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Neural Ordinary Differential Equations for Ecological and Evolutionary Time Series Analysis
  • Willem Bonnaffé,
  • Ben Sheldon,
  • Tim Coulson
Willem Bonnaffé
University of Oxford Department of Zoology
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Ben Sheldon
University of Oxford Department of Zoology
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Tim Coulson
University of Oxford Department of Zoology
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Abstract

We present a novel method, Neural Ordinary Differential Equations, for learning ecological and evolutionary processes from time series data. The method consists in modelling dynamical systems with Ordinary Differential Equations and dynamic functions with Artificial Neural Networks, which upon successful training converge to functional shapes that best describe the processes. We tested NODEs by inferring per-capita growth rates of hare and lynx in simulated and real time series, which revealed that prey-predator oscillations were mainly driven by stronger predation at low hare and lynx density, as well as negative density-dependence in lynx, in line with the literature, thus demonstrating the validity and utility of NODEs. The approach is applicable to any system that can be modelled with differential equations, and particularly suitable for linking ecological, evolutionary, and environmental dynamics where parametric approaches are too challenging to implement, opening new avenues for theoretical and empirical investigations.