Optimizing strategies for slowing the spread of invasive species
Fig 5
The annual cost of treatment decreases with the target speed v and increases with kλ0 (spongy moth population model). As in Fig 4, the main (middle) panel shows the annual cost of treatment associated with the optimal treatment, ACT*, as a function of the target propagation speed v for three choices of kλ0. ACT* decreases as v increases, and reaches zero when v equals the species’ natural propagation speed without treatment (v = v0≈12 km year−1). Higher kλ0 values, indicating a lower Allee threshold relative to carrying capacity, resulting in an increased ACT*, where ACT* is measured in units of thousands of USD per one-kilometer strip of land. The dashed black lines show, for each line, where the marginal cost of slowing the spread (slope of ACT*) equals the marginal benefit of slowing the spread by one kilometer over a one-kilometer strip, estimated as 16K USD per year by [62]. In particular, the optimal speed according to this estimation is v = ‒2.4 km/year if kλ0 = 100; v = 4.8 km/year if kλ0 = 300; and v = 9.6 km/year if kλ0 = 1000. In turn, the sub-panels demonstrate the optimal treatment profile (Aopt), and population density (nopt) across locations (x in units of σ = 10 km). Each sub-panel shows the optimal solution for a specific target speed v, with both treatment and population density advancing leftward at this speed (Eqs (9, 11)). All the parameters except α and v are the same in all the panels: Eq (2) is considered, where b is given by Eqs (6–8) with r = 2 and a = 0.08 USD‒1, and G is given by Eq (4). The raw data with the results of all the simulations for each kλ0 and v can be found Dryad [60].