Fast and flexible interpolation via PUM with applications in population dynamics

In this paper a new fast and flexible interpolation tool is shown. The Partition of Unity Method (PUM) is performed using Radial Basis Functions (RBFs) as local approximants. In particular, we present a new space-partitioning data structure extremely useful in applications because of its independence from the problem geometry. An application of such algorithm, in the context of wild herbivores in forests, shows that the ecosystem of the considered natural park is in a very delicate situation, for which the animal population could become extinguished. The determination of the so-called sensitivity surfaces, obtained with the new versatile partitioning structure, indicates some possible preventive measures to the park administrators.