56 



Fishery Bulletin 103(1) 



In 



SR = 



0.75° 

 1-0.75 5 



In 



0.25' ) 

 1-0.25 15 



simplifying to SR = — - — , when <5 = 1. 



All calculations were made on the basis of 2-mm-CL 

 size classes covering the entire size range for each fre- 

 quency distribution. The 2-mm-CL size classes were 

 used to ensure consistency across models, and also 

 to balance data resolution against the number of size 

 classes expected to have either zero catch or zero escape- 

 ment (Millar and Fryer, 1999). Wherever necessary, 

 hypothesis tests were conducted in accordance with the 

 recommendations of Millar and Walsh (1992) and Millar 

 and Fryer (1999). 



Results 



Morphometric relationships 



Least-squares regression analysis indicated highly sig- 

 nificant linear relationships between CL and each of 

 the other morphometric variables measured (Fig. 2). In 

 each case, at least 97% of the variability in the predic- 

 tor variable was explained by CL, indicating a high 

 degree of correlation among predictors. Nevertheless, for 

 any given CL, CB was consistently the largest variable 

 measured, whereas CD was the smallest. Furthermore, 

 CB increased more rapidly in response to increasing CL 

 than either CW or CD (ANCOVA: F=115.165; df=2, 167; 

 P<0.001). We therefore concluded that CB would likely 

 be the morphometric variable that limits escapement 

 through stretched square meshes. 



Theoretical calculation of escapement 



The mesh size that appeared (on the basis of visual inspec- 

 tion) to limit escapement was expressed as a function of 

 CL with a simple, linear, least-squares regression model 

 (Fig. 3). This relationship was highly significant and 

 explained 99% of the variability in critical mesh size. 



Using inverse prediction methods (Zar, 1999), we 

 calculated the critical CL (mean ±95% confidence inter- 

 val) from the regression model illustrated in Figure 3 

 for any mesh size. For 62-mm mesh, the critical CL is 

 estimated at 43.8 (±4.12) mm; for the 75-mm mesh the 

 estimate is 52.3 (±4.15) mm; whereas for the 100-mm 

 mesh it is 68.7 (±4.12) mm. Given the implicit assump- 

 tion that lobsters smaller than the critical CL can es- 

 cape, but that larger lobsters are retained, the mean 

 critical CL can be used as an estimate of L 50 . 



Aquarium trials 



No lobsters larger than 48 mm CL escaped the 62-mm 

 mesh traps in the aquarium and none smaller than 

 44 mm CL were retained. This finding resulted in an 

 extremely steep selection curve with a narrow SR (Fig. 

 4; Table 1). For the 75-mm mesh, no lobsters larger than 

 61 mm CL escaped and no lobsters smaller than 54 mm 

 CL were retained. This finding resulted in a slightly 

 more gentle selection curve, but with a reasonably tight 

 SR (Fig. 4, Table 1). Similarly, for the 100-mm mesh, no 

 lobsters larger than 79 mm CL escaped and no lobsters 

 smaller than 74 mm CL were retained. This finding 

 resulted in a selection curve that closely resembled that 

 for the 75-mm mesh, except that the curve shifted a few 

 size categories to the right (Fig. 4; Table 1). 



For all meshes, the symmetrical logistic model was se- 

 lected in preference to the asymmetrical Richards model 

 (Table 1), and in all cases the selected model fitted 

 the data reasonably well (Fig. 4). It should, 

 however, be noted that all hypothesis tests 

 were conducted by using the deviance residu- 

 als and their degrees of freedom for all size 

 classes sampled. This was necessary because 

 the very tight selection curves (especially for 

 the 62-mm mesh) resulted in relatively small 

 numbers of size classes in which retention 

 probability was neither zero nor one. 



The above results indicate that L 50 -esti- 

 mates for each mesh size are substantially 

 larger than the corresponding estimates of 

 critical CL from the theoretical escapement 

 model. In fact, assuming that the asymptotic 

 standard errors provided in Table 1 could be 

 converted to 95% confidence intervals by a 

 multiplication factor of two, only the confi- 

 dence intervals for these statistics from the 

 62 mm mesh would overlap. By contrast, con- 

 fidence intervals for the critical CL are well 

 below those for the L 50 for both the 75 mm 

 mesh and the 100-mm mesh. This impression 

 is confirmed by inspecting the probabilities of 



