Eur. Phys. J. B 65, 369-377 (2008)
https://doi.org/10.1140/epjb/e2008-00340-5

Dynamical inference of hidden biological populations

¹ NASA Ames Research Center, Mail Stop 269-2, Moffett Field, CA 94035, USA
² Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
³ Mission Critical Technologies Inc., 2041 Rosecrans Ave. Suite 225 El Segundo, CA 90245, USA

Corresponding author: ^a d.luchinsky@lancaster.ac.uk

Received: 4 February 2008
Revised: 10 July 2008
Published online: 10 September 2008

Abstract

Population fluctuations in a predator-prey system are analyzed for the case where the number of prey could be determined, subject to measurement noise, but the number of predators was unknown. The problem of how to infer the unmeasured predator dynamics, as well as the model parameters, is addressed. Two solutions are suggested. In the first of these, measurement noise and the dynamical noise in the equation for predator population are neglected; the problem is reduced to a one-dimensional case, and a Bayesian dynamical inference algorithm is employed to reconstruct the model parameters. In the second solution a full-scale Markov Chain Monte Carlo simulation is used to infer both the unknown predator trajectory, and also the model parameters, using the one-dimensional solution as an initial guess.