@article{RosenbaumRaatzWeithoffetal.2019,
  author    = {Rosenbaum, Benjamin and Raatz, Michael and Weithoff, Guntram and Fussmann, Gregor F. and Gaedke, Ursula},
  title     = {Estimating parameters from multiple time series of population dynamics using bayesian inference},
  series = {Frontiers in ecology and evolution},
  volume    = {6},
  journal   = {Frontiers in ecology and evolution},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {2296-701X},
  doi       = {10.3389/fevo.2018.00234},
  pages     = {14},
  year      = {2019},
  abstract  = {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.},
  language  = {en}
}
@article{MoenickesSchneiderMuehleetal.2011,
  author    = {Moenickes, Sylvia and Schneider, Anne-Kathrin and Muehle, Lesley and Rohe, Lena and Richter, Otto and Suhling, Frank},
  title     = {From population-level effects to individual response: modelling temperature dependence in Gammarus pulex},
  series = {The journal of experimental biology},
  volume    = {214},
  journal   = {The journal of experimental biology},
  number    = {21},
  publisher = {Company of Biologists Limited},
  address   = {Cambridge},
  issn      = {0022-0949},
  doi       = {10.1242/jeb.061945},
  pages     = {3678 -- 3687},
  year      = {2011},
  abstract  = {Population-level effects of global warming result from concurrent direct and indirect processes. They are typically described by physiologically structured population models (PSPMs). Therefore, inverse modelling offers a tool to identify parameters of individual physiological processes through population-level data analysis, e. g. the temperature dependence of growth from size-frequency data of a field population. Here, we make use of experiments under laboratory conditions, in mesocosms and field monitoring to determine the temperature dependence of growth and mortality of Gammarus pulex. We found an optimum temperature for growth of approximately 17 degrees C and a related temperature coefficient, Q(10), of 1.5 degrees C(-1), irrespective of whether we classically fitted individual growth curves or applied inverse modelling based on PSPMs to laboratory data. From a comparison of underlying data sets we conclude that applying inverse modelling techniques to population-level data results in meaningful response parameters for physiological processes if additional temperature-driven effects, including within-population interaction, can be excluded or determined independently. If this is not the case, parameter estimates describe a cumulative response, e. g. comprising temperature-dependent resource dynamics. Finally, fluctuating temperatures in natural habitats increased the uncertainty in parameter values. Here, PSPM should be applied for virtual monitoring in order to determine a sampling scheme that comprises important dates to reduce parameter uncertainty.},
  language  = {en}
}
@article{NueskenReichRozdeba2019,
  author    = {N{\"u}sken, Nikolas and Reich, Sebastian and Rozdeba, Paul J.},
  title     = {State and parameter estimation from observed signal increments},
  series = {Entropy : an international and interdisciplinary journal of entropy and information studies},
  volume    = {21},
  journal   = {Entropy : an international and interdisciplinary journal of entropy and information studies},
  number    = {5},
  publisher = {MDPI},
  address   = {Basel},
  issn      = {1099-4300},
  doi       = {10.3390/e21050505},
  pages     = {23},
  year      = {2019},
  abstract  = {The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors are correlated and both states and parameters need to be identified. Such scenarios arise from noisy and partial observations of Lagrangian particles which move under a stochastic velocity field involving unknown parameters. We take an appropriate class of McKean-Vlasov equations as the starting point to derive ensemble Kalman-Bucy filter algorithms for combined state and parameter estimation. We demonstrate their performance through a series of increasingly complex multi-scale model systems.},
  language  = {en}
}