Relación entre plastificante y duración del fraguado

4.5.1 Topographic Modelling

The survey data from Hobbister were entered into a GIS to allow a model of the pre-peat landscape to be created. To generate a continuous surface showing the topography of the pre-peat landscape it was necessary to interpolate between measured depths using functions within ESRI ArcMap 9.2.

Conolly and Lake (2006) note that simple linear interpolation using only two points along a straight line does not always result in accurate predictions of values at unsampled locations, and methods that use values and distances from a larger sample of surrounding known points give more reliable results. A commonly used method of linear interpolation is known as inverse distance weighting, which results in a simple, generally robust approximation of surfaces from a wide variety of point data (Wheatley and Gillings 2002).

Inverse distance weighting assumes that unknown values are more likely to resemble near values than distant ones, so the values of each point used to estimate the unknown value are weighted in inverse proportion to their distance from the unknown value (Wheatley and Gillings 2002). The effectiveness of this method of interpolation is dependent upon the number of neighbouring points (n) used in the calculation (Burrough 1986). Low values of n tend to produce quite a „blocky‟ surface, while very high values of n result in a very smooth background between data points, with the points themselves appearing as „peaks‟ above this (Wheatley and Gillings 2002). In this case a number of different values of n were tried in order to obtain the best compromise between the „blocky‟ result obtained with low values of n and the „peaky‟ result obtained with higher values, with a value of 10 giving the clearest result.

The resulting model of sub-peat topography at Hobbister is presented in the results chapter for the site.

4.5.2 Zonation

Pollen diagrams were subdivided into zones in order to simplify their description and aid in their discussion and interpretation. This was carried out using a function of psimpoll 4.25 (Bennett 2005) which generates zonation schemes based on both binary and optimal splitting, using either sum-of-squares or information content criteria (Birks and Gordon 1985), and on agglomeration using constrained cluster analysis (Grimm 1987). Zonation using this function was carried out on a subset of the pollen data from each site containing all main sum taxa that constituted 2% or more of at least one sample. The taxa included in the analysis for each site are listed in the relevant chapters.

Psimpoll 4.25 (Bennett 2005) also utilises a broken-stick model to determine the number of zones that can be reliably used from the output of a numerical zonation of pollen stratigraphical data, by separating variance resulting from structure in the dataset from that caused by stochastic processes (Bennett 1996). If the reduction in variance demonstrated that there is a strong positive correlation between palynological richness and palynological evenness (the degree to which taxon frequencies are similar) (Peros and Gajewsik 2008; Odgaard 2008). Evenness can be used as a measure of disturbance, since stable environments will tend to have uneven frequencies of different species due to one or two dominant species being more successful competitors. When disturbance is high, only species that can tolerate the environmental conditions will be present in high frequencies, again leading to low species evenness. Evenness will therefore be highest when disturbance occurs at an intermediate level (Grime 1973). Therefore the lower palynological richness, the more likely the environment is to have been either extremely unstable or extremely stable.

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While different pollen spectra do contain different numbers of pollen types, it is clear that the number of taxa recorded will be affected by the total number of grains counted, which will not be constant for all samples. Rarefaction analysis is a robust statistical technique that provides a minimum variance unbiased estimate of the expected number of taxa in a random sample of n individuals taken from N individuals containing T taxa, where n is less than or equal to N. The expected number of taxa in a count of size n is expressed as E(T_n) (Birks and Line 1992). Essentially, the technique standardises the pollen count to a single sum, removing the bias in richness estimates caused by differing count sizes and allowing meaningful comparison of palynological richness between samples. If the standardised count size and other conditions such as the pollen taxonomy used are kept constant between sequences, it should also be possible to compare palynological richness between sites.

Rarefaction analysis was carried out for each site using a function of psimpoll (Bennett 2005) and the results are presented in the percentage pollen diagram for each site. Since no sample counted contained fewer than 300 grains, this was the count size specified for standardisation.

4.5.4 Principal Components Analysis

Ordination techniques find axes of the greatest variability in species composition for a set of samples, and results can be plotted as an ordination diagram showing the similarity structure for the samples and species (Lepš and Šmilauer 2003). Principal components analysis (PCA) is an ordination technique that reduces multidimensional data to a low number of dimensions (Birks and Gordon 1985). The method measures the similarity between taxa, and then the resulting matrix is subjected to the PCA procedure, looking for major directions of variation within the dataset. The axes represent successively lower amounts of variation in the matrix. Transformations are usually applied to data before carrying out PCA in order to reduce the amount of difference between taxa with high and low pollen percentages, thereby preventing the analysis being dominated by taxa with high pollen productivities (Grimm 1987).

PCA was carried out on the covariance matrix derived from the combined dataset from all three sites in order to explore relationships between species and samples. The dataset contained all the main sum taxa that reached frequencies of 2% or more in at least one sample. A square-root transformation was applied to the data before carrying

out PCA using a function of psimpoll (Bennett 2005), since this is the most routinely used data transformation in pollen analysis (Grimm 1987). The results of the analysis were plotted using Microsoft Excel 2007 and the results are presented in Chapter 8, along with a list of taxa included in the analysis.

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