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6 / Hilborn et al.
1.2.5. Weight at age relationship
Weight at age is a vital piece of information in the assessment, because it is
involved in the vulnerable biomass calculations. It can be directly incorporated into the
model as observed data (design-based estimators) or by using a model-based approach
(parameters of the von Bertalanffy growth curve and the weight–length power function).
By default the program uses the observed data. The rest of the temporal weightat-age information arises from the following calculations:
a. If selectivity is a function of age, mean weight at age is predicted from the following
equation
 S s2 2
 bii σ a bii −1

2


(
s
a,t
S biiS
S
i
w = b (La ) e
)



where the exponential is a correction for the variance of the log-normal distribution of
size at age. If the survey selectivity is based on age, than the weight at age for the
commercial fleet is the same as the one for the surveys.
However, selectivity can be modeled as a function of fish size (only for surveys),
in which case the mean weight at age for the surveys is affected by selectivity at size
and the length–age relationship according to
∑ b (L )
=
∑s
S
i
s,g
wa,t
l
b iiS
s
sls,g
,t f l|a
l
s, g
l ,t
fl|as
l
Note: If you do not have model-based weight-at-age estimates, you will need to input
observed data for each year. The vulnerable biomass computation for the last year + 1 is
based by default on model-based estimates of weight-at-age, so if you do not have
those be sure to add one more line of observed weight-at-age data. If your model is in
numbers (catch, biomass, etc), you should enter nyear+1 vectors of weight-at-age data
filled out with values 1.
1.2.6. Selectivity
Selectivity is a process that can be modeled based on age or size. This model
supports an age-based selectivity for the fishing fleet and a size- or age-based selectivity
for the surveys. In this model the only sex-specific variation in the selectivity function
arises from the difference between ages of full recruitment.
1.2.6.1 Selectivity as a function of age
The selectivity function implemented in the model is a double half-Gaussian function of
age: