In 1994, (the World Conservation Union (IUCN) made new quantitative criteria for Red List Categories. Among these, criterion A is based on the reduction rate of population size and is not linked to absolute population size. This is because for most unexploited threatened species absolute population size is completely uncertain. Criterion E is directly concerned with the extinction probability within a specified period. Criterion A is applied to marine fish species, including tuna, which are exploited by commercial fishing. However, for many fish that are commercially exploited, the absolute number of mature individuals and the variance in its yearly reduction rate are often known. In addition, extinction probability depends on absolute population size. There is an inconsistency between criterion A and E when population size is large enough. This is the case for tuna. In this paper, we propose a new criterion for threatened species based on the average reduction rate and the current population size. Criterion A is consistent with criterion E as long as the population size is very small. We also propose a method for estimating the extinction risk of tuna based on the variance of the reduction rate. We investigated the sensitivity in the uncertain parameters involved in the models and concluded that tuna is unlikely to be listed as critically endangered but that southern bluefin tuna may be listed as vulnerable.
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