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ng (or mark-recapture) studies generally require the assumption that tagged and untagged individuals (of a particular demographic group) are equally likely to be captured. For tuna, this usually translates into the assumption that tagged fish released from a relatively small region (selected for logistical reasons) mix rapidly over a much broader region of interest. In this paper, we apply the Comparison of Paired Recovery Distribution (CPRD) analysis to skipjack (Katsuwonus pelamis), yellowfin (Thunnus albacares) and bigeye tuna (Thunnus obesus) from large-scale tagging programmes in the Western Pacific and Indian Oceans. The CPRD analysis uses chi-square and nearest neighbour permutation statistical tests to calculate the probability that two tag recovery distributions from different release events are drawn from the same spatial distribution. The release events were separated in space and/or time and recovered in the same time window. If there is evidence that the two recovery distributions differ, it follows that tags from the two release events are not fully mixed with each other, such that at least one would also not be mixed with the untagged population either. Recovery events were defined with spatial boundaries corresponding to the most recent stock assessments, and analyses were restricted to release areas that were entirely within the recovery region. In the WCPO, there was strong evidence of incomplete mixing for 5 quarters following release for skipjack and yellowfin tunas and 1 quarter for bigeye tuna. For all 3 species, the observed periods of incomplete mixing is clearly a minimum, as there were insufficient observations to make inferences with respect to longer periods at liberty. In the Indian Ocean, there is strong evidence for incomplete mixing for skipjack for 3 quarters following release, 2 quarters for yellowfin and 1 quarter for bigeye. In contrast to the WCPO, useful numbers of CPRD events of longer duration were identified but did not show consistent compelling evidence of incomplete mixing. The difference between the Pacific and Indian Ocean results may reflect genuine characteristics of mixing rates (e.g. tuna in archipelagic waters seem to migrate shorter distances on average that tuna in oceanic waters). However, the failure to detect incomplete mixing in the Indian Ocean may also reflect methodological limitations arising from the opportunistic nature of tag observations (e.g. the spatial distribution of Indian Ocean tag releases and recoveries was more restricted than in the WCPO). We expect that the mixing problem is serious enough to potentially introduce large biases to at least some of these stock assessments, but the magnitude of the biases may not be easy to quantify.
