Appendix A. (A) Details for assessing the persistence of a population with an integrodifference model and a discussion of the effect of the harvesting function on population persistence, (B) details for assessing population persistence with separable dispersal kernels, (C and D) derived expressions for the critical harvesting rate and rate of environmental shift for Gaussian and sinuosoidal dispersal kernels, (E) derived approximate expressions for these critical rates, (F) parameterized...

(A) Details for assessing the persistence of a population with an integrodifference model and a discussion of the effect of the harvesting function on population persistence, (B) details for assessing population persistence with separable dispersal kernels, (C and D) derived expressions for the critical harvesting rate and rate of environmental shift for Gaussian and sinuosoidal dispersal kernels, (E) derived approximate expressions for these critical rates, (F) parameterized model for black rockfish (Sebastes melanops) in the California Current and demonstrated results for parameters, and (G) details on differences between small and large MPA simulations.