Tradeoffs between bias, robustness, and common sense when choosing selectivity forms

Selectivity, as a combination of gear vulnerability and fish availability, can be modeled in age-structured assessment models with simple functions that range from those that employ a small number of parameters to those that use complex and highly parameterized functions. We conducted simulations across two life history types to test whether allowing more complicated selectivity forms is both estimable and justified when compared to simpler selectivity curves with a lower number of parameters. Operating models were constructed with asymptotic and dome-shaped fishery and survey selectivity and estimation models were evaluated that used a range of complexity in fishery selectivity from the 2-parameter logistic to the highly parameterized double normal function. Results indicated that in general, uncertainty and bias in final year spawning biomass was not consistent across the life history types, the parameterizations employed, or fishing to the left or right side of the maturity curve. For instance, estimating a dome shaped selectivity for the survey when the true selectivity was asymptotic did not result in positive bias in all cases, and, estimating asymptotic fishing selectivity was not always conservative. Overall, we find that more complex selectivity functions and even time-dependent parameterizations of selectivity may be robust for short-lived species, but may not be robust when applied to long-lived species.