Problem SE3

The ragweed (genus Ambrosia) is an alien species that has been unfortunately introduced to both Europe and Asia from North America. Ragweed pollen is notorious for causing allergic reactions in humans, specifically allergic rhinitis. Therefore, many countries have decided to employ biological control against ragweed, specifically by a leaf-eating beetle, Ophraella communa Le Sage (Fig. 1), which is quite effective (Fig. 2).

**Figure 1:** The defoliator Ophraella communa
$\includegraphics[width=0.5\linewidth]{Ophraella.eps}$

**Figure 2:** The ragweeds before biological control (left panel) and after biological control (right).
$\includegraphics[width=0.7\linewidth]{RagweedDefoliation.eps}$

Yamamura et al. (2007) studied the mobility of Ophraella communa in Japan. On August 8, 2000, they released a number of beetles which they have recaptured after 20 hours by means of traps located at various distances. Here below you can find a table with the results in terms of fractions of caught beetles (for instance, 7.6% is the percentage of beetles recaptured between 20 and 30 m).

Distance (m)	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90
Fraction (%)	50	14.5	7.6	10	5.2	4.8	3.2	2.4	2

Assume that beetles dispersed into the environment according to an isotropic two-dimensional model of diffusion. Estimate the diffusion coefficient D.