Coupling and Parameter Estimation for a Discrete Single-Species Metapopulation Model

• Published in: International journal of applied and computational mathematics Vol. 11; no. 3
• Main Authors: Giordani, Flávia Tereza, Bazán, Fermín S. V., Bedin, Luciano
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.06.2025; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Computational Science and Engineering; Coupling; Dynamics; Inverse problems; Least squares method; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nuclear Energy; Operations Research/Decision Theory; Parameter estimation; Population density; Reconstruction; Research Article; Theoretical; Metapopulations; Least squares method; Coupled map networks; Ricker map; Topology identification
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-025-01903-z

We address the inverse problem of simultaneous reconstruction of the parameters and coupling functions of a discrete single-species metapopulation from measured data of network dynamics. The unknown parameters include growth rates, total migration fractions and the entries of a circulating coupling matrix. From a practical point of view, the parameters are estimated by solving a least squares problem, using input data consisting of measurements of sub-population densities. The method of solution is based on a trust region reflective algorithm which allows the user to provide upper and lower limits on the system parameters. In contrast with many existing methods, our reconstruction procedure does not require any previous linearization, simplification or knowledge of the dynamics behaviour of the measured population densities. Another advantage of our approach is that it enables the simultaneous reconstruction by taking into account the entire metapopulation dynamics. Furthermore, the method is robust as it works well using input data with or without additive noise. The effectiveness of the method has been verified in reconstruction problems involving arbitrarily complex dynamics, such as chaotic or periodic, stationary, synchronous or asynchronous. Several numerical results are presented and discussed.