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

Laura Martín-Fernández; Gianni Gilioli; Ettore Lanzarone; Joaquín Míguez; Sara Pasquali; Fabrizio Ruggeri; Diego P. Ruiz

doi:10.3934/mbe.2014.11.573

Article Contents

2014, Volume 11, Issue 3: 573-597. Doi: 10.3934/mbe.2014.11.573

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

1.
Departamento de Física Aplicada, Universidad de Granada, Avda. Fuentenueva s/n, 18071 Granada
2.
Department of Molecular and Translational Medicine, University of Brescia, Viale Europa 11, 25125 Brescia
3.
CNR-IMATI, Via Bassini 15, 20133 Milano
4.
Departamento de Teoría de la Señal y Comunicaciones, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Madrid

Received: August 31, 2012

Revised: October 31, 2013

Published: December 2013

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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.

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Mathematics Subject Classification: Primary: 62F15, 65C35, 92D25; Secondary: 65C30.

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