Modeling Parameters in Stock Synthesis

1. Modeling Parameters in Stock Synthesis Modeling population processes2009 IATTC workshop

2. Outline • General framework • Bounds and priors • Temporal variation • Relationship among parameters

3. General framework • All parameter inputs have 14 or 7 elements • First 7: bounds, init value, prior info, phase • Next 7: advanced options for time variation • Conditional inputs depending on options #_LO HI INIT PRIOR PR_type SD PHASE env-var use_dev dev_minyr dev_maxyr dev_stddev Block Block_Fxn # Label 0.05 0.15 0.1 0.1 0 0.8 -3 0 0 0 0 0.5 0 0 # NatM_p_1_Fem_GP_1 -3 3 0 0 0 0.8 -3 0 0 0 0 0.5 0 0 # NatM_p_2_Fem_GP_1 10 45 36.0 36.0 0 10 2 0 0 0 0 0.5 0 0 # L_at_Amin_Fem_GP_1 40 90 70.0 70.0 0 10 2 0 0 0 0 0.5 0 0 # L_at_Amax_Fem_GP_1 0.05 0.25 0.15 0.15 0 0.8 3 0 0 0 0 0.5 0 0 # VonBert_K_Fem_GP_1 0.05 0.25 0.1 0.1 0 0.8 -3 0 0 0 0 0.5 0 0 # CV_young_Fem_GP_1 -3 3 0.25 0.25 0 0.8 -3 0 0 0 0 0.5 0 0 # CV_old_Fem_GP_1 -3 3 0 0 0 0.8 -3 0 0 0 0 0.5 0 0 # NatM_p_1_Mal_GP_1 -3 3 0 0 0 0.8 -3 0 0 0 0 0.5 0 0 # NatM_p_2_Mal_GP_1 -3 3 0 0 0 0.8 -3 0 0 0 0 0.5 0 0 # L_at_Amin_Mal_GP_1 -3 3 0 0 0 0.8 -2 0 0 0 0 0.5 0 0 # L_at_Amax_Mal_GP_1 -3 3 0 0 0 0.8 -3 0 0 0 0 0.5 0 0 # VonBert_K_Mal_GP_1 -3 3 0 0 0 0.8 -3 0 0 0 0 0.5 0 0 # CV_young_Mal_GP_1 -3 3 0.25 0.25 0 0.8 -3 0 0 0 0 0.5 0 0 # CV_old_Mal_GP_1 -3 3 2.0e-06 2.0e-06 0 0.8 -3 0 0 0 0 0.5 0 0 # Wtlen_1_Fem -3 4 3.0 3.0 0 0.8 -3 0 0 0 0 0.5 0 0 # Wtlen_2_Fem 50 60 55 55 0 0.8 -3 0 0 0 0 0.5 0 0 # Mat50%_Fem -3 3 -0.25 -0.25 0 0.8 -3 0 0 0 0 0.5 0 0 # Mat_slope_Fem -3 3 1 1 0 0.8 -3 0 0 0 0 0.5 0 0 # Eg/gm_inter_Fem

4. Bounds and priors • All parameters bounded • Prior options: uniform, normal, lognormal, symmetric and non-symmetric beta

5. Soft bounds • Optional penalty (set in starter file) applied to all parameters • Keeps ADMB from getting stuck on bounds • Acts along with user-specified priors • Equivalent to symmetric beta with shape parameter = 0.001

6. Temporal variation Deviations (N std. dev. pars.) Blocks (1 par. per block) Random walk (N -1 std. dev. pars.) Trend (3 pars.)

7. Temporal variation: blocks • Requires conditional input for extra parameters lines (same as other variation types) • Fixed time intervals specified in control file • Additional parameters may be: • Multiplicative offset from base value • Additive offset from base value • Replace base value for interval of years • May have random walk from one block to next

8. Temporal variation: deviations • Defined by • Type (base+dev or base∙edev) • Start and end years for • Normal distribution penalty • Not zero-centered Temporal variation: random walk • Similar to deviations, but one fewer parameter • Parameters represent differences • Normal distribution penalty

9. Temporal variation: trends • Only 3 parameters • Smooth alternative to blocks for cases that don’t support many parameters • Final value may be offset from base or new value

10. Parameter as function of covariate • Environmental variable: Ey • Pary = base+link∙Ey or base∙eEy • May be combined with other options (i.e. deviations around environmental index) • Covariate relationship to be used in future versions of SS for density dependence: • Mortality parameters as a function of biomass

11. Keeping time-varying parameters within bounds Options: • time varying parameters unconstrained by bounds on base parameter • logistic transformation to keep adjusted parameter value within bounds of base

12. Offsets from other parameters • Parameters for males often treated as offsets from females • growth • mortality • selectivity • Additive or multiplicative options • Makes hypothesis testing easy • To be covered in more detail in upcoming sessions of IATTC workshop