MEASUREMENT OF POPULATION MOVEMENT BY OBSERVATION OF 

 MERISTIC OR MORPHOMETRIC CHARACTERS 



By 



T. M. WidrigA/ 



and 

 Bruce A . Taft-/ 



INTRODUCTION 



When the general appearance of the 

 individual fish in the catch in a particular re- 

 gion suddenly changes in a short period of time, 

 clearly the populations fished have changed 

 composition. That is, new, different -looking 

 fish have moved into the region from somewhere 

 outside it, during the time that the change in 

 appearance took place. By measuring the char- 

 acters in which change is observed, it is possible 

 to state, under certain conditions and within 

 sampling limits, what percentage of the changed 

 population came from elsewhere. (The popula- 

 tions referred to will be defined ordinarily as 

 those fish in a given area at a given time; they 

 are not necessarily genetically specified popula- 

 tions.) 



Tag return data yield a complementary 

 measure of movement; the percentage of the 

 population in one region that moved to another 

 region . Both techniques depend upon a certain 

 lapse of time between observations, and the 

 percentage amounts in both cases are rates of 

 movement or exchange . They can therefore be 

 expected to vary with the length of the time in- 

 terval, and also at different time periods. 



In brief, we wish to propose a method 

 whereby the amount of mixing of two different 

 fish populations can be measured. (It is im- 

 portant to note that no judgment is made about 

 the nature, genotypic or phenotypic, of the dif- 

 ferences observed. This is a separate problem 

 whose solution depends on a different kind of 

 information.) We will give a hypothetical ex- 



1/ Analytical Statistician and 2/ Statistician, 

 South Pacific Fishery Investigations, U. S 

 Fish and Wildlife Service, P.O. Box 271, 

 La Jolla, California . 



ample and discuss the general application of the 

 method, including sampling and confidence 

 limits. An actual example will be drawn from 

 Pacific sardine data . Finally, the benefits of 

 combining this method with a tagging experiment 

 are mentioned. 



A SIMPLIFIED HYPOTHETICAL EXAMPLE 



Let there be two adjacent regions in- 

 habited by a certain species of fish of a single 

 year -class. Let the mean value of a certain 

 meristic character of the fish be different in the 

 two areas at a given time . Let the distribution 

 of this character in these two populations over- 

 lap considerably. 



Now let a certain number of fish in 

 Region A move into Region B within a certain 

 time, say a year. The mean value of the char- 

 acter in question will not have changed in 

 Region A, but it will have changed in Region B; 

 it will have shifted toward the mean value in 

 Region A. The amount of this shift is complete- 

 ly dependent upon two things: First, the per- 

 centage of fish now (in the second year) in Region 

 B that came from Region A, and, second, the 

 amount of the difference in means in the first 

 year between the two regions . To simplify the 

 expression of this situation, let 



Sili 



be the value of the character for the 

 ith fish in Region A in the first year, 



Mi be the mean in Region A of the character 

 in the first year 



X^jj be the value in Region B of the character 

 in the first year 



M hl be the mean in Region B of the character 

 in the first year 



X^i be the value in Region B of the character 

 in the second year 



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