optimal escapement policies. However, when harvesting immature fish, the addition of stochasticity can increase or decrease optimal escapement depending on the second and third derivative of the recruitment function. For logistic recruitment, stochasticity reduces optimal immature escapement by a multiplicative factor of one over one plus the variance of the environmental noise. Using hard clam, Mercenaria mercenaria, as an example and assuming Beverton-Holt recruitment, we show that optimal fishing of hard clam targets the immature stage class exclusively and that environmental stochasticity increases optimal escapement for low discount rates and decreases optimal escapement for high discount rates.