Trends in Fishing Mortality Rate along with Errors in Natural Mortality Rate can cause Spurious Time Trends in Fish Stock Abundances Estimated by Virtual Population Analysis (VPA)

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Abstract
Many researchers have reported biases in estimates offish abundance reconstructed by virtual population analysis (VPA). We document that VPA can produce changing levels of bias through time, thereby creating spurious time trends in recruitment and stock biomass estimates. We generated catch data from empirically based simulations of nine fish populations, estimated abundances using VPA with a deliberately mis-specified natural mortality rate, M, and compared the estimates to the models' "true" abundances. A period of increasing fishing mortality rate, F, combined with an overestimate of M produced spurious decreasing time trends in estimated abundance and recruitment, even when the true time series of F was known. Analogously, an underestimate of M led to a spurious increasing time trend. Bias was increased by a higher true M, and (for a given total change in F) by a slower increase in F. Because field estimates of M are uncertain and trends in F are common, some apparent trends (or lack of them) in abundances reconstructed by VPA may be artifacts. Therefore, inferences about the results of past management actions and about physical or biological effects on variability in recruitment must be made cautiously when VPA estimates are used.