# The missing theoretical part - influence of the stock efficiency in yield maximization, using Bluefin tuna as an example

The feed conversion ratio (FCR) or its reciprocal, the feed efficiency ratio (FER), is currently used to estimate the feed requirements in aquaculture. This has a serious disadvantage. The FCR is a function of feeding rate, initial and final mass at fattening, temperature and quality of feed. Therefore, the FCR is specific for any combination of these parameters and has to be adjusted whenever a parameter has changed. The feed costs and the fattening time influence the total costs significantly - a precise analysis of the relationships is necessary. For this purpose, the FER is divided into a feed efficiency factor, describing the assimilated percentage of consumed feed and a fish efficiency function, describing the percentage of assimilated food used for growth. The equation for the fish efficiency is derived from a novel growth equation, which involves the relationship between assimilation rate and mass growth. In a further step, an equation for the economic feed conversion ratio (eFCR) was derived. While doing this, it was noticeable that many relationships are already known. Aquaculture facilities can be regarded as ecosystems. It is obvious that corresponding equations should be used, and so the Beverton and Holt yield-per-recruit model and a very similar assimilated-food-per-recruit model were used for the calculations. It has been found that FCR is a special case of eFCR for M = 0 y-1, therefore the term FCR is sufficient. The numerical relationships are illustrated by the example of Bluefin tuna. The production of biomass by fishing is compared with the biomass production in aquaculture facilities. The competition for food is compared, as the feed for wild and farmed fish comes from the same ecosystem. Similar to the FCR, the faecal loss ratio (FLR) and the non-faecal loss ratio (NLR) are derived. These functions can be used to compute the quantities of waste products while fattening. Even if aquaculture has a bad reputation in the press, the biomass production by aquaculture is superior to the biomass production by fishing except for the workload. Finally, an important hint. The considerations presented here provide a closed theoretical picture. However, since the measurements of individual parameters are extremely difficult and error-prone, practical evidence and experiments are still lacking. The usefulness of the model will be proven hopefully by the use of the results in practice. The risk of errors can be minimized by crosschecking with other models.

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