Trend and fluctuations: analysis and design of population dynamics measurements in replicate ecosystems.
The dynamical evolution of complex systems is often intrinsically stochastic and subject to external random forces. In order to study the resulting variability in dynamics, it is essential to make measurements on replicate systems and to separate arbitrary variation of the average dynamics of these replicates from fluctuations around the average dynamics. Here we do so for population time-series data from replicate ecosystems sharing a common average dynamics or common trend. We explain how model parameters, including the effective interactions between species and dynamical noise, can be estimated from the data and how replication reduces errors in these estimates. For this, it is essential that the model can fit a variety of average dynamics. We then show how one can judge the quality of a model, compare alternate models, and determine which combinations of parameters are poorly determined by the data. In addition we show how replicate population dynamics experiments could be designed to optimize the acquired information of interest about the systems. Our approach is illustrated on a set of time series gathered from replicate microbial closed ecosystems.
Center for Studies in Physics and Biology and the Laboratory of Living Matter, The Rockefeller University, 1230 York Avenue, New York, New York 10065, USA.
Doeke R
DR
Hekstra
School of Natural Sciences, and The Simons Center for Systems Biology, The Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA and Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, 24, Rue Lhomond, 75231 Paris Cedex 05, France.
Simona
S
Cocco
School of Natural Sciences, and The Simons Center for Systems Biology, The Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA and Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24, Rue Lhomond, 75231 Paris Cedex 05, France.
Remi
R
Monasson
Center for Studies in Physics and Biology and the Laboratory of Living Matter, The Rockefeller University, 1230 York Avenue, New York, New York 10065, USA and School of Natural Sciences, and The Simons Center for Systems Biology, The Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA.
Stanislas
S
Leibler
D017753:Ecosystem; D008962:Models, Theoretical; D011157:Population Dynamics / Q000706:statistics & numerical data* / Q000639:trends*; D013269:Stochastic Processes