Maximum likelihood estimates of biological populations have been obtained on the basis of se-quential tagging experiments without replacement. At the time just before the
t-th sample (
t=1, 2, …,
T) is taken, the size of a population may be represented by
Nt-1 and the number of tagged individuals by
At-1. Let us assume
xt tagged individuals are found in
t-th sample of size
nt drawn at random from this population. Then,
mt individuals are taken out from the population again, tagged and released regardless whether or not they have been tagged before. If
yt among me has already been tagged, an actual increase in tagged individuals during the
t-th experiment is
mt-
yt-
xt.
Under usual circumstances it could be assumed that
Nt-l_??_
nt and
Nt-1_??_
At-1; hence
xt is ex-pected to follow Poisson distribution with mean of
ntAt-1/
Nt-1, and
yt is negligibly small. From these models the maximum likelihood estimates have been derived by using the successive approxi-mations as D
EL
URY did (formulae 1-6). Approximate coefficient of variation of estimated 1/
N0 or
F=
∑nt/
N0 is given by the reciprocal of square root of the total number recaptured (formulae 11 and 12).
If
At-1 is not too small in contrast with
Nt-1, the binomial distribution is more suitable than Poisson distribution to be used as a basic mathematical model. The estimates are obtained in the same procedure as before (formulae 7 and 8).
When data drawn from a constructed binomial population were analysed by using
At and
At', for both models of binomial and Poisson populations, it has been found that the effect of the difference of population models is small enough, and that the effect of neglecting
yt is not serious, though the results based on correct
At are always smaller than on approximate
At' (Tables 1 and 2).
For another example, the methods are applied to the data obtained from the marking experi-ments of fin whale which were carried out in the 1954 and 1955 seasons in one of three major whaling grounds of the northern North Pacific, located north of Aleutian Islands and east of 180° meridian. On the basis of biological surveys and tagging experiments it has been believed so far that there are a few different populations, each frequenting to one of these whaling grounds where they would stay for a considerable length of the season every year. This fact makes the situation simple for the statistical estimation by marking experiments. The data and results of calculations are shown in Tables 3-6. In addition, catch-effort records (Table 7) are analysed by D
EL
URY's method to compare them with the results of the marking experiments. Although these estimates have only a little reliability, it might be safely said that the size of the fin whale population in the region under study is 5, 000-50, 000.
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