surplus production model

surplus production model
Name	Surplus production model
Type	Population dynamics model
Field	Fisheries science
Introduced	1950s
Notable	Schaefer model, Fox model, Pella–Tomlinson model

surplus production model

Introduction

Surplus production models describe population-level biomass change using aggregate growth assumptions and harvest terms, originating in mid-20th century work that influenced fisheries regulation and biological assessment. Key contributors and contexts include Raymond Schaefer, Otto S. Pella, Harold B. Walford, International Whaling Commission, and early applications by national agencies such as the U.S. Fish and Wildlife Service and the International Council for the Exploration of the Sea. These models informed management decisions during events like the decline of Atlantic cod and assessments by institutions such as the Food and Agriculture Organization and the National Marine Fisheries Service.

Theoretical foundations

The theoretical foundations trace to classical logistic growth and harvest theory derived from Pierre François Verhulst and extensions by economists and biologists working in the context of resource use, including links to work by Gordon G. MacDonald and concepts employed by Hardin's tragedy of the commons proponents within institutional debates. Mathematical roots employ differential equations influenced by the logistic equation, reflecting density dependence and maximum sustainable yield concepts used in policy instruments like the Magnuson–Stevens Fishery Conservation and Management Act and discussed at fora such as the International Convention for the Regulation of Whaling. Theoretical debates involved scholars at institutions including Woods Hole Oceanographic Institution, Scripps Institution of Oceanography, and universities such as Harvard University and University of British Columbia.

Model formulations and variants

Canonical formulations include the Schaefer model (logistic-based), the Fox model (exponential density dependence), and the Pella–Tomlinson model (flexible shape parameter), each yielding distinct biomass dynamics and reference points like BMSY and FMSY used by agencies such as the National Oceanic and Atmospheric Administration and advisory panels like the International Council for the Exploration of the Sea. Variants incorporate age structure via links to methods advanced at Woods Hole Oceanographic Institution and cohort models used at Marine Stewardship Council assessments, while stochastic versions draw on techniques from Princeton University and University of Washington researchers. Multi-species and spatial extensions relate to modeling frameworks used by groups such as ICES Working Group and projects funded by the European Commission and United Nations Environment Programme.

Parameter estimation and fitting

Parameter estimation uses techniques including maximum likelihood, Bayesian inference, and least squares applied to catch, effort, and biomass indices, with software implementations developed at institutions like NOAA Fisheries and packages originating from research at Cornell University and University of Oxford. Fitting procedures account for observation error and process error using state-space frameworks influenced by work at Imperial College London and the Smithsonian Institution, while model selection criteria employ information-theoretic approaches popularized by researchers at University of Michigan and Australian Fisheries Management Authority. Diagnostic practices draw on retrospective analysis and simulation testing used by panels convened by the Food and Agriculture Organization and the World Wildlife Fund.

Applications in fisheries and resource management

Surplus production models have informed stock assessments, quota setting, and harvest control rules for stocks such as Atlantic cod, Pacific sardine, and Bluefin tuna, and have been used in management frameworks by bodies like the Northwest Atlantic Fisheries Organization, Commission for the Conservation of Antarctic Marine Living Resources, and national agencies including Fisheries and Oceans Canada. They underpin decision-support tools in regional programs such as Rebuilding Plans and international agreements including the Convention on Biological Diversity discussions where biomass reference points and MSY concepts are debated. Applied research linking models to ecosystem indicators has been advanced through collaborations with Pew Charitable Trusts and research centers such as CSIRO and Marine Scotland Science.

Limitations and criticisms

Criticisms highlight simplistic aggregation that can misrepresent age structure, recruitment variability, and trophic interactions, issues documented in reviews by World Bank fisheries projects and academic critiques from groups at Duke University and University of British Columbia. High uncertainty in parameter estimates, vulnerability to regime shifts observed in cases like the collapse of Northern cod, and sensitivity to unreported mortality have prompted scrutiny from panels convened by International Council for the Exploration of the Sea and policy debates within the European Commission. Critics advocate for precautionary approaches consistent with instruments such as the United Nations Fish Stocks Agreement.

Extensions and integrated approaches

Extensions integrate surplus production components within ecosystem models, size-structured frameworks, and multispecies management tools developed by consortia including ICES and research programs at NOAA and CSIRO. Integrated assessment models combine surplus production elements with age-structured data, stock-recruitment relationships from studies at University of Bergen and process-based submodels used in projects funded by the European Research Council. Adaptive management applications tie surplus production estimates to harvest control rules and monitoring programs implemented by agencies such as the New Zealand Ministry for Primary Industries and regional organizations like the Pacific Islands Forum.

Category:Fisheries science