Fast and flexible interpolation via PUM with applications in population dynamics

TL;DR

This paper introduces a fast, flexible interpolation method using Radial Basis Functions within the Partition of Unity framework, applied to ecological population dynamics to identify critical areas for conservation.

Contribution

It presents a novel space-partitioning data structure for PUM that is independent of problem geometry, enhancing efficiency and applicability.

Findings

The ecosystem is in a delicate state, risking species extinction.

Sensitivity surfaces reveal critical areas needing intervention.

The method provides a practical tool for ecological management.

Abstract

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.