Model development; explanatory variables

Three sets of explanatory variables were considered; landscape compositional variables, landscape connectivity variables and landscape structural variables. Correlations among each set of explanatory variables were explored prior to the formal modelling process. Correlations among the landscape compositional variables and landscape connectivity variables were assessed separately by means of spearman rank correlation (S). The landscape structure metrics were normalised by log10

transformation, unless otherwise stated, and correlations assessed by means of Pearson Product Moment Correlations (r). Pairs of variables with strongly significant correlations (absolute S > 0.8; absolute r >0.8) were identified and one of these variables was removed. All statistical analysis, unless otherwise stated, was conducted using the statistical package Genstat ® 13.2.

Landscape composition

Using the LCM 2000 and PH1 2000 data, total land cover/ habitat area (ha), landscape diversity (LSIDI) and landscape heterogeneity (NLAND) within each 1km grid square (see section 2.2.3) were used for the development of models using landscape compositional data. For the PH1 2000 data set total length of hedgerow in each grid square was also included (Table 2.6). Hedgerow data was obtained in addition to the Warwickshire Phase 1 Habitat Map as part of the Warwickshire Habitat Biodiversity Audit provided by Warwickshire County Council (see sections 1.6.1 and 2.1.2). Three classifications of hedgerows were identified; intact hedgerow, defunct hedgerow and hedge with trees (Table 2.6). All hedgerow types were considered in the analysis.

Hedgerow type PH1 Code Total frequency Proportion of total length (%) Intact hedge J21 129232.00 78.52 Defunct hedge J22 10473.00 7.28

Hedge with trees J23 22480.00 14.21 Table 2.6: The proportion and frequency of each hedgerow type within Warwickshire in 2001 according to the PH1 habitat classification.

43 Spearman rank correlations were calculated to identify significant correlations between the landscape compositional variables for the two data sets (LCM 2000 and PH1 2000). No correlations with an absolute coefficient greater than S ≥ 0.8 were identified amongst the landscape compositional variables for both data sets. As such no variables were omitted from the analysis on the basis of high spearman-rank correlations.

Landscape connectivity metrics

Land cover classes selected within the landscape compositional models are considered to be key land cover classes (see sections 4.2.2 and 4.2.6). The final landscape compositional models included 12 LCM land covers and 21 PH1 habitats. The connectivity of these key land cover classes was determined within each 1 km grid square using the software Conefor v2.6 (Saura and Torne, 2009). Two methods of obtaining measures of connectivity were considered; (1) connectivity of key land cover in isolated squares and (2) importance of patches within key land covers for maintaining connectivity across Warwickshire. For the computation of the connectivity variables, a border was applied to each 1 km grid square equal to the median dispersal distance for all butterfly species (325 m) and for those species comprising the ecological attribute groups 1-3 (250 m) (see section 2.2.2). A border was applied in order to include habitat patches present within the periphery of the square that may influence butterfly presence.

The spatial location of hedgerows was incorporated within the connectivity analysis for the key PH1 2000 habitats, in order to consider their role in providing additional habitat as well as providing conduits for movement of butterfly species associated with woodland and grassland habitats. The shelter foot print provided by hedgerows for butterflies has been identified to extend layward to four times the height of the hedge (Dover, et al., 2000; Lewis, 1969). Using data regarding hedgerow height available for the PH1 2010 data, the average height of 2.5 m was used as a surrogate for the 2000 hedgerow data set, and as such hedgerows were buffered by 5 m, providing a width of 10 m per hedgerow. Buffered hedgerows were then combined with the habitat ‘semi-natural broad-leaved woodland’ (PH-1), and with the

44 grassland habitats ‘unimproved neutral grassland’ (PH-15), ‘semi-improved neutral grassland’ (PH-16) and ‘calcareous grassland’ (PH-16).

Method 1

The binary connectivity metric, Integral Index of Connectivity (IIC), and the probabilistic metric, Probability of Connectivity (PC) (Pascual-Hortal and Saura, 2006; Saura and Pascual-Hortal, 2007), were computed for each key land cover class within each 1 km grid square using the median butterfly dispersal distances of 325 m and 250 m (see section 2.2.2) as thresholds for determining the network of connected patches (node component). For the LCM 2000 a total of 24 grid square connectivity metrics were computed (12 IIC metrics and 12 PC metrics) and for the PH1 2000 a total of 42 grid square connectivity metrics were computed (21 IIC metrics and 21 PC metrics).

Landscape connectivity variables were considered in addition to the compositional variables during the development of landscape connectivity models. The IIC and PC metrics exhibit weak correlations with total area for each key land cover class. However, metrics IIC and PC are strongly correlated at the 1 km scale, therefore only the metric IIC was used in further analyses (Eq1), as this is the simplest metric available. For the LCM 2000 a total of 12 IIC metrics were considered during the modeling procedure (Table 4.6) and for the PH1 2000 a total of 21 IIC metrics were considered during the modeling procedure (Table 4.18).

Eq 1 𝐼𝐼𝐶 = 𝐼𝐼𝐶𝑛𝑢𝑚 𝐴_𝐿2 = ∑ ∑ (𝑎𝑖 ∗ 𝑎𝑗 1 + 𝑛𝑙𝑖𝑗) 𝑛 𝑗=1 𝑛 𝑖=1 𝐴_𝐿2 Where:

ai and aj = area of pacthes i and j,

nlij = number of connections in the shortest path between patches i and j

AL2 = total class area

45 Method 2

In addition to computing IIC for each grid square for each key LCM/ PH1 land cover class, the importance of each patch for maintaining connectivity across the whole landscape of Warwickshire was calculated. Patch importance is obtained from calculating the change in IIC value with the removal of each patch in the landscape in turn (varIIC – Eq2) (Saura and Rubio, 2010). The metric varIIC was calculated using the distance thresholds of 325 m and 250 m to determine the network of connected patches for each key land cover class (see section 2.2.2). The importance of the nodes located within each 1 km grid square, as captured by varIIC, was then summed for each square providing a complementary assessment of habitat connectivity at the 1 km scale.

Eq 2

𝑣𝑎𝑟𝐼𝐼𝐶 =𝐼𝐼𝐶 − 𝐼𝐼𝐶𝑎𝑓𝑡𝑒𝑟 𝐴2_𝐿 Where:

AL2 = total class area

See Saura & Rubio (2010)

The varIIC metric can be partitioned into three components that contribute towards the overall connectivity value obtained (Saura and Rubio, 2010). The components of varIIC are (1) connectivity (varIICconn), which measures the importance of patches for maintaining overall connectivity (2) intra-connectivity (varIICintra) which considers connectivity within the patches and (3) dispersal flux (varIICflux) which measures how well connected a patch is to other patches (Saura and Rubio, 2010). The three components were computed for each key land cover class in addition to the overall varIIC metric.

For the LCM 2000 dataset a total of 48 metrics (12 classes x 4 metrics) were computed which measure the importance of patches in that landscape for maintaining connectivity across Warwickshire. Several of these metrics exhibited strong correlations (absolute S ≥ 0.8) with the area of the corresponding land cover class,

resulting in a final selection of only six additional varIIC metrics to be considered during the modelling procedure (Table 4.6). For the PH1 2000 a total of 84 metrics

46 (21 classes x 4 metrics) were computed which measure the importance of patches in that landscape for maintaining connectivity across Warwickshire. The majority of these 84 metrics exhibited strong correlations (absolute S ≥ 0.8) with the area of the

corresponding habitat, resulting in a final selection of only two additional varIIC metrics to be considered during the modelling procedure (Table 4.18).

Landscape Structure

Using the software FRAGSTATS (version 4) (McGarigal, et al., 2012) landscape structure metrics were calculated for each grid square landscape using land cover data derived from LCM 2000 and PH1 2000. A total of 69 metrics were initially computed which measured the landscape aspects area/ edge, shape, aggregation, and diversity (see section 1.6.2). The computation of landscape structure metrics followed the same procedure outlined in section 2.1.3.

Pearson Product Moment Correlations were used to assess the relationship between all landscape structure metrics, and pairs of metrics with an absolute correlation coefficient greater than r ≥ 0.8 were investigated further (0.01 % significance level).

Representative metrics of each significant pairwise correlation combination were chosen, with the simplest metric of the two chosen. A high correlation coefficient was chosen as in contrast to chapter 3 the number of data points was not a limiting factor (section 2.1.3) and as such a wider range of metrics could be considered. For all grid squares within the LCM 2000 dataset (n =2427) a total of 38 landscape structure metrics remained after removal of highly correlated metrics, and for the occupied squares used for the EAG models (n = 515) a total of 36 metrics remained (41 different metrics in total) (Table 4.10). For the PH1 2000, a total of 35 landscape structure metrics were selected from the correlation analysis for all grid squares (n = 2079) and 37 metrics were selected from the correlation analysis for the occupied squares (n = 466) (39 different metrics in total) (Table 4.22).