Population and community ecology traditionally has a very strong theoretical foundation with well-known models, such as the logistic and its many variations, and many modification of the classical Lotka-Volterra predator-prey and interspecific competition models. More and more, these classical models are confronted to data via fitting to empirical time-series, from the field or from the laboratory, for purposes of projections or for estimating model parameters of interest. However, the interface between mathematical population or community models and data, provided by a statistical model, is far from trivial. In order to help empiricists make informed decisions, we here ask which error structure one should use when fitting classical deterministic ODE models to empirical data, from single species to community dynamics and trophic interactions. We use both realistically simulated data and empirical data from microcosms to answer this question in a Bayesian framework. We find that pure observation error models mostly perform adequately overall. However, state-space models clearly outperform simpler approaches when observation errors are sufficiently large or biological models sufficiently complex. Finally, we provide a comprehensive tutorial for fitting these models in R.
Fitting deterministic population models to stochastic data: from trajectory matching to state-space models
