Table 1.
Parameter values for the eco-genetic model of Atlantic cod
| Description | Symbol | Equations | Value | Source |
|---|---|---|---|---|
| Initial mean genetic PMRN intercept (cm) |  |
– | 93 (90.3) | 1 |
| Initial mean genetic PMRN slope (cm year−1) |  |
– | −0.052 (−0.052) | 1 |
| Initial mean genetic gonado-somatic index |  |
– | 0.12 (0.12) | 1 |
| Initial mean genetic growth capacity (cm) |  |
– | 12.8 (12.9) | 1 |
| Initial genetic coefficient of variation | CG,0 | – | 0.08 | 2 |
| Initial heritability |  |
– | 0.2 | 2 |
| Default retention probability | q | 1a–d | 0.8 | 3 |
| PMRN width (cm) | w | 2c | 25.9 | 4 |
| Density-dependent growth constant (g−1) | b | 3a | 1.02 × 10−8 | 5 |
| Density-dependent growth exponent | c | 3a | 0.3 | 5 |
| Weight-specific oocyte density (g−1) | d | – | 4.4 × 103 | 6 |
| Conversion factor for gonado-somatic index | δ | 3c | 1.73 | 7 |
| Proportionality constant for weight (g cm−β) | α | 4a | 3.2 × 10−3 | 8 |
| Exponent of length–weight allometry | β | 4a | 3.24 | 8 |
| Density-independent stock-recruitment constant | k | 4b | 5.3 × 10−3 | 9 |
| Density-dependent stock-recruitment constant | j | 4b | 8.3 × 105 | 10 |
| Maximal growth increment (cm) | gmax | 5a | 80 | 11 |
| Background natural mortality probability | pB | – | 0.02 | 12 |
| Minimum-size limit on feeding grounds (cm) | lF | – | 60 | 13 |
Values in parentheses are mean prefishing equilibrium trait values, averaged over 30 independent model runs. PMRN, probabilistic maturation reaction norm.
Rationale and sources: (1) Set so that the prefishing equilibrium of evolving traits is reached within 2000 years and values are within empirical ranges for Atlantic cod reported for PMRNs (Heino et al. 2002b; Olsen et al. 2004), gonado-somatic indices (Lloret and Ratz 2000; McIntyre and Hutchings 2003; Rose and O'Driscoll 2002), and growth rates (ICES 2007; Marshall et al. 2004; Olsen et al. 2005). (2) Within the range reported by Houle (1992) and Mousseau and Roff (1987). (3) Model assumption. (4) Olsen et al. (2005). (5) Set so that the range of phenotypic growth rates predicted by the model is within the empirical range for Atlantic cod (ICES 2007; Marshall et al. 2004; Olsen et al. 2005). (6) Thorsen and Kjesbu (2001). (7) Lester et al. (2004). (8) From survey data for 1999–2007 collected by the Norwegian Institute of Marine Research (O.R. Kjesbu, pers. comm.). (9) Marshall et al. (2000). (10) Scaled from Marshall et al. (2000) so that population abundance at prefishing equilibrium is computationally manageable (ca. 20 000). (11) Set so that growth capacity at prefishing equilibrium produces phenotypic growth rates within the empirical range for Atlantic cod (ICES 2007; Marshall et al. 2004; Olsen et al. 2005). (12) Set so that the total natural mortality probability equals 0.18 (ICES 2007). (13) Model assumption as in Dunlop et al. (2009b).