Estimating Deep-Sea Fish Population Density From the Odour Extension Area: A Theoretical Basis and Comparison With the Conventional Methods - Aoki, Kunihiro; Fujiwara, Yoshihiro; Tsuchida, Shinji (Frontiers in Marine Science, 2022)
Accurately estimating the population density of deep-sea fish with a baited camera system has long been a significant challenge. Although several theoretical models have been developed using the first arrival time of an individual fish or time-varying fish abundance at the bait, none of the models allows for the spatio-temporal variability of the odour plume area extending from the bait. This study shows theoretically that the population density can be formulated as the inverse of the sample mean of the odour plume area extended until it reaches a first fish under the condition that fish at rest have a random dispersion. Each area estimate is governed by the homogeneous Poisson process and, hence, its probability density follows an exponential distribution. A large uncertainty can occur for each area estimate (sample), but the uncertainty decreases as the number of samples used to derive the sample mean increases by the law of large numbers. Numerical experiments conducted in the study indicate that the proposed method for inferring population density is also potentially applicable to cases in which the fish have a uniform or large-scale clumped dispersion. The experiments also show that the conventional method based on first arrival time fails to estimate the population density for any of the dispersion cases. This study also indicates that the reliability of the most popular inference method for estimating population density from the time-profile of fish abundance at the bait site was found to depend on the extension of the odour plume area and the dispersion pattern.