Simulation of the Population-Level Responses of Fish to Hypoxia: Should We Expect Sampling to Detect Responses?

Abstract

Our ability to use monitoring data to quantify the effects of hypoxia at the population level for fish remains elusive. We performed a simulation analysis similar to a power analysis to determine the probability that sampling would detect a known hypoxia effect on croaker recruitment for the northern Gulf of Mexico. We used 100 years of simulated annual recruitments of croaker from a population dynamics model under normoxic and hypoxia conditions to establish a credible magnitude of population response to historical hypoxia conditions. We also analyzed long-term monitoring data to determine realistic interannual variation in recruitment and used the fitted lognormal distributions to add variability to each year’s recruitment value from the population model. Segments of the two time series were randomly selected as 5-, 10-, and 25-year sequences of continuous years, variability added to the recruitment values, and then a t-test used to determine whether the known hypoxia effect would have been detected. Under field-estimated sampling variability, and 25 years of sampling with a generous cutoff p-value for detection of 0.1, there was still only a 50% chance of properly detecting the roughly 20% reduction in average croaker recruitment. Shorter time samples and use of the 0.05 cutoff resulted in lower probabilities of detection. When we artificially reduced the variability generated from the lognormal distributions, the probabilities of detection increased as expected and under the best conditions approached 85%. Despite the low probability of detecting the hypoxia effect with sampling, a 20% reduction in long-term average recruitment would be considered by most to be an ecologically significant impact.