Table 1. — Contrived data under conditions of low, inter- 

 mediate and high variability which are used to demon- 

 strate the indices /„ and 7^. 



c/f 



LOW VARIABILITY 

 Ig = 1.09 



Ir = 1.00 

 ( 2 data at each point) 



  I     I 



c/f 



INTERMEDIATE VARIABILITY 



I, 



1.09 

 r = 0.55 



I     I 



c/f 



HIGH VARIABILITY 

 Ig = 1.09 



o Ip » 0.44 



'  '  I     I 



Figure 1. — Comparisons of 7g and 7^ for c// and / re- 

 lations having different amounts of variability. The 

 data are from Table 1. 



of the amount of confidence that can be placed 

 in any estimate of Ir or in Ig. The question of 

 confidence can be resolved in the case of Ir if c/f 

 and / are both drawn from the same (at least 

 approximately) bivariate normal distribution. 

 In the likely event that c/f and / are not at least 

 approximately bivariate normal, then perhaps 

 a transformation might be useful. It is also 

 of interest to observe that since h is a corre- 

 lation coefficient then we can interpret Ir^ as the 

 percentage of the total variability in c/f which 

 is accounted for by regressing c/f upon /. 

 Furthermore there is no reason, of course, why 

 we could not extend this concept in multiple spe- 

 cies fisheries to consider these sorts of data in 

 a multiple correlation context. 



The idea of using the correlation coefficient 

 measuring the association between c/f and / as 

 a concentration index is intuitively quite obvious 

 and most likely would not be noteworthy except 

 to call attention to the similarity to a commonly 

 used index (Ig) which, in most instances, does 

 not aff'ord as large a scope for interpretation as 

 does Ir. There are some cautions, however, which 

 should be observed and these include, in addition 

 to bivariate normality if we wish to construct 

 confidence intervals, linearity in the relation be- 

 tween c/f and /. If, for example, the gear is 

 saturated or data are pooled from various sea- 

 sons, then linearity may not be a reasonable un- 

 derlying model. 



In the interpretation of either Ir or Ig it would 

 be helpful to have auxiliary information because 

 without this information it is impossible to de- 

 termine whether increases in these indices re- 

 sult from an increased concentration of fishing 

 on fish or fish on the location where fishermen 

 happen to be fishing. Thus, these indices alone 

 will not tell us whether changes in apparent 

 abundance result from changes in actual abund- 

 ance or changes in the skills of fishermen or both. 



We should also draw attention to the fact that 

 the relation of c/f and / is generally used in fish- 

 eries to determine "optimum" yield by regres- 

 sing, usually annual, values of c/f upon /. This 

 relation is frequently linear with a negative 

 slope and is usually transformed into a parabolic 

 function of c upon / indicating that level of / for 

 which c is a maximum. The procedure outlined 



513 



