1. Modeling Parameters in Stock Synthesis Modeling population processes 2009 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.) Random walk (N -1 std. dev. pars.) Blocks (1 par. per block) 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 Temporal variation: random walk Defined by –Type (base+dev or base∙e dev ) –Start and end years for –Normal distribution penalty Not zero-centered 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: E y –Par y = base+link∙E y or base∙e Ey –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