Geoscience Reference
In-Depth Information
The study area may be partitioned according to habitat features (e.g., so that
the open grassed areas are in one stratum and the shrubs in another). Other
considerations may be related to field logistics and natural features in the
field, such as catchment boundaries or fence lines, that can be used. The size
of primary units may represent what sampling can be achieved by the field
crew in one day, simplifying planning fieldwork to a primary unit per day.
One of the early applications of adaptive sampling to a stratified design is
the two-phase stratified design proposed by Francis (1984). In the initial phase,
the survey area is partitioned into strata, and an initial survey is conducted in
which effort is allocated among the strata according to an estimate of within-
stratum variability as in conventional stratified sampling. The initial phase
sample results are used to estimate within-stratum variance. The remaining
sample units are added one by one to an individual stratum. At each step of
this sequential allocation of sample units, the stratum that is allocated the unit
is chosen on the basis of where the greatest reduction in variance will be.
The design is adaptive in that the preliminary information is used to update
the estimate of the within-strata variability, and the remaining survey effort is
allocated to the strata that will be most effective in reducing the overall sample
variance. The adaptive allocation in the second phase is done to adjust or to
make up for any shortcomings in the initial allocation of effort. For some pop-
ulations, rather than using the within-stratum variance of the criteria for adap-
tive allocation, the square of the stratum mean is preferred (Francis, 1984). See
also the work of Jolly and Hampton (1990) for a discussion of a similar design.
The estimates of the population total and the sample variance are derived
from all the information collected in the two phases. There can be a small
bias in the sample estimate, but this can be corrected by bootstrapping
(Manly, 2004). Adaptive two-phase sampling has been compared favorably
with adaptive cluster sampling (Yu et al
.
, 2012; Brown, 1999). The design can
also be used for surveying multiple species populations (Manly et al
.
, 2002).
A related design was proposed by Smith and Lundy (2006) for a stratified
sample of sea scallops, with the within-stratum mean from the first phase
used to allocate a fixed amount of effort to strata where the mean was above a
threshold value. They used the Rao-Blackwell method (Thompson and Seber,
1996) to derive an unbiased estimate for the population. Harbitz et al
.
(2009)
used a similar design for surveys of Norwegian spring-spawning herring,
for which extra survey transects were added to strata that had fish densities
(estimated from acoustic data) over a threshold limit. Another recent design
suggested for fishery surveys uses an optimization approach to minimize
the average distance between sample points and then allocates second-phase
effort according to a predefined abundance threshold (Liu et al
.
, 2011).
Adaptive allocation has been used with two-stage sampling in a design
called adaptive two-stage sequential sampling (Brown et al., 2008; Moradi
and Salehi, 2010). Note that here two-stage sampling is used, whereas the
previous discussion was about two-phase sampling. The two concepts are
close. As in the two-phase stratified designs, an initial sample is taken from
