Size structure, not metabolic scaling rules, determines fisheries reference points

Impact assessments of fishing on a stock require parameterization of vital rates: growth, mortality and recruitment. For data-poor' stocks, vital rates may be estimated from empirical size-based relationships or from life-history invariants. However, a theoretical framework to synthesize these empirical relations is lacking. Here, we combine life-history invariants, metabolic scaling and size-spectrum theory to develop a general size- and trait-based theory for demography and recruitment of exploited fish stocks. Important concepts are physiological or metabolic scaled mortalities and flux of individuals or their biomass to size. The theory is based on classic metabolic relations at the individual level and uses asymptotic size W as a trait. The theory predicts fundamental similarities and differences between small and large species in vital rates and response to fishing. The central result is that larger species have a higher egg production per recruit than small species. This means that density dependence is stronger for large than for small species and has the consequence that fisheries reference points that incorporate recruitment do not obey metabolic scaling rules. This result implies that even though small species have a higher productivity than large species their resilience towards fishing is lower than expected from metabolic scaling rules. Further, we show that the fishing mortality leading to maximum yield per recruit is an ill-suited reference point. The theory can be used to generalize the impact of fishing across species and for making demographic and evolutionary impact assessments of fishing, particularly in data-poor situations.