さあ！諸君！捕鯨問題だ！

REP. INT. WHAL. COMMN 40, 1990 　　 pｐ.489―４９２

A Further Note on the Simultaneous Estimation of Natural
Mortality Rate and Population Trend from Catch-at-age Data
William K. de la Mare

INTRODUCTION
Japanese research involving the taking of minke whales in
the Antarctic under Special Permit has identified as its
major aim the estimation of age-dependent natural
mortality rates by an analysis of catch-at-age data. Central
to this aim is the use of a method of analysis of a time series
of catch-at-age data proposed by Tanaka (1988). De la
Mare (1989) has shown that the method of Tanaka, as
originally presented to the Scientific Committee, cannot
work in principle, because the problem is under-specified;
that is, the number of unknown parameters is greater than
the number of independent equations. That analysis
assumed negligible fishing mortality, as is inherent in the
design of the Japanese research program. Cooke (1988)
showed that the results of de la Mare (1989) apply even
when fishing mortality is not negligible.
Sakuramoto and Tanaka (1989) conducted simulation
trials showing that age-dependence in natural mortality
could be estimated from a time series of catch-at-age data.
However, this is not the same as estimating age-dependent
natural mortality, which was the original intention of the
Japanese research program and the method of Tanaka
(1988). The simulations are not tests of Tanaka's (1988)
method, because they do not implement the iterative
procedure using the 'multi-cohort method' (Sakuramoto
and Tanaka, 1985) to estimate average rate of population
increase, and then use that to modify the estimate of
average M, and so on. Sakuramoto and Tanaka (1989) in
fact propose using a time series of successive population
estimates as a component in estimating mortality. This, as
de la Mare (1989) showed is a necessary condition for
estimating natural mortality rates from catch-at-age data.

（つづく）