Williams and Shertzer: Effects of fishing on growth traits: a simulation analysis 



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fishery characteristics (Table 1). We then conducted a 

 variety of sensitivity analyses. 



In the base model, the natural mortality rate (M) was 

 set at 0.2/yr, a value common for many fish species. 

 Sensitivity analyses used M = 0.1, 0.4, or 0.8. The value 

 of M affects the values of A', A m , and L s , according to 

 the life-history invariant relationships (Table 1). The 

 relationship between M and K is often referred to as the 

 M/K ratio. Charnov (1993) suggested a central value for 

 fishes of M/A"=1.65, which we used in the base model. 

 Beverton (1992) examined the M/K ratio for fishes and 

 found a range of 0.5 to 2.5. We used this range in our 

 sensitivity analyses to examine the effect of the M/K 

 ratio on selection differentials (Table 2). 



The base model treated L x and K as independent 

 variables (p=0. Table 1). Often these parameters are 

 correlated. A meta-analysis by He and Stewart (2001) 

 of 235 fish populations indicated a correlation value of 

 -0.28. The negative correlation could be expected from 

 a trade-off between growth rate (represented by A'l 

 and maximum size (represented by L x ), as has been 

 suggested in studies of bioenergetics (Stearns, 1992; 

 Hutchings, 1993; Mangel, 1996). Our sensitivity analy- 

 ses considered negative values of correlation that range 

 from -0.25 to -1. 



With the base model, selectivity and maturity were 

 assumed to be "knife-edge," a functional form often used 

 in fisheries for convenience. Also, in the base model the 

 size at 50% selectivity (L s ) was assumed to occur at an 

 age equal to the age at 50% maturity (A m ). Although 



these fishery characteristics are common, selectivity 

 and maturity may not be knife-edge or coincide. In 

 sensitivity analyses, we examined different shapes of 

 selectivity and maturity curves (Fig. 2). We also ex- 

 amined the affect of shifting the age at 50% selectivity 

 from -2 to 2, in relation to the base case. This shift 

 corresponds to a range in L s values from 574 to 738. 

 For simplicity, we held F constant for these sensitivity 

 analyses, implying constant effort but resulting in dif- 

 ferent amounts of removals. 



Under logistic selectivity, the oldest, largest fish 

 receive the highest rate of exploitation. Yet often the 

 largest fish are unavailable to a fishery because of mi- 

 gration patterns or regulations (e.g., a maximum size 

 limit). Thus our sensitivity analyses included a cap on 

 susceptible sizes. The cap was set at 70, 80, or 907c of 



Using the base model, we examined the effects of an- 

 nual fishing mortality rate over values that range from 

 F=0 to F=10/yr, which is to 50 times the natural mor- 

 tality rate. Fishing mortality was applied continuously 

 throughout the year (i.e., D F =1). In sensitivity analyses, 

 we examined shorter fishing seasons ranging from one 

 to six months. The F was still an annual rate but was 

 applied over fewer months and adjusted so that the 

 number of fish removed was the same as when D F =1. 

 For seasons shorter than a full year, fishing was as- 

 sumed to occur at the beginning of the year. 



Like the fishing season, the duration of the spawn- 

 ing season was a full year in the base model (D s =l). 



