Symbolic Regression for Ecological Model Discovery

June 26, 2026

Symbolic regression offers an approach to ecological model discovery by generating mathematical expressions directly from data. However, existing frameworks emphasize equation discovery and provide limited support for comparing equations generated across repeated runs, datasets, or ecological groups. Consequently, substantial effort is required to organize candidate models, refit parameters consistently, assess robustness, and compare alternative symbolic structures. This thesis addresses this gap by introducing *leaf*, a framework that treats discovered equations as candidate ecological hypotheses requiring assessment rather than as final predictive outputs. The framework separates symbolic structure discovery from post-discovery evaluation. Candidate equations are generated across multiple data subsets or views, refitted using common parameter-estimation procedures, and compared through validation protocols, complexity measures, and Pareto-based analyses. It is evaluated in case studies involving species richness, species distributions, and the General Dynamic Model of island biogeography. The results show that symbolic regression outputs are sensitive to discovery conditions and that different data subsets can yield distinct equations with similar predictive performance. Repeated discovery therefore provides a broader view of the equation space than individual runs. Across case studies, predictive gains often plateaued at low or intermediate complexity, while simpler equations were more robust and interpretable. The framework also recovered compact alternatives to established General Dynamic Model formulations and repeatedly identified maximum island elevation as an informative predictor of species richness. These findings support viewing symbolic regression not as a method for identifying a single optimal equation, but as a tool for generating, comparing, and interpreting competing mathematical hypotheses in ecological research.

Authors in the community:

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  F

  Francisco Gabriel Thomaz Martins

  ist199068

Supervisors of this institution:

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  M

  Manuel Fernando Cabido Peres Lopes

  ist40208

electrical-engineering-electronic-engineering-information-engineering - Electrical engineering, electronic engineering, information engineering

eng - English

Instituto Superior Técnico