Model-free time series analysis detected the contributions of middle-age spawner biomass and the environment on Pacific bluefin tuna recruitment

The relationship between the biomass of Pacific bluefin tuna (PBF) spawners and the amount of recruitment (stock–recruitment relationship, SRR) is unclear. It is likely that environmental effects have masked the SRR of PBF. As the basis of constructing an effective SRR for PBF, we examined the effect of spawning biomass at different ages and the spatiotemporal patterns of environmental effects on the amount of recruitment, using a recently developed model-free nonlinear time series analysis method (empirical dynamic modelling, EDM). EDM revealed where, when, and how the environment affected the amount of recruitment. EDM also found a significant contribution of ages 8–9 spawners on recruitment dynamics and that the amount of recruitment plateaus with increase in ages 8–9 spawners. Based on knowledge obtained from EDM, we formulated several example SRRs that incorporated environmental effects (sea surface temperature). The newly developed SRR with information from EDM outperformed the SRR without this information. Finally, we interpreted the results based on preceding observational and experimental studies and discussed the potential of applying the combination of EDM and mathematical modelling towards the sustainable use of other stocks.