7116 ‎(2)‎

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

r

below. First, compute A = 2c, + C2 and T. y is
then estimated as

y = 6A2 - 3AT - T2 + T JT2 + 6AT - 3A2
18(A - T)
(11)

and p as

^ 3A - T - JT2 + 6A T - 3A 2
P = (12)
2A

1

The Standard Errors of these are given by (8) and
(9).

Example 2. c, = 244, c2 = 86 and C3 = 43. Then,
A = 574
T = 373
Y = 398.4
^ ^
SE(y) = 8.17
P = 0.600
If, instead, (10) and (7) are used,
p = 0.609
Y = 396.7

The case of 2 removals
In the case of 2 removals (e.g. Seber and LeCren,
1967) the estimators are

y = cif(c, - c2)

Y(y) = cfc~(cl + c2)
(c, - C2)4

P = 1 - c2/c,

Y(P> = c2(c, + c2)/cj

(13)

(14)

(15)
(16)

The Standard Errors of y and p are the square
roots of (14) and (16), and confidence limits as in
(3). (13) may be corrected for bias:

* ^ q (1 - q)
y = y -
^3
P

(13')

where y is calculated from (13).

23

Using an approximately known catchability
Under similar conditions a skilled electrofisher
may have an approximately constant efficiency or
catch ability. If this p is estimated by some of the
methods proposed above and can be assumed
constant, it can be used either to get population
estimates where only one removal has been
carried out, or to increase the precision in the case
of two or more removals. This method is espe-
cially valuable if the population size in a specific
area is very low (e.g. older fish), as the methods
above may fail or at least give poor precision in
this case. The rational is that q is estimated from
a large population (e.g. the pooled result from
several sections) where at least 2 or, better, 3
removals have been carried out. This q, which
thus has a good precision, is used in (7) to calcu-
late the size of the 'small' population or the popu-
lation in which few removals have been per-
formed. As an example (example 3), 3 removals
were carried out in each of 17 sections in a trout
stream, yielding, totally, 1002,213 and 68 trout of
age 1 +. From eq. (12) p is 0.761 and
q = 1- 0.761 = 0.239. In section No. 18 the fish-
ing had to be interrupted after 1 fishing, yielding
65 trout of this age class. Then from (7), y = 85.4
in section No. 18. Example 4. In section No. 19,
the catch from 3 removals was 2, 2 and O. The
population is too small to apply eq. (11) (see
below), so the p estimate from example 3 is used.
Using (7), a population size y = 4.06 is obtained
for section No. 19.
The precision in this case is partly determined
by the precision of the p estimate applied. Bohlin
(1981) showed that the sampling variance, pro-
vided that the population is not too small, is
approximately
^^k (~k^k-I)2
Y(^) = yq + yep) y q
y 1 ^k 1 ^k
-q -q
Using the data from example 3, the following
result is obtained:

(17)

y = 85.4
P = 0.761 (eq. 12), q = 1 - 0.761 = 0.239
7\
yep) = 0.000155 (eq. 9)
k = 1
^ ^ ^
V(y) = 28.77 (eq. 17), SE(y) = 5.36