さあ！諸君！捕鯨問題だ！

One aim of this note is to clarify the relationship between
the trials of Sakuramoto and Tanaka (1989) and the
general problem of estimating trend in recruitment and
age-dependent natural mortality. Some indications of the
likely precision of resultant estimates in recruitment trends
will be given.

The proposed Japanese catches are to be taken under a
sampling design which is intended to result in catch-at-age
distributions which are representative of the whole
population. While objections have been raised concerning
the ability of the proposed sampling method to achieve that
end (IWC, 1989a; IWC, 1989b, p. 55), for the purposes of
this paper, it is assumed that representative samples can be
obtained.
Sakuramoto and Tanaka (1989) correctly point out that
the difference between the age-dependent natural
mortality values and a 'Heincke-like' average value can be
determined from catch-at-age data alone. From this it
follows that the difference between any pair of
age-dependent natural mortalities can also be estimated.
Let:
Nr,t = the total number of animals in the population,
before catching, with ages r and greater in year t;
Cr,t = the catch of animals with ages r and greater in year t;
　　 ＝ 　 Σc a,t
　　　　　 a=r

where c a,t = the catch of animals in age class a in year t; and
k = the inter-sample interval, i.e. a sample (catch) is taken
every k years, and not in between.

It follows that, if negligible natural mortality occurs
during the period in which the catch is taken, the average
survivorship after natural mortality in the population of
animals aged r and greater in year t to year t + k is given by:

Sr = (N r+k,t+k)/(N r,t - Cr,t) (1)

（つづく）