さあ！諸君！捕鯨問題だ！

Now let n a,t be the number of animals, before catches, in
age class a in year t . The overall (age-dependent)
survivorship of animals aged a in year t to age a + k in year
t + k is given by:

~Sa = (n a+k, t+k)/(n a,t - c a,t) (2)

Let:

p a,t = the proportion of a sample taken in year t with age a
= c a,t/C 0,t
Pr,t = the proportion of a sample with ages r or greater in year t
= (ΣC a,t)/C 0,t
a=r

It is easily shown from (1) and (2) that:
~Sa = (p a+k,t+k . Sr)/(Pr+k,t+k * p a,t) (3)
and hence;
~M a - M r = lin [(P r+k, t+k * p a,t) / (p a+k,t+k)] (4)

（489/490頁）

which is the equivalent of equation (11) of Tanaka (1988).
From this it follows that the difference between average
age-dependent natural mortality, for ages a and j say, is
given by:
~Ma - ~Mj = log [(p a,t *. p j+k,t+k) / (p a+k,t+k * p j,t)] (5)*

This means that the shape of the age-dependent mortality
curve can be determined from catch-at-age data alone.
However, because the average level cannot be determined
without knowing the change in population size between the
two samples, the position of the age-dependent mortality
curve cannot be fixed from the catch-at-age data alone.
One of the main uses which the Japanese research
programme intends for age-dependent mortality rates is to
determine trends in recruitment from catch-at-age data.
___________
(5)* : log は自然対数

（つづく）