さあ！諸君！捕鯨問題だ！

The natural mortality estimates from 1,000 trials are
summarised in Table 1. ＃Fig. 1 shows the mean of the
estimates from the 1,000 trials with sample size 825, and
the 95% confidence intervals for the two sample sizes
and the confidence intervals associated with perfect
information on the population age structure. The results
show that the confidence intervals are very wide, even for
the case of perfect age data. In the perfect age data case it
can be seen that the confidence intervals have the same
shape as the true age-dependent mortality rates, but
shifted up or down. In the flat part of the mortality curve
the M a estimates have a CV of 0.21. The multinomial age
sample cases show wider confidence intervals which
expand for higher ages.

With stochastic catch-at-age data, pooling the indIvidual
age-dependent mortality rates, or fitting a more
parsimoniously parameterised curve to the data, would
reduce the width of the overall confidence intervals.
However, with perfect age data, the shape of the
age-dependent natural mortality curve is estimated
without error. In that case, estimation only involves fixing
the position of the natural mortality curve, and this
depends only on the variability in correcting for the effects
of the (non-constant) trends in the population over time
from the abundance data. Consequently, the perfect age
data confidence intervals represent a lower bound to
confidence intervals for the age-dependent natural
mortality curve, regardless of how its shape is estimated
from the data.

　 The time scale used in. these simulations is twenty years;
for the proposed Japanese research, which samples for half
the time in two different stock areas, the equivalent results
would require about 30 years of sampling. Producing
reasonably precise M a estimates (CV of 10%), even with
perfect age data would require the length of sampling
（491/492頁）
period to be increased by a factor of approximately 1.6, i.e.
to 48 years. Thus, there is no prospect of obtaining
reasonably precise estimates of age-dependent natural
mortality from the proposed Japanese research
programme in a reasonable time frame, even if much larger
sample sizes were used, unless very substantial
improvements can be made in the precision of population
abundance estimation. The same conclusion applies
regardless of whether the method of Nakamura et al.
(1989) is used or that of Sakuramoto and Tanaka (1989).

　 To examine the effect of the minimum level of
uncertainty on age-dependent mortality on trends in
recruitment calculated from the catch-at-age data, the M a
values corresponding to the confidence bounds from the
perfect age data case are used. In this case the calculated
trends represent the minimum 95% confidence bounds on
the trends themselves. The calculated trends for each
confidence bound are shown in ＃Fig. 2, along with the true
trend in recruitment. The three curves are arbitrarily.
scaled to pass through the same recruitment level in year
40. It can be seen that the calculated trends would not be
expected to give any reliable estimates of any trends in
recruitment in the real population.

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＃Fig. 1,＃Fig. 2 　 は表示不能

以下 　 No.42686 　　 の CONCLUSION AND DISCUSSIONへ続きます。