Sustainable fishing harvest rates for fluctuating fish and invertebrate stocks

Abstract

Ecological theory predicts fluctuations, such as oscillations and instabilities, in populations whose dynamics can be represented by discrete-time surplus production models, whenever the intrinsic rate of population growth (r) is too high. Many fished stocks may have sufficiently high r to undergo fluctuations under fishing. The maximum sustainable yield (MSY) is the fishing harvest rate concept that underlies United Nations Sustainable Development Goals and much of national fisheries administration around the world and yet in fluctuating stocks the MSY does not exist. This is because MSY's existence necessitates stable zero growth rates and in fluctuating stocks the growth rate switches from positive to negative over regular or irregular cycles, never staying put at zero. A more general surplus production concept is the total latent productivity (TLP). TLP averaged over years of negative and positive productivity has been proposed as a sustainable annual harvest rate for fluctuating stocks. We tested this theory assessing two harvested octopus populations inhabiting the Yucatan Peninsula with a 22-years time series of data, and a two-stages stock assessment methodology, with time-varying parameters at both stages. We find that parameters of the population dynamics changed in both species, dividing the time series in 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 octopus stocks, as shown by stochastic projections. Conversely, the average TLP yielded much lower and realistic annual harvest rates, closer to actual landings over the 22-years period. 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.

Fig 1. The study area of the application examples.

The Yucatan Peninsula, fishing grounds of the Mexican octopus fishery, and main communities involved in octopus fishing (CH, Champotón; SYB, Seybaplaya; CAMP, Campeche; IAR, Isla Arena; SI, Sisal; PR, Progreso; DB, Dzilam de Bravo; RL, Río Lagartos; CY, El Cuyo). Colored shaded areas and adjacent continental shelf correspond to the Campeche Bank.

Fig 2. IAGD estimates.

Maximum likelihood estimates of parameters and two standard errors bars of intra-annual generalized depletion models selected as best fits for the O. maya and O. americanus fisheries database in the Yucatan Peninsula, Mexico. a) Natural mortality rate, b) initial abundance, c) sum of abundance inputs during the season, d) scaling (note different multipliers for each species), e) effort response, f) abundance response.

Fig 3. Exploitation rates.

Weekly instantaneous exploitation rate (100*F/(F + M)) from intra-annual generalized depletion models applied to catch, effort and mean weight data in the fisheries for O. maya and O. americanus in the Yucatan Peninsula, Mexico. The thick black line marks the 40% exploitation rate.

Fig 4. Biomass dynamics.

Biomass dynamics (green dots and lines, black lines and surrounding bands) and realized (blue bars) and sustainable annual harvest rates (TLP: total latent productivity) of two octopus species in the Yucatan Peninsula, Mexico. The arrow points to the timing set to trigger changes in parameters of the biomass dynamics, the symmetry of the production function (p) in O. maya and the carrying capacity of the environment (K) in O. americanus. CatDyn biomass are weighted by q(1/CV(Biomass))/(1/min(CV(Biomass))) where q = 0.3 and 0.15 in O. maya and O. americanus respectively, so more precise estimates appear bigger.

Fig 5. Projections.

Stochastic biomass projections of the stock of O. maya and O. americanus in the Yucatan Peninsula 10 years into the future under five landings scenarios. Uncertainty bands (light blue polygons) correspond to two standard errors above and below the mean (blue lines) over 1000 replicates of the projections. These projections are implemented with parameters and standard errors of the selected Pella-Tomlinson model of each octopus species (Table 2). MSY: maximum sustainable yield; TLP: average total latent productivity; AL: average landings over the period 2000 to 2021.

Fig 6. Spatial distribution of fishing effort.

Spatial coverage of octopus fishing events over four periods in the VMS database for octopus fishing in the Yucatan Peninsula. The top left panel shows the coverage in the pre-expansion period while the other three panels show the coverage during the post-expansion period.