Two basic parameters of MSY are BMSY, the biomass required to produce that maximum yield, and the maximum fishing mortality (FMSY) that would not overfish the stock. A more intuitive and related metric to the latter is the rate of exploitation, which can be thought of as the proportion of fish killed in a given year that are removed by fishing activities. Yet, the instantaneous rate of fishing (F) is an important estimate produced by a stock assessment and also functions as a measure of fishing effort. For commercial fishing purposes, determining the “most bang for your buck” means maxing out the relationship of catch to fishing effort, such that you understand how much effort nets you the most yield, and beyond which it would be diminishing returns. An example relationship is illustrated below.
Beyond just catch, a more refined estimate with an eye toward the “sustainable” part of MSY is yield-per-recruit (Y/R). This method calculates a curve per cohort, or age class, to better understand what selectivity maximizes the yield while protecting the recruitment class. The graph below shows what the Y/R curve looks like when the fishery is selecting for ages 1-3. The marginal yield is the increase in total yield achieved by adding one extra unit of effort. The slope of the tangent of the curve is catch per unit effort (CPUE).
As is both evident from the graph and intuitive conceptually, the steepest slope occurs when you go from no fishing (F=0) to starting to fish (F > 0). Making an assumption that when marginal yield drops off to 10% of that initial maximum CPUE is where it becomes no longer worth it, stock assessment biologists can thereby estimate the corresponding fishing rate (F0.1) as a cutoff for how much effort to expend.
https://www.wolframcloud.com/objects/demonstrations/BevertonAndHoltsYieldPerRecruitModel-source.nb