Optimal bioeconomic management of changing marine resources by Emily Alison Moberg B.S., Massachusetts Institute of Technology (2011) Submitted to the MIT-WHOI Joint Program in Oceanography and Applied Ocean Science and Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY and the WOODS HOLE OCEANOGRAPHIC INSTITUTION September 2016 ○c 2016 Emily A. Moberg All rights reserved. The author hereby grants to MIT and WHOI permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part in any medium now known or hereafter created. Signature of author................................................................ MIT-WHOI Joint Program in Oceanography and Applied Ocean Science and Engineering Massachusetts Institute of Technology & Woods Hole Oceanographic Institution July 21, 2016 Certified by........................................................................ Dr. Michael G. Neubert Senior Scientist Woods Hole Oceanographic Institution Thesis Supervisor Accepted by....................................................................... Dr. Ann Tarrant Chairman, Joint Committee for Biological Oceanography Massachusetts Institute of Technology Woods Hole Oceanographic Institution 2 Optimal bioeconomic management of changing marine resources by Emily Alison Moberg Submitted to the MIT-WHOI Joint Program in Oceanography and Applied Ocean Science and Engineering Massachusetts Institute of Technology & Woods Hole Oceanographic Institution on July 21, 2016, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract Marine populations are increasingly subjected to changing conditions whether through har- vest or through broad-scale habitat change. Historically, few models have accounted for such trends over time, and even fewer have been used to study how trends affect optimal harvests. I developed and analyzed several models that explore, first, endogenous change caused by harvest and, second, exogenous change from factors (such as rising ocean temperatures) outside harvesters’ control. In these models, I characterized the profit–or yield–maximizing strategy when harvesting damages habitat in a multispecies fishery, when harvest creates a selective pressure on dispersal, and when rising temperatures cause changes in vital rates. I explore this last case in both deterministic and stochastic environments, and also allow the harvester to learn about unknown parameters of the stock recruitment model while harvesting. I also develop an unambiguous definition of and describe a statistical test for a shift in a species’ spatial distribution. My results demonstrate that optimal harvesting strategies in a changing environment differ in important ways from optimal strategies in a constant environment. Thesis Supervisor: Dr. Michael G. Neubert Title: Senior Scientist Woods Hole Oceanographic Institution 3 4 Acknowledgments This work was supported by NSF GRFP grant number 1122374, MIT’s Ida Green Fellow- ship, WHOI’sOceanVentureFund, andWHOIAcademicProgramsOffice. Iamalsograte- ful for travel support I received to attend the AARMS-Sustainability of Aquatic Ecosystem Networks and to the BIRS Impact of climate change on biological invasions and popula- tion distributions workshop. For Chapter 2, additional funding came from the The Seaver Institute and the National Science Foundation (OCE-1031256) through grants awarded to Julie Kellner and Michael Neubert. The co-authors of Chapter 3 received funding from The Woods Hole Oceanographic Institution’s Investment in Science Fund to MGN; The Recruitment Program of Global Experts to YL; The University of Tennessee Center for Business and Economics Research to SL; and the U.S. National Science Foundation (NSF) through grants OCE-1031256, DEB-1257545, and DEB-1145017 to MGN, CNH-0707961 to GEH, DMS-1411476 to YL. I also received incredible support during graduate school from friends and family in the form of advice and a sympathetic ear. This work would not have been possible without the loving support from my family–mom, dad, Maddy, and Amelia Rose. Thank you so much for your encouragement over the years, and for the many times you have read over drafts and listened to practice presentations. My family away from home on Cape Cod have been the New England Ballet Theatre and John Wesley United Methodist church. Being a part of these wonderful communities has been an integral part of keeping me grounded and sane while working on this thesis. Iwouldalsoliketothankmycommitteeandlab-mates, whohaveprovidedanincredible amount of support, advice, and feedback on this thesis from the nascent versions. They have also provided travel funding for conferences and collaboration; this work and my grad- uate experience would have been poorer without any of them. My lab-mates in particular answered my many questions and were great inspirations for me. Finally, I would like to thank Mr. Samilenko for inspiring my interest in environmental science and pushing me to become the best scholar I can be and to the late Mr. Malkovsky who shared his infectious love of science and encouraged me always to achieve my dreams. MIT’s Terrascope program, Dr. Jerolmack, Dr. Adams, Dr. Hemond, Dr. Linkov, and Dr. Sosik gave me invaluable introductions to research. None of this would have been possible without all of the people mentioned here, and I am eternally grateful to all of them. 5 6 Contents 1 Introduction 11 2 Bioeconomics and biodiversity in harvested metacommunities: a patch- occupancy approach 23 2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3 Patch Occupancy Framework . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4 Null Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4.1 Null Model: Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.4.2 Null Model: Diversity and Profit . . . . . . . . . . . . . . . . . . . . 35 2.4.3 Null Model: Spatial Management . . . . . . . . . . . . . . . . . . . . 40 2.5 Facilitation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.5.1 Facilitation Model: Equilibria . . . . . . . . . . . . . . . . . . . . . . 46 2.5.2 Facilitation Model: Diversity and Profit . . . . . . . . . . . . . . . . 47 2.5.3 Facilitation Model: Spatial Management . . . . . . . . . . . . . . . . 50 2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3 On the Bioeconomics of Marine Reserves when Dispersal Evolves 65 3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.4 Evolution of dispersal and the ESS . . . . . . . . . . . . . . . . . . . . . . . 71 3.4.1 Calculating the ESS . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 7 3.4.2 Convergence stability of the ESS . . . . . . . . . . . . . . . . . . . . 74 3.5 The ESOHS and effects of evolution on optimal management . . . . . . . . 75 3.5.1 Management with reserves . . . . . . . . . . . . . . . . . . . . . . . . 78 3.5.2 Is the ESOHS economically stable? . . . . . . . . . . . . . . . . . . . 78 3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4 Testing for an Unambiguous Shift in a Species Distribution 89 4.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.3.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.3.2 Statistical Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.5 Illustration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.7 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5 Optimal Harvest in a Deteriorating Environment 103 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.2 Optimal Harvest in a Constant Environment . . . . . . . . . . . . . . . . . 106 5.3 Optimal Harvest in a Deteriorating Environment . . . . . . . . . . . . . . . 108 5.3.1 Interior Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.3.2 Exiting the Fishery . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.3.3 Qualitative Behavior of Optimal Escapement Policy . . . . . . . . . 112 5.4 Example: Beverton-Holt Stock Recruitment Model . . . . . . . . . . . . . . 113 5.4.1 Increasing density-dependent mortality rate (𝜇 ) . . . . . . . . . . . 115 2 5.4.2 Decreasing fecundity (𝛼) . . . . . . . . . . . . . . . . . . . . . . . . . 115 5.5 Yield Maximizing Harvest . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.7 Appendix: Stochastic Case . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 8 6 Adaptive managment in stationary and changing environments 127 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 6.2 Stationary Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 6.2.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 6.3 Yield Maximizing Beverton-Holt Growth with Uniform, Multiplicative Shocks136 6.4 Sustainable or not? Yield Maximizing Piecewise Linear Growth Function with Multiplicative, Uniform Shocks . . . . . . . . . . . . . . . . . . . . . . 141 6.5 Non-stationary case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 6.6 Non-stationary Yield Maximizing Beverton-Holt Model . . . . . . . . . . . 146 6.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 7 Discussion 157 9 10