7116 ‎(2)‎

• UCREFRP Catalog Number: 7116
• Author: Baxter, G. and J. Simon
• Title: Editor
• USFW Year: Series
• USFW - Doc Type: 1970
• Copyright Material: YES

22

too small for individual tagging, and thus that
one may encounter problems separating
marked members from those that were marked
on previous occasions. If this is not a problem,
clipping of the adiposal fin may be the best
marking method. For short term studies, other
fins may be used, or various branding
methods.

The removal method

The second type of method used to estimate
population size in a small, closed area is the
removal method. This is the method most widely
used to estimate the population size of fish in
streams or the litoral zone of lakes when using
electrofishing and can be used if the capture is
efficient enough to reduce the population size
substantially.
To apply the removal method, the following
assumptions should be fulfilled (Seber, 1973;
p.312):

(1) The population is closed
(2) Equal catchability for all individuals
(3) Equal catch ability among the removals

The general case of k removals
To get estimates of population size from succes-
sive removals, one method is to use the maximum
likelihood estimator developed by Moran (1951)
and Zippin (1956). As there is no general explicite
solution, Zip pin (1956, 1958) provided graphs by
which the population size and the catchability can
be estimated in the case of 3, 4, 5 and 7 removals.
If k = the number of removals, c1 , c2. . . ck = the
catch in each consequtive removal,
T = (c, + c2 + ... + ck) = total catch, p = catch-
ability, and q ::::: 1 - p, a more flexible method is
to let a computer estimate q by iterative solution
of the expression

k
^ kqk L (i - l)cj
q i = 1 (6)
=
^ 1 ^k T
P -q

In (6), the sum in the last term is C2 + 2c) for
k = 3, and C2 + 2c) + 3c4 for k = 4 and so on. If
(6) is used for iterative solution, a first guess of
p = c,/T can be used. The population size y is
estimated by using the q value obtained in the
expreSSIOn

^ T
Y = (1 - qk)

(7)

The sampling variances of y and pare

^ y(1- qk)qk
V(y) = (1- qk)2 _ (pk)2qk-'

(8)

and

r

v ^ _ (qP)2 (1 - qk) (9)
(p) - y [q(1 - qk? _ (kP)2qk]

The Standard Errors are the square roots of (8)
and (9). For confidence limits, see (3).
Although (6) and (7) are readily programmed
into a computer, it is sometimes convenient, e.g.
in the field, to use simpler methods. One such,
yielding practically the same result as the method
above, and which to our knowledge has not been
previously used, is the following. An estimator of
q is(l)

^ T - c1
q=
T - ck

(10)

with the notation above. To obtain population
size, (7) is used.
Another simple method is Hayne's (1949) gra-
phical regression method. The relations (10) and
(7), however, are as simple to use, less subjective
and therefore recommended in favour of Hayne's
method.

.*
(

1

,

The case of 3 removals
Junge and Libosvarsky (1965) found explicite
solutions of y and p in the case of k = 3. As this
case is of special interest, the solutions are given

t.
(

(I) Derived in appendix I.