MATHEMATICAL DERIVATION OF CREEL CENSUS ESTIMATES 

 YELLOWSTOJIE LAKE SHORELINE 



The purpose of this section is to explain the details of the creel 

 census structure as done on Yellowstone Lake, Tlie primary components 

 of the structure are the complete census , which yields characteristics 

 of groups of fishermen in the fishery, and the incomplete census ^ wnich 

 furnishes a measure of the total fishing effort. The total catch and 

 total number of fishermen can be estimated from these (data) according 

 to the treatment which follows here, 



THE COMPLETE CENSUS 



The aim of the complete census is to obtain approximations of the 

 catch-per-unit-of-effort, average effort and catch-per-fisherman, and 

 frequency distribution of fishing effort for the entire Yellowstone 

 fishing group. These approximations can be deterndned by studying small 

 subgroups, if they are representative of the total fishing group. It is 

 practically impossible to choose samples that perfectly represent the 

 total group, because of the ever-changing pattern of angling distribu- 

 tion on Yellowstone Lake, A practical solution is the selection of four 

 areas, which when pooled are considered to be a representative sample of 

 the fishing population, both with respect to availability of fish and 

 fishing activity. During every biweekly period, each of these four 

 areas is observed for one entire fishing day. Randomization is sought 

 through a sampling schedule that treats each study area on a different 

 da^o The pooled observations are henceforth referred to as the com- 

 plete census, A sample complete census worksheet is given in fig-orellj 

 together with the numerical quantities which enter into the calciilations 

 and derivation, 



THE INCOMPLETE CENSUS 



In order to estimate the total number of hours of fishing effort 

 along the entire lakeshore during a given biweekly period, some mea- 

 sure of this must be found, A convenient measure is the count of fish- 

 er-men made by an observer driving along the lakeshore, tabulated accord- 

 ing to the time of day that the count is made. Since the frequency dis- 

 tribution is collected (from the complete census) in the pattern of an 

 hourly histogram, it is appropriate to divide the lakeshore into hypo- 

 thetical strips It , L2s L3, L[j, each strip being that area covered dur- 

 ing cne hour of the fovor hour driving trip. Thus each trip yields a 

 count for each strip. 



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