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Neural ordinary differential equations for ecological and evolutionary time‐series analysis
Author(s) -
Bonnaffé Willem,
Sheldon Ben C.,
Coulson Tim
Publication year - 2021
Publication title -
methods in ecology and evolution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.425
H-Index - 105
ISSN - 2041-210X
DOI - 10.1111/2041-210x.13606
Subject(s) - ordinary differential equation , dynamical systems theory , context (archaeology) , computer science , artificial neural network , series (stratigraphy) , population , stochastic differential equation , time series , dynamical system (definition) , equilibrium point , differential equation , mathematics , artificial intelligence , machine learning , physics , mathematical analysis , paleontology , demography , quantum mechanics , sociology , biology
Inferring the functional shape of ecological and evolutionary processes from time‐series data can be challenging because processes are often not describable with simple equations. The dynamical coupling between variables in time series further complicates the identification of equations through model selection as the inference of a given process is contingent on the accurate depiction of all other processes. We present a novel method, neural ordinary differential equations (NODEs), for learning ecological and evolutionary processes from time‐series data by modelling dynamical systems as ordinary differential equations and dynamical functions with artificial neural networks (ANNs). Upon successful training, the ANNs converge to functional shapes that best describe the biological processes underlying the dynamics observed, in a way that is robust to mathematical misspecifications of the dynamical model. We demonstrate NODEs in a population dynamic context and show how they can be used to infer ecological interactions, dynamical causation and equilibrium points. We tested NODEs by analysing well‐understood hare and lynx time‐series data, which revealed that prey–predator oscillations were mainly driven by the interspecific interaction, as well as intraspecific densitydependence, and characterised by a single equilibrium point at the centre of the oscillation. Our 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.