Assessment of two octopus stocks with fluctuating dynamics in Yucatán, Mexico
The total latent productivity surplus production model can be used in multilateral and national fisheries management policies to avoid overfishing stocks
In fluctuating populations of fished stocks – typically in tropical and sub-tropical regions and characterized by having an unstable equilibrium point where any small disturbance from the equilibrium point may bring the stock to oscillating or irregular shifts – the conditions are not present for the existence of the maximum sustainable yield (MSY, the theoretically largest yield or catch that can be taken from a species’ stock over an indefinite period, and a key concept in the generation of biological reference points to harvest fish stocks sustainably).
This is because the population growth rate is constantly switching from positive to negative at regular or irregular intervals so that surplus production is followed by deficit production in a persistent cycle, and MSY requires stable zero growth rates.
A more general surplus production concept is the total latent productivity (TLP). TLP averaged over years of negative and positive productivity has been considered as a sustainable annual harvest rate for fluctuating stocks. Roa-Ureta et al. proposed to use the total latent productivity (TLP), averaged over positive and negative growth rate periods, as limit harvest rate. Because unlike the MSY, the TLP is not a constant, varying year to year following the fluctuations of stock biomass, it was proposed as a novel solution to the well-known challenges that fluctuating stocks present when trying to determine their status with reference to MSY.
The nonexistence of the MSY in fluctuating stocks raises questions for fisheries management that are currently not addressed and that may become more important as more small-scale fisheries are assessed. This is because these fisheries usually harvest short-lived stocks and coastal stocks that may be more susceptible to enter into fluctuations.
Octopus stocks are interesting case studies of fluctuating dynamics and their consequences in fishery management. Our case study, the Yucatán octopus fishery is the third-largest octopus fishery in the world, and is based on two species, the Mexican four-eyed octopus (Octopus maya) and the common octopus (Octopus americanus). Landings of both species are comparable to landings from Western Africa and China, and landings of O. maya have been increasing in recent years.
This article – summarized from the original publication (Poot-Salazar, A. et al. 2024. Sustainable fishing harvest rates for fluctuating fish and invertebrate stocks. PLoS ONE 19(9): e0307836) – reports on a study that evaluated the utility of the average TLP to estimate sustainable harvest rates in stocks with fluctuating dynamics with two commercially-exploited populations of octopus in the Yucatán Peninsula in Mexico.
Might a new aging tool help improve octopus fishery management?
Study setup
The study area was the Yucatan Peninsula, located in the eastern part of Campeche Bank, in the southeast of the Gulf of Mexico (Fig 1). The main source of data used for stock assessment was a Mexican national fisheries database from fishing vessels less than 10 tons in weight. This database covers the whole fishery and is organized by fishing trip, so it is a database with fine-grain time resolution. For data analyses, we used the hierarchical statistical model developed in Roa-Ureta et al. This is a data-intermediate method requiring weekly time series of (1) total fishing effort in any unit, (2) total catch in weight, and (3) mean weight in the catch, in a time series of many years.
The data were used to test the utility of the average TLP to estimate sustainable harvest rates in stocks with fluctuating dynamics, using a stock assessment methodology that includes time-varying dynamics in both species. The test is conducted by projecting the stock ten years into the future to show that management based on the MSY would lead to collapse of the stocks while management based on the average TLP would lead to sustainable exploitation.
For detailed information on the study design, databases and data analyses, refer to the original publication.
Results and discussion
Our results show that parameters of the population dynamics changed in both species, dividing the time series into two periods, leading from single-point equilibrium to fluctuating dynamics in one species and increased amplitude and amplitude variability in the other species. These results mean that management based on the MSY would lead to overfishing and collapse of the two stocks of octopus, as shown by stochastic projections. Conversely, the average TLP yielded much lower and realistic annual harvest rates, closer to actual landings over the 22-year period.
Both assessed octopus stocks in the Yucatán Peninsula showed fluctuating dynamics: O. maya over the entire time series and O. americanus since 2011. This latter example serves as an empirical demonstration of the main argument that we present in this work, that the average total latent productivity (TLP) should replace the MSY for stocks that have oscillating or unstable dynamics.
Stock biomass projections show that implementation of the MSY as harvest rate would lead to stock collapse in both species, after the 10-year projections in O. maya and during the 10-year projection in O. americanus (Fig. 3). Conversely, implementation of the average TLP as annual harvest rate would lead to stable biomass in O. maya and to nearly stable though declining biomass in O. americanus.
Furthermore, the projection of O. maya biomass under the TLP policy has low uncertainty while the projection of O. americanus biomass is much more uncertain, with non-negligible probability to lead to stock collapse, a consequence of the higher statistical uncertainty in estimation of parameters for O. americanus. The other landings scenarios presented in Fig. 3 lead to stable though somewhat more fluctuating and more uncertain biomass in O. maya, and steeper declines and high uncertainty in O. americanus.
Our results are relevant for the management of numerous fish and invertebrate stocks under fishery exploitation, particularly short-lived species, but also long-lived species with special biological characteristics. The MSY should be replaced as a limit harvest rate and as a generator of limit biological reference points for all fish and invertebrate stocks that are suspected to have high intrinsic rates of population growth. This may include all cephalopods, small pelagic fish, some large pelagic fish with short life and fast dynamics such as the dolphinfish and some benthic invertebrate species.
In this study we discovered changes in the dynamics of O. maya and O. americanus around the Yucatán Peninsula. The biomass of O. americanus increased substantially in the second decade of our study period, during the 2010s. It is rather uncommon that wild fish and invertebrate stocks that are harvested constantly for decades increase in biomass. Based on indirect evidence it has been hypothesized that octopus and more generally cephalopods populations have been proliferating worldwide.
In the Yucatán Peninsula, Arreguín-Sánchez has argued that global warming trends and the fisheries depletion of finfish that are competitors or predators of octopus have created more favorable environmental conditions for octopus. Incidence of the upwelling derived from the Loop Current, present during spring and summer, cools the bottom water to 20 degrees-C throughout the sampling area, which would favor the events of population aggregations and reproduction, as shown at least for O. maya, which tends to present a uniform population abundance along the coastline of the Campeche Bank and a reported preference for cold temperate waters. We did not analyze environmental variables or the abundance of finfish during our study period so an environmentally-driven expansion of O. americanus around the Yucatán Peninsula cannot be ruled out.
Overall, we conclude that average TLP is the correct sustainable harvest rates for fluctuating stocks, which may include cephalopods, other invertebrates and small pelagic fish. This more general concept of surplus production needs to be incorporated in multilateral and national fisheries management policies to avoid overfishing stocks that have fluctuating population dynamics.
Perspectives
The stocks of O. maya and O. americanus in Yucatan appear not to be overfished or undergoing overfishing although the latter is experiencing wider fluctuations in biomass in recent years. Management measures such as mandatory use of a highly selective fishing gear and closing the fishing season for half of the year are certainly contributing to sustainability, but further measures to avoid too wide fluctuations in biomass might be necessary for O. americanus.
Establishing the upper catch limit of each species as the estimated TLP for each species would have positive ecological and economic consequences. From a population dynamics point of view, Fig. 2 shows that estimated TLPs minus an offset due to statistical uncertainty would imply removals that are below the low points in biomass fluctuations, which might be termed navigating under fluctuations, in order to avoid applying excessive rates when the stock is passing through low biomass states. In the years when the stocks are passing through the high biomass states, excessive production would just remain in the ecosystem, thus contributing to higher levels of transfers through trophic chains.
The recommended limit harvest rates would also keep total landings at the level of historical landings, which makes the Yucatán fishery the third largest octopus fishery in the world, thus securing the supply of markets that provide for significant revenue to Yucatán fishers. In addition, octopus markets would be supplied with greater expected stability, as we have demonstrated that the recommended limit harvest rates are sustainable in the long term.
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Authors
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Instituto Mexicano de Investigación en Pesca y Acuacultura Sustentables (IMIPAS), Mérida, Yucatán, México
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Corresponding author
Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (CINVESTAV), Mérida, Yucatán, México -
Unidad Multidisciplinaria de Investigación, Facultad de Ciencias, Universidad Nacional Autónoma de México (UNAM), Sisal, Yucatán, México
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COBI, Comunidad y Biodiversidad, Mérida, Yucatán, México
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Instituto Mexicano de Investigación en Pesca y Acuacultura Sustentables (IMIPAS), Mérida, Yucatán, México
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Instituto Mexicano de Investigación en Pesca y Acuacultura Sustentables (IMIPAS), Mérida, Yucatán, México
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Instituto Mexicano de Investigación en Pesca y Acuacultura Sustentables (IMIPAS), Mérida, Yucatán, México
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Instituto Mexicano de Investigación en Pesca y Acuacultura Sustentables (IMIPAS), Mérida, Yucatán, México
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Independent Consultant in Statistical Modelling, Marine Ecology and Fisheries, Portugalete, Bizkaia, Spain
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