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Mathematical Biosciences and Engineering

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: 01 September 2012 Accepted: 29 June 2018 Published: 01 January 2014

  • MSC : Primary: 62F15, 65C35, 92D25; Secondary: 65C30.

  • 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 responseand (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.

    Citation: Laura Martín-Fernández, Gianni Gilioli, Ettore Lanzarone, Joaquín Míguez, Sara Pasquali, Fabrizio Ruggeri, Diego P. Ruiz. A Rao-Blackwellized particle filter for joint parameter estimation and biomass tracking in a stochastic predator-prey system[J]. Mathematical Biosciences and Engineering, 2014, 11(3): 573-597. doi: 10.3934/mbe.2014.11.573

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  • 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 responseand (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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