McArdle, BrianPawley, Matthew David McDonald2006-12-132006-12-132006Thesis (PhD--Statistics and Biological Sciences)--University of Auckland, 2006.http://hdl.handle.net/2292/284Random 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.enItems in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated.https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htmThesisCopyright: The authorQ112868621