Neural ordinary differential equations for ecological and evolutionary time‐series analysis

Bonnaffé, Willem; Sheldon, Ben C.; Coulson, Tim

doi:10.1111/2041-210x.13606

Cited by 25 publications

(47 citation statements)

References 47 publications

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“…Valuable effort would therefore be expended in future work to consider the relationship of model flexibility to the parametric-and structural sensitivities of models when it comes to drawing inferences for population dynamics (e.g., Aldebert and Stouffer, 2018;Adamson and Morozov, 2020). Likewise, it would also be useful to clarify the relevance of model flexibility to the rapidly developing methods of scientific machine learning, including the use of symbolic regression, neural ordinary differential equations, and universal differential equations for model discovery (e.g., Martin et al, 2018;Guimerà et al, 2020;Rackauckas et al, 2020;Bonnaffé et al, 2021).…”

Section: Discussionmentioning

confidence: 99%

Geometric Complexity and the Information-Theoretic Comparison of Functional-Response Models

Novák

Stouffer

2021

Front. Ecol. Evol.

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The assessment of relative model performance using information criteria like AIC and BIC has become routine among functional-response studies, reflecting trends in the broader ecological literature. Such information criteria allow comparison across diverse models because they penalize each model's fit by its parametric complexity—in terms of their number of free parameters—which allows simpler models to outperform similarly fitting models of higher parametric complexity. However, criteria like AIC and BIC do not consider an additional form of model complexity, referred to as geometric complexity, which relates specifically to the mathematical form of the model. Models of equivalent parametric complexity can differ in their geometric complexity and thereby in their ability to flexibly fit data. Here we use the Fisher Information Approximation to compare, explain, and contextualize how geometric complexity varies across a large compilation of single-prey functional-response models—including prey-, ratio-, and predator-dependent formulations—reflecting varying apparent degrees and forms of non-linearity. Because a model's geometric complexity varies with the data's underlying experimental design, we also sought to determine which designs are best at leveling the playing field among functional-response models. Our analyses illustrate (1) the large differences in geometric complexity that exist among functional-response models, (2) there is no experimental design that can minimize these differences across all models, and (3) even the qualitative nature by which some models are more or less flexible than others is reversed by changes in experimental design. Failure to appreciate model flexibility in the empirical evaluation of functional-response models may therefore lead to biased inferences for predator–prey ecology, particularly at low experimental sample sizes where its impact is strongest. We conclude by discussing the statistical and epistemological challenges that model flexibility poses for the study of functional responses as it relates to the attainment of biological truth and predictive ability.

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Section: Discussionmentioning

confidence: 99%

Geometric Complexity and the Information-Theoretic Comparison of Functional-Response Models

Novák

Stouffer

2021

Front. Ecol. Evol.

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“…Since the inception of the Geber method by Hairston et al (2005) and Ellner et al (2011), a multiplicity of more sophisticated methods have flourished. These methods are based either on inferring parameters for dynamic models from data (Rudy et al 2017), on non-parametric approaches such as recurrent neural networks, or on hybrid approaches combining differential equations with neural networks (Bonnaffé et al 2021). Reviewing these methods is beyond the scope of this paper.…”

Section: Measuring the Trait Dependency Of Ecological Dynamics (Fig 1...mentioning

confidence: 99%

Size‐dependent eco‐evolutionary feedbacks in harvested systems

Édeline

Loeuille

2021

Oikos

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Harvesting may drive body downsizing along with population declines and decreased harvesting yields. These changes are commonly construed as consequences of direct harvest selection, where small‐bodied, early‐reproducing individuals are immediately favoured. However, together with directly selecting against a large body size, harvesting and body downsizing alter many ecological features, such as competitive and trophic interactions, and thus also indirectly reshape natural selection acting back on body sizes through eco‐evolutionary feedback loops (EEFLs). We sketch plausible scenarios of simple EEFLs in which one‐dimensional, density‐dependent natural selection acts either antagonistically or synergistically with direct harvest selection on body size. Antagonistic feedbacks favour body‐size stasis but erode genetic variability and associated body‐size evolvability, and may ultimately impair population persistence and recovery. In contrast, synergistic feedbacks drive fast evolution towards smaller body sizes and favour population resilience, but may have far‐reaching bottom–up or top–down effects. We illustrate the further complexities resulting from multiple environmental feedbacks using a co‐evolving predator–prey pair, in which case outcomes from EEFLs depend not only on population densities, but also on whether prey sit above or below the optimal predator/prey body‐size ratio, and whether prey are more or less evolvable than their predators. EEFLs improve our ability to understand and predict nature's response to harvesting, but their integration into the research agenda will require a full consideration of the effects and dynamics of natural selection.

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“…For instance, recently Dutta et al showed that NODE can generate the solutions for the various evolution problems of different fluid dynamics and further provide a promising potential to extrapolate [33]. Another attempt was to use NODE to learn ecological and evolutionary processes based on the time-series data generated by traditional ecological models [57]. Microbial communities are dynamical systems, in which microbes interact primarily through the metabolite consumption and production of byproduct metabolites [58, 34].…”

Section: Discussionmentioning

confidence: 99%

Predicting metabolomic profiles from microbial composition through neural ordinary differential equations

Wang

Lee-Sarwar

et al. 2022

Preprint

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Characterizing the metabolic profile of a microbial community is crucial for understanding its biological function and its impact on the host or environment. Metabolomics experiments directly measuring these profiles are difficult and expensive, while sequencing methods quantifying the species composition of microbial communities are well-developed and relatively cost-effective. Computational methods that are capable of predicting metabolomic profiles from microbial compositions can save considerable efforts needed for metabolomic profiling experimentally. Yet, despite existing efforts, we still lack a computational method with high prediction power, general applicability, and great interpretability. Here we develop a new method — mNODE (Metabolomic profile predictor using Neural Ordinary Differential Equations), based on a state-of-the-art family of deep neural network models. We show compelling evidence that mNODE outperforms existing methods in predicting the metabolomic profiles of human microbiomes and several environmental microbiomes. Moreover, in the case of human gut microbiomes, mNODE can naturally incorporate dietary information to further enhance the prediction of metabolomic profiles. Besides, susceptibility analysis of mNODE enables us to reveal microbe-metabolite interactions, which can be validated using both synthetic and real data. The presented results demonstrate that mNODE is a powerful tool to investigate the microbiome-diet-metabolome relationship, facilitating future research on precision nutrition.

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Neural ordinary differential equations for ecological and evolutionary time‐series analysis

Abstract: This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Cited by 25 publications

References 47 publications

Geometric Complexity and the Information-Theoretic Comparison of Functional-Response Models

Geometric Complexity and the Information-Theoretic Comparison of Functional-Response Models

Size‐dependent eco‐evolutionary feedbacks in harvested systems

Predicting metabolomic profiles from microbial composition through neural ordinary differential equations

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