Taylor and Hoenig: Effect of tag anchor location on Chionoecetes opilio 



327 



Table 2 



Incidence of necrosis around the tag anchor in male Chionoe- 

 cetes opilio tagged in Conception Bay, Newfoundland, with 

 t-bar tags. 



Tagging location 



Dorsal 

 muscle 



Body 

 cavity 



Shell 



Leg 



muscle 



Number with necrosis 1 1 



Number without necrosis 45 

 % necrotic 20 



4 7 7 



14 22 25 



22 24 22 



or 0.06 : 1. Hence animals with anchors loose in the body 

 cavity appear to have become less abundant relative 

 to those tagged in the dorsal musculature, and this 

 suggests lower tag retention and/or lower survival for 

 animals with anchors loose in the body cavity. In fact, 

 the relative retention/survival rate can be estimated 

 from the 1984 data as 



a = relative retention/survival (loose : dorsal) 



0.13. 



The estimator a is the cross-product ratio 

 used in survival analysis (Fienberg 1980). 



If all data were collected from animals 

 tagged in the same year, then it would be 

 a simple matter to use a x 2 test to test 

 the null hypothesis that the proportions 

 in each location are the same for the two 

 molt states (molted versus did not molt). 

 However, animals were tagged in two 

 separate years and there is at least a 

 reasonably strong possibility that the tag- 

 ging procedure varied between the years, 

 e.g., due to developing tagging skill. This 

 suggests that the interaction terms in- 

 volving year may be significant. If inter- 

 action terms are ignored and the data 

 from different years are pooled, then 

 associations between variables (i.e., be- 

 tween molt status and tagging location) 

 can be distorted and the apparent direc- 

 tion of the association can even reverse 

 (see Fienberg 1980, chap. 3). An analysis 

 which explicitly accounts for this possibil- 

 ity can be conducted using hierarchial 

 loglinear models. 



frequently 



The 16 counts in Table 1 for individual years 1983 

 and 1984 can be envisioned as comprising a 2 x 2 x 4 

 contingency table with main effects (categorizations) 

 due to year of tagging (Yr), molt status (Molt), and loca- 

 tion of tag within the body (Loc). There are nine log- 

 linear models that can be fitted to these data (Table 

 3) ranging from the model of complete independence 

 through seven models of partial dependence to the com- 

 pletely saturated model (see Fienberg 1980 for a dis- 

 cussion). The contingency table can be collapsed over 

 the year variable if one (or both) of the two-factor inter- 

 actions involving year is not significant. The hypothe- 

 sis that tagging location has no influence on retention/ 

 survival through molt can be rejected if it is necessary 

 to have an interaction between location and molt status 

 (Loc * Molt) to have a good fit to the data. 



Even the simplest model of main effects only (model 

 1) is not rejected by the likelihood ratio test (P = 

 0.2067, Table 3). It is still of interest to explore how 

 strong the evidence may be that location of the tag 

 affects survival/retention through the molt. We will 

 therefore examine the following four models in more 

 detail. 



model 1: 



Count = [Molt] [Yr] [Loc] 

 model 3: 



Count = [Molt] [Yr] [Loc] [Yr]*[Loc] 

 model 4: 



Count = [Molt] [Yr] [Loc] [Molt] * [Loc] 

 model 5: 



Count = [Molt] [Yr] [Loc] [Molt] * [Loc] [Yr]*[Loc] 



Table 3 



Loglinear model analysis of tagging count data in Table 1. C is the predicted 

 count, [Yr] represents year of tagging, [Molt] represents molt status, and [Loc] 

 represents location of the tag anchor within the body. Asterisk (*) indicates 

 an interaction between variables. To make the notation more compact, only 

 the highest-order interactions are given for each variable. For example, the 

 model C = [Loc] [Yr]«[Molt] represents main effects for location, year, and 

 molt, plus the interaction between year and molt. The order of presentation 

 of the variables has no significance in the model notation. 



Model 



1) C = [Yr] [Molt] [Loc] 



2) C = [Yr] * [Molt] [Loc] 



3) C = [Molt] [Yr] * [Loc] 



4) C = [Yr] [Molt] * [Loc] 



5) C = [Yr] * [Loc] [Molt] - 



6) C = [Yr]» [Molt] [Loc] < 



7) C = [Molt] * [Yr] [Loc] - 



8) C = [Molt] * [Yr] [Loc] • 



9) C = [Yr] • [Molt] * [Loc] 



[Loc] 



[Molt] 



[Yr] 



[Yr] [Molt]  



[Loc] 



