Appendix A. Robustness analysis. In addition to testing the effects of different minimum length limits and harvest probabilities as described in the main text, we also tested the robustness of model results to changes in several other functions and parameters.
The growthsurvival tradeoff (main text Eq. 2d) was expected to influence growth evolution: raising g_{max} reduces the severity of the tradeoff and causes a lower cost of faster growth. Therefore, not surprisingly, raising g_{max} elevated the genetic growth capacity after 100 years of harvest (Fig. A1a).
For the other robustness tests, we focused on effects on the PMRN intercept, because this trait consistently showed a large evolutionary response to harvest. Nevertheless, detailed results for all traits are presented in Table A1. The magnitude of evolution was positively correlated with changes in the parameter s_{0}, which determines the densitydependent mortality of newborn offspring (main text Eq. 3a); however, the overall difference in the position of the PMRN after 100 years of harvest was small (Fig. A1b). Higher values of s_{0} produce larger population abundances, which, in turn, produce smaller phenotypic length increments; possibly, there is then compensation in the evolution of the PMRN in response to this slower growth.
We also tested the effect of changing the relationship describing densitydependent growth by varying the parameter c_{11} (main text Eq. 3f) between 0 (densityindependent growth) and 21.5 × 10^{8} g–1(causing a strong reduction in growth with increasing population biomass). We observed an increase in the evolutionary response in the PMRN intercept when c_{11} was increased (Fig. A1c), so that the slowest evolutionary response occurred when the density dependence in growth was switched off entirely.
For the final component of our robustness analysis, we tested the effect of changing the assumed genetic coefficient of variance CV_{G} in the initial population on evolution of the PMRN: as expected, increasing CV_{G} between 0 and 12% accelerated the evolutionary reduction of the PMRN intercept (Fig. A1d).
TABLE A1. Detailed results of the robustness analysis. Results shown are the mean genetic trait values after 100 years of fishing with a harvest probability of 0.5 and a minimum size limit of 60 cm. Intercept and slope are the probabilistic maturation reaction norm (PMRN) intercept and slope, respectively. GSI is the gonadosomatic index.
Parameter name and value  (cm) 
(cm yr^{1}) 
(cm) 

Maximum length increment g_{max}  
40 cm  6.00 

50 cm  
60 cm  
70 cm  
80 cm  
90 cm  
100 cm  
Densitydependent mortality constant s_{0}  
1.0 × 10^{3}  
2.0 × 10^{3}  
3.0 × 10^{3}  
4.0 × 10^{3}  
5.0 × 10^{3}  
6.0 × 10^{3}  
7.0 × 10^{3}  
8.0 × 10^{3}  
9.0 × 10^{3}  
10.0 × 10^{3}  
Densitydependent growth constant c_{11}  
0 10^{8} g^{1}  
0.01 10^{8} g^{1}  
0.1 10^{8} g^{1}  
0.4 10^{8} g^{1}  
1.0 10^{8} g^{1}  
2.1 10^{8} g^{1}  
3.4 10^{8} g^{1}  
6.6 10^{8} g^{1}  
10.2 10^{8} g^{1}  
15.2 10^{8} g^{1}  
21.5 10^{8} g^{1}  
Genetic coefficient of variation CV_{G} in the initial population  
0%  
1%  
2%  
3%  
4%  
5%  
6%  
7%  
8%  
9%  
10%  
11%  
12% 
FIG. A1. Robustness analysis for the ecogenetic model of Atlantic cod. Panels show the (a) genetic growth capacity and the (bd) probabilistic maturation reaction norm (PMRN) intercept after 100 years of harvesting. Parameters varied are the (a) maximal length increment g_{max} (Eq. 2d), the (b) densitydependent mortality constant s_{0} (Eq. 3a), the (c) densitydependent growth constant c_{11} (Eq. 3f), and the (d) genetic coefficient of variation CV_{G} in the initial population. Harvest probability was 0.5, minimum length limit was 60 cm, and results show the means and standard deviations for 30 independent model runs. Triangles indicate the default parameter values from Table 2 and error bars show the standard deviations. 