Fisheries Stock Assessment Course

FAS 6932 ASSIGNMENT 5 DUE February 18, 2011

VPA AND STOCK SYNTHESIS: HOW INFORMATIVE ARE AGE STRUCTURE DATA?

The spreadsheet HERAGE.XLS has data on age composition and spawn survey abundance for a Pacific herring stock in the Georgia Strait, BC. Develop a VPA reconstruction of stock size from these data. Use results from the VPA to help develop an alternative assessment based on a forward (synthesis) model of the historical dynamics. Fit this model initially using a likelihood function only for the age composition data, then add a likelihood component for the predicted spawn survey index. Your forward simulation should predict Na+1,t+1=s(1-va,tut)Na,t where the natural survival rate s is given on the spreadsheet and exploitation rate ut is calculated each year from the total observed number of fish caught Ct (sum over ages of Ca,t data) as ut=min(1,Ct/ava,tNa,t) (Schnute-Richards approach to avoid treating ut as unknown parameter). Treat the following as unknown parameters to be estimated by Solver: (1) Na,1: numbers at age in year 1 (1951); (2) N0,t: numbers at age 0 in all years after 1951, i.e. recruitments; (3) va,1951-69: vulnerability at age to reduction fishery (assume 1.0 for older fish); (4) va,1969-97=ma: vulnerability/maturity at age to roe fishery (for spawn biomass calculations, assume maturity ma stable over all years, again 1.0 for older fish). Use the VPA results to provide initial estimates for these parameters.

In fitting the model, assume a multinomial log-likelihood function for sampled age proportions in the catch:

LogLage=at ntpa,tln(Pa,t) Where nt=effective sample size for age composition in year t (assume nt=100 or less) pa,t=observed proportion of age a fish in year t catch Pa,t=model predicted proportion of age a fish in year t catch (=utva,tNa,t/Ct) When you include the spawn survey data in the likelihood function, do so by constructing the toal log likelihood L=logLage+logLsurvey where you calculate the survey log likelihood component as 2 LogLsurvey= -(T-1)/2 ln(SS), SS=t(Zt-Zbar) , Zt=ln(bt/Bt) Where T=number of years survey data bt=observed spawn survey index in year t

Bt=predicted spawn biomass in year t, tmawaNa,t(1-utva,t) (wa=weight at age) Note you can change the “weight” placed on the age composition versus survey data in the overall likelihood function by changing the effective sample size nt for age data.

How well do the VPA and synthesis models agree about the stock history, especially when only the age composition data are used for fitting the synthesis model? Do both methods agree about the “current” or most recent (1997) spawning biomass? What happens to your results if you admit age-dependence in the natural survival rate (some age dependent estimates are included in the spreadsheet)?