NOAA Technical Memorandum NMFS-F/NWC-198 Determining Minimum Viable Populations under the Endangered Species Act by Grant G. Thompson National Marine Fisheries Service Alaska Fisheries Science Center Resource Ecology and Fisheries Management Division 7600 Sand Point Way NE, Bin C15700 Seattle, WA 98115-0070 June 1991 U.S. DEPARTMENT OF COMMERCE National Oceanic and Atmospheric Administration National Marine Fisheries Service

The Northwest Fisheries Science Center of the National Marine Fisheries Service, NOAA, uses the NOAA Technical Memorandum NMFS series to issue informal scientific and technical publications when complete formal review and editorial processing are not appropriate or feasible due to time constraints. Documents published in this series may be referenced in the scientific and technical literature.

The NMFS-NWFSC Technical Memorandum series of the Northwest Fisheries Science Center continues the NMFS-F/NWC series established in 1970 by the Northwest & Alaska Fisheries Science Center, which has since been split into the Northwest Fisheries Science Center and the Alaska Fisheries Science Center. The NMFS-AFSC Technical Memorandum series is now being used by the Alaska Fisheries Science Center.

Reference throughout this document to trade names does not imply endorsement by the National Marine Fisheries Service, NOAA.

This document should be cited as follows:

Thompson, G.G. 1991. Determining Minimum Viable Populations under the Endangered Species Act. U.S. Dep. Commer., NOAA Tech. Memo. NMFS F/NWC-198. 78 p.

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Conservation biologists have typically viewed population viability as a stochastic phenomenon. Although many factors can influence population viability, this paper focuses on the role of population size. More specifically, the paper addresses the "minimum viable population" question: As population size decreases, at what point does the risk of extinction become unacceptably high? In addition, the paper provides recommendations for conducting population viability analyses pursuant to petitions filed under the Endangered Species Act (ESA).

Three general techniques of population viability analysis are reviewed: rules of thumb, analytic approaches, and simulation approaches. Rules of thumb prescribe single "safe" levels of abundance. Analytic approaches give explicit solutions for quantities such as effective population size, mean time to extinction, and the probability of extinction as a function of time. Simulation approaches provide a flexible method for estimating nearly any quantity of interest.

All three approaches are shown to have advantages and disadvantages. The value of any particular approach is likely to vary from case to case, depending on data availability and other factors. In general, it is advisable to make use of as many methods as possible, recognizing the strengths and weaknesses of each.

Introduction

Overview of Approaches to Population Viability Analysis

Discussion

Acknowledgments

Citations

Appendix A:

Evaluation of Nominal and Expected Utilities From a Minimum Viable Population

Appendix B:

Elasticity of Expected Extinction Time in a Special Case of the Birth-and-Death Process Mode

The following individuals provided helpful comments on an earlier draft of the manuscript: Nic Bax (Pentec Environmental), Jim Berkson (Columbia River Inter-Tribal Fish Commission), Mitch Friedman (Greater Ecosystem Alliance), Jim Lannan (Oregon State University), Bruce Marcot (U.S. Forest Service), Ben Sandford and Robin Waples (National Marine Fisheries Service), and Hal Weeks (Oregon Department of Fish and Wildlife).

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