The transfer function method reveals how age‐structured populations respond to environmental fluctuations with serious implications for fisheries management

Fluctuations in wild fish populations result from interaction between population dynamics and environmental forcing. Age‐structured populations can magnify or dampen particular frequencies of these fluctuations, depending on life cycle and species traits. The transfer function (TF) gives a detailed analytical description of these phenomena. In this study, we derive a generalized form of TF to investigate the fluctuations of fish populations in response to species traits and environmental noise characteristics. We found that for semelparous species, fluctuations in fish stocks log‐size are directly proportional to the recruitment elasticity and inversely proportional to the age of maturity, and for iteroparous species, fluctuations in fish stocks log‐size are inversely proportional to the adult lifespan. In addition to the already known effect of cohort resonance (increased sensitivity to environmental fluctuations on cohort timescales in the elastic range of recruitment elasticity), we find a stock resonance effect (increased sensitivity to environmental fluctuations on double cohort timescales in the inelastic range of recruitment elasticity). These results were then applied to fisheries management. The relationship between fishing mortality and species‐specific variability of fish stocks was formalized. In accordance with this analysis, precautionary levels for different catches were estimated. Using the method of transfer functions, we derive general (for any lifecycle and any stock–recruitment relation) formulas describing the spectrum of population variations induced by the stochastic environment, which are then analyzed for spectral features. Our results specify the conditions for such a well‐documented phenomenon as cohort resonance, as well reveal the conditions for a previously undescribed phenomenon as stock resonance.