Relationships between the specific growth rate and the thermal-unit growth coefficient applied to cultured juvenile fish

The growth of cultured juvenile fish is usually quantified by two indexes, the specific growth rate or SGR, and the thermal-unit growth coefficient or TGC. The SGR is a relative growth index based on logarithms of body weights, and it decreases with body weight. The classical TGC is based on one-third powers of body weights and the summation of temperature over time. It can also depend on body weight, but it is possible to release this dependency by empirically adjusting the power function in its mathematical definition. These two indexes are usually presented in the same article to compare the growth attained by different groups of fish subjected to different experimental treatments. However, no formal framework linking both indexes is available for researchers up to the moment, the meanings of SGR and TGC remaining unrelated. The present work shows that the TGC of a group of fish growing at a given temperature can be expressed as a function of the SGR. In addition, the relationship between SGR and TGC here reported provides the basis to re-defined the TGC as a size-independent index with application to fish culture.