Modeling Parameters in Stock Synthesis

Modeling population processes2009 IATTC workshop

Outline

• General framework

• Bounds and priors

• Temporal variation

• Relationship among parameters

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

Bounds and priors

• All parameters bounded

• Prior options: uniform, normal, lognormal, symmetric and non-symmetric beta

Parameter value

Pri

or

de

nsi

ty

Pmin Pmax

UniformNormalLog-normalSymmetric betaNon-symmetric beta

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

Parameter value

-lo

g(L

)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

00

0.0

05

0.0

10

Temporal variationDeviations (N std. dev. pars.)

Random walk (N -1 std. dev. pars.)

Blocks (1 par. per block)

Trend (3 pars.)

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

Temporal variation: deviations

Temporal variation: random walk

• Defined by – Type (base+dev or base∙edev) – Start and end years for – Normal distribution penalty

• Not zero-centered

• Similar to deviations, but one fewer parameter

• Parameters represent differences• Normal distribution penalty

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

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

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

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