COS 72-1 - Using neural ordinary differential equations to predict complex ecological dynamics from population density data

Abstract: Simple mathematical models have been used to describe ecological processes for over a century. However, the inherent complexity of ecological systems makes simple models subject to modeling bias due to simplifying assumptions or unaccounted factors, limiting their predictive power for complex ecological communities. Neural Ordinary Differential Equations (NODEs) have surged recently as a machine-learning algorithm that preserves the dynamic nature of the data. NODEs consist of dynamical models where populations are modeled using a neural network instead of a parametric function. This preservation of the data dynamics is an advantage for modeling ecological time series in comparison to other state-of-the-art methods. However, the question of how NODEs perform as a forecasting tool of ecological communities is still unanswered. Here we explore this question using simulated time series of population densities of multiple competing species in a time-varying environment. We explore the performance of NODEs by fitting them using time series of different community sizes and different training data sizes. We find that NODEs provide less uncertain forecasts than the standard ARIMA models. In addition, we find that combining NODEs with parametric models can recover the final community size of our simulated time series better than ARIMA or NODE models. We also discuss ways to improve the forecasting performance of NODEs. The power of a forecasting tool such as NODEs is that it can provide insights into population dynamics and should thus broaden the approaches to studying time series of ecological communities.