The effect of random and density-dependent variation in sampling efficiency on variance of abundance estimates from fishery surveys

Abundance indices (AIs) provide information on population abundance and trends over time, while AI variance (AIV) provides information on reliability or quality of the AI. AIV is an important output from surveys and is commonly used in formal assessments of survey quality, in survey comparison studies, and in stock assessments. However, uncertainty in AIV estimates is poorly understood and studies on the precision and bias in survey AIV estimates are lacking. Typically, AIV estimates are "design based" and are derived from sampling theory under some aspect of randomized samples. Inference on population density in these cases can be confounded by unaccounted process errors such as those due to variable sampling efficiency (q). Here, we simulated fish distribution and surveys to assess the effect of q and variance in q on design-based estimates of AIV. Simulation results show that the bias and precision of AIV depend on the mean q and variance in q. We conclude that to fully evaluate the reliability of AI, both observation error and variability in q must be accounted for when estimating AIV. A decrease in mean q and an increase in the variance in q results in increased bias and decreased precision in survey AIV estimates. These effects are likely small in surveys with mean q >= 1. However, for surveys where q <= 0.5, these effects can be large. Regardless of the survey type, AIV estimates can be improved with knowledge of q and variance in q.