Fast and flexible interpolation via PUM with applications in population dynamics
For ecologists and park administrators, this provides a new interpolation tool to assess population dynamics and inform conservation strategies.
The paper presents a fast and flexible interpolation method using Partition of Unity with Radial Basis Functions, applied to population dynamics of wild herbivores. The analysis reveals a delicate ecosystem where animal population could become extinct, and sensitivity surfaces suggest preventive measures.
In this paper the Partition of Unity Method (PUM) is efficiently 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. Moreover, we study, in the context of wild herbivores in forests, an application of such algorithm. This investigation 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 fast and flexible interpolation tool, indicates some possible preventive measures to the park administrators.