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Mathematical Biosciences and Engineering (MBE)
 

A Rao-Blackwellized particle filter for joint parameter estimation and biomass tracking in a stochastic predator-prey system

Pages: 573 - 597, Volume 11, Issue 3, June 2014

doi:10.3934/mbe.2014.11.573       Abstract        References        Full Text (531.1K)       Related Articles

Laura Martín-Fernández - Departamento de Física Aplicada, Universidad de Granada, Avda. Fuentenueva s/n, 18071 Granada, Spain (email)
Gianni Gilioli - Department of Molecular and Translational Medicine, University of Brescia, Viale Europa 11, 25125 Brescia, Italy (email)
Ettore Lanzarone - CNR-IMATI, Via Bassini 15, 20133 Milano, Italy (email)
Joaquín Míguez - Departamento de Teoría de la Señal y Comunicaciones, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Madrid, Spain (email)
Sara Pasquali - CNR-IMATI, Via Bassini 15, 20133 Milano, Italy (email)
Fabrizio Ruggeri - CNR-IMATI, Via Bassini 15, 20133 Milano, Italy (email)
Diego P. Ruiz - Departamento de Física Aplicada, Universidad de Granada, Avda. Fuentenueva s/n, 18071 Granada, Spain (email)

Abstract: Functional response estimation and population tracking in predator-prey systems are critical problems in ecology. In this paper we consider a stochastic predator-prey system with a Lotka-Volterra functional response and propose a particle filtering method for: (a) estimating the behavioral parameter representing the rate of effective search per predator in the functional response and (b) forecasting the population biomass using field data. In particular, the proposed technique combines a sequential Monte Carlo sampling scheme for tracking the time-varying biomass with the analytical integration of the unknown behavioral parameter. In order to assess the performance of the method, we show results for both synthetic and observed data collected in an acarine predator-prey system, namely the pest mite Tetranychus urticae and the predatory mite Phytoseiulus persimilis.

Keywords:  Prey-predator system, parameter estimation, population tracking, state-space model, Rao-Blackwellized particle filter.
Mathematics Subject Classification:  Primary: 62F15, 65C35, 92D25; Secondary: 65C30.

Received: September 2012;      Accepted: November 2013;      Published: January 2014.

 References