Deriving an Ecological Risk Assessment Criterion Concentration for Populations with Seasonal Variation: Reconsidering and Improving the Algorithm

Population-level ecological risk assessment (PLERA) for chemicals has been advocated for broader application in chemicals´ risk management. The persistence capability, indicated by the finite growth rate (lambda) of certain population is scientifically soundly founded and is an appropriate risk assessment endpoint. In accordance, the concentration by which a population vitality is so stressed that its lambda value is reduced to be one, can serve as a criterion concentration, denoted as C_lambda=1. Nonetheless, seasonal variation is desirably taken into account when deriving C_lambda=1 for better ecological relevance. This paper revisited the algorithm for C_lambda=1 derivation and proposed an improved algorithm for faster calculation. Specifically, in the algorithm, the age-structured projection matrix (namely Leslie matrix) was collapsed into a much smaller stage-structured projection matrix. The new algorithm was compared to the normal algorithm with a case study of nonylphenol on Japanese medaka (Oryzias latipes), and the simulation results suggest that the new algorithm can save computation time by around three quarters with a small underestimation of the variance and slight bias. The proposed algorithm is considered useful for a fast or screening stage of PLERA.