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



397 



10 



0.8 

 06 

 4 

 0.2 

 0.0' 



10 



Age 



o 



200 400 600 800 



Length 



1000 



Figure 2 



Effect of the slope parameter on (A) the prob- 

 ability of maturity and (B) the probability of 

 selection. (A) Maturity slope parameter /3 m = 0.25 

 (light dash), /i„, = 0.5 (light solid!, ft,, = 1.0 (heavy 

 dash), and P m =°° (heavy solid). (B) Selectivity 

 slope parameter /3 S = 0.01 (light dash). /3 S = 0.05 

 (light solid), /3 S = 0.1 (heavy dashl, and /3 S = ^ 

 (heavv solid). 



increases, the selection differential on size increases 

 or decreases monotonically toward an asymptote, the 

 selection differential on L x . Thus selection differentials 

 on size across all ages are bounded by those at L _, + K 

 + L x K and L x . The selection differential on the small- 

 est fish (age approaching t ) is an upper bound when 

 the selection differential on K is positive, and a lower 

 bound when negative. These properties are important 

 for interpreting how selection differentials on size-at-age 

 correspond to differentials on L x and K. 



Using the base model, we computed selection differen- 

 tials on L x and K as functions of fishing mortality, over 

 the range F=Q to F=10/yr. The selection differentials 

 increased with F nonlinearly, resulting in a concave 

 relationship (Fig. 4). However for F<2.0, the relation- 

 ship is nearly linear. 



The alternative models also revealed linear relation- 

 ships between selection differentials and F, for F<2.0 

 (figures not shown). In addition, those relationships 

 have a zero intercept (by definition, no fishing, no selec- 

 tion differential). Because the relationships are (nearly) 

 linear and have a common intercept, the rank of selec- 



1000 



800 



£ 600 



400 



200 



~i 1 1 r~ 



5 10 15 20 



5 10 15 20 

 Age 



Figure 3 



Hypothetical changes in 

 length, given changes in 

 growth parameters. (Ai 

 Growth trajectories in the 

 base model (solid), a 59c de- 

 crease in growth parameter 

 K (dash), a 5 r/ r decrease in 

 growth parameter L ^ (dot), 

 and b c /< decrease in both 

 parameters (dash-dot). (B) 

 The corresponding reductions 

 in length are relative to the 

 base model. 



tion differentials among models does not change across 

 values of F. A model that bears the highest selection dif- 

 ferential at F=0.2 does so at F=2.0. We therefore present 

 results of sensitivity analyses for a single value of F 

 (F=0.8/yr), with the understanding that for other values 

 of F (up to 2.0), magnitudes of selection differentials can 

 be inferred and ranks among models are maintained. 



Increased variation in L x and K tended to increase 

 the selection differentials, and interaction between the 

 two growth parameters (Tables 2 and 3). Selection dif- 

 ferentials on L x were generally larger than those on K. 

 In the base model, the largest selection differential on 

 each growth parameter occurred when variation in the 

 focal parameter was highest and variation in the other 

 parameter was zero. The selection differentials on size- 

 at-age were largest when variation in both parameters 

 was highest (20% CV for both L x and K). 



