Bottom Trawl Surveys - Proceedings of a Workshop Held at Ottawa ...

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The uncertainties of weight estimates are, on
the other hand, a result of the sampling design
and sampling rate of commercial catch.
The above analysis considers that the Fo.1
fishing levels and the partial recruitment
coefficients, i.e. our controls, are known
quantities. For instance, our results are valid
for an instantaneous rate of fishing mortality
of 0.195. In practice, the Fo.1 fishing level
is estimated from mean weight-at-age and from
partial recruitment coefficients; this estimate
is not without errors. We can assess the effect
of the uncertainties of the FQ.1 reference level
on catch projections by extending the projection
algorithm so as to include the simultaneous
evaluation of FQ.1· By definition, Fo.1 is the
value of F.,T which ensures that the first
partial derivative of yield per recruit with
respect to F.,T is equal to one tenth the value
of the slope of the yield per recruit curve at
the origin. Rivard (1980) suggests the use of
the method of false position for estimating Fo.1
from age-specific weights and from the
coefficients of partial recruitment; we used
that method for estimating the Fo.1 reference
level in the projection algorithm. Variances of
catch projections with the extended method are
given in Table 9. While the relative error for
the 1981 stock size estimate is not modified by
this extension of the projection algorithm, the
relative error of the 1981 catch biomass (TAG)
goes from 15% to 18%. This 3% difference
represents the increase in relative error due to
the fact that Fo.1 is now estimated from input
data. It is interesting to note that the
variances of age-specific weights now account
for 74% of the total variance of 1981 catch
biomass, in comparison to 60% with 'fixed'
projections. These results re-enforce the
conclusions presented in the preceding paragraph
regarding the importance of age-specific weight
estimates for catch projections.
Similarly, various methods are used for
estimating the coefficients of partial
recruitment but the precision and the accuracy
of such estimates are generally unknown. In
general, we expect a negative correlation
between estimates of partial recruitment and
stock size estimates for the current year.
Consequently, the results presented hereabove
regarding the uncertainties of catch projections
will not be affected if the covariance term due
to this negative correlation is of the same
order of magnitude than the variance term due to
partial recruitment estimates. There is,
however, an additional source of error which is
related to the use of current estimates of
partial recruitment for the years of projection:
the current approach assumes that the fleet
composition, the gears being used and fish
availability are constant for the period of
projection. Such error, which is not random and
which is independent of stock size estimates,
does not cancel out and could introduce
inaccuracies in catch projections. In general,
such an error will influence more seriously the
estimates of partial recruitment for the
youngest age-groups, which age-groups do not
TABLE 9
Effect of various options on the relative error
of calculated quantities in catch projections:
example is for cod in 4T-4Vn.
A. Current methods (24%)*
B. Projecting from
estimates of stock
size at the beginning
of the current year
(Doubleday's method):
a. FQ·1 known
Relative error for
1981 1981
stock size catch
biomass
1. with historical data 11% 15%
2. annual mean
weight at age
calculated from a
von Bertalanff
growth curve 11% 14%
3. 25% reduction of the
within-year variance
of research survey
estimates 10% 14%
4. the relative error
for mean weight at
age reduced to 10% 11% 11%
5. Application of 3
and 4 above 10% 10%
b. FQ·1 expressed as a
function of input
information (with
historical datal 11% 18%
c. Effect of some systematic
(non random) errors when
method B is applied.
1. 100% increase of
partial recruitment
coefficient at age 3
and 45%, at age 4
for 1980 and 1981** 0.1% -2%
2. In 1979, unreported
50% discard at sea
for age 3, 25% for
age 4 0.1% 0.1%
3. Unreported 80%
discard at sea for
age 3, from 1970
to 1979 -0.5% -0.6%
4. In 1979, 20% 'underreporting'
for
a 11 age groups 0.7% 2.5%
*See Table 1; refers to the 1977 stock size.
**Results also valid for method A; considers
the effect of a change in r 1 on Fo.l·