Abstract:
Random start systematic sampling (SYS) is a survey design that is simple (it selects
the whole sample with one random start), easy to implement and that can, in theory,
give precise estimates of ecological abundance in the presence of positive spatial
autocorrelation. However, SYS suffers from a serious defect, namely, that it is not
possible to obtain an unbiased estimator of sampling variance (θSYS) on the basis of a
single sample. A variety of approximations have been suggested, and unbiased modelbased
methods have been calculated, but validation of these estimators has been
limited within the ecological literature.
The heart of any spatial problem is how to deal with spatial autocorrelation. We show
that the scale of spatial inference gives a framework that unifies the commonly
reported, discordant views about autocorrelation (i.e. ‘autocorrelation increases the
power of the analysis’ vs ‘autocorrelation decreases the power of the analysis’). The
scale of spatial inference is rarely discussed or considered, but we suggest that it
should be the first step in any (spatial) analysis.
The thesis then uses computer simulation to compare the performance of eleven
previously proposed SYS estimators (including simple random sampling, 4SRS). The
computer simulations are designed to recreate the spatial distribution characteristics
that are common within ecological abundances. We also develop and test a novel
method of estimating θSYS based on ‘Krige’s Additivity Relationship’ and variography
(geostatistics). This estimator was labelled 4KAR.
We found that if the right spatial model (i.e. a reference theoretical variogram) is
used, then 4KAR appears to be an unbiased estimator of θ. Without a priori knowledge
about the spatial structure (so the theoretical variogram is constructed solely from SYS
data), 4KAR was generally one of the least biased and most stable estimators out of
those examined. The other estimator that fared well, 4r1, was also model-based; it
used an estimate of the first order autocorrelation in its estimate of θ. 4SRS performed
comparatively well on untransformed ecological simulations, but was the worst
performing estimator after a log(x+1) transformation.