7116 ‎(2)‎

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

I'

.
I

Note that it is not necessary to estimate V(y;);
they are automatically included. If population
density is to be estimated, just divide Y and
^ ^
SE(Y) by M.

Estimation of population changes

,

So far we have only discussed some methods to
estimate total stock or density. Both in fishery
management and environment monitoring, how-
ever, population change is often of greater interest
than absolute values.
We can use all methods above to estimate the
absolute population change D = X - Y, where Y is
the population size in one occation and X in
another. To do this, however, the best method is
probably to use as input variables a. = ~. - y^.
^ 1 I I
ip.stead of Y i, and instead of V (y;) the sum
V(~;) + V(yJ.
^
The result is an estimate D and its variance
^ ^ ^ ^
V(D) or Standard Error SE(D). In this case
the comparison is based on 'paired'observations,
viz. the same sections on each occasion. This
design is often the best one when the main aim is
to monitor changes, and the reason is that there
is often a positive correlation between y and x
('good' sections in one year are often 'better' than
the average even in the following year). This tends
to reduce the (spatial) variance of the a. values
I ^
and therefore also the sampling error of D.
There are two practical consequences of this:
1. The gain in precision is probably larger when
using the SRS design with no auxiliary variable
(Eqs. (21-22)), than if SRS with an auxiliary
variable is used (egs. (23-24)) or in the case of
PPS (eqs. (25-26)). In practice this means that
SRS without the use of an auxiliary variable,
being the cheapest method, may perform as
well as the other two methods and should be
tried when estimation of absolute population
change "is the main aim.
2. When using SRS without an auxiliary variable,
the gain in precision by using paired observa-
tions depends on both the variances V (y) and
Vex) and on the correlation between x and y.
Using the data on which Table 3 is based,

33

Table 5. Sample size n required to reach a given precision
class (see 3.3.) for various combinations of coefficients of
correlation r and total number of units N. Cp = 0.8 in all
cases. Paired observations assume& Sample size and precision
classes. paired data.

N = 25 N = 50 N = 100 N = 00

Class 1 r=O 22 38 60 160
r = 0.6 19 29 40 64
r = 0.8 16 21 27 34
Class 2 r=O 16 22 26 34
r = 0.6 II 13 15 17
r = 0.8 9 10 II 11
Class 3 r=O 10 12 14 14
r = 0.6 8 9 9 9
r = 0.8 6 7 7 7

covering a wide range of stream types, we
found strikingly similar correlation coefficients
r between population size per section year 1
and year 2 (r = 0.63-0.79) for salmon and
trout older than one summer. Further, if we
assume a Cp value of 0.8, we can make a crude
calculation of the sample size required to reach
precision class 1-3 in the case of paired
observation. The result (Table 5) can be com-
pared with the sample sizes in Table 4. This
comparison shows that considerably smaller
sample sizes n are required to 'discover' popu-
lation changes of a given magnitude (Table 4)
than to 'discover' differences between popu-
lations (Table 3). It appears that a sample size
of about 15 would be sufficient to reach
Class 2 even in large streams (N large).

^
To test whether an observed difference D is
statistically significant, the safest way is to use a
non-parametric test, e.g. Wilcoxon match-paired
signed-ranks test, which is powerful but very
simple to use (see e.g. Siegel, 1958; p. 75).
Finally, the relative population change R = X/V
(e.g. finite survival) is often of interest. As pointed
out by Youngs and Robson (1978), however, the
sampling variance of such a ratio 'is much more
complex and has not been delt with to any greater
extent in fishery literature'. We therefore know
little about sampling designs where the main aim