BAYLIFF: INTEGRITY OF SKIPJACK TUNA SCHOOLS 



X"/df values do not appear to decrease consistent- 

 ly with time, as would be expected if the fish tend 

 to mix gradually with time. If, however, only the 

 values corresponding to date of release-month of 

 recapture strata with more than 10 tag returns are 

 considered the x"/df values tend to decrease with 

 time. The x~ values corresponding to these strata 

 are summed at the bottoms of the first five sections 

 of Table 6, and these sums are divided by the sums 

 of the degrees of freedom to obtain total x"/df 

 values. It can be seen that these also tend to 

 decrease with time. In addition, the x" values and 

 degrees of freedom for the strata with more than 

 10 tag returns for all the experiments are summed 

 in the last section of Table 6; the x"/df values again 

 tend to decrease with time. It thus appears that the 

 fish were gradually mixing as time passed. 



One thousand Monte Carlo simulations were run 

 for each stratum with more than 10 tags, using com- 

 puter program MONTCARL, to determine the prob- 

 ability of obtaining an equal or greater value of 

 X-/df, if the tagged and untagged fish were ran- 

 domly mixed with one another. The results are 

 shown in the last column of Table 6. In most cases 

 these indicated that the tagged and untagged fish 



were not randomly mixed. These data tend to in- 

 dicate less rapid mixing with time than do the data 

 for the Chi- square contingency tests. 



DISCUSSION 



There is a fundamental difference between the 

 two methods. The Chi-square contingency tests test 

 whether the tagged fish occurred in many or few 

 of the schools, whereas the binomial tests test 

 whether the ratios of tagged to total fish are con- 

 sistent among schools. For example, if there was 

 a total of 15 returns of tagged fish obtained from 

 15 different sets from a total of 20 25-ton sets and 

 20 1-ton sets, it would make no difference for the 

 Chi-square contingency tests which sets the tagged 

 fish occurred in. For the binomial homogeneity tests, 

 however, the x'/df value would be much greater 

 if the tagged fish occurred in 15 of the 20 1-ton 

 sets than if they occurred in 15 of the 20 25-ton 

 sets. 



The Chi-square contingency tests are adversely 

 affected by the small numbers of tag returns, which 

 makes them rather low powered. For example, for 

 the releases of 19 June 1962, and 28 June 1963, 



Table 6. — Results of binomial homogeneity tests with skipjack tuna tag return 



data. 



639 



