Variable Natural Mortality Rates Inflate Variance of Recruitments Estimated from Virtual Population Analysis (VPA)

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Abstract
We used a simulation model to determine whether estimates offish recruitment obtained from virtual population analysis (VPA) (1) have the correct interannual variability and (2) yield high statistical power (>0.8) when correlated with an environmental factor, given that the "true" instantaneous adult natural mortality rate (M) likely varies over time but a constant M is used in VPA (MVPA). Under such circumstances, VPA exaggerates variability in recruitment, which reduces the probability of correctly detecting environmental correlates with recruitment. The magnitude of these effects increases with increases in (1) the absolute value of the true mean M, (2) the variation in M over time, (3) the relative error in MVPA, and (4) the magnitude of MVPA relative to FL (instantaneous terminal fishing mortality rate) and decreases with increases in magnitude of the true variation of recruitment or the true correlation with the environmental factor (all else being equal). This bias is not large under most conditions, but it is likely to be more important in short-lived, high-M species than the similar but counteracting bias caused by aging errors. Sensitivity analyses can demonstrate how various MVPA values affect conclusions about environmental correlates with recruitment.