1 Introduction

Working at the level of municipalities. Data results from a survey conducted in 155 municipalities in Corsica. It includes counts of the number of pigs found in each of 5 types of farms, that were clustered according to their biosecurity practices (C1, …, C5), in decreasing order of disease transmission.

2 Description of the survey data

2.1 Distribution of the types of breeding

Figure 2.1: Number and density of pigs in municipalities, by cluster. Excluding zeroes, which are the most prevalent values in all clusters.

2.2 Spatial distribution of types of breeding

The following maps represent the number and density of pigs by cluster and municipality.

Figure 2.2: Number pigs in each farm cluster, by municipality.

Figure 2.3: Pig density in each farm cluster, by municipality

In order to prevent a perceptual bias due to the varying sizes of the municipalities the following cartogram represents the municipalities as hexagons of equal size.

Pig density in each farm cluster, by municipality, as a cartogram.

2.3 Distribution of pigs over municipalities

Regardless of the cluster

Figure 2.4: Number and density of pigs by municipality.

Figure 2.5: Pig density by municipality, as a cartogram.

3 Profiles of municipalities

We conducted a Principal Components Analysis using the number and density of pigs in each cluster and the surface area in order to identify the main patterns of municipalities.

Figure 3.1: Percent variance explained by the principal components. The line shows the cumulative percent variance.

Figure 3.4: Projection of variables on the first two principal components.

Figure 3.5: Density and PC values for the most extreme municipalities.

The Figures above show that about 42 % of the variability in the densities and numbers of pigs and in the area of municipalities can be explained in 2 dimensions.

Municipalities can be arranged along 2 principal axes determined mainly by the density and numbers of pigs in clusters 1 and 2 in one case, and by the density and numbers of pigs in clusters 4 and 5 in the other.

Densities and absolute numbers are very correlated and independent from the area in the first factorial plane. Meaning that high densities tend to be explained by large numbers rather than by small surface areas. In contrast, the density of pigs in the third cluster is explained to a larger extent by smaller areas.

The first principal component measures volume: number and density regardless of the cluster, whereas the second component measures specificity: concentration on either clusters 1 and 2 or in clusters 4 and 5.

While most municipalities have rather average volumes (number and density of pigs) in all clusters, there are a few that are particularly concentrated on either group of clusters.

For ulterior analyses, the municipalities can be reasonably characterised using only two quantitative variables such as the densities of pigs in clusters 1-2 and 4-5, or equivalently the principal components 1 and 2. A third principal component should be added to explain more that 50 % of the variability.

Figure 3.6: Profile of municipalities according to a 9-class bivariate group based on the first factorial plane. Municipalities in red have relatively more farms in clusters 1 and 2, whereas blue is associated to clusters 4 and 5. Intensity represents density and absolute quantity.

Figure 3.6 shows a map of municipalities with a bivariate colour scale where intensity is mapped to volume (PC1) and tone is mapped to clusters (PC2).

4 Degree of interaction

Two measures of interaction have been used, by weighted average of the animal densities. Different set of weights have been elicited for assessing the risk of direct and indirect interactions (Figure 4.1).

Both measures are very similar, giving a decreasing weight trend with respect to cluster number, except for the switched weights for clusters 2 and 3 for the direct interaction.

This produced measures of risk that are quite similar at a municipality level (Figures 4.2, 4.3)

Figure 4.3: Direct and indirect interactions as estimated by the custom weighted averages of cluster densities.

5 Contrasting municipalities with similar risks

Here we consider the question as to what extent the custom measure of risk of interaction represents the profiles of municipalities. In other words, how does variation look like, among municipalities with similar estimates of risk.

For so doing, we considered the projections of municipalities on the first three principal components and computed the cosine of the angles (as a measure of similarity of profiles) for all pairs of municipalities, as well as the absolute difference in their estimated risk of direct interaction.

Figure 5.1 shows the risk estimates, projections, and cluster-densities of 10 pairs of municipalities that are almost orthogonal in the factorial space (i.e. very different profiles, with cosines < 0.05) but still share a similar risk estimate (difference in risk below 0.2).

Figure 5.1: Contrasting municipalities with similar levels of risk. Cluster densities are expressed in km⁻²

6 Conclusions

• I find the measures of interaction rather appropriate, as they can be readily interpreted as a number of animals at risk per square kilometre.

• One possible improvement is to propagate the variability in the experts’ risk elicitations into a quantification of uncertainty in the estimation of risk.

• The PCA axes provide a different characterisation of municipalities, designed for capturing the main trends. This can be useful for clustering or studying patterns, but it’s not necessarily informative about the risk of interaction. Indeed, the interaction scores are barely correlated with the principal components.