Table 1.
Demographic parameters and their numerical values in the model
| Parameter | Description | Unit | Value | Equation | Source |
|---|---|---|---|---|---|
| p | Length–mass coefficient | mm g−u | 77 | – | Based on P. Magnan and M. Plante, unpublished data, and R. Curry et al. (1993) |
| u | Length–mass exponent | – | 0.30 | – | Based on P. Magnan and M. Plante, unpublished data, and R. Curry et al. (1993) |
| d | PMRN width | mm | 110.3 | (2) | Based on P. Magnan and M. Plante, unpublished data |
| ν0 | Initial mean value of PMRN intercept | mm | 200 | (3) | Based on P. Magnan and M. Plante, unpublished data |
| σ0 | Initial mean value of PMRN slope | mm year−1 | 7.68 | (3) | Based on P. Magnan and M. Plante, unpublished data |
| W0 | Average mass of an egg | g | 0.01 | (4) | Based on P. Magnan and M. Plante, unpublished data R. Curry et al. (1993) |
| υf | Nonlinearity of female reproductive success | – | 2 | (5) | Model assumption |
| υm | Nonlinearity of male reproductive success | – | 2 | (6) | Model assumption |
| κ1 | Beverton–Holt constant | – | 0.0076 | (7) | Chosen to be consistent with M. Power and G. Power (1995) |
| κ2 | Beverton–Holt constant | – | 1 117 391 | (7) | Chosen to be consistent with M. Power and G. Power (1995) |
| βs | Strength of condition-specific effects on mortality | – | 4 | (8) | N. Broekhuizen et al. (1994) |
| β1 | Strength of size-unspecific effects on mortality | – | −1.90 | (8) | Based on P. Magnan and M. Plante, unpublished data |
| β2 | Strength of size-specific effects on mortality | cm−1 | 0.011 | (8) | Based on P. Magnan and M. Plante, unpublished data |
| α | Size-specific consumption coefficient | g1−γ day−1 | 0.07 | ((9) | Based on P. Magnan and M. Plante, unpublished data |
| γ | Size-specific consumption exponent | – | 0.68 | (9) | Based on P. Magnan and M. Plante, unpublished data |
| ϑ1 | Maximum consumption rate | liter−1 day−1 | 164 | (10) | M. L. Koski and B. M. Johnson (2002) |
| ϑ2 | Half-saturation resource density in consumption rate | liter−1 | 42.2 | (10) | M. L. Koski and B. M. Johnson (2002) |
| L | Volume of shared habitat | liter | 1.8 × 107 | (10) | Chosen to be consistent with P. Magnan et al. (2005) |
| r | Intrinsic growth rate of resource | day−1 | 0.1 | (11) | D. Claessen et al. (2000) and consistent with F. Marchand et al. (2002) |
| K | Carrying capacity of unharvested resource | – | 1.8 × 109 | (11) | Chosen to be consistent with F. Marchand et al. (2002) and P. Magnan et al. (2005) and D. Claessen et al. (2000) |
| λ | Product of zooplankton mass (50 μg and a dimensionless trophic conversion factor (0.61) | g | 0.00003 | (11) | D. Claessen et al. (2000) and A. E. Gamble et al. (2006) |
| δ | Metabolic rate | day−1 | 0.005 | (13) | Based on P. Magnan and M. Plante, unpublished data |
| T | Length of the year | day | 365 | (16) | |
| σ | Standard deviation of the stochastic component of the growth equation | g1−γ | 0.700 | (14) | Based on P. Magnan and M. Plante, unpublished data |
| ρJ | Juvenile maximum condition | – | 1.6 | – | G. Broekhuizen et al. (1994) |
| ε | Fraction of energy intake allocated to reversible mass used for reproduction | – | 0.32 | (17) | Chosen to be consistent with P. Magnan and M. Plante, unpublished data |
Appendices A and B describe the estimation of parameters based on unpublished data sets.
PMRN; probabilistic maturation reaction norm.