Calculation of MSY

Estimation of MSY can be achieved by direct experimentation, observation of natural systems, deduction from

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Biomass as a fraction of carrying capacity — Schaefer Pella-Tomlinson

Figure 2 Yield (equal to the surplus production) as a proportion of MSY for the Schaefer and Pella-Tomlinson models. The shape parameter of the Pella-Tomlinson model is fixed so that the biomass that supports MSY is 30% of the carrying capacity.

Figure 2 Yield (equal to the surplus production) as a proportion of MSY for the Schaefer and Pella-Tomlinson models. The shape parameter of the Pella-Tomlinson model is fixed so that the biomass that supports MSY is 30% of the carrying capacity.

biological understanding, or a combination of the three. Unfortunately, many natural resource systems are not amenable to replication, the contrast in treatments is limited, or the life histories require time frames that are too great. In addition, the resource must be overfished at some stage to determine MSY and this may not be desirable. Therefore, MSY is often an uncertain quantity.

Early understanding of MSY in fisheries came from the Schaefer surplus production model, which is based on logistic population growth. This theory suggested that MSY occurs when the population is depleted to half of its carrying capacity (K) and MSY = rK/4, where r is the (intrinsic) rate of population increase when the population density is low. However, it quickly became recognized that the symmetrical production function of the Schaefer model was not consistent with the population dynamics of many fish populations. This resulted in the development of the Pella-Tomlinson surplus production model, which contains an additional parameter that allows the production function to be asymmetrical. Unfortunately, it is difficult to estimate this additional parameter for most populations (Figure 2).

Surplus production, and therefore MSY, is dependent on the life history characteristics of the population and the total available habitat. As mentioned previously, surplus production is equal to reproduction and growth less natural mortality. Surplus production models do not explicitly model these population processes, but represent them using a single function. Modern analyses use more detailed models that explicitly represent the different population dynamics processes, and also the characteristics of the fishery. These analyses often estimate that MSY occurs when the population is depleted to around 30% of its carrying capacity, but this level varies depending on the characteristics of the population and the fishery.

MSY can be estimated from a combination of two fundamental theories in fisheries science, yield-per-recruit (YPR) and the stock-recruitment (SR)

relationship. MSY is a tradeoff between maximizing YPR and ensuring there are enough recruits to provide the individuals to harvest. When individuals are young, they generally have high growth rates, and the average gain in biomass through growth for a cohort is greater than the losses due to natural mortality. As they age, growth slows and the losses due to natural mortality become greater than the gains due to growth. Theoretically, there is an age, the critical age, at which the gains due to growth equal the losses due to natural mortality. If all individuals were harvested at this age, the YPR would be maximized. However, in most situations it is not possible to catch all individuals at the critical age, so optimization of YPR is achieved through applying a minimum legal size or restriction on fishing methods (e.g., minimum mesh sizes for fishing nets).

The other component of MSY is the SR relationship. YPR only maximizes the yield based on a given number of recruits; however, as a population is depleted by fishing the potential of that population to reproduce is also affected. Generally, the fishing mortality levels required to maximize YPR will result in reduced recruitment and therefore maximizing yield requires a tradeoff between maximizing YPR and maximizing recruitment. Unfortunately, the SR relationship is often the most uncertain factor because of (1) natural variability in recruitment, (2) uncertainty in the estimates of stock size and recruitment, and (3) lack of contrast in the stock size (Figure 3).

MSY is dependent on the age or length-specific selectivity of the fishing method used. Both the YPR and the reproductive potential are influenced by the age or size of the fish that are captured. Fishing methods differ in the MSY that they can produce depending on the selectivity

Figure 3 YPR, yield, and recruitment as a proportion of their maximum realized under equilibrium fishing mortality plotted against the equilibrium biomass as a fraction of the carrying capacity. The yield decreases faster than YPR at low biomass levels because the recruitment reduces as the biomass decreases.

Figure 3 YPR, yield, and recruitment as a proportion of their maximum realized under equilibrium fishing mortality plotted against the equilibrium biomass as a fraction of the carrying capacity. The yield decreases faster than YPR at low biomass levels because the recruitment reduces as the biomass decreases.

of the fishing gear. In general, methods that catch juveniles before they can reproduce have lower YPR and lower reproductive potential, and therefore produce less MSY. Conversely, methods that catch mature individuals generally have greater YPR and greater adult biomass, and produce greater MSY. In many fisheries there are multiple fishing methods employed and the MSY will depend on the relative amount of effort allocated to each method.

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