Mechanistic models for panel data: Analysis of ecological experiments with four interacting species

TL;DR

This paper introduces a likelihood-based statistical approach using iterated particle filtering for analyzing complex ecological panel data, enabling better modeling of nonlinear, stochastic, and partially observed ecological systems.

Contribution

It develops a new methodology applying iterated particle filtering to ecological panel data, allowing for improved parameter estimation and model evaluation of complex ecological dynamics.

Findings

Successfully applied to freshwater plankton data

Enabled likelihood maximization for nonlinear models

Provided tools for hypothesis testing and model diagnostics

Abstract

In an ecological context, panel data arise when time series measurements are made on a collection of ecological processes. Each process may correspond to a spatial location for field data, or to an experimental ecosystem in a designed experiment. Statistical models for ecological panel data should capture the high levels of nonlinearity, stochasticity, and measurement uncertainty inherent in ecological systems. Furthermore, the system dynamics may depend on unobservable variables. This study applies iterated particle filtering techniques to explore new possibilities for likelihood-based statistical analysis of these complex systems. We analyze data from a mesocosm experiment in which two species of the freshwater planktonic crustacean genus, Daphnia, coexist with an alga and a fungal parasite. Time series data were collected on replicated mesocosms under six treatment conditions. Iterated filtering enables maximization of the likelihood for scientifically motivated nonlinear partially observed Markov process models, providing access to standard likelihood-based methods for parameter estimation, confidence intervals, hypothesis testing, model selection and diagnostics. This toolbox allows scientists to propose and evaluate scientifically motivated stochastic dynamic models for panel data, constrained only by the requirement to write code to simulate from the model and to specify a measurement distribution describing how the system state is observed.