SPSS version 16 and Pisces Conservation Ltd ‘Species Diversity and Richness IV v. 4.0’ were used for the statistical analysis.
To test the hypothesis that all sites would have the same invertebrate
abundance, a chi-square test for differences was carried out (Tabachnick and Fidell, 2007) (Objective 3.2). The mean abundance of morpho-species was examined using one-way ANOVA, testing the hypothesis that all sites have the same mean invertebrate abundance. Where significant differences were found, Tukey tests were used a posteriori to identify the source of the significance (Ennos, 2007). The same procedure was then used to examine any variation between the individual taxa at each site i.e. were similar proportions of beetles, for example, found at all sites?
j = H(s) H(max)
Correlation analysis, using the Pearson product-moment correlation coefficient, was then used to explore the strength and direction of any linear relationship between the total numbers of individuals found to the principal components, which represent the urban-rural gradients (Objective 3.3).
The Species Richness & Diversity III v. 3.0 package (Pisces Conservation Ltd) was used to test the hypothesis that all sites would have the same species diversity and evenness, the diversity among the different taxa was examined using a range of indices (Objective 3.4). The most commonly used diversity measure is the Shannon-Wiener diversity index (H), which measures the rarity and commonness of species in a community (Magurran, 2004). As the
methods used in this study may be replicated to allow a quick assessment of similar sites, it was useful to use indices that were both familiar and popular, therefore, the Shannon-Wiener diversity index (Equation 1) and Pielou’s
evenness index (Equation 2) were used to assess relative species diversity and evenness in this section of the study.
H = - Σ pi ln ( pi) Equation 1
where pi = the proportion of a particular species in a sample which is multiplied
by the natural logarithm of itself (Fowler and Cohen, 1990).
Pielou’s equitability index (Clarke and Warwick, 2001) was then calculated: where H(s) = the Shannon-Wiener index H(s); H(max) = the theoretical maximum value for H(s) if all species in the sample were equally abundant:
Equation 2
One-way ANOVAs were then used to examine any differences in taxa diversity (DV) along the urban-rural gradient (IV) (Objective 3.5). The null hypothesis
tested was that all taxa would be found in similar proportion regardless of position on the gradient. Again, where significant differences were found, Tukey tests were used a posteriori to identify the source of the significance.
3.9 RESULTS
3.10 Establishing the urban-rural gradient
A ‘common sense’ approach to classify the chosen allotment sites as urban, suburban or rural, based mainly on population and size, would suggest that the most urban sites would be in Hull (Newland and Bude), a large city, possibly with Bridlington being classified as relatively urban too. The most rural sites would likely be Driffield and Hunmanby, due to their location on the edge of small villages or towns, whilst Cottingham and Beverley were most likely to be classed as suburban. The range of data gathered to support these
assumptions is summarized in Table 3.1 (see Methods Section 3.5 for details). These data show considerable variation between the physical parameters of each allotment site and are used to assess whether or not these assumptions were true or not regarding the presence of an urban-rural gradient.
Table 3.1 Physical parameters for each allotment site used for PCA.
(HN=Hunmanby; BR=Bridlington; DR=Driffield; BV=Beverley; CT=Cottingham; BD=Bude; NW=Newland.) (See Section 3.5 for details.)
HN BR DR BV CT BD NW
Population 6000 33837 11477 17549 17263 243589 243589 Site area (ha) 1.00 1.50 3.10 2.50 1.40 2.24 8.30
No. of plots 10 56 113 17 9 74 280
Ave. plot size 76 300 300 270 200 250 350
% hard surface 500m 66.25 82.50 37.50 95.00 93.75 70.00 87.50 % hard surface 1km 45.63 85.94 31.56 71.56 70.00 76.88 91.56 % hard surface 2km 12.31 60.38 25.77 54.62 48.85 75.77 95.00
No. of trees on site 1 0 0 1 0 0 62
No. of trees in 100m 400 22 208 11 23 1 180
No. allotment sites 1 2 2 3 3 22 22
% famland 1 km 40 0 75 0 5 0 0
Land allocation: site 1 3 1 2 1 5 3
The thirteen physical variables were subjected to Principle Components Analysis with Varimax rotation using both SPSS Version 16 and CAP 3.1 to establish the relationships between allotment sites. Although the data matrix was relatively small (ninety-one cases), most of the loading values exceeded 0.8 (see Appendix A3.4), therefore the test was sufficiently robust (see Tabachnick and Fidell, 2007), as the objective of the PCA was simply data exploration, to confirm whether or not distinct urban-rural groupings existed.
Prior to performing PCA the suitability of data for factor analysis was assessed. Inspection of the weightings of the twelve variables in a correlation matrix
revealed the presence of many coefficients of R = > 0.3 and above (the cut-off threshold suggested by Tabachnick and Fidell, (2007)), therefore their
factorability was suitable.
PCA revealed the presence of three components with eigenvalues greater than 1, explaining 52.32, 24.18 and 13.13 % of the variance respectively. An
inspection of the screeplot (see Appendix A3.5) revealed a clear break after the second component and as these two components accounted for 76.49 % of the variation, this was the most parsimonious explanation of the data variance (Tabachnick and Fidell, 2007). The regression factor scores for the first two components are shown in Table 3.2.
Table 3.2 Regression factor scores for the two highest components for a PCA of allotment physical characteristics.
1 2
Area of hard surface (%) within 2 km radius 0.973
Population 0.893
No. of allotment sites per town 0.867
Hard surface (%) 1 km 0.825 -0.481
Land allocation: site 0.821
Farmland (%) 1 km -0.797 0.582
Ave. plot size 0.713
Site area (ha) 0.706 0.575
Hard surface (%) 500 m 0.455 -0.751
No. of plots 0.680 0.728
No. of trees 100 m -0.459 0.654
Land allocation: surrounding 0.622
No. of trees on site 0.620 0.397
Component
The regression factor scores of the individual sites for the first two principle components are plotted in Figure 3.2a. PC1 clearly splits the sites into urban, suburban and rural, showing the relative distance apart between the sites (Objective 3.1). The very clearly separated Hull site, Newland (NW) allotments, equates to an ‘urban’ classification; Beverley (BV), Cottingham (CT) and
Bridlington (BR) group together in a ‘suburban’ group, with Bude (BD) slightly separated from this group, whilst Driffield (DR) is in a ‘rural’ classification, with Hunmanby (HN) somewhat separated from it, but still in the rural category.
Figure 3.2a Principle Components Analysis plot of physical data to
highlight any potential urban-rural gradient. PC1 and PC2 account for 82.7
% of the variance between sites. Distance grouping values based on Euclidean distance. NW represents the most urban site; BD, BR, BV & CT represent suburban sites; DR and HN, represent the most rural sites (see text for details). To show the key factors defining the urban-suburban-rural gradient, the PCA results are re-plotted showing the thirteen factors in Figure 3.2b. The results show that most urban site(s) are most likely to have a higher proportion of hard surface in the surrounding 2 km diameter of the allotment site; higher human population; a greater number of allotment sites; a higher proportion of hard surface in the surrounding 1 km diameter of the allotment site; surrounding land allocated as residential; a higher site and higher plot area and finally, to a slightly lesser degree, a higher number of trees on the allotment site. In this case, Newland allotments is by far the most urban.
The rural sites are most likely to have the highest percentage of farmland in the surrounding 1 km diameter of the allotment site; the least amount of hard
surface in the surrounding 500m; a higher number of trees surrounding the site PCA for Allotment Physical Data
-4 -2 0 2 4 PC1 -4 -2 0 2 PC 2 Distance 2 4 HN BR DR BV CT BD NW DR Driffield HN Hunmanby CT Cottingham BV Beverley BR Bridlington BD Bude NW Newland
PCA Plot - Correlation - Allotment Environmental Variables Principal - Axis 1 (52.32%) 4 3 2 1 0 -1 -2 -3 -4 Vector - Axis 1 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 P rin ci pa l - A xi s 2 ( 24. 18% ) 4 3.5 3 2.5 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -2.5 -3 -3.5 -4 Ve cto r - Ax is 2 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 -0.25 -0.3 -0.35 -0.4 -0.45 -0.5 -0.55 Population
Site area (ha) No. of plots Ave. plot size
% hard surface 500m
% hard surface 1km
% hard surface 2k
No. of trees on site
No. of trees 100m No. of allotment sites
% farmland 1km Land allocation site
Land allocation surrounding
HN DR BR BV CT BD NW DR Driffield HN Hunmanby CT Cottingham BV Beverley BR Bridlington BD Bude NW Newland and the surrounding land classed as “unallocated”. In this case, Driffield and Hunmanby would be classed as rural. Intermediate characteristics are classified by the site area and the number of plots. Under these groupings, Cottingham, Beverley, Bridlington and to a lesser extent, Bude, would be classed as suburban, although Bude lies somewhat towards the more urban category than the former three sites.
Figure 3.2b Principle Components Analysis plot of physical data to
highlight any potential urban-rural gradient, showing contribution of each vector (see text for details; full vector details are in Section 3.5).
As shown above, two principle components were optimal and were therefore subject to Varimax rotation. The rotated solution identified the nature of the underlying latent variable represented by each component i.e. were they mainly urban, suburban or rural (see Table 3.3). There were a number of strong
loadings, with some variables loading substantially on only one component, although some variables did have cross loadings. The two-component solution explained a total of 76.50 % of the variance, (the same as the un-rotated PCA)
Characteristic
1 2
No. of plots 0.991
Site area (ha) 0.910
Population 0.773 0.475
No. of allotment sites 0.755 0.455 No. of trees on site 0.728
Ave. plot size 0.726
Land allocation: surrounding 0.568 -0.328
Farmland (%) 1km -0.964
Hard surface (%) 1km 0.907 Hard surface (%) 500m 0.864
No. of trees 100m -0.794
Hard surface (%) 2k 0.632 0.755 Land allocation: site 0.522 0.648
Rotated Component Matrix
Component
with Component 1 contributing 39.98% and Component 2 contributing 36.52%. Thus, the rotated solution shows that the number of plots, site area and number of trees on site were the highest three contributors to urban sites respectively, with no cross loading. This was followed by population and number of allotment sites contributing equally, but both had a level of cross loading. The percentage of farmland and the number of trees within 100m were the highest two
contributors to rural sites respectively, with no cross loading. The amount of hard surface within 1 km, 500m and 2 km respectively were effectively double negative values, indicating that rural sites has the least amount of hard standing surrounding the sites.
Table 3.3 Pattern/structure for coefficients: Varimax Rotation with Kaiser Normalization of Two Factor Solution for Allotment Physical
Characteristics. Component 1 indicates urban loadings, component 2 rural
3.10.1 PCA results summary
To summarize, most of the environmental factors measured played a part in explaining the variation in the urban-suburban-rural gradient. The number of plots, site area and number of trees on site respectively contributed the highest three factors to describe urban sites. The amount of farmland in the
surrounding 1 km and the number of trees surrounding the site contributed most of the variation to describe rural sites, whilst the other factors were intermediate. It appears therefore that an urban-rural gradient was apparent to some extent in the study sites chosen, based on the physical data. Newland is therefore
classed as the urban site, Bude, Bridlington, Beverley and Cottingham the suburban sites, whilst Driffield and Hunmanby were classed as rural. These classifications will be used throughout the remaining Chapters.