Dr. Victor Boussange

Ecosystem response to climate change is complex. In order to forecast ecosystem dynamics, we need high-quality data on changes in past species abundance that can inform process-based models. Sedimentary ancient DNA (sedaDNA) has revolutionised our ability to document past ecosystems' dynamics. It provides time series of increased taxonomic resolution compared to microfossils (pollen, spores), and can often give species-level information, especially for past vascular plant and mammal abundances. Time series are much richer in information than contemporary spatial distribution information, which have been traditionally used to train models for predicting biodiversity and ecosystem responses to climate change. Here, we outline the potential contribution of sedaDNA to forecast ecosystem changes. We showcase how species-level time series may allow quantification of the effect of biotic interactions in ecosystem dynamics, and be used to estimate dispersal rates when a dense network of sites is available. By combining palaeo-time series, process-based models, and inverse modelling, we can recover the biotic and abiotic processes underlying ecosystem dynamics, which are traditionally very challenging to characterise. Dynamic models informed by sedaDNA can further be used to extrapolate beyond current dynamics and provide robust forecasts of ecosystem responses to future climate change.
This article is part of the theme issue 'Ecological novelty and planetary stewardship: biodiversity dynamics in a transforming biosphere'.

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. Non-local nonlinear PDE models can accurately capture these phenomena, but traditional numerical approximation methods are infeasible when the considered non-local PDE is high-dimensional. 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 non-local 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.

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.

Differentiation mechanisms are influenced by the properties of the landscape over which individuals interact, disperse and evolve. Here, we investigate how habitat connectivity and habitat heterogeneity affect phenotypic differentiation by formulating a stochastic eco-evolutionary model where individuals are structured over a spatial graph. We combine analytical insights into the eco-evolutionary dynamics with numerical simulations to understand how the graph topology and the spatial distribution of habitat types affect differentiation. We show that not only low connectivity but also heterogeneity in connectivity promotes neutral differentiation, due to increased competition in highly connected vertices. Habitat assortativity, a measure of habitat spatial auto-correlation in graphs, additionally drives differentiation under habitat-dependent selection. While assortative graphs systematically amplify adaptive differentiation, they can foster or depress neutral differentiation depending on the migration regime. By formalising the eco-evolutionary and spatial dynamics of biological populations on graphs, our study establishes fundamental links between landscape features and phenotypic differentiation.