さあ！諸君！捕鯨問題だ！

（つづき）
Simulations were run using a cohort model, with density
dependence on pregnancy rate given by a Pella-Tomlinson
function, leading to an MSY rate of approximately 3% at
MSY population level of 60% of the unexploited
population size. The age-dependent natural mortality
schedule for the population is given in Table 1. The same
constant catch is removed from the previously unexploited
population for ten years prior to the first collection of
catch-at-age samples. Three cases are examined: (1)
sample size of 825 in each year, (2) sample size of 8250 in
each year and (3) perfect age data (i.e. free of sampling
variability). In all cases, ages are determined without
error. The rate of exploitation is kept constant in each case
by rescaling the total population size. That is, the catch of
825 animals is taken from a population with an unexploited
size of 100,000, and the catches of 8,250 from a population
of 1,000,000. The rate of exploitation is less than 1 %, and
hence comparable with the situation thought to apply for
the Japanese research program, at least in Area V.
However, the estimator used does not require the
assumption that the rate of exploitation is low.

　 The stochastic catch-at-age samples have a multinomial
distribution. The yearly estimates of population size have a
lognormal distribution with expected value equal to the
true population size and a constant coefficient of variation
(CV) of 0.15. The CV is at the low end of the range
currently achieved in the IDCR sightings surveys (IWC,
1985). The CV's of sightings estimates currently available
may underestimate the true CV of a series of sightings
estimates since they consider only the effect of sampling
variability. In practice other year to year sources of
variation may affect sightings estimates. The samples are
collected every year for twenty years (i.e. k = 1), and
include 40 age classes. Equation (7) shows that the
precision of results obtained would be the same for the case
where the time series of estimates of abundance were an
index rather than absolute values, but this would introduce
bias if the rate of exploitation was not corrected for.
（つづく）