This logistic model of growth is produced by a population introduced to a new habitat or with very poor numbers going through a lag phase of slow growth at first. Once it reaches a foothold population it will go through a rapid growth rate that will start to level off once the species approaches carrying capacity. The idea of maximum sustained yield is to decrease population density to the point of highest growth rate possible. This changes the number of the population, but the new number can be maintained indefinitely, ideally.
MSY is extensively used for fisheries management. Unlike the logistic (Schaefer) model, MSY in most modern fisheries models 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.
Unfortunately errors in estimating the population dynamics of a species can lead to setting the maximum sustainable yield too high (or too low). An example of this was the New Zealand Orange roughy fishery. Early quotas were based on an assumption that the orange roughy had a fairly short lifespan and bred relatively quickly. However, it was later discovered that the orange roughy lived a long time and had bred slowly (~30 years). By this stage stocks had been largely depleted.