Problem SE10

The European tree frog (Hyla arborea, Fig. 7) although it is arboreal does anyway need water bodies for reproduction. Carlson and Edenhamn (2000) studied a metapopulation of this frog in Sweden (378 ponds over an area of about 1200 km $^2$

) and estimated in subsequent years the fraction of occupied ponds and the rate of colonization, namely the fraction of empty ponds being colonized in the course of each year (see Fig. 8)

**Figure 7:** The European tree frog swimming in a pond.
$\includegraphics[width=0.5\linewidth]{Hyla.eps}$

**Figure 8:** Data of a Swedish metapopulation of H. arborea between 1989-1992. Top panel: fraction of occupied ponds in subsequent years. Bottom panel: fraction of ponds that were empty in the previous year and turn out to be occupied in the current year.
$\includegraphics[width=0.5\linewidth]{FrogMetapopulation.eps}$

Assume that the values recorded in 1992 can be considered as values at equilibrium. Use the Levins model in order to estimate the extinction parameter e and the colonization parameter c. If 40% of the ponds were dried up, what effect would this disturbance have on the frog metapopulation?