Lotka-Volterra-like model of the interaction of phytoplankton (prey) and zooplankton (predator), for LibBi.
Matlab Shell
Switch branches/tags
Nothing to show
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Permalink
Failed to load latest commit information.
data
oct
LICENSE
MANIFEST
META.yml
PZ.bi
PZ.md
README.md
VERSION.md
config.conf
filter.conf
init.sh
optimise.conf
posterior.conf
prior.conf
run.sh

README.md

Synopsis

./run.sh

This samples from the prior and posterior distributions. The oct/ directory contains a few functions for plotting these results (GNU Octave and OctBi required).

A synthetic data set is provided, but a new one one may be generated with init.sh (GNU Octave and OctBi required).

Description

This package is based on a Lotka-Volterra model of the interaction between phytoplankton $P$ (prey) and zooplankton $Z$ (predator). It differs from the classic Lotka-Volterra by having a stochastic growth term for phytoplankton, and quadratic mortality term for zooplankton.

The process model is given by the equations: \begin{eqnarray} \frac{dP}{dt} &=& \alpha_t P - cPZ \\ \frac{dZ}{dt} &=& ecPZ - m_lZ - m_q Z^2, \end{eqnarray} where $t$ is time in days, and the stochastic growth term $a_t$ is drawn daily as $\alpha_t \sim \mathcal{N}(\mu,\sigma)$, with $\mu$ and $\sigma$ being the two parameters of the model.

This version of the model was originally used in Jones, Parslow & Murray (2010). Its behaviour under sampling with the particle marginal Metropolis-Hastings (PMMH) sampler is also studied in Murray, Jones & Parslow (2013).

References

Jones, E.; Parslow, J. & Murray, L. M. A Bayesian approach to state and parameter estimation in a Phytoplankton-Zooplankton model. Australian Meteorological and Oceanographic Journal, 2010, 59, 7-16.

Murray, L. M.; Jones, E. M. & Parslow, J. On collapsed state-space models and the particle marginal Metropolis-Hastings sampler, 2013.