Constraining nonlinear time series modeling with the metabolic theory of ecology

Abstract

Forecasting the response of ecological systems to environmental change is a critical challenge for sustainable management. The metabolic theory of ecology (MTE) posits scaling of biological rates with temperature, but it has had limited application to population dynamic forecasting. Here we use the temperature dependence of the MTE to constrain empirical dynamic modeling (EDM), an equation-free nonlinear machine learning approach for forecasting. By rescaling time with temperature and modeling dynamics on a “metabolic time step,” our method (MTE-EDM) improved forecast accuracy in 18 of 19 empirical ectotherm time series (by 19% on average), with the largest gains in more seasonal environments. MTE-EDM assumes that temperature affects only the rate, rather than the form, of population dynamics, and that interacting species have approximately similar temperature dependence. A review of laboratory studies suggests these assumptions are reasonable, at least approximately, though not for all ecological systems. Our approach highlights how to combine modern data-driven forecasting techniques with ecological theory and mechanistic understanding to predict the response of complex ecosystems to temperature variability and trends.

Predicting multiple observations in complex systems through low-dimensional embeddings

“…System details are often unknown, and only their time series data are accessible. Therefore, a variety of data-driven techniques are designed for the prediction task 4 , 5 , including traditional statistical models (e.g., autoregressive integrated moving average (ARIMA)) 6 , state space-based methods (e.g., sequential locally weighted global linear maps (S-maps) 7 and multiview embedding (MVE)) 8 , machine learning algorithms (e.g., support vector machine (SVM) 9 , long short-term memory (LSTM) 10 , and reservoir computing (RC) 11 , 12 , and state-of-the-art combination frameworks (e.g., multitask learning-based Gaussian process regression machine (MT-GPRM) 13 , randomly distribution embedding (RDE) 14 and autoreservoir neural network (ARNN) 15 ). These advanced approaches have shown potential for several significant tasks, e.g., one-step and multistep ahead predictions of a target time series variable 16 .…”