Confronting population models with experimental microcosm data: from trajectory matching to state-space models

Population and community ecology traditionally has a very strong theoretical foundation with well-known models, such as the logistic and its variations, and many modification of the classical Lotka-Volterra predator-prey and interspecific competition models. More and more, these classical models are being confronted to data via fitting to empirical time-series 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, especially researchers working with experimental laboratory populations in micro- and mesocosms, make informed decisions, we here compare different error structures one could 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 investigate this question in a Bayesian framework. We find that many model parameters can be estimated precisely with an appropriate choice of error structure using pure observation error or state-space models, if observation errors are not too high. However, Allee effect models are typically hard to identify and state-space models should be preferred with when model complexity increases. Our work shows that, at least in the context of experimental laboratory populations, deterministic models can be used to describe stochastic population dynamics that include process variability and observation error. We discuss when more complex state-space model formulations may be required for obtaining accurate parameter estimates. Finally, we provide a comprehensive tutorial for fitting these models in R.