Ecosystems are involved in global biogeochemical cycles that regulate climate and provide essential services to human societies. Mechanistic models are required to describe ecosystem dynamics and anticipate their response to anthropogenic pressure, but their adoption has been limited in practice because of issues with parameter identification and because of model inaccuracies. While observations could be used to directly estimate parameters and improve models, model nonlinearities as well as shallow, incomplete and noisy datasets complicate this process. Here, we propose a machine learning (ML) framework relying on a mini-batch method combined with automatic differentiation and state-of-the-art optimizers. By splitting the data into mini-batches with a short time horizon, we show both analytically and numerically that the mini-batch method regularizes the learning problem. When combined with the proposed numerical implementation, the resulting ML framework can efficiently learn the parameter of complex dynamical models and is a workhorse for model selection. We evaluate the performance of the ML framework in recovering the dynamics of a simulated food-web. We show that it can efficiently learn from noisy, incomplete and independent time series, accurately estimating the model parameters and providing reliable short-term forecasts. We further show that the ML framework can provide statistical support for the true generating model among several candidates. In summary, the proposed ML framework can efficiently learn from data and elucidate mechanistic pathways to improve our understanding and predictions of ecosystem dynamics.

Faunal turnover in Indo-Australia across Wallace’s Line is one of the most recognizable patterns in biogeography and has catalyzed debate about the role of evolutionary and geoclimatic history in biotic interchanges. Here, analysis of more than 20,000 vertebrate species with a model of geoclimate and biological diversification shows that broad precipitation tolerance and dispersal ability were key for exchange across the deep-time precipitation gradient spanning the region. Sundanian (Southeast Asian) lineages evolved in a climate similar to the humid “stepping stones” of Wallacea, facilitating colonization of the Sahulian (Australian) continental shelf. By contrast, Sahulian lineages predominantly evolved in drier conditions, hampering establishment in Sunda and shaping faunal distinctiveness. We demonstrate how the history of adaptation to past environmental conditions shapes asymmetrical colonization and global biogeographic structure.

Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately account for certain non-local phenomena such as, e.g., interactions at a distance. In order to properly capture these phenomena non-local nonlinear PDE models are frequently employed in the literature. In this article we propose two numerical methods based on machine learning and on Picard iterations, respectively, to approximately solve non-local nonlinear PDEs. The proposed machine learning-based method is an extended variant of a deep learning-based splitting-up type approximation method previously introduced in the literature and utilizes neural networks to provide approximate solutions on a subset of the spatial domain of the solution. The Picard iterations-based method is an extended variant of the so-called full history recursive multilevel Picard approximation scheme previously introduced in the literature and provides an approximate solution for a single point of the domain. Both methods are mesh-free and allow non-local nonlinear PDEs with Neumann boundary conditions to be solved in high dimensions.In the two methods, the numerical difficulties arising due to the dimensionality of the PDEs are avoided by (i) using the correspondence between the expected trajectory of reflected stochastic processes and the solution of PDEs (given by the Feynman-Kac formula) and by (ii) using a plain vanilla Monte Carlo integration to handle the nonlocal term. We evaluate the performance of the two methods on five different PDEs arising in physics and biology. In all cases, the methods yield good results in up to 10 dimensions with short run times. Our work extends recently developed methods to overcome the curse of dimensionality in solving PDEs.