Estimating co-extinction threats in terrestrial ecosystems

The biosphere is changing rapidly due to human endeavour. Because ecological communities underlie networks of interacting species, changes that directly affect some species can have indirect effects on others. Accurate tools to predict these direct and indirect effects are therefore required to guide conservation strategies. However, most extinction-risk studies only consider the direct effects of global change-such as predicting which species will breach their thermal limits under different warming scenarios-with predictions of trophic cascades and co-extinction risks remaining mostly speculative. To predict the potential indirect effects of primary extinctions, data describing community interactions and network modelling can estimate how extinctions cascade through communities. While theoretical studies have demonstrated the usefulness of models in predicting how communities react to threats like climate change, few have applied such methods to real-world communities. This gap partly reflects challenges in constructing trophic network models of real-world food webs, highlighting the need to develop approaches for quantifying co-extinction risk more accurately. We propose a framework for constructing ecological network models representing real-world food webs in terrestrial ecosystems and subjecting these models to co-extinction scenarios triggered by probable future environmental perturbations. Adopting our framework will improve estimates of how environmental perturbations affect whole ecological communities. Identifying species at risk of co-extinction (or those that might trigger co-extinctions) will also guide conservation interventions aiming to reduce the probability of co-extinction cascades and additional species losses.

A roadmap towards predicting species interaction networks (across space and time)

Networks of species interactions underpin numerous ecosystem processes, but comprehensively sampling these interactions is difficult. Interactions intrinsically vary across space and time, and given the number of species that compose ecological communities, it can be tough to distinguish between a true negative (where two species never interact) from a false negative (where two species have not been observed interacting even though they actually do). Assessing the likelihood of interactions between species is an imperative for several fields of ecology. This means that to predict interactions between species-and to describe the structure, variation, and change of the ecological networks they form-we need to rely on modelling tools. Here, we provide a proof-of-concept, where we show how a simple neural network model makes accurate predictions about species interactions given limited data. We then assess the challenges and opportunities associated with improving interaction predictions, and provide a conceptual roadmap forward towards predictive models of ecological networks that is explicitly spatial and temporal. We conclude with a brief primer on the relevant methods and tools needed to start building these models, which we hope will guide this research programme forward. This article is part of the theme issue 'Infectious disease macroecology: parasite diversity and dynamics across the globe'.

Automated Discovery of Relationships, Models, and Principles in Ecology

Ecological systems are the quintessential complex systems, involving numerous high-order interactions and non-linear relationships. The most used statistical modeling techniques can hardly accommodate the complexity of ecological patterns and processes. Finding hidden relationships in complex data is now possible using massive computational power, particularly by means of artificial intelligence and machine learning methods. Here we explored the potential of symbolic regression (SR), commonly used in other areas, in the field of ecology. Symbolic regression searches for both the formal structure of equations and the fitting parameters simultaneously, hence providing the required flexibility to characterize complex ecological systems. Although the method here presented is automated, it is part of a collaborative human–machine effort and we demonstrate ways to do it. First, we test the robustness of SR to extreme levels of noise when searching for the species-area relationship. Second, we demonstrate how SR can model species richness and spatial distributions. Third, we illustrate how SR can be used to find general models in ecology, namely new formulas for species richness estimators and the general dynamic model of oceanic island biogeography. We propose that evolving free-form equations purely from data, often without prior human inference or hypotheses, may represent a very powerful tool for ecologists and biogeographers to become aware of hidden relationships and suggest general theoretical models and principles.

Neural hierarchical models of ecological populations

Neural networks are increasingly being used in science to infer hidden dynamics of natural systems from noisy observations, a task typically handled by hierarchical models in ecology. This article describes a class of hierarchical models parameterised by neural networks - neural hierarchical models. The derivation of such models analogises the relationship between regression and neural networks. A case study is developed for a neural dynamic occupancy model of North American bird populations, trained on millions of detection/non-detection time series for hundreds of species, providing insights into colonisation and extinction at a continental scale. Flexible models are increasingly needed that scale to large data and represent ecological processes. Neural hierarchical models satisfy this need, providing a bridge between deep learning and ecological modelling that combines the function representation power of neural networks with the inferential capacity of hierarchical models.