Empirical weight-at-age and aging error/bias

[Steve Barbeaux - NOAA Federal]

For Pacific cod we have substantial aging error and then aging bias pre-2007. We also have a stock that at a given length, can be quite a bit heavier by age. We were hoping to use  empirical weight-at-age data (ewaa), but dealing with error and bias in the  ewaa seems challenging. How does the ewaa interact, if at all, with aging error/bias as it is configured in stock synthesis and has anyone else dealt with this in a stock synthesis model? Any examples out there that we could learn from?

Thanks, Steve 

[Kelli Johnson]

We use empirical weight-at-age data for Pacific Hake, the model also has an ageing error matrix. I do not believe that the empirical weight-at-age data are linked at all to the ageing error matrices just the age-composition data that are used to estimate selectivity. Sorry I am not more help. At first thought, you could resample the empirical weight-at-age data giving the ageing error to generate different matrices of empirical weight-at-age to go into the assessment and see if it makes a difference. Or, we could do a simulation that looks at how big the ageing error has to be for it to matter? I do not think either has been done before.

[Richard Methot - NOAA Federal]

Great question Steve.  As Kelli says, EWAA data is treated as exactly true.

Instead of entering the body weight as EWAA, enter it as data on mean weight-at age'.  This is in the data file after the agecomp data.  For each observation enter the ageerr with a negative so the model will treat the obs as weight-at-age', not length-at-age'.  I use ' because they are now treated as weight at observed age', not weight at true age.

1 #_Use_MeanSize-at-Age_obs (0/1)
# sex codes:  0=combined; 1=use female only; 2=use male only; 3=use both as joint sex x length distribution
# partition codes:  (0=combined; 1=discard; 2=retained
# ageerr codes:  positive means mean length-at-age; negative means mean bodywt_at_age
#_yr month fleet sex part ageerr ignore datavector(female-male)

Now, SS3 will take into account size selectivity and ageing error when deriving the expected values for data of this type.

SS3 will also account for weight-at-length.

If you give the model both length-at-age' and weight-at-age' observations, then it is conceivable that the weight-at-length parameters could be estimated.

The challenge is that the model will need to estimate growth parameters, probably with time varying characteristics, in order to match these obs.

The result will be model estimates of length and weight at true age that will be used in the population dynamics.

Rick

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[Ian Taylor - NOAA Federal]

One additional thought on ageing error and empirical weight-at-age.

To test the impact of ageing error on empirical weight at age, you could follow Rick's suggestion to create mean weight-at-age observations, but just enter dummy data, set the lambda to 0 and not estimate time-varying growth.

Then compare the expected values of mean bodyweight at age (output in CompReport.sso with Kind = "W@A" and returned by r4ss::SS_output() as $wadbase) to the values in wtatage.ss_new, which will be the mean weight at the true age for each fleet. Selectivity will be included in the fleet specific values in each case.

An example of setting up length-at-age observations with lambda = 0 is available in this model: https://github.com/nmfs-ost/ss3-test-models/tree/main/models/BigSkate_2019 (where the ageing error inputs for the length-at-age are positive but as Rick said would need to be negative to make it weight-at-age instead of length).

My guess is that bias in the ageing process which you have prior to 2007 could have a big impact, but variability in ages won't be that big a deal since weight-at-age is often reasonably linear across a small range of ages, so the overestimates and underestimates will cancel each other out. Assuming that the bias is negative (underageing fish), then length-based selectivity could also counteract it by increasing the average weight of the selected fish at younger ages to be more similar to the weight of the fish at the true age.

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