In population ecology and economics, maximum sustainable yield (MSY) is theoretically, the largest yield (or catch) that can be taken from a species' stock over an indefinite period. Fundamental to the notion of sustainable harvest, the concept of MSY aims to maintain the population size at the point of maximum growth rate by harvesting the individuals that would normally be added to the population, allowing the population to continue to be productive indefinitely. Under the assumption of logistic growth, resource limitation does not constrain individuals' reproductive rates when populations are small, but because there are few individuals, the overall yield is small. At intermediate population densities, also represented by half the carrying capacity, individuals are able to breed to their maximum rate. At this point, called the maximum sustainable yield, there is a surplus of individuals that can be harvested because growth of the population is at its maximum point due to the large number of reproducing individuals. Above this point, density dependent factors increasingly limit breeding until the population reaches carrying capacity. At this point, there are no surplus individuals to be harvested and yield drops to zero. The maximum sustainable yield is usually higher than the optimum sustainable yield and maximum economic yield. MSY is extensively used for fisheries management. Unlike the logistic (Schaefer) model, MSY has been refined in most modern fisheries models and occurs at around 30% of the unexploited population size. This fraction differs among populations depending on the life history of the species and the age-specific selectivity of the fishing method.
History The concept of MSY as a fisheries management strategy developed in Belmar, New Jersey, in the early 1930s. It increased in popularity in the 1950s with the advent of surplus-production models with explicitly estimate MSY. As an apparently simple and logical management goal, combined with the lack of other simple management goals of the time, MSY was adopted as the primary management goal by several international organizations (e.g., IWC, IATTC, ICCAT, ICNAF), and individual countries. Between 1949 and 1955, the U.S. maneuvered to have MSY declared the goal of international fisheries management (Johnson 2007). The international MSY treaty that was eventually adopted in 1955 gave foreign fleets the right to fish off any coast. Nations that wanted to exclude foreign boats had to first prove that its fish were overfished. As experience was gained with the model, it became apparent to some researchers that it lacked the capability to deal with the real world operational complexities and the influence of trophic and other interactions. In 1977, Peter Larkin wrote its epitaph, challenging the goal of maximum sustained yield on several grounds: It put populations at too much risk; it did not account for spatial variability in productivity; it did not account for species other than the focus of the fishery; it considered only the benefits, not the costs, of fishing; and it was sensitive to political pressure. In fact, none of these criticisms was aimed at sustainability as a goal. The first one noted that seeking the absolute MSY with uncertain parameters was risky. The rest point out that the goal of MSY was not holistic; it left out too many relevant features. Some managers began to use more conservative quota recommendations, but the influence of the MSY model for fisheries management still prevailed. Even while the scientific community was beginning to question the appropriateness and effectiveness of MSY as a management goal, it was incorporated into the 1982 United Nations Convention for the Law of the Sea, thus ensuring its integration into national and international fisheries acts and laws.
Modelling MSY
Population growth
The key assumption behind all sustainable harvesting models such as MSY is that populations of organisms grow and replace themselves – that is, they are renewable resources. Additionally it is assumed that because the growth rates, survival rates, and reproductive rates increase when harvesting reduces population density, they produce a surplus of biomass that can be harvested. Otherwise, sustainable harvest would not be possible. Another assumption of renewable resource harvesting is that populations of organisms do not continue to grow indefinitely; they reach an equilibrium population size, which occurs when the number of individuals matches the resources available to the population (i.e., assume classic logistic growth). At this equilibrium population size, called the carrying capacity, the population remains at a stable size.
The logistic model (or logistic function) is a function that is used to describe bounded population growth under the previous two assumptions. The logistic function is bounded at both extremes: when there are not individuals to reproduce, and when there is an equilibrium number of individuals (i.e., at carrying capacity). Under the logistic model, population growth rate between these two limits is most often assumed to be sigmoidal (Figure 1). There is scientific evidence that some populations do grow in a logistic fashion towards a stable equilibrium – a commonly cited example is the logistic growth of yeast. The equation describing logistic growth is:
N t = K 1 + K − N 0 N 0 e − r t {\displaystyle N_{t}={\frac {K}{1+{\frac {K-N_{0}}{N_{0}}}e^{-rt}}}} (equation 1.1) The parameter values are:
N t {\displaystyle N_{t}} =The population size at time t
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