growth slows to an extent that distributions of 

 lengths from different cohorts cannot be distinguish- 

 ed. A growth curve can then be fitted to the month- 

 ly mean lengths. 



Since the analysis of Perrin et al. (1976), the sam- 

 ple of measured lengths from offshore spotted 

 dolphins has increased from about 3,500 to over 

 15,000. Consequently, we were able to analyze the 

 available data more extensively than had been done 

 previously. 



Methods 



Length measurements from all postnatal 

 specimens, made between 1968 and 1982, were used 

 in the analyses except for three specimens <68 

 cm which were judged to have been erroneously 

 identified as calves. The data were stratified 

 into eight areas based upon apparent hiatuses in 

 distribution from examination of sightings and ef- 

 fort data (Fig. 1). Areas 1 and 2 comprise the 

 southern population and areas 3-8 the northern 

 population. 



For the northern data, no consistency could be 

 found in preliminary analyses of lengths when data 

 from all areas were included. When area 3 was ex- 

 cluded, consistency was much improved. When areas 

 4 and 5 were also excluded, consistency was improved 

 further for the months of February through June 

 This indicated that there were nonseasonal or 

 seasonal but asynchronous elements in areas 3, 4, 

 and 5 at least at certain times of the year. Conse- 

 quently, in our analyses of northern data we used 

 lengths from areas 6, 7, and 8 only for February 

 through June and lengths from areas 4-8 for January 

 and July through December. A similar situation 

 occurred for the southern data where the elimina- 

 tion of area 2 improved consistency for January 

 through May. In our analyses of southern data, 

 therefore, we used lengths only from area 1 for these 

 months. 



The data were grouped in interval widths of 4 cm. 

 This gave four possible ways of grouping the data 

 because lengths were measured to the nearest whole 

 centimeter. Each of these four groupings were in- 

 vestigated, there being no reason to prefer a start- 

 ing point of the first interval as, for example, 76, 77, 

 78, or 79 cm. 



A mixture of normal distributions was fitted to 

 each data set using a version of the computer pro- 

 gram NORMSEP (Hasselblad 1966). The program 

 requires the number of distributions to be specified, 

 and this was varied in order to determine the most 

 likely number of distributions present. The model 



FISHERY BULLETIN: VOL. 83, NO. 4 



selected as most representative of the length- 

 frequency data was that which gave the highest x" 

 value, and therefore the highest probability that a 

 greater ^ value could be obtained by chance alone, 

 and also gave biologically feasible results based on 

 prior knowledge of delphinid growth. (Some model 

 fits had a very high probability of a greater ^, but 

 the mean lengths could not be accounted for by any 

 reasonable regime of growth.) 



We chose Laird's (1969) form of the Gompertz 

 (1825) growth equation to fit to the monthly mean 

 lengths. A linear model is clearly inadequate to 

 describe growth except over a very short time period. 

 We also investigated the use of the von Bertalanffy 

 (1934) growth equation but found it to be less flexi- 

 ble than the Gompertz model. 



Each model of growth was fitted to the mean 

 lengths using the midpoint of the first month as time 

 zero. In fact, this is not necessarily the time of birth 

 so we fixed time of birth by substituting our estimate 

 of length at birth into the fitted equation. Lengths 

 at age were then calculated by substituting that age 

 plus the difference between the midpoint of the first 

 month and our calculated time of birth into the fit- 

 ted equation. 



Results 



Northern Population 



Figure 4 shows, as examples, the fitted mixture 

 of normal distributions to the length-frequency data 

 for August and October. The arrows indicate the 

 positions of the means of the fitted distributions. 



Ihble 2 shows the estimates of mean length of the 

 fitted normal distributions for each month. The 

 estimates are presented so that the increases from 

 month to month can be clearly seen. The two final 

 columns of Tkble 2 are mean lengths of the two 

 distributions to the right of the length-frequency 

 plots. These mean lengths are consistent from month 

 to month. The table shows that there are actually 

 two series of mean lengths: one beginning at 86.7 

 cm in September and continuing through columns 

 2 and 4 of the mean lengths, and the other begin- 

 ning at 84.5 cm in April (the estimate of 92.7 cm for 

 March is an anomaly for which we have no explana- 

 tion) and continuing through columns 1, 3, and 5. 

 These represent two cohorts born each year about 

 6 mo apart in the spring and autumn. Note that each 

 series of mean lengths continues only for about 24 

 mo. This is because after this time growth has slow- 

 ed to an extent that it is not possible to distinguish 

 distributions of length from different cohorts. The 



558 



