TEGNER ET AL.: BIOLOGY AND MANAGEMENT OF RED ABALONES 



CO 



10- 



Octopus spp predation 

 N = 53 



20- 



UJ 

 X 

 CO 10 



o 

 cr 



10- 



Rock crab {Cancer spp.) predation 

 N = 209 



Cliona ce/afa-\nfesie6 shells 

 N = 56 



— I 1 I i~ 



35 65 95 125 155 185 215 



SIZE (mm) 



Figure 6.— Size-frequency distributions of red abalone shells re- 

 covered in the tagging area 1980-82 which could be attributed to 

 a specific predator. 



Natural mortality rate must be less than the esti- 

 mated Z. Commercial exploitation begins at 197 mm, 

 recreational exploitation at 178 mm, and mortality 

 associated with exploitation (bar-cutting) reduces 

 the number of individuals smaller than legal size 

 (Fig. 5). The method used here suggests a value of 

 M around 0.15. 



Yield-Per-Recruit Analysis 



Isopleth diagrams for red abalones using M = 0.10 

 and 0.15 are shown in Figure 7A and B respective- 

 ly. The minimum size associated with the maximum 

 yield-per-recruit estimate is sensitive to the value 

 of M used: it is 176 mm when M = 0.10, and 164 

 mm when M = 0.15. Both sets of estimates show 

 the pattern described by Breen (1986): except at 

 very low values of F, the yield estimates are not sen- 

 sitive to variation in F; conversely at low values of 

 F, the yield estimates are insensitive to variation 

 in minimum size. 



For pink abalones, yield isopleths are shown in 

 Figure 7C and D. The minimum size producing the 

 greatest estimated yield is very sensitive to the 

 estimate of M. If M = 0.35, as Doi et al. (1977) sug- 

 gested, then the best minimum size is 116 mm; if 



Table 6.— Effect of cfianging input parameters and initial conditions on estimated total mor- 

 tality rate Z in red abalones, using ttie data in Figure 3 and Table 1. 7 is the value of the 

 objective function; the goal is to minimize this function in con|unction with realistic mortality 

 rate estimates. Unless specified, bounds in the first and last standard deviations of lengths- 

 at-age for the first and last cohorts are 7.5 and 8.5. 



Effect of varying the total number of age classes 



NK 16 15 14 13 12 



Z 0.196 0.194 0193 0.182 0.165 



T 481 483 486 492 500 



Effect of releasing constraints on estimated mean length of the last age class 

 Constrained Unconstrained 



Z 

 T 



0.196 

 481 



0.195 

 481 



Effect of changing upper and lower bounds on the estimated standard deviations of lengths- 

 at-age around the mean length-at-age. Bounds on the first line are those for the first cohort; 

 those on the second line are for the last cohort. The asterisk indicates when the model was 

 not actually constrained by the bound. 



Bounds 



Z 

 T 



Effect of varying the age of the first age class, NFULL. included in the calculation of total 

 mortality rate {NK = 16) 

 12 3 4 5 6 7 



0,206 0.196 180 0.180 0.177 0.181 0.174 



NFULL 



Z 



481 



481 



480 



480 



480 



480 



480 



327 



