Because it uses a simple empirical formula, the TOFA method has been widely applied for inferences regarding population density ( Yau et al., 2001 Premke et al., 2006 Linley et al., 2017 Devine et al., 2018). One approach is to use an empirical relation between population density and the “time of first arrival” (TOFA), that is, the elapsed time between the landing of the baited camera system and the arrival of the first fish at the bait ( Priede and Merrett, 1996). Multiple efforts have been made to develop a method for estimating population density from two general perspectives. However, the former method is infeasible in the deep sea and the latter carries the risk of damaging the ecosystem around the sea floor ( Bailey et al., 2007).Ī baited camera system, consisting of a lander equipped with bait and a camera, is seen as a promising means to conduct an efficient census of fish populations leading to a further evaluation of fish diversity or community composition (e.g., Cappo et al., 2003 Jamieson, 2016). Similarly, various approaches have been used for estimating fish in the ocean, including underwater visual census (e.g., Caldwell et al., 2016) and trawl sampling ( Fitzpatrick et al., 2012 Johnson et al., 2013). These methods include quadrat, removal, and mark-recapture approaches (e.g., Molles, 2015). Various methods have been used to estimate population density, mainly targeting living creatures on land and in rivers. Estimating the abundance of higher predators as well as endangered, low fecundity, and commercial species in the deep sea is especially crucial to sustaining the vulnerable deep-sea ecosystem ( Norse et al., 2012 Watson and Morato, 2013 Clark et al., 2016 Nielsen et al., 2016 Fujiwara et al., 2021a). The accurate estimation of population density is necessary for a precise understanding of the population dynamics of constituent species, the level of diversity, and the underlying ecosystem, all of which vary in response to surrounding environmental changes. 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. 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. 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. 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. Each area estimate is governed by the homogeneous Poisson process and, hence, its probability density follows an exponential distribution. 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. 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.
![clumped dispersio clumped dispersio](https://image.slidesharecdn.com/ch-130728100621-phpapp01/95/apes-ch-5-part-2-9-638.jpg)
![clumped dispersio clumped dispersio](https://biologybrains.weebly.com/uploads/5/9/1/1/59119249/4502843_orig.jpg)
![clumped dispersio clumped dispersio](https://image.slidesharecdn.com/populationecology2014-140815081451-phpapp01/95/population-ecology-2014-7-638.jpg)
Kunihiro Aoki 1*, Yoshihiro Fujiwara 2 and Shinji Tsuchida 2