7116 ‎(2)‎

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

30

Yi = Ydmj population density in a unit i, esti-
mated as

!l ^ ^
Yi = Ydmj

Y = Y /M mean population density in the
stratum or target area, estimated as

^ n n

Yi = L Yd L mj
Pi == mdM probability of selecting unit i when
using proportional probability
sampling with replacement.

This section is organized in the following way.
First, 3 general methods of total stock assessment
are outlined and examplified without much
reference to their limitations. Then we continue
with a discussion on how to estimate population
changes rather than population size; this is often
a main goal. Finally, the application of the
methods proposed are discussed with special
reference to large streams.

Methods based on simple random sampling (SRS)
within strata

Regardless whether the areas are of equal or
unequal size, one way to obtain a sample is to use
simple random sampling. This is usually carried
out by numbering all the N sections and then
using a table of random numbers drawing a
sample of size n. The population size Yj in each of
these n sections is then estimated by electro-
fishing, e.g. by some of the methods proposed
above, as Y i with a sampling variance V (y i)'
If sections of (approximately) equal size (e.g.
length) are used, the following method can be
employed to estimate total population Y.
Compute the mean per section as

n ^
.:. (^ ('; ^)/ "Yi
y= Y'+.Y2+"',+Yn n=L.,-
n

and the estimated (spatial) variance between the
areas in the usual way as

v (y) = f (y i - Y )2
n - 1

The total population in the stratum is then esti-
mated as

^ -
Y = Ny

(21)

^ ^
and the sampling variance V(Y) of Y as

^ ^ N ^ N~ ^
V(Y) = - (N - n) V(y) + - L., V(yJ (22)
n n

^
SE(Y) is estimated as the square root of this
expressIOn.
This method will be referred to as SRS esti-
mation without auxiliary variable.
In eq. (22), the first term is the error generated
by the spatial variation of the fish population, and
the second the additional error due to the fact that
each Yi is estimated, not known.
Ifmore than 1 stratum is used, the total popula-
tion in the target area is the sum of the total
populations in each stratum. As the sampling
variances are also additive, this leads to
h
^ ^
Y lOt = L Yj
where h is the number of strata and Yj the total
population in the j : th stratum, and
h
^ ^ ^ ^
V(Ytot) = L V(Y)

(

^ ^
As usuaJIy, SE(Ytot) is the square root of
^ ^
V(Ytot)'

Example 5. 7 sections of approximately equal
length (n = 7) were drawn at random from a
stratum with N = 37. The populations Yi were
estimated using 3 removals and applying eq. (11)
and (8). The input data c, , c2, C3 and the result
is then:

.>

r

^ ^ ^
i c, C2 C3 Yi V(yJ
1 178 31 7 217.4 1.76
2 69 18 7 96.5 4.35
3 107 13 5 125.6 0.68
4 88 26 6 122.6 4.20
5 104 27 9 143.1 5.19
6 111 24 7 143.9 2.68
7 28 8 3 40.2 2.22

.~

h

l