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

Abstract

Population and community ecology traditionally has a very strong theoretical foundation with well-known dynamical models, such as the logistic and its variations, and many modifications of the classical Lotka-Volterra predator-prey and interspecific competition models. More and more, these classical models are being confronted with data via fitting to empirical time series for purposes of projections or for estimating model parameters of interest. However, using statistical models to fit theoretical models to data is far from trivial, especially for time series data where subsequent measurements are not independent. This raises the question of whether statistical inferences using pure observation error models, such as simple (non-)linear regressions, are biased, and whether more elaborate process error models or state-space models have to be used to address this complexity. In order to help empiricists, especially researchers working with experimental laboratory populations in micro-and mesocosms, make informed decisions about the sta-

Partitioning time series to improve process-based models with machine learning

“…Our work contributes to the ongoing effort to better assimilate observational data into process-based models [Schartau et al, 2017, Raissi et al, 2019, Kashinath et al, 2021, Auger-Méthé et al, 2021, Rosenbaum and Fronhofer, 2023, Paredes et al, 2023, Bolibar et al, 2023], with a specific focus on the parametrization of differential equation-based models with strong nonlinearities. Recently, Yazdani et al [2020] proposed an alternative framework dubbed “systems biology informed deep learning”, where a neural network is fitted to the data and the additional process-based model constraints are integrated.…”

“…We observe that our segmentation method resembles state-space modelling approaches (see [Auger-Méthé et al, 2021] and references therein). As such, it should not only regularise the inverse problem and the problem’s memory requirements, but also reduce bias arising from observation and process errors [Rosenbaum and Fronhofer, 2023]. Overall, the inverse modelling framework successfully blends ML methods with process-based models to learn from ecological time series.…”

“…A variety of data assimilation methods are increasingly being used to parametrize community models. Bayesian inference with Markov Chain Monte Carlo methods, used in Lignell et al [2013], Higgins et al [2010], Xu et al [2006], Fiechter et al [2013], Rosenbaum et al [2019], Heiland et al [2023], Rosenbaum and Fronhofer [2023], Pagel and Schurr [2012], offer the advantage of quantifying uncertainties by inferring the full posterior probability distribution of the unknown parameters. This is achieved by a global exploration of the parameter space, which makes Bayesian methods computationally expensive and particularly prone to the curse of dimensionality [Gosh et al, 2021].…”

The shape of density dependence and the relationship between population growth, intraspecific competition and equilibrium population density

“…7 remain qualitatively unchanged, however diagnostic values (Pareto k) indicate that fits may be sensitive to differences in model validation, that is, which data points are left out. One possibility to reduce the issue of overfitting is to fit multiple replicate time series at once using a joint likelihood function (see Rosenbaum and Fronhofer 2023 for more advanced fitting strategies).…”

“…The disadvantage of these more mechanistic consumerresource models is an increased complexity and number of parameters. Importantly, the quality and quantity of empirical data is often not sufficient for confronting such models with data (Rosenbaum and Fronhofer 2023). In an attempt to simplify, some studies have explored under what conditions population level growth models (e.g.…”