234 



Fishery Bulletin 102(2) 



calf sizes. Because of this approach, it was not possible to 

 derive a single estimate of the number of missing calves 

 or to extrapolate their estimate to sets not used in this 

 analysis. 



In the current study, we present a different method of 

 estimating the number of missing calves in each set where 

 offshore spotted dolphins (S. attenuate! attenuata) were 

 killed. For brevity, we call the shortage of calves in the kill 

 in relation to the number of lactating females in the kill 

 the "calf deficit." We examined the western-southern and 

 northeastern offshore stocks separately according to the 

 geographic boundaries described by Dizon et al. (1994). 

 As they age, spotted dolphins change color through five 

 color phases (Perrin, 1970). We used the color-phase 

 frequency distribution of the kill in conjunction with age- 

 and color-based frequency distributions from a sample of 

 the kill to estimate the total number of missing calves in 

 each stock, along with confidence intervals derived from 

 bootstrap replications. This method also allowed us to 

 examine the calf deficit from sets in recent years from 

 which we did not have biological samples and to examine 

 the time series of available years for evidence of a trend 

 in the calf deficit. 



Methods 



Since 1973, observers have been randomly placed on tuna 

 purse-seine vessels. For each spotted dolphin killed during 

 an observed set, observers attempted to record the sex and 

 the color phase of the dolphin ( neonate, two-tone, speckled, 

 mottled, and fused, see Perrin, 1970). From the National 

 Marine Fisheries Service (NMFS) set log database, we 

 obtained the number of northeastern and western-south- 

 ern offshore spotted dolphins (by gender and color phase) 

 killed in every observed set from 1973 to 1990. The Inter- 

 American Tropical Tuna Commission (IATTC) provided 

 the same data from 1996 to 2000. 



Proration 



In each set, color phase or gender (or both) may not have 

 been recorded for some dolphins. Assuming that the distri- 

 bution of the demographic composition of this missing data 

 is equivalent to the overall demographic composition of the 

 kill, we allocated the number of dolphins cf unknown color 

 phase (nu) to unknown gender in each color phase (jigu) 

 according to the following formula, 



ngu : = ngu, + 



N. 



I", 



(1) 



where c = one of the five color phases (neonate to fused I; 

 N c = the total number of dolphins in each color 

 phase in the entire data set; and 

 ngu\. = the new number of dolphins in each color phase 

 where gender is unknown, including the indi- 

 viduals of prorated unknown color phase 



The number of male (nm' c ) or female (nf' c ) dolphins in a 

 color phase was calculated as 



nm,. = nm + 



ngu,  



Nm. 



Nni + Nf\ j 



nf c '=nf t + 



ngu 



w 



Nm c +Nf r 



(2) 



(3) 



where Nm c and Nf c are the total number of males and 

 females, respectively, observed in that color phase in 

 the entire data. Table 1 gives the sample size of sets for 

 both stocks by year, as well as the fraction of the kill of 

 unknown gender and color phase that were prorated as 

 described above. 



Number of suckling calves 



As time permitted, NMFS observers would also collect 

 biological data from a subset of the kill. For this study, 

 we used ages estimated from teeth collected for a study of 

 spotted dolphin growth and reproduction (Myrick et al., 

 1986 ). The specimens used were a random sample of all 

 male and female spotted dolphins collected between 1973 

 and 1978 for which total body length was recorded and 

 teeth were collected. However, additional specimens with 

 lengths less than 150 cm were selected in order to match 

 as closely as possible the length distribution of the aged 

 sample to the underlying length distribution of the spotted 

 dolphins in the kill. This was necessary because observ- 

 ers did not generally collect teeth from smaller, younger 

 animals. Later, another sample of female spotted dolphins 

 was selected from specimens collected in 1981. Specimens 

 were aged as described in Myrick et al. ( 1986 ). 



The final data set used in our analyses included age 

 estimates for 1094 female spotted dolphin specimens and 

 798 male specimens. Of these, 649 females and 457 males 

 belonged to the northeastern stock and had color phase re- 

 corded. These 1 106 dolphins were used to generate the age 

 frequency distribution for each color phase (F , Table 2). 



(4) 



'""Is,, 



where S ac = the number of samples of age a in color phase c. 



The oldest age recorded was 36 years. 



To derive an age distribution for the dolphins killed in 

 each tuna set, we estimated the number of dolphins in each 

 age class (n a ) as 



»,,=x^„ 



i 5) 



where n' 



the sum of nm' c and «/' (the number of males 

 and females in each color phase after prora- 

 tion from Equations 2 and 3). 



