236 



Fishery Bulletin 102(2) 



Calf deficit 



As described in Archer et al. (2001), the calf deficit (D) 

 in each set was calculated by subtracting the number of 

 calves (iV ca ;J from the number of lactating females (N [ac ). 

 If this value was zero or less, then D was set to zero to 

 indicate that there were enough calves to account for all 

 lactating females killed ( Fig. 1 1, 



D- 



if7V„„<iV„ i;/ - 



(10) 



We calculated three deficit-based fractions: 1) the mean 

 deficit per set (D s ); 2) the mean deficit per dolphin killed 

 (D k ); and 3), the mean deficit per lactating female killed 

 CD,): 



D 



D, = 



D,= 



1° 



ObsSets 



ObsKill 



!*> 



EstLacKill 



(11) 



(12) 



(13) 



where ZD = the total observed calf deficit in each year; 

 ObsSets = the number of observed sets used in the 

 analysis, including those sets without a 

 dolphin kill; 

 ObsKill = the number of dolphins killed in the observed 

 sets; and 

 EstLacKill = the total estimated number of lactating 

 females killed. 



The above analysis was conducted each year. Estima- 

 tion error was evaluated with 20,000 bootstrap replicates 

 for each year. For each replicate, the sets within that year 

 were randomly resampled. The frequency tables F ni . and 

 Flac t were also recalculated by resampling the list of bio- 

 logical specimens. The parameters for the weaning model, 

 P(milk) a , were estimated again by resampling the 29 

 calves and by fitting the logistic model to the new data set 

 as described in Archer and Robertson (in press). All resa- 

 mpling was done with replacement. N ral p N lac , and D were 

 estimated as described above for each set, and D s , D h , and 

 Dj were calculated for the replicate. The 95°; confidence 

 intervals for Af n// , N lac , D, D s , D k , and D/ were estimated 

 from the 2.5'; and 97.5% quantiles of the distributions of 

 the bootstrap replicate values. 



The total calf deficit (D total ) was estimated as the deficit 

 per dolphin killed (D k ) multiplied by the total number of 

 dolphins killed [N kiUed ) by stock each year, 



For the period 1973-84, annual values of N hlllcil for each 

 stock were provided by the IATTC (Joseph 2 ). For 1984-90 

 and 1996-2000. values were published by IATTC (2002). 

 In the bootstrap estimation of the 959? CI around D lntal , for 

 the 1973-90 period, each replicate was randomly sampled 

 from a normal distribution by using the estimated total 

 kill standard error. For 1996-2000, the total kill was 

 reported to be exact; therefore the total kill was used 

 without variance in all replicates. 



D 



total 



D l; * N kmd 



(1 li 



- Joseph. J. 1994. Letter of September 6 to Michael Tillman. 

 2 p. Southwest Fisheries Science Center. 8604 La Jolla Shores 

 Dr., LaJolla. CA 92037. 



