CAUSAS DE LA VIOLENCIA FAMILIAR

6.1. Introduction.

The non-conformity of several of the profiles to an exponential distribution suggest th a t processes of preferential selection take place w ithin the soil profiles of the study area. Although this is problematic, it does not render th e ^^^Cs technique inadequate for quantifying soil redistribution. The potential exists to correct the profiles for this effect by modelling the profile shape. Unfortunately, ^^^Cs profiles are not available a t every site and the provision of a reliable n et soil flux m ap based on ^^^Cs profiles would be prohibitively time-consuming (Longmore et al., 1983). Although ^^^Cs éluviation cannot be totally overcome w ithin the present study, the use of depth-bulked samples provides several logistical advantages.

Results from the PCA of soil profile samples showed th at, although ^^^Cs contributed to the explanation of variance in the first principal component, other properties were more im portant. The low importance of ^^^Cs on the principal components is surprising since it was thought to be associated w ith erosion and deposition. By conducting the same analyses on depth-bulked samples it is hoped th a t the ^^^Cs loading will be more dominant and provide a greater explanation of variation in the principal components. If so, the depth-bulked samples m ight provide a more useful sam pling approach for mapping ^^^Cs and calculating n et soil flux.

6.2. P rin cip a l com ponents an alysis.

The soil properties of the depth-bulked samples were standardised following the method of Odeh et al. (1991) as described above (Section 5.2). The results of the PCA for samples bulked w ith depth from the entire study area (global) are shown in Table

6.2.1. Most variance is explained by the first eigenvalue b ut the proportion of variance explained by subsequent eigenvalues does not decrease rapidly. Thus, the

first two explain approximately 57 % of the variance. This suggests a large am ount of inter-correlation between soil properties. Sites were divided between Plain and P lateau in an attem pt to increase the percentage variance explained. Direct comparison between the explained variance for these regions is not possible because bulk density and soil strength variables were not available on the Plateau. Despite this, the percentage variance explained by the P lateau is sim ilar to th a t for the global region (Table 6.2.1). The results suggest th a t the PCA of the global region m ay be dominated by variation in data from the Plateau.

Table 6.2.1. Comparison of eigenvalues and explained variance accounted for by PCA of sites from w ithin the study area.

Principal components Global Eigenvalues 5.48 3.14 1.53 1.21 1.06 0.73 Variance 36.52 20.97 10.17 8.05 7.06 4.86 Plain Eigenvalues 4.89 2.50 1.59 1.42 1.06 0.92 Variance % 32.59 16.69 10.59 9.47 7.09 6.12 Plateau Eigenvalues 3.90 1.93 1.56 1.44 0.96 0.79 Variance % 35.41 17.56 14.21 13.07 8.74 7.14

Since th e data were standardised prior to the PCA the highlighted dom inant component loadings (Table 6.2.2) plotted in the plane of th e first two principal components (Figure 6.2.1) may be used for interpretation. As w ith the profile sam ples, the first principal component of the depth-bulked saniples is dom inated by percentage silt and sand content, pH and organic m atter, and to a lesser extent by soil strength at 15 cm depth, bulk density and the mass expression of ^^^Cs.

Table 6.2.2. Principal component loadings of soil properties from sites w ithin regions of the study area.

Principal component loadings

Global Plateau Plain

1 2 1 2 1 2 Soil Property % Organic m atter -0.356 0.058 -0.118 0.017 -0.294 0.142 Bulk density 0.293 0.355 - - 0.221 -0.037 (Bq k g ') -0.291 -0.379 -0.446 0.314 0.093 0.528 ""Cs (Bq m ") -0.207 -0.391 -0.446 0.318 0.101 0.527 Strength (5 cm) -0.200 0.332 - - -0.205 -0.126 Strength (10 cm) -0.123 0.282 - - -0.159 0.348 Strength (15 cm) -0.305 -0.254 - - -0.138 0.424 % L f -0.222 0.313 -0.254 -0.515 -0.370 0.162 Hue -0.118 0.224 -0.044 -0.223 -0.284 -0.173 Value 0.117 0.086 0.425 -0.335 -0.090 -0.078 Chroma 0.242 -0.042 0.185 0.166 0.100 -0.047 pH -0.376 0.147 0.040 -0.134 0.238 0.200 % Silt content -0.376 0.147 -0.345 -0.182 -0.407 -0.010 % Sand content 0.374 -0.150 0.344 0,185 0.405 0.009

A sim ilar set of loadings exerts an influence on principal component two due to the large proportion of variance explained by this component. The im portant loadings include both expressions of ^^^Cs, bulk density, soil strength and Notably, an inverse relationship between bulk density and ^^^Cs exists. Although not strongly loaded on either component, soil hue is positively related to %Lf and soil strength, soil chroma to sand content and soil value to bulk density. These relationships w ere also identified in the profile analysis where they were interpreted as being linked to drainage qualities.

Plateau and Plain regions it is not surprising to find the same loadings dom inating the first two principal components. It is clear from the sim ilarity in the dom inant loadings and the ordering of these loadings th a t the PCA of th e global region is a generalisation of the sm aller Plateau and Plain regions. Furtherm ore, the associations th a t have been made for each PCA are sufficiently sim ilar to avoid conducting this analysis on the separate regions.

0.4 _Bd 0.3 sm Q . - 0 . I a -0.2 -0 .3 -0 .4 0.1 0.2 0.3 -0 .1 -0 .0 0.4 -0 .4

Principal com ponent 1

Figure 6.2.1 Depth-bulked soil eigenvectors labelled for each property plotted in the plane of the first two principal components.

6.3. N o n -h iera rc h ic al m u ltiv a ria te classific atio n .

The principal component site scores for the global region are plotted in the plane of the first two principal components in Figure 6.3.1. Despite the only slight clustering, non-hierarchical classification of the m ultivariate dataset was performed.

Selection of the optimal classification was hindered by th e lack of Wilks’s criterion which was due to the inability of the program to handle m issing data. The sum of squares (SS) was used as an alternative (Figure 6.3.2). However, it is still difficult to identify the optimal classification. Principal component scores m ay be used in place of the m ultivariate dataset to replace the missing values. Thus, both W ilks’s and SS criteria became available. By comparison between these criteria for the classification using the principal component scores, the use of the w eaker SS

criterion was validated for the identification of the optimal classification using the m ultivariate dataset (Figure 6.3.2). Slight clustering in the data is evident in the trough at g = 6. This suggests that if there are weak clusters, then there are six classes (Oliver and Webster, 1987a).

An interpretation of principal components for the global region is provided by inspection of the site scores plotted in the plane of the first two principal components (Figure 6.3.1) and labelled using the six classes. To aid interpretation of the principal components and to summarise the soil in the study area the average of each soil property for each class was produced (Table 6.3.1).

0.4 0.3 0.2 0.1 -0 .1 o - 0 . 2 0- -01 - 0 4 -0.5 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 Principal com ponent I

-0 .0 0.2

Figure 6.3.1 Principal component scores for depth-bulked samples of the global region plotted in the plane of the first two principal components and labelled using the multivariate classification.

Principal component one represents variation mainly in particle size, organic m atter and pH. Finer more organically rich material with higher pH levels is found on the left (classes 2, 3, 4 and 6), whilst coarser soil with less organic m atter and lower pH levels is found on the right (classes 1 and 5). Principal component two represents variation in ^^^Cs, Xlf soil compaction. Lower ^^^Cs but higher soil compaction and

Xu are found in the upper portion of the diagram (classes 1, 3 and 4), whilst higher ^^^Cs and lower soil and compaction and ^Lf are found on the lower portion (classes 2, 5 and 6).

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