Performance of stock assessments with misspecified age- and time-varying natural mortality

Natural mortality (M) in fish likely varies with age (size) and among years, and while M is often assumed constant over these factors in stock assessments, several methods have been applied to estimate age- or year-specific values. Including age- or time-varying M in stock assessments, however, may not produce less biased parameter estimates, despite the increased realism. Two generic fish populations (long- and short-lived) subject to size- and year-varying M were simulated, along with data used to fit statistical catch-at-age (SCAA) models. The SCAA models assumed M was constant, age-varying, or year-varying, and the bias in estimates of spawning stock biomass (SSB), fully selected fishing mortality (F), and recruitment was recorded. The scale and trends among years in the bias of parameter estimates were generally driven by how the true values of M varied among years and how M was treated in the SCAA model. Bias was unaffected by how fishing mortality rates varied among years. The scale and trends among years in the bias of parameter estimates were generally similar when specifying a constant M and an age-varying M in the SCAA model. Using an annually varying M in the SCAA model generally improved the scale, and reduced trends among years in the bias of parameter estimates relative to constant M and age-varying M. Trends among years in bias were generally more pronounced for estimates of SSB than recruitment for long-lived life history simulations, but the opposite was true for short-lived life history simulations. These results suggested that the biases induced by not accounting for age-variation in M are likely secondary to those caused by the misspecification of temporal trends (trend and annual fluctuations in this case) in M. More time should be dedicated to accounting for temporal shifts in M than accounting for age-variation in M. The consequences of misspecification of M may also partially depend on life history.