Sustainable fishing harvest rates for fluctuating fish and invertebrate stocks.

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.