Estimating parameters from multiple time series of population dynamics using Bayesian inference

Abstract

1 1. Empirical time series of interacting entities, e.g. species abundances, are highly 2 useful to study ecological mechanisms. Mathematical models are valuable tools to 3 further elucidate those mechanisms and underlying processes. However, obtaining 4 an agreement between model predictions and experimental observations remains a 5 demanding task. As models always abstract from reality one parameter often sum-6 marizes several properties. Parameter measurements are performed in additional 7 experiments independent of the ones delivering the time series. Transferring these 8 parameter values to different settings may result in incorrect parametrizations. On 9 top of that, the properties of organisms and thus the respective parameter values 10 may vary considerably. These issues limit the use of a priori model parametriza-11 tions. 12 2. In this study, we present a method suited for a direct estimation of model parame-13 ters and their variability from experimental time series data. We combine numer-14 ical simulations of a continuous-time dynamical population model with Bayesian 15 inference, using a hierarchical framework that allows for variability of individual 16 parameters. The method is applied to a comprehensive set of time series from a 17 laboratory predator-prey system that features both steady states and cyclic pop-18 ulation dynamics. 19 3. Our model predictions are able to reproduce both steady states and cyclic dynamics 20 of the data. Additionally to the direct estimates of the parameter values, the 21Bayesian approach also provides their uncertainties. We found that fitting cyclic 22 population dynamics, which contain more information on the process rates than 23 steady states, yields more precise parameter estimates. We detected significant 24 variability among parameters of different time series and identified the variation 25 in the maximum growth rate of the prey as a source for the transition from steady 26 2 states to cyclic dynamics. 27 4. By lending more flexibility to the model, our approach facilitates parametrizations 28 and shows more easily which patterns in time series can be explained also by 29 simple models. Applying Bayesian inference and dynamical population models in 30 conjunction may help to quantify the profound variability in organismal properties 31 in nature. 32 Keywords 33 Bayesian inference, chemostat experiments, hierarchical model, ordinary differential 34 equation, parameter estimation, population dynamics, predator prey, time series analy-35 sis, trait variability, Stan 36