TY  - JOUR
A1  - Rosenbaum, Benjamin
A1  - Raatz, Michael
A1  - Weithoff, Guntram
A1  - Fussmann, Gregor F.
A1  - Gaedke, Ursula
T1  - Estimating parameters from multiple time series of population dynamics using bayesian inference
JF  - Frontiers in ecology and evolution
N2  - Empirical time series of interacting entities, e.g., species abundances, are highly useful to study ecological mechanisms. Mathematical models are valuable tools to further elucidate those mechanisms and underlying processes. However, obtaining an agreement between model predictions and experimental observations remains a demanding task. As models always abstract from reality one parameter often summarizes several properties. Parameter measurements are performed in additional experiments independent of the ones delivering the time series. Transferring these parameter values to different settings may result in incorrect parametrizations. On top of that, the properties of organisms and thus the respective parameter values may vary considerably. These issues limit the use of a priori model parametrizations. In this study, we present a method suited for a direct estimation of model parameters and their variability from experimental time series data. We combine numerical simulations of a continuous-time dynamical population model with Bayesian inference, using a hierarchical framework that allows for variability of individual parameters. The method is applied to a comprehensive set of time series from a laboratory predator-prey system that features both steady states and cyclic population dynamics. Our model predictions are able to reproduce both steady states and cyclic dynamics of the data. Additionally to the direct estimates of the parameter values, the Bayesian approach also provides their uncertainties. We found that fitting cyclic population dynamics, which contain more information on the process rates than steady states, yields more precise parameter estimates. We detected significant variability among parameters of different time series and identified the variation in the maximum growth rate of the prey as a source for the transition from steady states to cyclic dynamics. By lending more flexibility to the model, our approach facilitates parametrizations and shows more easily which patterns in time series can be explained also by simple models. Applying Bayesian inference and dynamical population models in conjunction may help to quantify the profound variability in organismal properties in nature.
KW  - Bayesian inference
KW  - chemostat experiments
KW  - ordinary differential equation
KW  - parameter estimation
KW  - population dynamics
KW  - predator prey
KW  - time series analysis
KW  - trait variability
Y1  - 2019
U6  - https://doi.org/10.3389/fevo.2018.00234
SN  - 2296-701X
VL  - 6
PB  - Frontiers Research Foundation
CY  - Lausanne
ER  - 
TY  - JOUR
A1  - Massie, Thomas Michael
A1  - Ryabov, Alexei
A1  - Blasius, Bernd
A1  - Weithoff, Guntram
A1  - Gaedke, Ursula
T1  - Complex transient dynamics of stage-structured populations in response to environmental changes
JF  - The American naturalist : a bi-monthly journal devoted to the advancement and correlation of the biological sciences
N2  - Stage structures of populations can have a profound influence on their dynamics. However, not much is known about the transient dynamics that follow a disturbance in such systems. Here we combined chemostat experiments with dynamical modeling to study the response of the phytoplankton species Chlorella vulgaris to press perturbations. From an initially stable steady state, we altered either the concentration or dilution rate of a growth-limiting resource. This disturbance induced a complex transient response-characterized by the possible onset of oscillations-before population numbers relaxed to a new steady state. Thus, cell numbers could initially change in the opposite direction of the long-term change. We present quantitative indexes to characterize the transients and to show that the dynamic response is dependent on the degree of synchronization among life stages, which itself depends on the state of the population before perturbation. That is, we show how identical future steady states can be approached via different transients depending on the initial population structure. Our experimental results are supported by a size-structured model that accounts for interplay between cell-cycle and population-level processes and that includes resource-dependent variability in cell size. Our results should be relevant to other populations with a stage structure including organisms of higher order.
KW  - chemostat experiments
KW  - Chlorella vulgaris
KW  - environmental changes
KW  - population dynamics
KW  - stage structure
KW  - transient dynamics
Y1  - 2013
U6  - https://doi.org/10.1086/670590
SN  - 0003-0147
SN  - 1537-5323
VL  - 182
IS  - 1
SP  - 103
EP  - 119
PB  - Univ. of Chicago Press
CY  - Chicago
ER  -