According to Graham (1939), the maximum yield that can be extracted from a wild stock is found at the half of the virgin size of that population, as seen in Fig. 1A, B. A similar view is commented by Zabel et al. (2003). After this premise, a simplistic approach can be adopted by assuming that when the catch trend shows a maximum, followed by a decline, then that

maximum yield corresponds to the half of the population size at the virgin stock. Stock assessment based upon this approach is very limited and despite that its ecological principles as background are valid, there are many factors constraining the validity of this procedure and therefore other approaches more accurate and based upon age structure have been adopted over time.

By following the former statements, a simple approach to roughly estimate the stock biomass is by just fitting a parabola to the catch records of some fisheries or regions, even deliberately ignoring a relationship of the stock density of populations, just by usually using the catch per unit of effort as an indicator of stock density. In this case, time was used as an indirect indicator of fishing effort, because the information on this variable is not easily available and because it is beyond the scope of this paper. Therefore, second degree regressions were used to several fisheries and regions just to have an idea on when the maximum yields, presumably equivalent to the Maximum Sustainable Yields (MSY), were attained. It is assumed that the stock biomass is at least twice bigger than the maximum yield attained in a certain time, and in that point is supposed that the exploitation rate E, is 50 per cent. This approach is conservative, because the intrinsic growth rate is not provided, given that many populations are involved. In the stock assessment process, the E value is usually lower than 0.5; however, by considering that many species are involved in the procedure is analysis, is likely to expect that in this collection there may be species which are overexploited, as well as others which may be underexploited. For this reason, it is reasonable to adopt a conservative criterion instead of being too optimistic assuming that the biomass could reach higher values. It is pertinent to mention that most of the regressions applied and described in the following paragraphs excepting three, provided high and significant R2 coefficients.

On being consistent with this idea, estimations of the MSY by applying a parabola were fitted to catch data of the world fisheries exploited and recorded for different regions as shown in Fig. 2 (A — F) and in Table 1. The time scale of catch extracted from FAO (2010), data goes from 1950 to 2010. It is evident that in most cases the catch has attained a maximum yield, which for practical purposes; it can be considered as equivalent to the MSY level.