1 Introduction

The present document describes the data and methodology used to derive the risk-map of contact opportunities with domestic pigs, as well as the results and their interpretation.

2 Data description

In the investigated area, we have information on farm-sites with presence of domestic pigs, their number, the farming practices and the geographic area where they wander.

The farming practices were summarised into five groups with different relative risk levels. Below is the map of farming-sites by type of practice. Figure 2.1 displays the relative risk scores for each farming type, relative to the safest group.

Figure 2.1: Relative risk scores of farming practice types relative to the last group.

3 Methodology

We postulate the following hypotheses:

1. The probability of interaction between a wild-boar approaching a pig-site and one of the pigs therein is proportional to the pig-density and to the risk-score of the site: \[ \begin{equation} \tag{1} P(\text{contact}\,|\,\text{approach}) \propto r\, N / A, \end{equation} \] where \(r\) is the risk score relative to farming practices, \(N\) is the number of pigs in the site and \(A\) is the surface area of the site.

   It is useful to verify this assumption in a few concrete scenarios. For instance, this means that an approaching wild boar has the same chance to interact with a pig in any of the following situations:

   Site	N_pigs	Area (ha)	Type score	Type desc.
   1	80	0.1	1.0	Closed building
   2	800	1.0	1.0	Closed building
   3	100	1.0	8.0	Open air half-year
   4	800	23.5	23.5	Open air

   If these situations seem equivalent to experts from a risk perspective, the we can move on. Having seen the results, I feel that Site 4 should be assigned far more risk than Sites 1 or 2. Moreover, for closed buildings, I wonder whether risk should really increase with pig-density.

   In the meanwhile, I propose as an alternative model using the squared-root of density, instead of the density in Eq. 1: \[ \begin{equation} \tag{2} P(\text{contact}\,|\,\text{approach}) \propto r\, \sqrt{N / A}. \end{equation} \]

   This gives the following risk values for the previous scenarios, which look more sensible to me:

   Site	Alter. risk
   1	28
   2	28
   3	80
   4	137

   This calibration of the density needs to be discussed. For the moment, I will show and compare results with both models.

2. The probability that a wild boar approaches a farm-site is a exponentially-decaying function of the distance from the centroid of its habitat to the site. \[ \begin{equation} \tag{3} P(\text{approach}\,|\,\rho) = p(d\,|\,\rho) = \exp{\{-d\,\log(100) / \rho\}}, \end{equation} \] where \(d\) is the distance to the site and \(\rho\) is the range of activity of the wild boar. Note that for \(x = 0\) (i.e. the wild boar lives basically next to the site) the probability of approach is 1, for any value of \(\rho\). On the other hand, the probability of approach at \(x = \rho\) drops to \(0.01\)

   

   Figure 3.1: Probability of a wild boar approaching a pig-site as a function of the distance from the centroid of its habitat.

   The parameter \(\rho\) of activity range is arbitrary and, lacking data, needs to be determined based on the literature and expert opinion. I have used \(\rho = 10\) km for the results that follow. It would be good to perform a sensitivity analsys on this parameter.

Given these two hypotheses, the probability of contact with a pig from a given site is the product of Equations 1 (or 2) and 3, while the probability of contact with a pig from any of the sites is the sum across all sites, \(P(\text{contact} \,|\, \rho) \propto R(x)\), where: \[ \begin{equation} \tag{4} R(x) = \sum_{s_i \in \text{sites}} r_i\, f(\delta_i)\, p(d(x, s_i)\,|\,\rho). \end{equation} \]

We call this the risk-of-contact function for a wild boar at location \(x\), where \(\delta_i\) is the pig-density of site \(i\). This can be represented spatially as a map, and is what is shown next.

4 Results

First, the component of the risk due to each farm’s density and practices is shown below, under models 1 and 2. This can be interpreted as an animal density adjusted by practices. However, note that the scales under both models are not comparable.

As you can see, from the distance, all polygons seem of rather low values on both sides. The small sites, less visible, produce very high densities and some are adjusted by a factor of 10 or 20 according to their practices. You can have fun finding the small polygons with greatest values.

Figure 4.1 displays the distribution of the animal density and its square-root, for comparison. You can see how there are three sites with remarkably high values that are somewhat moderated in the square-root model.

Figure 4.1: Distribution of animal-density and its square-root acroos farm-sites.

Below is the risk-map using model (1). The farms are overlayed with transparency for reference, but they can be removed entirely from the layer control on the top-left corner.

In contrast, here is the risk-map using the alternative model (2).

5 Conclusions

• Discuss the problem of calibration of the animal density with experts. See Methodology.

• Discuss the wild boar range of activity to be used (or range of sensible values for sensitivity analysis).