171 



Dr. Fox. In the current level of population or from the initial level 

 of population ? 



Mr. de la Garza. Either one? Do you estimate that to what per- 

 centage of accuracy? Within 10 percent or 25 percent? 



Dr. Fox. With the two standard errors that would be 95 percent 

 confidence limits that the current stock size is approximately plus or 

 minus 40 percent of the stock size. 



Mr. de la Garza. You allow a margin of error of 40 percent? 



Dr. Fox. That is the statistical margin of error in the estimate. 



Dr. White. There is a 95 percent chance that the true value of 

 the. stock levels will fall between those limits. If you are willing to be 

 satisfied with a lower level of chance, you could select one standard 

 error and, hence, there would be a 67* percent chance of its falling 

 between narrower limits. Statisticians usually use the 95 percent 

 confidence limit. 



Mr. Anderson. Is that what you have used, 95 percent ? 



Dr. White. We have used these estimates, yes. 

 _ Mr. Leggett. What you have said is that the maximum popula- 

 tion of the eastern spinner has been estimated from 2.2 to 2.7 million ? 



Dr. Fox. Yes. 



Mr. Leggett. Congressional counsel says original. Is there a dif- 

 ference between original and maximum? 



Dr. Fox. We assume the stock size prior to exploitation is the 

 original. 



Mr. Leggett. 2.2 to 2.7 million eastern spinners located in the 

 world ? 



Dr. Fox. No, sir, in the eastern tropical Pacific Ocean. That would 

 be eastern spinners because eastern spinners is a stock of spinner 

 dolphin found there. 



Mr. Leggett. Is that in the CYRA area? 



Dr. Fox. Some are found slightly outside. 



Mr. Leggett. How far outside the CYRA area did your study 

 entail, Dr. Fox? 



Dr. Fox. Well, the information comes from areas as far west as 

 approximately 150 degrees west longitude, a little before you get to 

 Hawaii. 



Mr. Leggett. And 150 degrees west longitude is what? It goes as 

 far as Honolulu or farther ? 



Dr. Fox. It is getting within a few degrees of Hawaii on a vertical 

 plane. 



Mr. Leggett. That is north and south? 



Dr. Fox. Yes. 



Mr. Leggett. Dr. Fox, how do you effect that estimate? 



Dr. Fox. We estimated current stock levels, and then by the use 

 of a model of the response of the population to exploitation, by the 

 use of the current net reproductive rate, and by the estimates of 

 fishing mortality for previous years, we are able to start with the 

 current population size and back calculate what the original stock 

 size was. 



Mr. Leggett. All right. 



So you had no original information as to what the stock was in 

 the area? 



