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Cattoni V, South LF, Warne DJ, Boettiger C, Thakran B, Holden MH. Revisiting Fishery Sustainability Targets. Bull Math Biol 2024; 86:127. [PMID: 39284973 PMCID: PMC11405477 DOI: 10.1007/s11538-024-01352-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Accepted: 08/26/2024] [Indexed: 09/22/2024]
Abstract
Density-dependent population dynamic models strongly influence many of the world's most important harvest policies. Nearly all classic models (e.g. Beverton-Holt and Ricker) recommend that managers maintain a population size of roughly 40-50 percent of carrying capacity to maximize sustainable harvest, no matter the species' population growth rate. Such insights are the foundational logic behind most sustainability targets and biomass reference points for fisheries. However, a simple, less-commonly used model, called the Hockey-Stick model, yields very different recommendations. We show that the optimal population size to maintain in this model, as a proportion of carrying capacity, is one over the population growth rate. This leads to more conservative optimal harvest policies for slow-growing species, compared to other models, if all models use the same growth rate and carrying capacity values. However, parameters typically are not fixed; they are estimated after model-fitting. If the Hockey-Stick model leads to lower estimates of carrying capacity than other models, then the Hockey-Stick policy could yield lower absolute population size targets in practice. Therefore, to better understand the population size targets that may be recommended across real fisheries, we fit the Hockey-Stick, Ricker and Beverton-Holt models to population time series data across 284 fished species from the RAM Stock Assessment database. We found that the Hockey-Stick model usually recommended fisheries maintain population sizes higher than all other models (in 69-81% of the data sets). Furthermore, in 77% of the datasets, the Hockey-Stick model recommended an optimal population target even higher than 60% of carrying capacity (a widely used target, thought to be conservative). However, there was considerable uncertainty in the model fitting. While Beverton-Holt fit several of the data sets best, Hockey-Stick also frequently fit similarly well. In general, the best-fitting model rarely had overwhelming support (a model probability of greater than 95% was achieved in less than five percent of the datasets). A computational experiment, where time series data were simulated from all three models, revealed that Beverton-Holt often fit best even when it was not the true model, suggesting that fisheries data are likely too small and too noisy to resolve uncertainties in the functional forms of density-dependent growth. Therefore, sustainability targets may warrant revisiting, especially for slow-growing species.
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Affiliation(s)
- Vincent Cattoni
- The University of Queensland School of Mathematics and Physics, Saint Lucia, Australia
| | - Leah F South
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- Centre for Data Science, Queensland University of Technology, Brisbane, Australia
| | - David J Warne
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- Centre for Data Science, Queensland University of Technology, Brisbane, Australia
| | - Carl Boettiger
- Department of Environmental Science, Policy and Management, University of California, Berkeley, Berkeley, USA
| | - Bhavya Thakran
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
| | - Matthew H Holden
- The University of Queensland School of Mathematics and Physics, Saint Lucia, Australia.
- Centre for Biodiversity and Conservation Science, The University of Queensland, Saint Lucia, Australia.
- Centre for Marine Science, The University of Queensland, Saint Lucia, Australia.
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Holden MH, Plagányi EE, Fulton EA, Campbell AB, Janes R, Lovett RA, Wickens M, Adams MP, Botelho LL, Dichmont CM, Erm P, Helmstedt KJ, Heneghan RF, Mendiolar M, Richardson AJ, Rogers JGD, Saunders K, Timms L. Cost-benefit analysis of ecosystem modeling to support fisheries management. JOURNAL OF FISH BIOLOGY 2024; 104:1667-1674. [PMID: 38553910 DOI: 10.1111/jfb.15741] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2023] [Revised: 03/03/2024] [Accepted: 03/15/2024] [Indexed: 06/27/2024]
Abstract
Mathematical and statistical models underlie many of the world's most important fisheries management decisions. Since the 19th century, difficulty calibrating and fitting such models has been used to justify the selection of simple, stationary, single-species models to aid tactical fisheries management decisions. Whereas these justifications are reasonable, it is imperative that we quantify the value of different levels of model complexity for supporting fisheries management, especially given a changing climate, where old methodologies may no longer perform as well as in the past. Here we argue that cost-benefit analysis is an ideal lens to assess the value of model complexity in fisheries management. While some studies have reported the benefits of model complexity in fisheries, modeling costs are rarely considered. In the absence of cost data in the literature, we report, as a starting point, relative costs of single-species stock assessment and marine ecosystem models from two Australian organizations. We found that costs varied by two orders of magnitude, and that ecosystem model costs increased with model complexity. Using these costs, we walk through a hypothetical example of cost-benefit analysis. The demonstration is intended to catalyze the reporting of modeling costs and benefits.
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Affiliation(s)
- Matthew H Holden
- School of Mathematics and Physics, University of Queensland, St Lucia, Queensland, Australia
- Centre for Biodiversity and Conservation Science, University of Queensland, St Lucia, Queensland, Australia
| | - Eva E Plagányi
- CSIRO Environment, Brisbane, Queensland, Australia
- Centre for Marine Socioecology, University of Tasmania, Hobart, Tasmania, Australia
| | - Elizabeth A Fulton
- Centre for Marine Socioecology, University of Tasmania, Hobart, Tasmania, Australia
- CSIRO Environment, Hobart, Tasmania, Australia
| | - Alexander B Campbell
- Fisheries Queensland, Department of Agriculture and Fisheries, Brisbane, Queensland, Australia
| | - Rachel Janes
- Fisheries Queensland, Department of Agriculture and Fisheries, Brisbane, Queensland, Australia
| | - Robyn A Lovett
- Fisheries Queensland, Department of Agriculture and Fisheries, Brisbane, Queensland, Australia
| | - Montana Wickens
- Fisheries Queensland, Department of Agriculture and Fisheries, Brisbane, Queensland, Australia
| | - Matthew P Adams
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Chemical Engineering, The University of Queensland, St Lucia, Queensland, Australia
| | - Larissa Lubiana Botelho
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
- Securing Antarctica's Environmental Future, Queensland University of Technology, Brisbane, Queensland, Australia
| | | | - Philip Erm
- Conservation Science Group, Department of Zoology, University of Cambridge, Cambridge, UK
| | - Kate J Helmstedt
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
- Securing Antarctica's Environmental Future, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Ryan F Heneghan
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Manuela Mendiolar
- School of Mathematics and Physics, University of Queensland, St Lucia, Queensland, Australia
- Centre for Biodiversity and Conservation Science, University of Queensland, St Lucia, Queensland, Australia
| | - Anthony J Richardson
- School of Mathematics and Physics, University of Queensland, St Lucia, Queensland, Australia
- Centre for Biodiversity and Conservation Science, University of Queensland, St Lucia, Queensland, Australia
- CSIRO Environment, Brisbane, Queensland, Australia
| | | | - Kate Saunders
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- Department of Econometrics and Business Statistics, Monash University, Melbourne, Victoria, Australia
| | - Liam Timms
- School of Mathematics and Physics, University of Queensland, St Lucia, Queensland, Australia
- Centre for Biodiversity and Conservation Science, University of Queensland, St Lucia, Queensland, Australia
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Filar JA, Holden MH, Mendiolar M, Streipert SH. Overcoming the impossibility of age-balanced harvest. Math Biosci 2024; 367:109111. [PMID: 37996065 DOI: 10.1016/j.mbs.2023.109111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Revised: 10/30/2023] [Accepted: 11/20/2023] [Indexed: 11/25/2023]
Abstract
In many countries, sustainability targets for managed fisheries are often expressed in terms of a fixed percentage of the carrying capacity. Despite the appeal of such a simple quantitative target, an unintended consequence may be a significant tilting of the proportions of biomass across different ages, from what they would have been under harvest-free conditions. Within the framework of a widely used age-structured model, we propose a novel quantitative definition of "age-balanced harvest" that considers the age-class composition relative to that of the unfished population. We show that achieving a perfectly age-balanced policy is impossible if we harvest any fish whatsoever. However, every non-trivial harvest policy has a special structure that favours the young. To quantify the degree of age-imbalance, we propose a cross-entropy function. We formulate an optimisation problem that aims to attain an "age-balanced steady state", subject to adequate yield. We demonstrate that near balanced harvest policies are achievable by sacrificing a small amount of yield. These findings have important implications for sustainable fisheries management by providing insights into trade-offs and harvest policy recommendations.
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Affiliation(s)
- Jerzy A Filar
- School of Mathematics and Physics, The University of Queensland, Australia.
| | - Matthew H Holden
- School of Mathematics and Physics, The University of Queensland, Australia.
| | - Manuela Mendiolar
- School of Mathematics and Physics, The University of Queensland, Australia.
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McGowan J, Weary R, Carriere L, Game ET, Smith JL, Garvey M, Possingham HP. Prioritizing debt conversion opportunities for marine conservation. CONSERVATION BIOLOGY : THE JOURNAL OF THE SOCIETY FOR CONSERVATION BIOLOGY 2020; 34:1065-1075. [PMID: 32424907 PMCID: PMC8129986 DOI: 10.1111/cobi.13540] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2019] [Revised: 01/30/2020] [Accepted: 03/04/2020] [Indexed: 05/28/2023]
Abstract
Incentivized debt conversion is a financing mechanism that can assist countries with a heavy debt burden to bolster their long-term domestic investment in nature conservation. The Nature Conservancy, an international conservation-based nongovernmental organization, is adapting debt conversions to support marine conservation efforts by small island developing states and coastal countries. Prioritizing debt conversion opportunities according to their potential return on investment can increase the impact and effectiveness of this finance mechanism. We developed guidance on how to do so with a decision-support approach that relies on a novel threat-based adaptation of cost-effectiveness analysis. We constructed scenarios by varying parameters of the approach, including enabling conditions, expected benefits, and threat classifications. Incorporating both abatable and unabatable threats affected priorities across planning scenarios. Similarly, differences in scenario construction resulted in unique solution sets for top priorities. We show how environmental organizations, private entities, and investment banks can adopt structured prioritization frameworks for making decisions about conservation finance investments, such as debt conversions. Our guidance can accommodate a suite of social, ecological, and economic considerations, making the approach broadly applicable to other conservation finance mechanisms or investment strategies that seek to establish a transparent process for return-on-investment decision-making.
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Affiliation(s)
- Jennifer McGowan
- The Nature Conservancy4245 Fairfax Dr #100ArlingtonVA22203U.S.A.
| | - Rob Weary
- NatureVestThe Nature Conservancy4245 Fairfax Dr #100ArlingtonVA22203U.S.A.
| | - Leah Carriere
- NatureVestThe Nature Conservancy4245 Fairfax Dr #100ArlingtonVA22203U.S.A.
| | - Edward T. Game
- The Nature Conservancy48 Montague RoadSouth BrisbaneQld4101Australia
| | - Joanna L. Smith
- Nature UnitedThe Nature Conservancy366 Adelaide Street East, Suite 331TorontoONM5A 3X9Canada
| | - Melissa Garvey
- The Nature Conservancy4245 Fairfax Dr #100ArlingtonVA22203U.S.A.
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