DISCUSSION 



The condition that the only fish new to 

 San Pedro were those from Monterey should be 

 examined. The next port of landing south of 

 San Pedro is Ensenada, Mexico; however, no 

 samples are available for the season 1947-48. 

 If there had been samples, one should have ex- 

 amined the "1" distribution of the 1945 class, 

 since if the mean 1, there happened to be also 

 less than that at San Pedro, the change at San 

 Pedro between the two seasons could alternative- 

 ly have been due to an influx of fish from the 

 south, as well as from the north . No unique 

 solution would exist in such a situation, but if 

 one considered the fish moving only from the 

 south, the portion necessary to alter the San 

 Pedro mean as much as observed could be cal- 

 culated in the same fashion as has been done 

 here for Monterey . Similarly, offshore regions, 

 if they contained fish whose 1 was less than 

 that at San Pedro, could be responsible for the 

 decreased San Pedro mean. If the mean in all 

 outlying regions but one were greater, the one 

 region would necessarily be responsible. 



change in means would be referred to the locality 

 of tagging and that to which tagged fish moved, 

 in computing the movement on the basis of fish 

 attributes . The movement of the tagged fish 

 provides a basis for deciding where the immigrant 

 fish came from that produced the observed change 

 in fish attributes' mean. Since the analysis of 

 time changes in the mean value of fish attributes 

 can yield estimates of population movement only 

 if assumptions are made about the direction of 

 movement, the method is far more powerful if 

 tagging data for adiacent regions are available. 



SUMMARY 



One of the persistent problems of fishery 

 biology has been the determination of movement 

 of fish within a population occupying a given geo- 

 graphical area . We have proposed a method for 

 estimation of the amount of interchange between 

 sub-areas based on the time differences in mean 

 values of attributes of the fish. Since mixing is 

 a dynamic process, conclusions about its magni- 

 tude must be based upon observations taken in 

 succeeding time periods . 



Other combinations of mixing from other 

 regions are possible: the technique above re- 

 quires the condition that one region at a time be 

 considered. 



TECHNIQUES COMBINED WITH TAGGING 



If the populations are tagged, the above 

 study yields useful complementary measures of 

 population movement . The tagged fish, when 

 recovered, tell one what portion of an outside 

 area's population moves into a given area. The 

 change in the mean of the fish's attribute tells 

 one what portion of the given region's population 

 came from a given outside area. The ratio of 

 the population size in the tagged area to that in 

 the untagged but recovered area can then be 

 estimated. If P, is the proportion of fish in the 

 recovery area that came from the tagged area 

 and P„ is the proportion of fish of the tagged 

 area tnat moved from the tagged area into the 

 recovery area, then the relative population size 

 is N : /N 2 ? P2/P1 . If, further, the size of the 

 population in the tagged area is known (from tag- 

 ging and recovering there), the population size 

 in the non -tagged area can be estimated. The 



The true difference in an attribute's mean 

 between time periods of a region subject to migra- 

 tion from an adjacent area depends on both the 

 difference in means of the mixing fish and the 

 extent of the migration into the region. Providing 

 first that the migrating fish are representative 

 of the fish in the adjacent area, second, that the 

 attribute is constant with the passage of time, 

 and third, that the change in mean between years 

 may be solely attributed to mixing from a given 

 adjacent region, then a simple method of estima- 

 ting the magnitude of mixing has been presented. 

 Confidence limits for an estimate of the proportion 

 of fish in the local region that have moved from 

 the adjacent region have been written out. It is 

 important to remember that this technique will 

 not yield an estimate unless real differences in 

 the two regions' means are established. For 

 this reason consideration should be given to the 

 number of fish sampled from the regions, and 

 they should be taken in such a manner that the 

 samples are representative of the fish populations. 



The main difficulty in application of the 

 method lies in establishing the source of immi- 

 grants, and the usefulness of tagging data in this 

 regard has been described. 



32 



